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Michael Herzberg
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f5af1116db |
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output
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An overview of the formalization is given in:
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Achim D. Brucker and Michael Herzberg. A Formal Semantics of the Core DOM
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in Isabelle/HOL. In The 2018 Web Conference Companion (WWW). Pages 741-749,
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ACM Press, 2018. doi:10.1145/3184558.3185980
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A BibTeX entry for LaTeX users is
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@InProceedings{ brucker.ea:core-dom:2018,
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abstract = {At its core, the Document Object Model (DOM) defines a tree-like
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data structure for representing documents in general and HTML
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documents in particular. It forms the heart of any rendering engine
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of modern web browsers. Formalizing the key concepts of the DOM is
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a pre-requisite for the formal reasoning over client-side JavaScript
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programs as well as for the analysis of security concepts in modern
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web browsers. In this paper, we present a formalization of the core DOM,
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with focus on the node-tree and the operations defined on node-trees,
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in Isabelle/HOL. We use the formalization to verify the functional
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correctness of the most important functions defined in the DOM standard.
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Moreover, our formalization is (1) extensible, i.e., can be extended without
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the need of re-proving already proven properties and (2) executable, i.e.,
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we can generate executable code from our specification.},
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address = {New York, NY, USA},
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author = {Achim D. Brucker and Michael Herzberg},
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booktitle= {The 2018 Web Conference Companion (WWW)},
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conf_date= {April 23-27, 2018},
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doi = {10.1145/3184558.3185980},
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editor = {Pierre{-}Antoine Champin and Fabien L. Gandon and Mounia Lalmas and Panagiotis G. Ipeirotis},
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isbn = {978-1-4503-5640-4/18/04},
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keywords = {Document Object Model, DOM, Formal Semantics, Isabelle/HOL},
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location = {Lyon, France},
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pages = {741--749},
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pdf = {https://www.brucker.ch/bibliography/download/2018/brucker.ea-core-dom-2018.pdf},
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publisher= {ACM Press},
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title = {A Formal Semantics of the Core {DOM} in {Isabelle/HOL}},
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url = {https://www.brucker.ch/bibliography/abstract/brucker.ea-core-dom-2018},
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year = {2018},
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}
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chapter AFP
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session "Core_DOM" (AFP) = "HOL-Library" +
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options [timeout = 1200, document = pdf, document_variants="document:outline=/proof,/ML",document_output=output]
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directories
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"common"
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"common/classes"
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"common/monads"
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"common/pointers"
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"common/preliminaries"
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"common/tests"
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"standard"
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"standard/classes"
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"standard/pointers"
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theories
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Core_DOM
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Core_DOM_Tests
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document_files (in "document")
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"root.tex"
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"root.bib"
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(***********************************************************************************
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* Copyright (c) 2016-2018 The University of Sheffield, UK
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*
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
|
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* modification, are permitted provided that the following conditions are met:
|
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*
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* * Redistributions of source code must retain the above copyright notice, this
|
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* list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above copyright notice,
|
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* this list of conditions and the following disclaimer in the documentation
|
||||
* and/or other materials provided with the distribution.
|
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* SPDX-License-Identifier: BSD-2-Clause
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***********************************************************************************)
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theory Testing_Utils
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imports Main
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begin
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ML \<open>
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val _ = Theory.setup
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(Method.setup @{binding timed_code_simp}
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(Scan.succeed (SIMPLE_METHOD' o (CHANGED_PROP oo (fn a => fn b => fn tac =>
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let
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val start = Time.now ();
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val result = Code_Simp.dynamic_tac a b tac;
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val t = Time.now() - start;
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in
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(if length (Seq.list_of result) > 0 then Output.information ("Took " ^ (Time.toString t)) else ());
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result
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end))))
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"timed simplification with code equations");
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val _ = Theory.setup
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(Method.setup @{binding timed_eval}
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(Scan.succeed (SIMPLE_METHOD' o (fn a => fn b => fn tac =>
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let
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val eval = CONVERSION (Conv.params_conv ~1 (K (Conv.concl_conv ~1 (Code_Runtime.dynamic_holds_conv a))) a) THEN'
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resolve_tac a [TrueI];
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val start = Time.now ();
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val result = eval b tac
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val t = Time.now() - start;
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in
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(if length (Seq.list_of result) > 0 then Output.information ("Took " ^ (Time.toString t)) else ());
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result
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end)))
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"timed evaluation");
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val _ = Theory.setup
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(Method.setup @{binding timed_eval_and_code_simp}
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(Scan.succeed (SIMPLE_METHOD' o (fn a => fn b => fn tac =>
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let
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val eval = CONVERSION (Conv.params_conv ~1 (K (Conv.concl_conv ~1 (Code_Runtime.dynamic_holds_conv a))) a) THEN'
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resolve_tac a [TrueI];
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val start = Time.now ();
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val result = eval b tac
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val t = Time.now() - start;
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val start2 = Time.now ();
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val result2_opt =
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Timeout.apply (seconds 600.0) (fn _ => SOME (Code_Simp.dynamic_tac a b tac)) ()
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handle Timeout.TIMEOUT _ => NONE;
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val t2 = Time.now() - start2;
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in
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if length (Seq.list_of result) > 0 then (Output.information ("eval took " ^ (Time.toString t));
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File.append (Path.explode "/tmp/isabellebench") (Time.toString t ^ ",")) else ();
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(case result2_opt of
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SOME result2 =>
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(if length (Seq.list_of result2) > 0 then (Output.information ("code_simp took " ^ (Time.toString t2));
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File.append (Path.explode "/tmp/isabellebench") (Time.toString t2 ^ "\n")) else ())
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| NONE => (Output.information "code_simp timed out after 600s"; File.append (Path.explode "/tmp/isabellebench") (">600.000\n")));
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result
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end)))
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"timed evaluation and simplification with code equations with file output");
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\<close>
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(* To run the DOM test cases with timing information output, simply replace the use *)
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(* of "eval" with either "timed_code_simp", "timed_eval", or, to run both and write the results *)
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(* to /tmp/isabellebench, "timed_eval_and_code_simp". *)
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end
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File diff suppressed because it is too large
Load Diff
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@ -1,328 +0,0 @@
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(***********************************************************************************
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* Copyright (c) 2016-2018 The University of Sheffield, UK
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*
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* All rights reserved.
|
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*
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* Redistribution and use in source and binary forms, with or without
|
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* modification, are permitted provided that the following conditions are met:
|
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*
|
||||
* * Redistributions of source code must retain the above copyright notice, this
|
||||
* list of conditions and the following disclaimer.
|
||||
*
|
||||
* * Redistributions in binary form must reproduce the above copyright notice,
|
||||
* this list of conditions and the following disclaimer in the documentation
|
||||
* and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
||||
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
||||
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
||||
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* SPDX-License-Identifier: BSD-2-Clause
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***********************************************************************************)
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section\<open>Element\<close>
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text\<open>In this theory, we introduce the types for the Element class.\<close>
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theory ElementClass
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imports
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"NodeClass"
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"ShadowRootPointer"
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begin
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text\<open>The type @{type "DOMString"} is a type synonym for @{type "string"}, define
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in \autoref{sec:Core_DOM_Basic_Datatypes}.\<close>
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type_synonym attr_key = DOMString
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type_synonym attr_value = DOMString
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type_synonym attrs = "(attr_key, attr_value) fmap"
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type_synonym tag_name = DOMString
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record ('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr) RElement = RNode +
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nothing :: unit
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tag_name :: tag_name
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child_nodes :: "('node_ptr, 'element_ptr, 'character_data_ptr) node_ptr list"
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attrs :: attrs
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shadow_root_opt :: "'shadow_root_ptr shadow_root_ptr option"
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type_synonym
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('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element) Element
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= "('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option)
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RElement_scheme"
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register_default_tvars
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"('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element) Element"
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type_synonym
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('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Node, 'Element) Node
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= "(('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option) RElement_ext
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+ 'Node) Node"
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register_default_tvars
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"('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Node, 'Element) Node"
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type_synonym
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('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) Object
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= "('Object, ('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option)
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RElement_ext + 'Node) Object"
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register_default_tvars
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"('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) Object"
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type_synonym
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('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr,
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'Object, 'Node, 'Element) heap
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= "('document_ptr document_ptr + 'shadow_root_ptr shadow_root_ptr + 'object_ptr,
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'element_ptr element_ptr + 'character_data_ptr character_data_ptr + 'node_ptr, 'Object,
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('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option) RElement_ext +
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'Node) heap"
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register_default_tvars
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"('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr,
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'Object, 'Node, 'Element) heap"
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type_synonym heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l = "(unit, unit, unit, unit, unit, unit, unit, unit, unit) heap"
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definition element_ptr_kinds :: "(_) heap \<Rightarrow> (_) element_ptr fset"
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where
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"element_ptr_kinds heap =
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the |`| (cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r |`| (ffilter is_element_ptr_kind (node_ptr_kinds heap)))"
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lemma element_ptr_kinds_simp [simp]:
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"element_ptr_kinds (Heap (fmupd (cast element_ptr) element (the_heap h))) =
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{|element_ptr|} |\<union>| element_ptr_kinds h"
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apply(auto simp add: element_ptr_kinds_def)[1]
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by force
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definition element_ptrs :: "(_) heap \<Rightarrow> (_) element_ptr fset"
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where
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"element_ptrs heap = ffilter is_element_ptr (element_ptr_kinds heap)"
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definition cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) Node \<Rightarrow> (_) Element option"
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where
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"cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node =
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(case RNode.more node of Inl element \<Rightarrow> Some (RNode.extend (RNode.truncate node) element) | _ \<Rightarrow> None)"
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adhoc_overloading cast cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
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abbreviation cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) Object \<Rightarrow> (_) Element option"
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where
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"cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t obj \<equiv> (case cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e obj of Some node \<Rightarrow> cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node | None \<Rightarrow> None)"
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adhoc_overloading cast cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
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definition cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e :: "(_) Element \<Rightarrow> (_) Node"
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where
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"cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e element = RNode.extend (RNode.truncate element) (Inl (RNode.more element))"
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adhoc_overloading cast cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e
|
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abbreviation cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t :: "(_) Element \<Rightarrow> (_) Object"
|
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where
|
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"cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr \<equiv> cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t (cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr)"
|
||||
adhoc_overloading cast cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t
|
||||
|
||||
consts is_element_kind :: 'a
|
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definition is_element_kind\<^sub>N\<^sub>o\<^sub>d\<^sub>e :: "(_) Node \<Rightarrow> bool"
|
||||
where
|
||||
"is_element_kind\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr \<longleftrightarrow> cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr \<noteq> None"
|
||||
|
||||
adhoc_overloading is_element_kind is_element_kind\<^sub>N\<^sub>o\<^sub>d\<^sub>e
|
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lemmas is_element_kind_def = is_element_kind\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
|
||||
|
||||
abbreviation is_element_kind\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t :: "(_) Object \<Rightarrow> bool"
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where
|
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"is_element_kind\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr \<equiv> cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr \<noteq> None"
|
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adhoc_overloading is_element_kind is_element_kind\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t
|
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lemma element_ptr_kinds_commutes [simp]:
|
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"cast element_ptr |\<in>| node_ptr_kinds h \<longleftrightarrow> element_ptr |\<in>| element_ptr_kinds h"
|
||||
apply(auto simp add: node_ptr_kinds_def element_ptr_kinds_def)[1]
|
||||
by (metis (no_types, lifting) element_ptr_casts_commute2 ffmember_filter fimage_eqI
|
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fset.map_comp is_element_ptr_kind_none node_ptr_casts_commute3
|
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node_ptr_kinds_commutes node_ptr_kinds_def option.sel option.simps(3))
|
||||
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||||
definition get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) element_ptr \<Rightarrow> (_) heap \<Rightarrow> (_) Element option"
|
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where
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"get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr h = Option.bind (get\<^sub>N\<^sub>o\<^sub>d\<^sub>e (cast element_ptr) h) cast"
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adhoc_overloading get get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
|
||||
locale l_type_wf_def\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
begin
|
||||
definition a_type_wf :: "(_) heap \<Rightarrow> bool"
|
||||
where
|
||||
"a_type_wf h = (NodeClass.type_wf h \<and> (\<forall>element_ptr \<in> fset (element_ptr_kinds h).
|
||||
get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr h \<noteq> None))"
|
||||
end
|
||||
global_interpretation l_type_wf_def\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t defines type_wf = a_type_wf .
|
||||
lemmas type_wf_defs = a_type_wf_def
|
||||
|
||||
locale l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t = l_type_wf type_wf for type_wf :: "((_) heap \<Rightarrow> bool)" +
|
||||
assumes type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t: "type_wf h \<Longrightarrow> ElementClass.type_wf h"
|
||||
|
||||
sublocale l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t \<subseteq> l_type_wf\<^sub>N\<^sub>o\<^sub>d\<^sub>e
|
||||
apply(unfold_locales)
|
||||
using NodeClass.a_type_wf_def
|
||||
by (meson ElementClass.a_type_wf_def l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_axioms l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
|
||||
locale l_get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas = l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
begin
|
||||
sublocale l_get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_lemmas by unfold_locales
|
||||
|
||||
lemma get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_type_wf:
|
||||
assumes "type_wf h"
|
||||
shows "element_ptr |\<in>| element_ptr_kinds h \<longleftrightarrow> get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr h \<noteq> None"
|
||||
using l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_axioms assms
|
||||
apply(simp add: type_wf_defs get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
by (metis NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf bind_eq_None_conv element_ptr_kinds_commutes notin_fset
|
||||
option.distinct(1))
|
||||
end
|
||||
|
||||
global_interpretation l_get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas type_wf
|
||||
by unfold_locales
|
||||
|
||||
definition put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) element_ptr \<Rightarrow> (_) Element \<Rightarrow> (_) heap \<Rightarrow> (_) heap"
|
||||
where
|
||||
"put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr element = put\<^sub>N\<^sub>o\<^sub>d\<^sub>e (cast element_ptr) (cast element)"
|
||||
adhoc_overloading put put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
|
||||
lemma put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ptr_in_heap:
|
||||
assumes "put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr element h = h'"
|
||||
shows "element_ptr |\<in>| element_ptr_kinds h'"
|
||||
using assms
|
||||
unfolding put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def element_ptr_kinds_def
|
||||
by (metis element_ptr_kinds_commutes element_ptr_kinds_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_ptr_in_heap)
|
||||
|
||||
lemma put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_put_ptrs:
|
||||
assumes "put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr element h = h'"
|
||||
shows "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|cast element_ptr|}"
|
||||
using assms
|
||||
by (simp add: put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_put_ptrs)
|
||||
|
||||
|
||||
|
||||
lemma cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_inject [simp]:
|
||||
"cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e x = cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e y \<longleftrightarrow> x = y"
|
||||
apply(simp add: cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def RObject.extend_def RNode.extend_def)
|
||||
by (metis (full_types) RNode.surjective old.unit.exhaust)
|
||||
|
||||
lemma cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_none [simp]:
|
||||
"cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node = None \<longleftrightarrow> \<not> (\<exists>element. cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e element = node)"
|
||||
apply(auto simp add: cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def RObject.extend_def RNode.extend_def
|
||||
split: sum.splits)[1]
|
||||
by (metis (full_types) RNode.select_convs(2) RNode.surjective old.unit.exhaust)
|
||||
|
||||
lemma cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_some [simp]:
|
||||
"cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node = Some element \<longleftrightarrow> cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e element = node"
|
||||
by(auto simp add: cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def RObject.extend_def RNode.extend_def
|
||||
split: sum.splits)
|
||||
|
||||
lemma cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_inv [simp]: "cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t (cast\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e element) = Some element"
|
||||
by simp
|
||||
|
||||
lemma get_elment_ptr_simp1 [simp]:
|
||||
"get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr (put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr element h) = Some element"
|
||||
by(auto simp add: get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
lemma get_elment_ptr_simp2 [simp]:
|
||||
"element_ptr \<noteq> element_ptr'
|
||||
\<Longrightarrow> get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr (put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr' element h) = get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr h"
|
||||
by(auto simp add: get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
|
||||
|
||||
abbreviation "create_element_obj tag_name_arg child_nodes_arg attrs_arg shadow_root_opt_arg
|
||||
\<equiv> \<lparr> RObject.nothing = (), RNode.nothing = (), RElement.nothing = (),
|
||||
tag_name = tag_name_arg, Element.child_nodes = child_nodes_arg, attrs = attrs_arg,
|
||||
shadow_root_opt = shadow_root_opt_arg, \<dots> = None \<rparr>"
|
||||
|
||||
definition new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) heap \<Rightarrow> ((_) element_ptr \<times> (_) heap)"
|
||||
where
|
||||
"new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h =
|
||||
(let new_element_ptr = element_ptr.Ref (Suc (fMax (finsert 0 (element_ptr.the_ref
|
||||
|`| (element_ptrs h)))))
|
||||
in
|
||||
(new_element_ptr, put new_element_ptr (create_element_obj '''' [] fmempty None) h))"
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ptr_in_heap:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
shows "new_element_ptr |\<in>| element_ptr_kinds h'"
|
||||
using assms
|
||||
unfolding new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def
|
||||
using put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ptr_in_heap by blast
|
||||
|
||||
lemma new_element_ptr_new:
|
||||
"element_ptr.Ref (Suc (fMax (finsert 0 (element_ptr.the_ref |`| element_ptrs h)))) |\<notin>| element_ptrs h"
|
||||
by (metis Suc_n_not_le_n element_ptr.sel(1) fMax_ge fimage_finsert finsertI1 finsertI2 set_finsert)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ptr_not_in_heap:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
shows "new_element_ptr |\<notin>| element_ptr_kinds h"
|
||||
using assms
|
||||
unfolding new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
|
||||
by (metis Pair_inject element_ptrs_def ffmember_filter new_element_ptr_new is_element_ptr_ref)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_new_ptr:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
shows "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|cast new_element_ptr|}"
|
||||
using assms
|
||||
by (metis Pair_inject new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_put_ptrs)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_is_element_ptr:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
shows "is_element_ptr new_element_ptr"
|
||||
using assms
|
||||
by(auto simp add: new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t [simp]:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
assumes "ptr \<noteq> cast new_element_ptr"
|
||||
shows "get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr h = get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr h'"
|
||||
using assms
|
||||
by(auto simp add: new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_get\<^sub>N\<^sub>o\<^sub>d\<^sub>e [simp]:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
assumes "ptr \<noteq> cast new_element_ptr"
|
||||
shows "get\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr h = get\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr h'"
|
||||
using assms
|
||||
by(auto simp add: new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t [simp]:
|
||||
assumes "new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t h = (new_element_ptr, h')"
|
||||
assumes "ptr \<noteq> new_element_ptr"
|
||||
shows "get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr h = get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr h'"
|
||||
using assms
|
||||
by(auto simp add: new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def)
|
||||
|
||||
locale l_known_ptr\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
begin
|
||||
definition a_known_ptr :: "(_) object_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"a_known_ptr ptr = (known_ptr ptr \<or> is_element_ptr ptr)"
|
||||
|
||||
lemma known_ptr_not_element_ptr: "\<not>is_element_ptr ptr \<Longrightarrow> a_known_ptr ptr \<Longrightarrow> known_ptr ptr"
|
||||
by(simp add: a_known_ptr_def)
|
||||
end
|
||||
global_interpretation l_known_ptr\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t defines known_ptr = a_known_ptr .
|
||||
lemmas known_ptr_defs = a_known_ptr_def
|
||||
|
||||
|
||||
locale l_known_ptrs\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t = l_known_ptr known_ptr for known_ptr :: "(_) object_ptr \<Rightarrow> bool"
|
||||
begin
|
||||
definition a_known_ptrs :: "(_) heap \<Rightarrow> bool"
|
||||
where
|
||||
"a_known_ptrs h = (\<forall>ptr \<in> fset (object_ptr_kinds h). known_ptr ptr)"
|
||||
|
||||
lemma known_ptrs_known_ptr:
|
||||
"ptr |\<in>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> known_ptr ptr"
|
||||
apply(simp add: a_known_ptrs_def)
|
||||
using notin_fset by fastforce
|
||||
|
||||
lemma known_ptrs_preserved:
|
||||
"object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved known_ptrs_subset known_ptrs_new_ptr l_known_ptrs_def by blast
|
||||
|
||||
end
|
||||
|
|
@ -1,186 +0,0 @@
|
|||
(***********************************************************************************
|
||||
* Copyright (c) 2016-2018 The University of Sheffield, UK
|
||||
*
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions are met:
|
||||
*
|
||||
* * Redistributions of source code must retain the above copyright notice, this
|
||||
* list of conditions and the following disclaimer.
|
||||
*
|
||||
* * Redistributions in binary form must reproduce the above copyright notice,
|
||||
* this list of conditions and the following disclaimer in the documentation
|
||||
* and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
||||
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
||||
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
||||
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
* SPDX-License-Identifier: BSD-2-Clause
|
||||
***********************************************************************************)
|
||||
|
||||
section\<open>ShadowRoot\<close>
|
||||
text\<open>In this theory, we introduce the typed pointers for the class ShadowRoot. Note that, in
|
||||
this document, we will not make use of ShadowRoots nor will we discuss their particular properties.
|
||||
We only include them here, as they are required for future work and they cannot be added alter
|
||||
following the object-oriented extensibility of our data model.\<close>
|
||||
theory ShadowRootPointer
|
||||
imports
|
||||
"DocumentPointer"
|
||||
begin
|
||||
|
||||
datatype 'shadow_root_ptr shadow_root_ptr = Ref (the_ref: ref) | Ext 'shadow_root_ptr
|
||||
register_default_tvars "'shadow_root_ptr shadow_root_ptr"
|
||||
type_synonym ('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr,
|
||||
'document_ptr, 'shadow_root_ptr) object_ptr
|
||||
= "('shadow_root_ptr shadow_root_ptr + 'object_ptr, 'node_ptr, 'element_ptr,
|
||||
'character_data_ptr, 'document_ptr) object_ptr"
|
||||
register_default_tvars "('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr,
|
||||
'document_ptr, 'shadow_root_ptr) object_ptr"
|
||||
|
||||
definition cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) shadow_root_ptr \<Rightarrow> (_) shadow_root_ptr"
|
||||
where
|
||||
"cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r = id"
|
||||
|
||||
definition cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_)shadow_root_ptr \<Rightarrow> (_) object_ptr"
|
||||
where
|
||||
"cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = object_ptr.Ext (Inr (Inr (Inl ptr)))"
|
||||
|
||||
definition cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) object_ptr \<Rightarrow> (_) shadow_root_ptr option"
|
||||
where
|
||||
"cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = (case ptr of
|
||||
object_ptr.Ext (Inr (Inr (Inl shadow_root_ptr))) \<Rightarrow> Some shadow_root_ptr
|
||||
| _ \<Rightarrow> None)"
|
||||
|
||||
adhoc_overloading cast cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
|
||||
|
||||
definition is_shadow_root_ptr_kind :: "(_) object_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"is_shadow_root_ptr_kind ptr = (case cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of Some _ \<Rightarrow> True
|
||||
| None \<Rightarrow> False)"
|
||||
|
||||
consts is_shadow_root_ptr :: 'a
|
||||
definition is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) shadow_root_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = (case ptr of shadow_root_ptr.Ref _ \<Rightarrow> True
|
||||
| _ \<Rightarrow> False)"
|
||||
|
||||
abbreviation is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) object_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> (case cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of
|
||||
Some shadow_root_ptr \<Rightarrow> is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr
|
||||
| None \<Rightarrow> False)"
|
||||
adhoc_overloading is_shadow_root_ptr is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
lemmas is_shadow_root_ptr_def = is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
|
||||
consts is_shadow_root_ptr_ext :: 'a
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> \<not> is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr"
|
||||
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> (case cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of
|
||||
Some shadow_root_ptr \<Rightarrow> is_shadow_root_ptr_ext\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr
|
||||
| None \<Rightarrow> False)"
|
||||
adhoc_overloading is_shadow_root_ptr_ext is_shadow_root_ptr_ext\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr_ext\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
|
||||
instantiation shadow_root_ptr :: (linorder) linorder
|
||||
begin
|
||||
definition
|
||||
less_eq_shadow_root_ptr :: "(_::linorder) shadow_root_ptr \<Rightarrow> (_) shadow_root_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"less_eq_shadow_root_ptr x y \<equiv> (case x of Ext i \<Rightarrow> (case y of Ext j \<Rightarrow> i \<le> j | Ref _ \<Rightarrow> False)
|
||||
| Ref i \<Rightarrow> (case y of Ext _ \<Rightarrow> True | Ref j \<Rightarrow> i \<le> j))"
|
||||
definition less_shadow_root_ptr :: "(_::linorder) shadow_root_ptr \<Rightarrow> (_) shadow_root_ptr \<Rightarrow> bool"
|
||||
where "less_shadow_root_ptr x y \<equiv> x \<le> y \<and> \<not> y \<le> x"
|
||||
instance
|
||||
apply(standard)
|
||||
by(auto simp add: less_eq_shadow_root_ptr_def less_shadow_root_ptr_def
|
||||
split: shadow_root_ptr.splits)
|
||||
end
|
||||
|
||||
|
||||
lemma is_shadow_root_ptr_ref [simp]: "is_shadow_root_ptr (shadow_root_ptr.Ref n)"
|
||||
by(simp add: is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma is_shadow_root_ptr_not_node_ptr[simp]: "\<not>is_shadow_root_ptr (cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr)"
|
||||
by(simp add: is_shadow_root_ptr_def cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma cast_shadow_root_ptr_not_node_ptr [simp]:
|
||||
"cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr \<noteq> cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr"
|
||||
"cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr \<noteq> cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr"
|
||||
unfolding cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def by auto
|
||||
|
||||
lemma cast_shadow_root_ptr_not_document_ptr [simp]:
|
||||
"cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr \<noteq> cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr"
|
||||
"cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr \<noteq> cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr"
|
||||
unfolding cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def by auto
|
||||
|
||||
lemma shadow_root_ptr_no_node_ptr_cast [simp]:
|
||||
"\<not> is_shadow_root_ptr_kind (cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr)"
|
||||
by(simp add: cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def is_shadow_root_ptr_kind_def)
|
||||
lemma node_ptr_no_shadow_root_ptr_cast [simp]:
|
||||
"\<not> is_node_ptr_kind (cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr)"
|
||||
using is_node_ptr_kind_obtains by fastforce
|
||||
|
||||
lemma shadow_root_ptr_no_document_ptr_cast [simp]:
|
||||
"\<not> is_shadow_root_ptr_kind (cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr)"
|
||||
by(simp add: cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def is_shadow_root_ptr_kind_def)
|
||||
lemma document_ptr_no_shadow_root_ptr_cast [simp]:
|
||||
"\<not> is_document_ptr_kind (cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr)"
|
||||
using is_document_ptr_kind_obtains by fastforce
|
||||
|
||||
lemma shadow_root_ptr_shadow_root_ptr_cast [simp]:
|
||||
"is_shadow_root_ptr_kind (cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr)"
|
||||
by (simp add: cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def is_shadow_root_ptr_kind_def)
|
||||
|
||||
lemma shadow_root_ptr_casts_commute [simp]:
|
||||
"cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = Some shadow_root_ptr \<longleftrightarrow> cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr = ptr"
|
||||
unfolding cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
by(auto split: object_ptr.splits sum.splits)
|
||||
|
||||
lemma shadow_root_ptr_casts_commute2 [simp]:
|
||||
"(cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r (cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr) = Some shadow_root_ptr)"
|
||||
by simp
|
||||
|
||||
lemma shadow_root_ptr_casts_commute3 [simp]:
|
||||
assumes "is_shadow_root_ptr_kind ptr"
|
||||
shows "cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r (the (cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr)) = ptr"
|
||||
using assms
|
||||
by(auto simp add: is_shadow_root_ptr_kind_def cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
split: object_ptr.splits sum.splits)
|
||||
|
||||
lemma is_shadow_root_ptr_kind_obtains:
|
||||
assumes "is_shadow_root_ptr_kind ptr"
|
||||
obtains shadow_root_ptr where "ptr = cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr"
|
||||
using assms is_shadow_root_ptr_kind_def
|
||||
by (metis case_optionE shadow_root_ptr_casts_commute)
|
||||
|
||||
lemma is_shadow_root_ptr_kind_none:
|
||||
assumes "\<not>is_shadow_root_ptr_kind ptr"
|
||||
shows "cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = None"
|
||||
using assms
|
||||
unfolding is_shadow_root_ptr_kind_def cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
by (auto split: object_ptr.splits sum.splits)
|
||||
|
||||
lemma cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_inject [simp]:
|
||||
"cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r x = cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r y \<longleftrightarrow> x = y"
|
||||
by(simp add: cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_ext_none [simp]:
|
||||
"cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r (object_ptr.Ext (Inr (Inr (Inr object_ext_ptr)))) = None"
|
||||
by(simp add: cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma is_shadow_root_ptr_kind_simp1 [dest]: "is_document_ptr_kind ptr \<Longrightarrow> \<not>is_shadow_root_ptr_kind ptr"
|
||||
by (metis document_ptr_no_shadow_root_ptr_cast shadow_root_ptr_casts_commute3)
|
||||
|
||||
lemma is_shadow_root_ptr_kind_simp2 [dest]: "is_node_ptr_kind ptr \<Longrightarrow> \<not>is_shadow_root_ptr_kind ptr"
|
||||
by (metis node_ptr_no_shadow_root_ptr_cast shadow_root_ptr_casts_commute3)
|
||||
|
||||
end
|
||||
|
|
@ -216,7 +216,7 @@ lemma get_child_nodes_reads: "reads (get_child_nodes_locs ptr) (get_child_nodes
|
|||
intro!: reads_bind_pure reads_subset[OF return_reads] )[1]
|
||||
apply(auto simp add: get_child_nodes\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def intro: reads_subset[OF reads_singleton]
|
||||
reads_subset[OF check_in_heap_reads] intro!: reads_bind_pure reads_subset[OF return_reads]
|
||||
split: option.splits)[1]
|
||||
split: option.splits)
|
||||
done
|
||||
end
|
||||
|
||||
|
|
@ -618,70 +618,8 @@ lemma set_child_nodes_get_child_nodes_different_pointers:
|
|||
apply(auto)[1]
|
||||
apply(auto)[1]
|
||||
apply(rule is_element_ptr_kind_obtains)
|
||||
apply(auto)[1]
|
||||
apply(auto)[1]
|
||||
apply(auto)
|
||||
done
|
||||
|
||||
lemma set_child_nodes_element_ok [simp]:
|
||||
assumes "known_ptr ptr"
|
||||
assumes "type_wf h"
|
||||
assumes "ptr |\<in>| object_ptr_kinds h"
|
||||
assumes "is_element_ptr_kind ptr"
|
||||
shows "h \<turnstile> ok (set_child_nodes ptr children)"
|
||||
proof -
|
||||
have "is_element_ptr ptr"
|
||||
using \<open>known_ptr ptr\<close> assms(4)
|
||||
by(auto simp add: known_ptr_impl known_ptr_defs CharacterDataClass.known_ptr_defs
|
||||
ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
|
||||
then show ?thesis
|
||||
using assms
|
||||
apply(auto simp add: set_child_nodes_def a_set_child_nodes_tups_def set_child_nodes\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
split: option.splits)[1]
|
||||
by (simp add: DocumentMonad.put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok local.type_wf_impl)
|
||||
qed
|
||||
|
||||
lemma set_child_nodes_document1_ok [simp]:
|
||||
assumes "known_ptr ptr"
|
||||
assumes "type_wf h"
|
||||
assumes "ptr |\<in>| object_ptr_kinds h"
|
||||
assumes "is_document_ptr_kind ptr"
|
||||
assumes "children = []"
|
||||
shows "h \<turnstile> ok (set_child_nodes ptr children)"
|
||||
proof -
|
||||
have "is_document_ptr ptr"
|
||||
using \<open>known_ptr ptr\<close> assms(4)
|
||||
by(auto simp add: known_ptr_impl known_ptr_defs CharacterDataClass.known_ptr_defs
|
||||
ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
|
||||
then show ?thesis
|
||||
using assms
|
||||
apply(auto simp add: set_child_nodes_def a_set_child_nodes_tups_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
split: option.splits)[1]
|
||||
by (simp add: DocumentMonad.put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok local.type_wf_impl)
|
||||
qed
|
||||
|
||||
lemma set_child_nodes_document2_ok [simp]:
|
||||
assumes "known_ptr ptr"
|
||||
assumes "type_wf h"
|
||||
assumes "ptr |\<in>| object_ptr_kinds h"
|
||||
assumes "is_document_ptr_kind ptr"
|
||||
assumes "children = [child]"
|
||||
assumes "is_element_ptr_kind child"
|
||||
shows "h \<turnstile> ok (set_child_nodes ptr children)"
|
||||
proof -
|
||||
have "is_document_ptr ptr"
|
||||
using \<open>known_ptr ptr\<close> assms(4)
|
||||
by(auto simp add: known_ptr_impl known_ptr_defs CharacterDataClass.known_ptr_defs
|
||||
ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
|
||||
then show ?thesis
|
||||
using assms
|
||||
apply(auto simp add: set_child_nodes_def a_set_child_nodes_tups_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)[1]
|
||||
apply(split invoke_splits, rule conjI)+
|
||||
apply(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]
|
||||
apply(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]
|
||||
apply (simp add: local.type_wf_impl put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok)
|
||||
apply(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]
|
||||
by(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]
|
||||
qed
|
||||
end
|
||||
|
||||
locale l_set_child_nodes_get_child_nodes = l_get_child_nodes + l_set_child_nodes +
|
||||
|
|
@ -1178,8 +1116,7 @@ begin
|
|||
|
||||
definition a_set_disconnected_nodes :: "(_) document_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> (_, unit) dom_prog"
|
||||
where
|
||||
"a_set_disconnected_nodes document_ptr disc_nodes =
|
||||
put_M document_ptr disconnected_nodes_update disc_nodes"
|
||||
"a_set_disconnected_nodes document_ptr disc_nodes = put_M document_ptr disconnected_nodes_update disc_nodes"
|
||||
lemmas set_disconnected_nodes_defs = a_set_disconnected_nodes_def
|
||||
|
||||
definition a_set_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
|
|
@ -1203,13 +1140,10 @@ locale l_set_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\
|
|||
assumes set_disconnected_nodes_locs_impl: "set_disconnected_nodes_locs = a_set_disconnected_nodes_locs"
|
||||
begin
|
||||
lemmas set_disconnected_nodes_def = set_disconnected_nodes_impl[unfolded a_set_disconnected_nodes_def]
|
||||
lemmas set_disconnected_nodes_locs_def =
|
||||
set_disconnected_nodes_locs_impl[unfolded a_set_disconnected_nodes_locs_def]
|
||||
lemmas set_disconnected_nodes_locs_def = set_disconnected_nodes_locs_impl[unfolded a_set_disconnected_nodes_locs_def]
|
||||
lemma set_disconnected_nodes_ok:
|
||||
"type_wf h \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h \<Longrightarrow>
|
||||
h \<turnstile> ok (set_disconnected_nodes document_ptr node_ptrs)"
|
||||
by (simp add: type_wf_impl put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok
|
||||
set_disconnected_nodes_impl[unfolded a_set_disconnected_nodes_def])
|
||||
"type_wf h \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_disconnected_nodes document_ptr node_ptrs)"
|
||||
by (simp add: type_wf_impl put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok set_disconnected_nodes_impl[unfolded a_set_disconnected_nodes_def])
|
||||
|
||||
lemma set_disconnected_nodes_ptr_in_heap:
|
||||
"h \<turnstile> ok (set_disconnected_nodes document_ptr disc_nodes) \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h"
|
||||
|
|
@ -1244,17 +1178,13 @@ end
|
|||
|
||||
locale l_set_disconnected_nodes = l_type_wf + l_set_disconnected_nodes_defs +
|
||||
assumes set_disconnected_nodes_writes:
|
||||
"writes (set_disconnected_nodes_locs document_ptr)
|
||||
(set_disconnected_nodes document_ptr disc_nodes) h h'"
|
||||
"writes (set_disconnected_nodes_locs document_ptr) (set_disconnected_nodes document_ptr disc_nodes) h h'"
|
||||
assumes set_disconnected_nodes_ok:
|
||||
"type_wf h \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h \<Longrightarrow>
|
||||
h \<turnstile> ok (set_disconnected_nodes document_ptr disc_noded)"
|
||||
"type_wf h \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_disconnected_nodes document_ptr disc_noded)"
|
||||
assumes set_disconnected_nodes_ptr_in_heap:
|
||||
"h \<turnstile> ok (set_disconnected_nodes document_ptr disc_noded) \<Longrightarrow>
|
||||
document_ptr |\<in>| document_ptr_kinds h"
|
||||
"h \<turnstile> ok (set_disconnected_nodes document_ptr disc_noded) \<Longrightarrow> document_ptr |\<in>| document_ptr_kinds h"
|
||||
assumes set_disconnected_nodes_pointers_preserved:
|
||||
"w \<in> set_disconnected_nodes_locs document_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow>
|
||||
object_ptr_kinds h = object_ptr_kinds h'"
|
||||
"w \<in> set_disconnected_nodes_locs document_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> object_ptr_kinds h = object_ptr_kinds h'"
|
||||
assumes set_disconnected_nodes_types_preserved:
|
||||
"w \<in> set_disconnected_nodes_locs document_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
|
||||
|
|
@ -1271,8 +1201,7 @@ declare l_set_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D
|
|||
lemma set_disconnected_nodes_is_l_set_disconnected_nodes [instances]:
|
||||
"l_set_disconnected_nodes type_wf set_disconnected_nodes set_disconnected_nodes_locs"
|
||||
apply(simp add: l_set_disconnected_nodes_def)
|
||||
using set_disconnected_nodes_ok set_disconnected_nodes_writes
|
||||
set_disconnected_nodes_pointers_preserved
|
||||
using set_disconnected_nodes_ok set_disconnected_nodes_writes set_disconnected_nodes_pointers_preserved
|
||||
set_disconnected_nodes_ptr_in_heap set_disconnected_nodes_typess_preserved
|
||||
by blast+
|
||||
|
||||
|
|
@ -1314,8 +1243,7 @@ interpretation i_set_disconnected_nodes_get_disconnected_nodes?:
|
|||
by unfold_locales
|
||||
declare l_set_disconnected_nodes_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_disconnected_nodes_get_disconnected_nodes_is_l_set_disconnected_nodes_get_disconnected_nodes
|
||||
[instances]:
|
||||
lemma set_disconnected_nodes_get_disconnected_nodes_is_l_set_disconnected_nodes_get_disconnected_nodes [instances]:
|
||||
"l_set_disconnected_nodes_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs
|
||||
set_disconnected_nodes set_disconnected_nodes_locs"
|
||||
using set_disconnected_nodes_is_l_set_disconnected_nodes get_disconnected_nodes_is_l_get_disconnected_nodes
|
||||
|
|
@ -1362,17 +1290,17 @@ subsubsection \<open>get\_tag\_name\<close>
|
|||
|
||||
locale l_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
begin
|
||||
definition a_get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_name) dom_prog"
|
||||
definition a_get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_type) dom_prog"
|
||||
where
|
||||
"a_get_tag_name element_ptr = get_M element_ptr tag_name"
|
||||
"a_get_tag_name element_ptr = get_M element_ptr tag_type"
|
||||
|
||||
definition a_get_tag_name_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
|
||||
where
|
||||
"a_get_tag_name_locs element_ptr \<equiv> {preserved (get_M element_ptr tag_name)}"
|
||||
"a_get_tag_name_locs element_ptr \<equiv> {preserved (get_M element_ptr tag_type)}"
|
||||
end
|
||||
|
||||
locale l_get_tag_name_defs =
|
||||
fixes get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_name) dom_prog"
|
||||
fixes get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_type) dom_prog"
|
||||
fixes get_tag_name_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
|
||||
|
||||
locale l_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
|
|
@ -1380,7 +1308,7 @@ locale l_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^
|
|||
l_get_tag_name_defs get_tag_name get_tag_name_locs +
|
||||
l_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
for type_wf :: "(_) heap \<Rightarrow> bool"
|
||||
and get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_name) dom_prog"
|
||||
and get_tag_name :: "(_) element_ptr \<Rightarrow> (_, tag_type) dom_prog"
|
||||
and get_tag_name_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set" +
|
||||
assumes type_wf_impl: "type_wf = DocumentClass.type_wf"
|
||||
assumes get_tag_name_impl: "get_tag_name = a_get_tag_name"
|
||||
|
|
@ -1482,7 +1410,7 @@ begin
|
|||
lemma set_child_nodes_get_tag_name:
|
||||
"\<forall>w \<in> set_child_nodes_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_tag_name_locs ptr'. r h h'))"
|
||||
by(auto simp add: set_child_nodes_locs_def get_tag_name_locs_def all_args_def
|
||||
intro: element_put_get_preserved[where getter=tag_name and setter=child_nodes_update])
|
||||
intro: element_put_get_preserved[where getter=tag_type and setter=child_nodes_update])
|
||||
end
|
||||
|
||||
locale l_set_child_nodes_get_tag_name = l_set_child_nodes + l_get_tag_name +
|
||||
|
|
@ -1505,209 +1433,162 @@ lemma set_child_nodes_get_tag_name_is_l_set_child_nodes_get_tag_name [instances]
|
|||
|
||||
subsubsection \<open>set\_tag\_type\<close>
|
||||
|
||||
locale l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
locale l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
begin
|
||||
|
||||
definition a_set_tag_name :: "(_) element_ptr \<Rightarrow> tag_name \<Rightarrow> (_, unit) dom_prog"
|
||||
definition a_set_tag_type :: "(_) element_ptr \<Rightarrow> tag_type \<Rightarrow> (_, unit) dom_prog"
|
||||
where
|
||||
"a_set_tag_name ptr tag = do {
|
||||
"a_set_tag_type ptr tag = do {
|
||||
m \<leftarrow> get_M ptr attrs;
|
||||
put_M ptr tag_name_update tag
|
||||
put_M ptr tag_type_update tag
|
||||
}"
|
||||
lemmas set_tag_name_defs = a_set_tag_name_def
|
||||
lemmas set_tag_type_defs = a_set_tag_type_def
|
||||
|
||||
definition a_set_tag_name_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
definition a_set_tag_type_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
where
|
||||
"a_set_tag_name_locs element_ptr \<equiv> all_args (put_M element_ptr tag_name_update)"
|
||||
"a_set_tag_type_locs element_ptr \<equiv> all_args (put_M element_ptr tag_type_update)"
|
||||
end
|
||||
|
||||
locale l_set_tag_name_defs =
|
||||
fixes set_tag_name :: "(_) element_ptr \<Rightarrow> tag_name \<Rightarrow> (_, unit) dom_prog"
|
||||
fixes set_tag_name_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
locale l_set_tag_type_defs =
|
||||
fixes set_tag_type :: "(_) element_ptr \<Rightarrow> tag_type \<Rightarrow> (_, unit) dom_prog"
|
||||
fixes set_tag_type_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
|
||||
locale l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
locale l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_type_wf type_wf +
|
||||
l_set_tag_name_defs set_tag_name set_tag_name_locs +
|
||||
l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
l_set_tag_type_defs set_tag_type set_tag_type_locs +
|
||||
l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
for type_wf :: "(_) heap \<Rightarrow> bool"
|
||||
and set_tag_name :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> (_, unit) dom_prog"
|
||||
and set_tag_name_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set" +
|
||||
and set_tag_type :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> (_, unit) dom_prog"
|
||||
and set_tag_type_locs :: "(_) element_ptr \<Rightarrow> (_, unit) dom_prog set" +
|
||||
assumes type_wf_impl: "type_wf = DocumentClass.type_wf"
|
||||
assumes set_tag_name_impl: "set_tag_name = a_set_tag_name"
|
||||
assumes set_tag_name_locs_impl: "set_tag_name_locs = a_set_tag_name_locs"
|
||||
assumes set_tag_type_impl: "set_tag_type = a_set_tag_type"
|
||||
assumes set_tag_type_locs_impl: "set_tag_type_locs = a_set_tag_type_locs"
|
||||
begin
|
||||
|
||||
lemma set_tag_name_ok:
|
||||
"type_wf h \<Longrightarrow> element_ptr |\<in>| element_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_tag_name element_ptr tag)"
|
||||
lemma set_tag_type_ok:
|
||||
"type_wf h \<Longrightarrow> element_ptr |\<in>| element_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_tag_type element_ptr tag)"
|
||||
apply(unfold type_wf_impl)
|
||||
unfolding set_tag_name_impl[unfolded a_set_tag_name_def] using get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok
|
||||
unfolding set_tag_type_impl[unfolded a_set_tag_type_def] using get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_ok
|
||||
by (metis (no_types, lifting) DocumentClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ElementMonad.get_M_pure bind_is_OK_E
|
||||
bind_is_OK_pure_I is_OK_returns_result_I)
|
||||
|
||||
lemma set_tag_name_writes:
|
||||
"writes (set_tag_name_locs element_ptr) (set_tag_name element_ptr tag) h h'"
|
||||
by(auto simp add: set_tag_name_impl[unfolded a_set_tag_name_def]
|
||||
set_tag_name_locs_impl[unfolded a_set_tag_name_locs_def] intro: writes_bind_pure)
|
||||
lemma set_tag_type_writes:
|
||||
"writes (set_tag_type_locs element_ptr) (set_tag_type element_ptr tag) h h'"
|
||||
by(auto simp add: set_tag_type_impl[unfolded a_set_tag_type_def]
|
||||
set_tag_type_locs_impl[unfolded a_set_tag_type_locs_def] intro: writes_bind_pure)
|
||||
|
||||
lemma set_tag_name_pointers_preserved:
|
||||
assumes "w \<in> set_tag_name_locs element_ptr"
|
||||
lemma set_tag_type_pointers_preserved:
|
||||
assumes "w \<in> set_tag_type_locs element_ptr"
|
||||
assumes "h \<turnstile> w \<rightarrow>\<^sub>h h'"
|
||||
shows "object_ptr_kinds h = object_ptr_kinds h'"
|
||||
using assms(1) object_ptr_kinds_preserved[OF writes_singleton2 assms(2)]
|
||||
by(auto simp add: all_args_def set_tag_name_locs_impl[unfolded a_set_tag_name_locs_def]
|
||||
by(auto simp add: all_args_def set_tag_type_locs_impl[unfolded a_set_tag_type_locs_def]
|
||||
split: if_splits)
|
||||
|
||||
lemma set_tag_name_typess_preserved:
|
||||
assumes "w \<in> set_tag_name_locs element_ptr"
|
||||
lemma set_tag_type_typess_preserved:
|
||||
assumes "w \<in> set_tag_type_locs element_ptr"
|
||||
assumes "h \<turnstile> w \<rightarrow>\<^sub>h h'"
|
||||
shows "type_wf h = type_wf h'"
|
||||
apply(unfold type_wf_impl)
|
||||
using assms(1) type_wf_preserved[OF writes_singleton2 assms(2)]
|
||||
by(auto simp add: all_args_def set_tag_name_locs_impl[unfolded a_set_tag_name_locs_def]
|
||||
by(auto simp add: all_args_def set_tag_type_locs_impl[unfolded a_set_tag_type_locs_def]
|
||||
split: if_splits)
|
||||
end
|
||||
|
||||
locale l_set_tag_name = l_type_wf + l_set_tag_name_defs +
|
||||
assumes set_tag_name_writes:
|
||||
"writes (set_tag_name_locs element_ptr) (set_tag_name element_ptr tag) h h'"
|
||||
assumes set_tag_name_ok:
|
||||
"type_wf h \<Longrightarrow> element_ptr |\<in>| element_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_tag_name element_ptr tag)"
|
||||
assumes set_tag_name_pointers_preserved:
|
||||
"w \<in> set_tag_name_locs element_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> object_ptr_kinds h = object_ptr_kinds h'"
|
||||
assumes set_tag_name_types_preserved:
|
||||
"w \<in> set_tag_name_locs element_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
locale l_set_tag_type = l_type_wf + l_set_tag_type_defs +
|
||||
assumes set_tag_type_writes:
|
||||
"writes (set_tag_type_locs element_ptr) (set_tag_type element_ptr tag) h h'"
|
||||
assumes set_tag_type_ok:
|
||||
"type_wf h \<Longrightarrow> element_ptr |\<in>| element_ptr_kinds h \<Longrightarrow> h \<turnstile> ok (set_tag_type element_ptr tag)"
|
||||
assumes set_tag_type_pointers_preserved:
|
||||
"w \<in> set_tag_type_locs element_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> object_ptr_kinds h = object_ptr_kinds h'"
|
||||
assumes set_tag_type_types_preserved:
|
||||
"w \<in> set_tag_type_locs element_ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
|
||||
|
||||
global_interpretation l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs defines
|
||||
set_tag_name = l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_set_tag_name and
|
||||
set_tag_name_locs = l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_set_tag_name_locs .
|
||||
global_interpretation l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs defines
|
||||
set_tag_type = l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_set_tag_type and
|
||||
set_tag_type_locs = l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_set_tag_type_locs .
|
||||
interpretation
|
||||
i_set_tag_name?: l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf set_tag_name set_tag_name_locs
|
||||
i_set_tag_type?: l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf set_tag_type set_tag_type_locs
|
||||
apply(unfold_locales)
|
||||
by (auto simp add: set_tag_name_def set_tag_name_locs_def)
|
||||
declare l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
by (auto simp add: set_tag_type_def set_tag_type_locs_def)
|
||||
declare l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_tag_name_is_l_set_tag_name [instances]:
|
||||
"l_set_tag_name type_wf set_tag_name set_tag_name_locs"
|
||||
apply(simp add: l_set_tag_name_def)
|
||||
using set_tag_name_ok set_tag_name_writes set_tag_name_pointers_preserved
|
||||
set_tag_name_typess_preserved
|
||||
lemma set_tag_type_is_l_set_tag_type [instances]:
|
||||
"l_set_tag_type type_wf set_tag_type set_tag_type_locs"
|
||||
apply(simp add: l_set_tag_type_def)
|
||||
using set_tag_type_ok set_tag_type_writes set_tag_type_pointers_preserved
|
||||
set_tag_type_typess_preserved
|
||||
by blast
|
||||
|
||||
paragraph \<open>get\_child\_nodes\<close>
|
||||
|
||||
locale l_set_tag_name_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
|
||||
locale l_set_tag_type_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
|
||||
l_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M
|
||||
begin
|
||||
lemma set_tag_name_get_child_nodes:
|
||||
"\<forall>w \<in> set_tag_name_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_child_nodes_locs ptr'. r h h'))"
|
||||
by(auto simp add: set_tag_name_locs_impl[unfolded a_set_tag_name_locs_def]
|
||||
lemma set_tag_type_get_child_nodes:
|
||||
"\<forall>w \<in> set_tag_type_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_child_nodes_locs ptr'. r h h'))"
|
||||
by(auto simp add: set_tag_type_locs_impl[unfolded a_set_tag_type_locs_def]
|
||||
get_child_nodes_locs_impl[unfolded a_get_child_nodes_locs_def] all_args_def
|
||||
intro: element_put_get_preserved[where setter=tag_name_update and getter=child_nodes])
|
||||
intro: element_put_get_preserved[where setter=tag_type_update and getter=child_nodes])
|
||||
end
|
||||
|
||||
locale l_set_tag_name_get_child_nodes = l_set_tag_name + l_get_child_nodes +
|
||||
assumes set_tag_name_get_child_nodes:
|
||||
"\<forall>w \<in> set_tag_name_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_child_nodes_locs ptr'. r h h'))"
|
||||
locale l_set_tag_type_get_child_nodes = l_set_tag_type + l_get_child_nodes +
|
||||
assumes set_tag_type_get_child_nodes:
|
||||
"\<forall>w \<in> set_tag_type_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_child_nodes_locs ptr'. r h h'))"
|
||||
|
||||
interpretation
|
||||
i_set_tag_name_get_child_nodes?: l_set_tag_name_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf
|
||||
set_tag_name set_tag_name_locs known_ptr
|
||||
i_set_tag_type_get_child_nodes?: l_set_tag_type_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf
|
||||
set_tag_type set_tag_type_locs known_ptr
|
||||
get_child_nodes get_child_nodes_locs
|
||||
by unfold_locales
|
||||
declare l_set_tag_name_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
declare l_set_tag_type_get_child_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_tag_name_get_child_nodes_is_l_set_tag_name_get_child_nodes [instances]:
|
||||
"l_set_tag_name_get_child_nodes type_wf set_tag_name set_tag_name_locs known_ptr get_child_nodes
|
||||
lemma set_tag_type_get_child_nodes_is_l_set_tag_type_get_child_nodes [instances]:
|
||||
"l_set_tag_type_get_child_nodes type_wf set_tag_type set_tag_type_locs known_ptr get_child_nodes
|
||||
get_child_nodes_locs"
|
||||
using set_tag_name_is_l_set_tag_name get_child_nodes_is_l_get_child_nodes
|
||||
apply(simp add: l_set_tag_name_get_child_nodes_def l_set_tag_name_get_child_nodes_axioms_def)
|
||||
using set_tag_name_get_child_nodes
|
||||
using set_tag_type_is_l_set_tag_type get_child_nodes_is_l_get_child_nodes
|
||||
apply(simp add: l_set_tag_type_get_child_nodes_def l_set_tag_type_get_child_nodes_axioms_def)
|
||||
using set_tag_type_get_child_nodes
|
||||
by fast
|
||||
|
||||
|
||||
paragraph \<open>get\_disconnected\_nodes\<close>
|
||||
|
||||
locale l_set_tag_name_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
|
||||
locale l_set_tag_type_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_set_tag_type\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
|
||||
l_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M
|
||||
begin
|
||||
lemma set_tag_name_get_disconnected_nodes:
|
||||
"\<forall>w \<in> set_tag_name_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_disconnected_nodes_locs ptr'. r h h'))"
|
||||
by(auto simp add: set_tag_name_locs_impl[unfolded a_set_tag_name_locs_def]
|
||||
lemma set_tag_type_get_disconnected_nodes:
|
||||
"\<forall>w \<in> set_tag_type_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_disconnected_nodes_locs ptr'. r h h'))"
|
||||
by(auto simp add: set_tag_type_locs_impl[unfolded a_set_tag_type_locs_def]
|
||||
get_disconnected_nodes_locs_impl[unfolded a_get_disconnected_nodes_locs_def]
|
||||
all_args_def)
|
||||
end
|
||||
|
||||
locale l_set_tag_name_get_disconnected_nodes = l_set_tag_name + l_get_disconnected_nodes +
|
||||
assumes set_tag_name_get_disconnected_nodes:
|
||||
"\<forall>w \<in> set_tag_name_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_disconnected_nodes_locs ptr'. r h h'))"
|
||||
locale l_set_tag_type_get_disconnected_nodes = l_set_tag_type + l_get_disconnected_nodes +
|
||||
assumes set_tag_type_get_disconnected_nodes:
|
||||
"\<forall>w \<in> set_tag_type_locs ptr. (h \<turnstile> w \<rightarrow>\<^sub>h h' \<longrightarrow> (\<forall>r \<in> get_disconnected_nodes_locs ptr'. r h h'))"
|
||||
|
||||
interpretation
|
||||
i_set_tag_name_get_disconnected_nodes?: l_set_tag_name_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf
|
||||
set_tag_name set_tag_name_locs get_disconnected_nodes
|
||||
i_set_tag_type_get_disconnected_nodes?: l_set_tag_type_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf
|
||||
set_tag_type set_tag_type_locs get_disconnected_nodes
|
||||
get_disconnected_nodes_locs
|
||||
by unfold_locales
|
||||
declare l_set_tag_name_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
declare l_set_tag_type_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_tag_name_get_disconnected_nodes_is_l_set_tag_name_get_disconnected_nodes [instances]:
|
||||
"l_set_tag_name_get_disconnected_nodes type_wf set_tag_name set_tag_name_locs get_disconnected_nodes
|
||||
lemma set_tag_type_get_disconnected_nodes_is_l_set_tag_type_get_disconnected_nodes [instances]:
|
||||
"l_set_tag_type_get_disconnected_nodes type_wf set_tag_type set_tag_type_locs get_disconnected_nodes
|
||||
get_disconnected_nodes_locs"
|
||||
using set_tag_name_is_l_set_tag_name get_disconnected_nodes_is_l_get_disconnected_nodes
|
||||
apply(simp add: l_set_tag_name_get_disconnected_nodes_def
|
||||
l_set_tag_name_get_disconnected_nodes_axioms_def)
|
||||
using set_tag_name_get_disconnected_nodes
|
||||
using set_tag_type_is_l_set_tag_type get_disconnected_nodes_is_l_get_disconnected_nodes
|
||||
apply(simp add: l_set_tag_type_get_disconnected_nodes_def
|
||||
l_set_tag_type_get_disconnected_nodes_axioms_def)
|
||||
using set_tag_type_get_disconnected_nodes
|
||||
by fast
|
||||
|
||||
|
||||
paragraph \<open>get\_tag\_type\<close>
|
||||
|
||||
locale l_set_tag_name_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M = l_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M
|
||||
+ l_set_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M
|
||||
begin
|
||||
lemma set_tag_name_get_tag_name:
|
||||
assumes "h \<turnstile> a_set_tag_name element_ptr tag \<rightarrow>\<^sub>h h'"
|
||||
shows "h' \<turnstile> a_get_tag_name element_ptr \<rightarrow>\<^sub>r tag"
|
||||
using assms
|
||||
by(auto simp add: a_get_tag_name_def a_set_tag_name_def)
|
||||
|
||||
lemma set_tag_name_get_tag_name_different_pointers:
|
||||
assumes "ptr \<noteq> ptr'"
|
||||
assumes "w \<in> a_set_tag_name_locs ptr"
|
||||
assumes "h \<turnstile> w \<rightarrow>\<^sub>h h'"
|
||||
assumes "r \<in> a_get_tag_name_locs ptr'"
|
||||
shows "r h h'"
|
||||
using assms
|
||||
by(auto simp add: all_args_def a_set_tag_name_locs_def a_get_tag_name_locs_def
|
||||
split: if_splits option.splits )
|
||||
end
|
||||
|
||||
locale l_set_tag_name_get_tag_name = l_get_tag_name + l_set_tag_name +
|
||||
assumes set_tag_name_get_tag_name:
|
||||
"h \<turnstile> set_tag_name element_ptr tag \<rightarrow>\<^sub>h h'
|
||||
\<Longrightarrow> h' \<turnstile> get_tag_name element_ptr \<rightarrow>\<^sub>r tag"
|
||||
assumes set_tag_name_get_tag_name_different_pointers:
|
||||
"ptr \<noteq> ptr' \<Longrightarrow> w \<in> set_tag_name_locs ptr \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
|
||||
\<Longrightarrow> r \<in> get_tag_name_locs ptr' \<Longrightarrow> r h h'"
|
||||
|
||||
interpretation i_set_tag_name_get_tag_name?:
|
||||
l_set_tag_name_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf get_tag_name
|
||||
get_tag_name_locs set_tag_name set_tag_name_locs
|
||||
by unfold_locales
|
||||
declare l_set_tag_name_get_tag_name\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_tag_name_get_tag_name_is_l_set_tag_name_get_tag_name [instances]:
|
||||
"l_set_tag_name_get_tag_name type_wf get_tag_name get_tag_name_locs
|
||||
set_tag_name set_tag_name_locs"
|
||||
using set_tag_name_is_l_set_tag_name get_tag_name_is_l_get_tag_name
|
||||
apply(simp add: l_set_tag_name_get_tag_name_def
|
||||
l_set_tag_name_get_tag_name_axioms_def)
|
||||
using set_tag_name_get_tag_name
|
||||
set_tag_name_get_tag_name_different_pointers
|
||||
by fast+
|
||||
|
||||
|
||||
subsubsection \<open>set\_val\<close>
|
||||
|
||||
locale l_set_val\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs
|
||||
|
|
@ -1848,8 +1729,7 @@ interpretation
|
|||
declare l_set_val_get_disconnected_nodes\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
lemma set_val_get_disconnected_nodes_is_l_set_val_get_disconnected_nodes [instances]:
|
||||
"l_set_val_get_disconnected_nodes type_wf set_val set_val_locs get_disconnected_nodes
|
||||
get_disconnected_nodes_locs"
|
||||
"l_set_val_get_disconnected_nodes type_wf set_val set_val_locs get_disconnected_nodes get_disconnected_nodes_locs"
|
||||
using set_val_is_l_set_val get_disconnected_nodes_is_l_get_disconnected_nodes
|
||||
apply(simp add: l_set_val_get_disconnected_nodes_def l_set_val_get_disconnected_nodes_axioms_def)
|
||||
using set_val_get_disconnected_nodes
|
||||
|
|
@ -2483,9 +2363,7 @@ lemma remove_child_child_in_heap:
|
|||
assumes "h \<turnstile> remove_child ptr' child \<rightarrow>\<^sub>h h'"
|
||||
shows "child |\<in>| node_ptr_kinds h"
|
||||
using assms
|
||||
apply(auto simp add: remove_child_def
|
||||
elim!: bind_returns_heap_E bind_returns_heap_E2[rotated, OF get_child_nodes_pure, rotated]
|
||||
split: if_splits)[1]
|
||||
apply(auto simp add: remove_child_def elim!: bind_returns_heap_E bind_returns_heap_E2[rotated, OF get_child_nodes_pure, rotated] split: if_splits)
|
||||
by (meson is_OK_returns_result_I local.get_owner_document_ptr_in_heap node_ptr_kinds_commutes)
|
||||
|
||||
|
||||
|
|
@ -2503,8 +2381,7 @@ proof -
|
|||
using assms(1)
|
||||
apply(auto simp add: remove_child_def
|
||||
elim!: bind_returns_heap_E
|
||||
dest!: returns_result_eq[OF assms(2)]
|
||||
pure_returns_heap_eq[rotated, OF get_owner_document_pure]
|
||||
dest!: returns_result_eq[OF assms(2)] pure_returns_heap_eq[rotated, OF get_owner_document_pure]
|
||||
pure_returns_heap_eq[rotated, OF get_child_nodes_pure]
|
||||
split: if_splits)[1]
|
||||
by (metis get_disconnected_nodes_pure pure_returns_heap_eq)
|
||||
|
|
@ -2527,8 +2404,7 @@ lemma remove_child_writes [simp]:
|
|||
intro!: writes_bind)
|
||||
|
||||
lemma remove_writes:
|
||||
"writes (remove_child_locs (the |h \<turnstile> get_parent child|\<^sub>r) |h \<turnstile> get_owner_document (cast child)|\<^sub>r)
|
||||
(remove child) h h'"
|
||||
"writes (remove_child_locs (the |h \<turnstile> get_parent child|\<^sub>r) |h \<turnstile> get_owner_document (cast child)|\<^sub>r) (remove child) h h'"
|
||||
by(auto simp add: remove_def intro!: writes_bind_pure split: option.splits)
|
||||
|
||||
lemma remove_child_children_subset:
|
||||
|
|
@ -2612,8 +2488,7 @@ end
|
|||
locale l_remove_child = l_type_wf + l_known_ptrs + l_remove_child_defs + l_get_owner_document_defs
|
||||
+ l_get_child_nodes_defs + l_get_disconnected_nodes_defs +
|
||||
assumes remove_child_writes:
|
||||
"writes (remove_child_locs object_ptr |h \<turnstile> get_owner_document (cast child)|\<^sub>r)
|
||||
(remove_child object_ptr child) h h'"
|
||||
"writes (remove_child_locs object_ptr |h \<turnstile> get_owner_document (cast child)|\<^sub>r) (remove_child object_ptr child) h h'"
|
||||
assumes remove_child_pointers_preserved:
|
||||
"w \<in> remove_child_locs ptr owner_document \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> object_ptr_kinds h = object_ptr_kinds h'"
|
||||
assumes remove_child_types_preserved:
|
||||
|
|
@ -2811,8 +2686,7 @@ proof -
|
|||
obtain old_document parent_opt h2 where
|
||||
old_document: "h \<turnstile> get_owner_document (cast node) \<rightarrow>\<^sub>r old_document" and
|
||||
parent_opt: "h \<turnstile> get_parent node \<rightarrow>\<^sub>r parent_opt" and
|
||||
h2: "h \<turnstile> (case parent_opt of Some parent \<Rightarrow> do { remove_child parent node } |
|
||||
None \<Rightarrow> do { return ()}) \<rightarrow>\<^sub>h h2"
|
||||
h2: "h \<turnstile> (case parent_opt of Some parent \<Rightarrow> do { remove_child parent node } | None \<Rightarrow> do { return ()}) \<rightarrow>\<^sub>h h2"
|
||||
and
|
||||
h': "h2 \<turnstile> (if owner_document \<noteq> old_document then do {
|
||||
old_disc_nodes \<leftarrow> get_disconnected_nodes old_document;
|
||||
|
|
@ -2860,8 +2734,7 @@ None \<Rightarrow> do { return ()}) \<rightarrow>\<^sub>h h2"
|
|||
next
|
||||
case (Some option)
|
||||
then show ?case
|
||||
using assms(2) \<open>h2 \<turnstile> get_child_nodes ptr \<rightarrow>\<^sub>r children'\<close> remove_child_children_subset known_ptrs
|
||||
type_wf
|
||||
using assms(2) \<open>h2 \<turnstile> get_child_nodes ptr \<rightarrow>\<^sub>r children'\<close> remove_child_children_subset known_ptrs type_wf
|
||||
by simp
|
||||
qed
|
||||
qed
|
||||
|
|
@ -2895,8 +2768,7 @@ lemma adopt_node_types_preserved:
|
|||
by (auto split: if_splits)
|
||||
end
|
||||
|
||||
locale l_adopt_node = l_type_wf + l_known_ptrs + l_get_parent_defs + l_adopt_node_defs +
|
||||
l_get_child_nodes_defs + l_get_owner_document_defs +
|
||||
locale l_adopt_node = l_type_wf + l_known_ptrs + l_get_parent_defs + l_adopt_node_defs + l_get_child_nodes_defs + l_get_owner_document_defs +
|
||||
assumes adopt_node_writes:
|
||||
"writes (adopt_node_locs |h \<turnstile> get_parent node|\<^sub>r
|
||||
|h \<turnstile> get_owner_document (cast node)|\<^sub>r document_ptr) (adopt_node document_ptr node) h h'"
|
||||
|
|
@ -3092,8 +2964,7 @@ locale l_insert_before\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<
|
|||
and get_disconnected_nodes :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"
|
||||
and get_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
|
||||
and get_owner_document :: "(_) object_ptr \<Rightarrow> ((_) heap, exception, (_) document_ptr) prog"
|
||||
and insert_before ::
|
||||
"(_) object_ptr \<Rightarrow> (_) node_ptr \<Rightarrow> (_) node_ptr option \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and insert_before :: "(_) object_ptr \<Rightarrow> (_) node_ptr \<Rightarrow> (_) node_ptr option \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and insert_before_locs :: "(_) object_ptr \<Rightarrow> (_) object_ptr option \<Rightarrow> (_) document_ptr
|
||||
\<Rightarrow> (_) document_ptr \<Rightarrow> (_, unit) dom_prog set"
|
||||
and append_child :: "(_) object_ptr \<Rightarrow> (_) node_ptr \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
|
|
@ -3115,8 +2986,8 @@ lemma insert_before_list_in_set: "x \<in> set (insert_before_list v ref xs) \<lo
|
|||
by(auto)
|
||||
|
||||
lemma insert_before_list_distinct: "x \<notin> set xs \<Longrightarrow> distinct xs \<Longrightarrow> distinct (insert_before_list x ref xs)"
|
||||
apply(induct x ref xs rule: insert_before_list.induct)
|
||||
by(auto simp add: insert_before_list_in_set)
|
||||
by (induct x ref xs rule: insert_before_list.induct)
|
||||
(auto simp add: insert_before_list_in_set)
|
||||
|
||||
lemma insert_before_list_subset: "set xs \<subseteq> set (insert_before_list x ref xs)"
|
||||
apply(induct x ref xs rule: insert_before_list.induct)
|
||||
|
|
@ -3156,9 +3027,8 @@ lemma insert_before_ptr_in_heap:
|
|||
assumes "h \<turnstile> ok (insert_before ptr node reference_child)"
|
||||
shows "ptr |\<in>| object_ptr_kinds h"
|
||||
using assms
|
||||
apply(auto simp add: insert_before_def elim!: bind_is_OK_E)[1]
|
||||
by (metis (mono_tags, lifting) ensure_pre_insertion_validity_pure is_OK_returns_result_I
|
||||
local.get_owner_document_ptr_in_heap next_sibling_pure pure_returns_heap_eq return_returns_heap)
|
||||
apply(auto simp add: insert_before_def elim!: bind_is_OK_E)
|
||||
by (metis (mono_tags, lifting) ensure_pre_insertion_validity_pure is_OK_returns_result_I local.get_owner_document_ptr_in_heap next_sibling_pure pure_returns_heap_eq return_returns_heap)
|
||||
|
||||
lemma insert_before_child_in_heap:
|
||||
assumes "h \<turnstile> ok (insert_before ptr node reference_child)"
|
||||
|
|
@ -3277,7 +3147,7 @@ subsubsection \<open>create\_element\<close>
|
|||
locale l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs =
|
||||
l_get_disconnected_nodes_defs get_disconnected_nodes get_disconnected_nodes_locs +
|
||||
l_set_disconnected_nodes_defs set_disconnected_nodes set_disconnected_nodes_locs +
|
||||
l_set_tag_name_defs set_tag_name set_tag_name_locs
|
||||
l_set_tag_type_defs set_tag_type set_tag_type_locs
|
||||
for get_disconnected_nodes ::
|
||||
"(_) document_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"
|
||||
and get_disconnected_nodes_locs ::
|
||||
|
|
@ -3286,16 +3156,16 @@ locale l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\
|
|||
"(_) document_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and set_disconnected_nodes_locs ::
|
||||
"(_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
|
||||
and set_tag_name ::
|
||||
and set_tag_type ::
|
||||
"(_) element_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and set_tag_name_locs ::
|
||||
and set_tag_type_locs ::
|
||||
"(_) element_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
|
||||
begin
|
||||
definition a_create_element :: "(_) document_ptr \<Rightarrow> tag_name \<Rightarrow> (_, (_) element_ptr) dom_prog"
|
||||
definition a_create_element :: "(_) document_ptr \<Rightarrow> tag_type \<Rightarrow> (_, (_) element_ptr) dom_prog"
|
||||
where
|
||||
"a_create_element document_ptr tag = do {
|
||||
new_element_ptr \<leftarrow> new_element;
|
||||
set_tag_name new_element_ptr tag;
|
||||
set_tag_type new_element_ptr tag;
|
||||
disc_nodes \<leftarrow> get_disconnected_nodes document_ptr;
|
||||
set_disconnected_nodes document_ptr (cast new_element_ptr # disc_nodes);
|
||||
return new_element_ptr
|
||||
|
|
@ -3303,29 +3173,28 @@ definition a_create_element :: "(_) document_ptr \<Rightarrow> tag_name \<Righta
|
|||
end
|
||||
|
||||
locale l_create_element_defs =
|
||||
fixes create_element :: "(_) document_ptr \<Rightarrow> tag_name \<Rightarrow> (_, (_) element_ptr) dom_prog"
|
||||
fixes create_element :: "(_) document_ptr \<Rightarrow> tag_type \<Rightarrow> (_, (_) element_ptr) dom_prog"
|
||||
|
||||
global_interpretation l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs get_disconnected_nodes get_disconnected_nodes_locs
|
||||
set_disconnected_nodes set_disconnected_nodes_locs
|
||||
set_tag_name set_tag_name_locs
|
||||
set_tag_type set_tag_type_locs
|
||||
defines
|
||||
create_element = "l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_create_element get_disconnected_nodes
|
||||
set_disconnected_nodes set_tag_name"
|
||||
set_disconnected_nodes set_tag_type"
|
||||
.
|
||||
|
||||
locale l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs get_disconnected_nodes get_disconnected_nodes_locs
|
||||
set_disconnected_nodes set_disconnected_nodes_locs set_tag_name set_tag_name_locs +
|
||||
l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_tag_type set_tag_type_locs +
|
||||
l_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs +
|
||||
l_set_tag_name type_wf set_tag_name set_tag_name_locs +
|
||||
l_set_tag_type type_wf set_tag_type set_tag_type_locs +
|
||||
l_create_element_defs create_element +
|
||||
l_known_ptr known_ptr
|
||||
for get_disconnected_nodes :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"
|
||||
and get_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
|
||||
and set_disconnected_nodes :: "(_) document_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and set_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
|
||||
and set_tag_name :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and set_tag_name_locs :: "(_) element_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
|
||||
and set_tag_type :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, unit) prog"
|
||||
and set_tag_type_locs :: "(_) element_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
|
||||
and type_wf :: "(_) heap \<Rightarrow> bool"
|
||||
and create_element :: "(_) document_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr) prog"
|
||||
and known_ptr :: "(_) object_ptr \<Rightarrow> bool" +
|
||||
|
|
@ -3345,7 +3214,7 @@ proof -
|
|||
obtain new_element_ptr h2 h3 disc_nodes_h3 where
|
||||
new_element_ptr: "h \<turnstile> new_element \<rightarrow>\<^sub>r new_element_ptr" and
|
||||
h2: "h \<turnstile> new_element \<rightarrow>\<^sub>h h2" and
|
||||
h3: "h2 \<turnstile> set_tag_name new_element_ptr tag \<rightarrow>\<^sub>h h3" and
|
||||
h3: "h2 \<turnstile> set_tag_type new_element_ptr tag \<rightarrow>\<^sub>h h3" and
|
||||
disc_nodes_h3: "h3 \<turnstile> get_disconnected_nodes document_ptr \<rightarrow>\<^sub>r disc_nodes_h3" and
|
||||
h': "h3 \<turnstile> set_disconnected_nodes document_ptr (cast new_element_ptr # disc_nodes_h3) \<rightarrow>\<^sub>h h'"
|
||||
by(auto simp add: create_element_def
|
||||
|
|
@ -3356,9 +3225,8 @@ proof -
|
|||
using new_element_new_ptr h2 new_element_ptr by blast
|
||||
|
||||
moreover have object_ptr_kinds_eq_h2: "object_ptr_kinds h3 = object_ptr_kinds h2"
|
||||
apply(rule writes_small_big[where P="\<lambda>h h'. object_ptr_kinds h' = object_ptr_kinds h",
|
||||
OF set_tag_name_writes h3])
|
||||
using set_tag_name_pointers_preserved
|
||||
apply(rule writes_small_big[where P="\<lambda>h h'. object_ptr_kinds h' = object_ptr_kinds h", OF set_tag_type_writes h3])
|
||||
using set_tag_type_pointers_preserved
|
||||
by (auto simp add: reflp_def transp_def)
|
||||
moreover have "document_ptr |\<in>| document_ptr_kinds h3"
|
||||
by (meson disc_nodes_h3 is_OK_returns_result_I local.get_disconnected_nodes_ptr_in_heap)
|
||||
|
|
@ -3373,21 +3241,18 @@ lemma create_element_known_ptr:
|
|||
proof -
|
||||
have "is_element_ptr new_element_ptr"
|
||||
using assms
|
||||
apply(auto simp add: create_element_def elim!: bind_returns_result_E)[1]
|
||||
apply(auto simp add: create_element_def elim!: bind_returns_result_E)
|
||||
using new_element_is_element_ptr
|
||||
by blast
|
||||
then show ?thesis
|
||||
by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs
|
||||
ElementClass.known_ptr_defs)
|
||||
by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs)
|
||||
qed
|
||||
end
|
||||
|
||||
locale l_create_element = l_create_element_defs
|
||||
|
||||
interpretation
|
||||
i_create_element?: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs
|
||||
set_disconnected_nodes set_disconnected_nodes_locs set_tag_name set_tag_name_locs type_wf
|
||||
create_element known_ptr
|
||||
i_create_element?: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_tag_type set_tag_type_locs type_wf create_element known_ptr
|
||||
by(auto simp add: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms_def create_element_def instances)
|
||||
declare l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
|
||||
|
||||
|
|
@ -3426,8 +3291,7 @@ global_interpretation l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^
|
|||
.
|
||||
|
||||
locale l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
|
||||
l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs set_val set_val_locs get_disconnected_nodes
|
||||
get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs +
|
||||
l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs set_val set_val_locs get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs +
|
||||
l_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs +
|
||||
l_set_val type_wf set_val set_val_locs +
|
||||
l_create_character_data_defs create_character_data +
|
||||
|
|
@ -3468,8 +3332,7 @@ proof -
|
|||
using new_character_data_new_ptr h2 new_character_data_ptr by blast
|
||||
|
||||
moreover have object_ptr_kinds_eq_h2: "object_ptr_kinds h3 = object_ptr_kinds h2"
|
||||
apply(rule writes_small_big[where P="\<lambda>h h'. object_ptr_kinds h' = object_ptr_kinds h",
|
||||
OF set_val_writes h3])
|
||||
apply(rule writes_small_big[where P="\<lambda>h h'. object_ptr_kinds h' = object_ptr_kinds h", OF set_val_writes h3])
|
||||
using set_val_pointers_preserved
|
||||
by (auto simp add: reflp_def transp_def)
|
||||
moreover have "document_ptr |\<in>| document_ptr_kinds h3"
|
||||
|
|
@ -3480,28 +3343,24 @@ proof -
|
|||
qed
|
||||
|
||||
lemma create_character_data_known_ptr:
|
||||
assumes "h \<turnstile> create_character_data document_ptr text \<rightarrow>\<^sub>r new_character_data_ptr"
|
||||
assumes "h \<turnstile> create_character_data document_ptr tag \<rightarrow>\<^sub>r new_character_data_ptr"
|
||||
shows "known_ptr (cast new_character_data_ptr)"
|
||||
proof -
|
||||
have "is_character_data_ptr new_character_data_ptr"
|
||||
using assms
|
||||
apply(auto simp add: create_character_data_def elim!: bind_returns_result_E)[1]
|
||||
apply(auto simp add: create_character_data_def elim!: bind_returns_result_E)
|
||||
using new_character_data_is_character_data_ptr
|
||||
by blast
|
||||
then show ?thesis
|
||||
by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs
|
||||
ElementClass.known_ptr_defs)
|
||||
by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs)
|
||||
qed
|
||||
end
|
||||
|
||||
locale l_create_character_data = l_create_character_data_defs
|
||||
|
||||
interpretation
|
||||
i_create_character_data?: l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes
|
||||
get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_val set_val_locs
|
||||
type_wf create_character_data known_ptr
|
||||
by(auto simp add: l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms_def
|
||||
create_character_data_def instances)
|
||||
i_create_character_data?: l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_val set_val_locs type_wf create_character_data known_ptr
|
||||
by(auto simp add: l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms_def create_character_data_def instances)
|
||||
declare l_create_character_data\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms [instances]
|
||||
|
||||
|
||||
|
|
@ -3697,11 +3556,11 @@ definition a_get_elements_by_class_name :: "(_) object_ptr \<Rightarrow> attr_va
|
|||
|
||||
definition a_get_elements_by_tag_name :: "(_) object_ptr \<Rightarrow> attr_value \<Rightarrow> (_, (_) element_ptr list) dom_prog"
|
||||
where
|
||||
"a_get_elements_by_tag_name ptr tag = to_tree_order ptr \<bind>
|
||||
"a_get_elements_by_tag_name ptr tag_name = to_tree_order ptr \<bind>
|
||||
map_filter_M (\<lambda>ptr. (case cast ptr of
|
||||
Some element_ptr \<Rightarrow> do {
|
||||
this_tag_name \<leftarrow> get_M element_ptr tag_name;
|
||||
(if this_tag_name = tag then return (Some element_ptr) else return None)
|
||||
this_tag_name \<leftarrow> get_M element_ptr tag_type;
|
||||
(if this_tag_name = tag_name then return (Some element_ptr) else return None)
|
||||
}
|
||||
| _ \<Rightarrow> return None))"
|
||||
end
|
||||
|
|
@ -3716,8 +3575,7 @@ global_interpretation
|
|||
defines
|
||||
get_element_by_id = "l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_get_element_by_id first_in_tree_order get_attribute"
|
||||
and
|
||||
get_elements_by_class_name = "l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_get_elements_by_class_name
|
||||
to_tree_order get_attribute"
|
||||
get_elements_by_class_name = "l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_get_elements_by_class_name to_tree_order get_attribute"
|
||||
and
|
||||
get_elements_by_tag_name = "l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs.a_get_elements_by_tag_name to_tree_order" .
|
||||
|
||||
|
|
@ -3728,17 +3586,13 @@ locale l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\
|
|||
l_to_tree_order to_tree_order +
|
||||
l_get_attribute type_wf get_attribute get_attribute_locs
|
||||
for to_tree_order :: "(_::linorder) object_ptr \<Rightarrow> ((_) heap, exception, (_) object_ptr list) prog"
|
||||
and first_in_tree_order ::
|
||||
"(_) object_ptr \<Rightarrow> ((_) object_ptr \<Rightarrow> ((_) heap, exception, (_) element_ptr option) prog)
|
||||
and first_in_tree_order :: "(_) object_ptr \<Rightarrow> ((_) object_ptr \<Rightarrow> ((_) heap, exception, (_) element_ptr option) prog)
|
||||
\<Rightarrow> ((_) heap, exception, (_) element_ptr option) prog"
|
||||
and get_attribute :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, char list option) prog"
|
||||
and get_attribute_locs :: "(_) element_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
|
||||
and get_element_by_id ::
|
||||
"(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr option) prog"
|
||||
and get_elements_by_class_name ::
|
||||
"(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr list) prog"
|
||||
and get_elements_by_tag_name ::
|
||||
"(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr list) prog"
|
||||
and get_element_by_id :: "(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr option) prog"
|
||||
and get_elements_by_class_name :: "(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr list) prog"
|
||||
and get_elements_by_tag_name :: "(_) object_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr list) prog"
|
||||
and type_wf :: "(_) heap \<Rightarrow> bool" +
|
||||
assumes get_element_by_id_impl: "get_element_by_id = a_get_element_by_id"
|
||||
assumes get_elements_by_class_name_impl: "get_elements_by_class_name = a_get_elements_by_class_name"
|
||||
|
|
@ -3786,7 +3640,7 @@ lemma get_elements_by_tag_name_result_in_tree_order:
|
|||
intro!: map_filter_M_pure map_M_pure_I bind_pure_I
|
||||
split: option.splits list.splits if_splits)
|
||||
|
||||
lemma get_elements_by_tag_name_pure [simp]: "pure (get_elements_by_tag_name ptr tag) h"
|
||||
lemma get_elements_by_tag_name_pure [simp]: "pure (get_elements_by_tag_name ptr tag_name) h"
|
||||
by(auto simp add: get_elements_by_tag_name_def
|
||||
intro!: bind_pure_I map_filter_M_pure
|
||||
split: option.splits)
|
||||
|
|
@ -3796,7 +3650,7 @@ locale l_get_element_by = l_get_element_by_defs + l_to_tree_order_defs +
|
|||
assumes get_element_by_id_result_in_tree_order:
|
||||
"h \<turnstile> get_element_by_id ptr iden \<rightarrow>\<^sub>r Some element_ptr \<Longrightarrow> h \<turnstile> to_tree_order ptr \<rightarrow>\<^sub>r to
|
||||
\<Longrightarrow> cast element_ptr \<in> set to"
|
||||
assumes get_elements_by_tag_name_pure [simp]: "pure (get_elements_by_tag_name ptr tag) h"
|
||||
assumes get_elements_by_tag_name_pure [simp]: "pure (get_elements_by_tag_name ptr tag_name) h"
|
||||
|
||||
interpretation
|
||||
i_get_element_by?: l_get_element_by\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M to_tree_order first_in_tree_order get_attribute
|
||||
File diff suppressed because it is too large
Load Diff
|
|
@ -1,37 +0,0 @@
|
|||
An overview of the formalization is given in:
|
||||
|
||||
Achim D. Brucker and Michael Herzberg. A Formal Semantics of the Core DOM
|
||||
in Isabelle/HOL. In The 2018 Web Conference Companion (WWW). Pages 741-749,
|
||||
ACM Press, 2018. doi:10.1145/3184558.3185980
|
||||
|
||||
A BibTeX entry for LaTeX users is
|
||||
@InProceedings{ brucker.ea:core-dom:2018,
|
||||
abstract = {At its core, the Document Object Model (DOM) defines a tree-like
|
||||
data structure for representing documents in general and HTML
|
||||
documents in particular. It forms the heart of any rendering engine
|
||||
of modern web browsers. Formalizing the key concepts of the DOM is
|
||||
a pre-requisite for the formal reasoning over client-side JavaScript
|
||||
programs as well as for the analysis of security concepts in modern
|
||||
web browsers. In this paper, we present a formalization of the core DOM,
|
||||
with focus on the node-tree and the operations defined on node-trees,
|
||||
in Isabelle/HOL. We use the formalization to verify the functional
|
||||
correctness of the most important functions defined in the DOM standard.
|
||||
Moreover, our formalization is (1) extensible, i.e., can be extended without
|
||||
the need of re-proving already proven properties and (2) executable, i.e.,
|
||||
we can generate executable code from our specification.},
|
||||
address = {New York, NY, USA},
|
||||
author = {Achim D. Brucker and Michael Herzberg},
|
||||
booktitle= {The 2018 Web Conference Companion (WWW)},
|
||||
conf_date= {April 23-27, 2018},
|
||||
doi = {10.1145/3184558.3185980},
|
||||
editor = {Pierre{-}Antoine Champin and Fabien L. Gandon and Mounia Lalmas and Panagiotis G. Ipeirotis},
|
||||
isbn = {978-1-4503-5640-4/18/04},
|
||||
keywords = {Document Object Model, DOM, Formal Semantics, Isabelle/HOL},
|
||||
location = {Lyon, France},
|
||||
pages = {741--749},
|
||||
pdf = {https://www.brucker.ch/bibliography/download/2018/brucker.ea-core-dom-2018.pdf},
|
||||
publisher= {ACM Press},
|
||||
title = {A Formal Semantics of the Core {DOM} in {Isabelle/HOL}},
|
||||
url = {https://www.brucker.ch/bibliography/abstract/brucker.ea-core-dom-2018},
|
||||
year = {2018},
|
||||
}
|
||||
|
|
@ -1,20 +0,0 @@
|
|||
chapter AFP
|
||||
|
||||
session "Core_SC_DOM" (AFP) = "HOL-Library" +
|
||||
options [timeout = 1200, document = pdf, document_variants="document:outline=/proof,/ML",document_output=output]
|
||||
directories
|
||||
"common"
|
||||
"common/classes"
|
||||
"common/monads"
|
||||
"common/pointers"
|
||||
"common/preliminaries"
|
||||
"common/tests"
|
||||
"safely_composable"
|
||||
"safely_composable/classes"
|
||||
"safely_composable/pointers"
|
||||
theories
|
||||
Core_DOM
|
||||
Core_DOM_Tests
|
||||
document_files (in "document")
|
||||
"root.tex"
|
||||
"root.bib"
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../Core_DOM/common/Core_DOM.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../Core_DOM/common/Core_DOM_Basic_Datatypes.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../Core_DOM/common/Core_DOM_Functions.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../Core_DOM/common/Core_DOM_Tests.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/classes/BaseClass.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/classes/CharacterDataClass.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/classes/DocumentClass.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/classes/NodeClass.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/classes/ObjectClass.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/BaseMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/CharacterDataMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/DocumentMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/ElementMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/NodeMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/monads/ObjectMonad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/CharacterDataPointer.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/DocumentPointer.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/ElementPointer.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/NodePointer.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/ObjectPointer.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/pointers/Ref.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/preliminaries/Heap_Error_Monad.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/preliminaries/Hiding_Type_Variables.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/preliminaries/Testing_Utils.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Core_DOM_BaseTest.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document-adoptNode.html
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document-adoptNode.html.orig
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document-getElementById.html
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document-getElementById.html.orig
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document_adoptNode.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Document_getElementById.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node-insertBefore.html
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node-insertBefore.html.orig
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node-removeChild.html
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node-removeChild.html.orig
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node_insertBefore.thy
|
||||
|
|
@ -1 +0,0 @@
|
|||
../../../Core_DOM/common/tests/Node_removeChild.thy
|
||||
|
|
@ -1,508 +0,0 @@
|
|||
@STRING{j-fac = "Formal Aspects of Computing" }
|
||||
@STRING{pub-springer={Springer-Verlag} }
|
||||
@STRING{pub-springer:adr={Heidelberg} }
|
||||
@STRING{s-lncs = "Lecture Notes in Computer Science" }
|
||||
|
||||
@Book{ nipkow.ea:isabelle:2002,
|
||||
author = {Tobias Nipkow and Lawrence C. Paulson and Markus Wenzel},
|
||||
title = {Isabelle/HOL---A Proof Assistant for Higher-Order Logic},
|
||||
publisher = pub-springer,
|
||||
address = pub-springer:adr,
|
||||
series = s-lncs,
|
||||
volume = 2283,
|
||||
doi = {10.1007/3-540-45949-9},
|
||||
abstract = {This book is a self-contained introduction to interactive
|
||||
proof in higher-order logic (HOL), using the proof
|
||||
assistant Isabelle2002. It is a tutorial for potential
|
||||
users rather than a monograph for researchers. The book has
|
||||
three parts.
|
||||
|
||||
1. Elementary Techniques shows how to model functional
|
||||
programs in higher-order logic. Early examples involve
|
||||
lists and the natural numbers. Most proofs are two steps
|
||||
long, consisting of induction on a chosen variable followed
|
||||
by the auto tactic. But even this elementary part covers
|
||||
such advanced topics as nested and mutual recursion. 2.
|
||||
Logic and Sets presents a collection of lower-level tactics
|
||||
that you can use to apply rules selectively. It also
|
||||
describes Isabelle/HOL's treatment of sets, functions and
|
||||
relations and explains how to define sets inductively. One
|
||||
of the examples concerns the theory of model checking, and
|
||||
another is drawn from a classic textbook on formal
|
||||
languages. 3. Advanced Material describes a variety of
|
||||
other topics. Among these are the real numbers, records and
|
||||
overloading. Advanced techniques are described involving
|
||||
induction and recursion. A whole chapter is devoted to an
|
||||
extended example: the verification of a security protocol.
|
||||
},
|
||||
year = 2002,
|
||||
acknowledgement={brucker, 2007-02-19},
|
||||
bibkey = {nipkow.ea:isabelle:2002}
|
||||
}
|
||||
|
||||
@Misc{ dom-specification,
|
||||
year = 2016,
|
||||
month = {DOM Living Standard -- Last Updated 20 October 2016},
|
||||
day = 20,
|
||||
url = {https://dom.spec.whatwg.org/},
|
||||
organization = {Web Hypertext Application Technology Working Group
|
||||
(WHATWG)},
|
||||
note = {An archived copy of the version from 20 October 2016 is
|
||||
available at
|
||||
\url{https://git.logicalhacking.com/BrowserSecurity/fDOM-idl/}.}
|
||||
}
|
||||
|
||||
@InProceedings{ brucker.ea:core-dom:2018,
|
||||
author = {Achim D. Brucker and Michael Herzberg},
|
||||
title = {A Formal Semantics of the Core {DOM} in {Isabelle/HOL}},
|
||||
booktitle = {Proceedings of the Web Programming, Design, Analysis, And
|
||||
Implementation (WPDAI) track at WWW 2018},
|
||||
location = {Lyon, France},
|
||||
url = {https://www.brucker.ch/bibliography/abstract/brucker.ea-fdom-2018},
|
||||
year = {2018},
|
||||
abstract = {At its core, the Document Object Model (DOM) defines a
|
||||
tree-like data structure for representing documents in
|
||||
general and HTML documents in particular. It forms the
|
||||
heart of any rendering engine of modern web browsers.
|
||||
Formalizing the key concepts of the DOM is a pre-requisite
|
||||
for the formal reasoning over client-side JavaScript
|
||||
programs as well as for the analysis of security concepts
|
||||
in modern web browsers. In this paper, we present a
|
||||
formalization of the core DOM, with focus on the node-tree
|
||||
and the operations defined on node-trees, in Isabelle/HOL.
|
||||
We use the formalization to verify the functional
|
||||
correctness of the most important functions defined in the
|
||||
DOM standard. Moreover, our formalization is (1)
|
||||
extensible, i.e., can be extended without the need of
|
||||
re-proving already proven properties and (2) executable,
|
||||
i.e., we can generate executable code from our
|
||||
specification. },
|
||||
keywords = {Document Object Model, DOM, Formal Semantics,
|
||||
Isabelle/HOL},
|
||||
classification= {conference},
|
||||
areas = {formal methods, software},
|
||||
public = {yes}
|
||||
}
|
||||
@Article{ klein:operating:2009,
|
||||
author = {Gerwin Klein},
|
||||
title = {Operating System Verification --- An Overview},
|
||||
journal = {S\={a}dhan\={a}},
|
||||
publisher = pub-springer,
|
||||
year = 2009,
|
||||
volume = 34,
|
||||
number = 1,
|
||||
month = feb,
|
||||
pages = {27--69},
|
||||
abstract = {This paper gives a high-level introduction to the topic of
|
||||
formal, interactive, machine-checked software verification
|
||||
in general, and the verification of operating systems code
|
||||
in particular. We survey the state of the art, the
|
||||
advantages and limitations of machine-checked code proofs,
|
||||
and describe two specific ongoing larger-scale verification
|
||||
projects in more detail.}
|
||||
}
|
||||
|
||||
|
||||
@InProceedings{ gardner.ea:securing:2009,
|
||||
author = {Ryan W. Gardner and Sujata Garera and Matthew W. Pagano
|
||||
and Matthew Green and Aviel D. Rubin},
|
||||
title = {Securing medical records on smart phones},
|
||||
booktitle = {ACM workshop on Security and privacy in medical and
|
||||
home-care systems (SPIMACS)},
|
||||
year = 2009,
|
||||
isbn = {978-1-60558-790-5},
|
||||
pages = {31--40},
|
||||
location = {Chicago, Illinois, USA},
|
||||
doi = {10.1145/1655084.1655090},
|
||||
address = pub-acm:adr,
|
||||
publisher = pub-acm,
|
||||
abstract = {There is an inherent conflict between the desire to
|
||||
maintain privacy of one's medical records and the need to
|
||||
make those records available during an emergency. To
|
||||
satisfy both objectives, we introduce a flexible
|
||||
architecture for the secure storage of medical records on
|
||||
smart phones. In our system, a person can view her records
|
||||
at any time, and emergency medical personnel can view the
|
||||
records as long as the person is present (even if she is
|
||||
unconscious). Our solution allows for efficient revocation
|
||||
of access rights and is robust against adversaries who can
|
||||
access the phone's storage offline.}
|
||||
}
|
||||
|
||||
@InProceedings{ raad.ea:dom:2016,
|
||||
author = {Azalea Raad and Jos{\'{e}} Fragoso Santos and Philippa
|
||||
Gardner},
|
||||
title = {{DOM:} Specification and Client Reasoning},
|
||||
booktitle = {Programming Languages and Systems - 14th Asian Symposium,
|
||||
{APLAS} 2016, Hanoi, Vietnam, November 21-23, 2016,
|
||||
Proceedings},
|
||||
pages = {401--422},
|
||||
year = 2016,
|
||||
crossref = {igarashi:programming:2016},
|
||||
doi = {10.1007/978-3-319-47958-3_21},
|
||||
abstract = {We present an axiomatic specification of a key fragment of
|
||||
DOM using structural separation logic. This specification
|
||||
allows us to develop modular reasoning about client
|
||||
programs that call the DOM.}
|
||||
}
|
||||
|
||||
|
||||
@InProceedings{ bohannon.ea:featherweight:2010,
|
||||
author = {Aaron Bohannon and Benjamin C. Pierce},
|
||||
title = {Featherweight {F}irefox: {F}ormalizing the Core of a Web
|
||||
Browser},
|
||||
booktitle = {Usenix Conference on Web Application Development
|
||||
(WebApps)},
|
||||
year = 2010,
|
||||
month = jun,
|
||||
url = {http://www.cis.upenn.edu/~bohannon/browser-model/},
|
||||
abstract = {We offer a formal specification of the core functionality
|
||||
of a web browser in the form of a small-step operational
|
||||
semantics. The specification accurately models the asyn-
|
||||
chronous nature of web browsers and covers the basic as-
|
||||
pects of windows, DOM trees, cookies, HTTP requests and
|
||||
responses, user input, and a minimal scripting lan- guage
|
||||
with first-class functions, dynamic evaluation, and AJAX
|
||||
requests. No security enforcement mechanisms are
|
||||
included{\^a}instead, the model is intended to serve as a
|
||||
basis for formalizing and experimenting with different
|
||||
security policies and mechanisms. We survey the most
|
||||
interesting design choices and discuss how our model re-
|
||||
lates to real web browsers.}
|
||||
}
|
||||
|
||||
@Proceedings{ joyce.ea:higher:1994,
|
||||
editor = {Jeffrey J. Joyce and Carl-Johan H. Seger},
|
||||
title = {Higher Order Logic Theorem Proving and Its Applications
|
||||
(HUG)},
|
||||
booktitle = {Higher Order Logic Theorem Proving and Its Applications
|
||||
(HUG)},
|
||||
publisher = pub-springer,
|
||||
address = pub-springer:adr,
|
||||
series = s-lncs,
|
||||
abstract = {Theorem proving based techniques for formal hardware
|
||||
verification have been evolving constantly and researchers
|
||||
are getting able to reason about more complex issues than
|
||||
it was possible or practically feasible in the past. It is
|
||||
often the case that a model of a system is built in a
|
||||
formal logic and then reasoning about this model is carried
|
||||
out in the logic. Concern is growing on how to consistently
|
||||
interface a model built in a formal logic with an informal
|
||||
CAD environment. Researchers have been investigating how to
|
||||
define the formal semantics of hardware description
|
||||
languages so that one can formally reason about models
|
||||
informally dealt with in a CAD environment. At the
|
||||
University of Cambridge, the embedding of hardware
|
||||
description languages in a logic is classified in two
|
||||
categories: deep embedding and shallow embedding. In this
|
||||
paper we argue that there are degrees of formality in
|
||||
shallow embedding a language in a logic. The choice of the
|
||||
degree of formality is a trade-off between the security of
|
||||
the embedding and the amount and complexity of the proof
|
||||
effort in the logic. We also argue that the design of a
|
||||
language could consider this verifiability issue. There are
|
||||
choices in the design of a language that can make it easier
|
||||
to improve the degree of formality, without implying
|
||||
serious drawbacks for the CAD environment.},
|
||||
volume = 780,
|
||||
year = 1994,
|
||||
doi = {10.1007/3-540-57826-9},
|
||||
isbn = {3-540-57826-9},
|
||||
acknowledgement={brucker, 2007-02-19}
|
||||
}
|
||||
|
||||
|
||||
@Misc{ whatwg:dom:2017,
|
||||
key={whatwg},
|
||||
author={{WHATWG}},
|
||||
url={https://dom.spec.whatwg.org/commit-snapshots/6253e53af2fbfaa6d25ad09fd54280d8083b2a97/},
|
||||
month=mar,
|
||||
year=2017,
|
||||
day=24,
|
||||
title={{DOM} -- Living Standard},
|
||||
note={Last Updated 24 {March} 2017},
|
||||
institution = {WHATWG},
|
||||
}
|
||||
|
||||
@Misc{ whatwg:html:2017,
|
||||
key={whatwg},
|
||||
author={{WHATWG}},
|
||||
url={https://html.spec.whatwg.org/},
|
||||
month=apr,
|
||||
year=2017,
|
||||
day=13,
|
||||
title={{HTML} -- Living Standard},
|
||||
note={Last Updated 13 {April} 2017},
|
||||
institution = {WHATWG},
|
||||
}
|
||||
|
||||
|
||||
@Misc{ w3c:dom:2015,
|
||||
key={w3c},
|
||||
author={{W3C}},
|
||||
url={https://www.w3.org/TR/dom/},
|
||||
month=nov,
|
||||
year=2015,
|
||||
day=19,
|
||||
title={{W3C} {DOM4}},
|
||||
institution = {W3C},
|
||||
}
|
||||
|
||||
|
||||
@Proceedings{ igarashi:programming:2016,
|
||||
editor = {Atsushi Igarashi},
|
||||
title = {Programming Languages and Systems - 14th Asian Symposium,
|
||||
{APLAS} 2016, Hanoi, Vietnam, November 21-23, 2016,
|
||||
Proceedings},
|
||||
series = {Lecture Notes in Computer Science},
|
||||
volume = 10017,
|
||||
year = 2016,
|
||||
doi = {10.1007/978-3-319-47958-3},
|
||||
isbn = {978-3-319-47957-6}
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@InProceedings{ gardner.ea:dom:2008,
|
||||
author = {Philippa Gardner and Gareth Smith and Mark J. Wheelhouse
|
||||
and Uri Zarfaty},
|
||||
title = {{DOM:} Towards a Formal Specification},
|
||||
booktitle = {{PLAN-X} 2008, Programming Language Technologies for XML,
|
||||
An {ACM} {SIGPLAN} Workshop colocated with {POPL} 2008, San
|
||||
Francisco, California, USA, January 9, 2008},
|
||||
year = 2008,
|
||||
crossref = {plan-x:2008},
|
||||
url = {http://gemo.futurs.inria.fr/events/PLANX2008/papers/p18.pdf},
|
||||
abstract = {The W3C Document Object Model (DOM) specifies an XML up-
|
||||
date library. DOM is written in English, and is therefore
|
||||
not compo- sitional and not complete. We provide a first
|
||||
step towards a compo- sitional specification of DOM. Unlike
|
||||
DOM, we are able to work with a minimal set of commands and
|
||||
obtain a complete reason- ing for straight-line code. Our
|
||||
work transfers O{\^a}Hearn, Reynolds and Yang{\^a}s
|
||||
local Hoare reasoning for analysing heaps to XML, viewing
|
||||
XML as an in-place memory store as does DOM. In par-
|
||||
ticular, we apply recent work by Calcagno, Gardner and
|
||||
Zarfaty on local Hoare reasoning about a simple tree-update
|
||||
language to DOM, showing that our reasoning scales to DOM.
|
||||
Our reasoning not only formally specifies a significant
|
||||
subset of DOM Core Level 1, but can also be used to verify
|
||||
e.g. invariant properties of simple Javascript programs.}
|
||||
}
|
||||
|
||||
|
||||
|
||||
@InProceedings{ jang.ea:establishing:2012,
|
||||
author = {Dongseok Jang and Zachary Tatlock and Sorin Lerner},
|
||||
title = {Establishing Browser Security Guarantees through Formal
|
||||
Shim Verification},
|
||||
booktitle = {Proceedings of the 21th {USENIX} Security Symposium,
|
||||
Bellevue, WA, USA, August 8-10, 2012},
|
||||
pages = {113--128},
|
||||
year = 2012,
|
||||
crossref = {kohno:proceedings:2012},
|
||||
url = {https://www.usenix.org/conference/usenixsecurity12/technical-sessions/presentation/jang},
|
||||
abstract = { Web browsers mediate access to valuable private data in
|
||||
domains ranging from health care to banking. Despite this
|
||||
critical role, attackers routinely exploit browser
|
||||
vulnerabilities to exfiltrate private data and take over
|
||||
the un- derlying system. We present Q UARK , a browser
|
||||
whose kernel has been implemented and verified in Coq. We
|
||||
give a specification of our kernel, show that the
|
||||
implementation satisfies the specification, and finally
|
||||
show that the specification implies several security
|
||||
properties, including tab non-interference, cookie
|
||||
integrity and confidentiality, and address bar integrity.
|
||||
}
|
||||
}
|
||||
|
||||
@Proceedings{ kohno:proceedings:2012,
|
||||
editor = {Tadayoshi Kohno},
|
||||
title = {Proceedings of the 21th {USENIX} Security Symposium,
|
||||
Bellevue, WA, USA, August 8-10, 2012},
|
||||
publisher = {{USENIX} Association},
|
||||
year = 2012,
|
||||
timestamp = {Thu, 15 May 2014 09:12:27 +0200}
|
||||
}
|
||||
|
||||
|
||||
|
||||
@Proceedings{ plan-x:2008,
|
||||
title = {{PLAN-X} 2008, Programming Language Technologies for XML,
|
||||
An {ACM} {SIGPLAN} Workshop colocated with {POPL} 2008, San
|
||||
Francisco, California, USA, January 9, 2008},
|
||||
year = 2008,
|
||||
timestamp = {Fri, 18 Jan 2008 13:01:04 +0100}
|
||||
}
|
||||
|
||||
|
||||
@Article{ brucker.ea:extensible:2008-b,
|
||||
abstract = {We present an extensible encoding of object-oriented data models into HOL. Our encoding is supported by a datatype package that leverages the use of the shallow embedding technique to object-oriented specification and programming languages. The package incrementally compiles an object-oriented data model, i.e., a class model, to a theory containing object-universes, constructors, accessor functions, coercions (casts) between dynamic and static types, characteristic sets, and co-inductive class invariants. The package is conservative, i.e., all properties are derived entirely from constant definitions, including the constraints over object structures. As an application, we use the package for an object-oriented core-language called IMP++, for which we formally prove the correctness of a Hoare-Logic with respect to a denotational semantics.},
|
||||
address = {Heidelberg},
|
||||
author = {Achim D. Brucker and Burkhart Wolff},
|
||||
doi = {10.1007/s10817-008-9108-3},
|
||||
issn = {0168-7433},
|
||||
issue = {3},
|
||||
journal = {Journal of Automated Reasoning},
|
||||
keywords = {object-oriented data models, HOL, theorem proving, verification},
|
||||
language = {USenglish},
|
||||
pages = {219--249},
|
||||
pdf = {https://www.brucker.ch/bibliography/download/2008/brucker.ea-extensible-2008-b.pdf},
|
||||
publisher = {Springer-Verlag},
|
||||
title = {An Extensible Encoding of Object-oriented Data Models in HOL},
|
||||
url = {https://www.brucker.ch/bibliography/abstract/brucker.ea-extensible-2008-b},
|
||||
volume = {41},
|
||||
year = {2008},
|
||||
}
|
||||
|
||||
@PhDThesis{ brucker:interactive:2007,
|
||||
abstract = {We present a semantic framework for object-oriented specification languages. We develop this framework as a conservative shallow embedding in Isabelle/HOL. Using only conservative extensions guarantees by construction the consistency of our formalization. Moreover, we show how our framework can be used to build an interactive proof environment, called HOL-OCL, for object-oriented specifications in general and for UML/OCL in particular.\\\\Our main contributions are an extensible encoding of object-oriented data structures in HOL, a datatype package for object-oriented specifications, and the development of several equational and tableaux calculi for object-oriented specifications. Further, we show that our formal framework can be the basis of a formal machine-checked semantics for OCL that is compliant to the OCL 2.0 standard.},
|
||||
abstract_de = {In dieser Arbeit wird ein semantisches Rahmenwerk f{\"u}r objektorientierte Spezifikationen vorgestellt. Das Rahmenwerk ist als konservative, flache Einbettung in Isabelle/HOL realisiert. Durch die Beschr{\"a}nkung auf konservative Erweiterungen kann die logische Konsistenz der Einbettung garantiert werden. Das semantische Rahmenwerk wird verwendet, um das interaktives Beweissystem HOL-OCL f{\"u}r objektorientierte Spezifikationen im Allgemeinen und insbesondere f{\"u}r UML/OCL zu entwickeln.\\\\Die Hauptbeitr{\"a}ge dieser Arbeit sind die Entwicklung einer erweiterbaren Kodierung objektorientierter Datenstrukturen in HOL, ein Datentyp-Paket f{\"u}r objektorientierte Spezifikationen und die Entwicklung verschiedener Kalk{\"u}le f{\"u}r objektorientierte Spezifikationen. Zudem zeigen wir, wie das formale Rahmenwerk verwendet werden kann, um eine formale, maschinell gepr{\"u}fte Semantik f{\"u}r OCL anzugeben, die konform zum Standard f{\"u}r OCL 2.0 ist.},
|
||||
author = {Achim D. Brucker},
|
||||
keywords = {OCL, UML, formal semantics, theorem proving, Isabelle, HOL-OCL},
|
||||
month = {mar},
|
||||
note = {ETH Dissertation No. 17097.},
|
||||
pdf = {https://www.brucker.ch/bibliography/download/2007/brucker-interactive-2007.pdf},
|
||||
school = {ETH Zurich},
|
||||
title = {An Interactive Proof Environment for Object-oriented Specifications},
|
||||
url = {https://www.brucker.ch/bibliography/abstract/brucker-interactive-2007},
|
||||
year = {2007},
|
||||
}
|
||||
|
||||
@InCollection{ brucker.ea:standard-compliance-testing:2018,
|
||||
talk = {talk:brucker.ea:standard-compliance-testing:2018},
|
||||
abstract = {Most popular technologies are based on informal or
|
||||
semiformal standards that lack a rigid formal semantics.
|
||||
Typical examples include web technologies such as the DOM
|
||||
or HTML, which are defined by the Web Hypertext Application
|
||||
Technology Working Group (WHATWG) and the World Wide Web
|
||||
Consortium (W3C). While there might be API specifications
|
||||
and test cases meant to assert the compliance of a certain
|
||||
implementation, the actual standard is rarely accompanied
|
||||
by a formal model that would lend itself for, e.g.,
|
||||
verifying the security or safety properties of real
|
||||
systems.
|
||||
|
||||
Even when such a formalization of a standard exists, two
|
||||
important questions arise: first, to what extend does the
|
||||
formal model comply to the standard and, second, to what
|
||||
extend does the implementation comply to the formal model
|
||||
and the assumptions made during the verification? In this
|
||||
paper, we present an approach that brings all three
|
||||
involved artifacts - the (semi-)formal standard, the
|
||||
formalization of the standard, and the implementations -
|
||||
closer together by combining verification, symbolic
|
||||
execution, and specification based testing.},
|
||||
keywords = {standard compliance, compliance tests, DOM},
|
||||
location = {Toulouse, France},
|
||||
author = {Achim D. Brucker and Michael Herzberg},
|
||||
booktitle = {{TAP} 2018: Tests And Proofs},
|
||||
language = {USenglish},
|
||||
publisher = pub-springer,
|
||||
address = pub-springer:adr,
|
||||
series = s-lncs,
|
||||
number = 10889,
|
||||
editor = {Cathrine Dubois and Burkhart Wolff},
|
||||
title = {Formalizing (Web) Standards: An Application of Test and
|
||||
Proof},
|
||||
categories = {holtestgen, websecurity},
|
||||
classification= {conference},
|
||||
areas = {formal methods, software engineering},
|
||||
public = {yes},
|
||||
year = 2018,
|
||||
doi = {10.1007/978-3-319-92994-1_9},
|
||||
pages = {159--166},
|
||||
isbn = {978-3-642-38915-3},
|
||||
pdf = {http://www.brucker.ch/bibliography/download/2018/brucker.ea-standard-compliance-testing-2018.pdf},
|
||||
url = {http://www.brucker.ch/bibliography/abstract/brucker.ea-standard-compliance-testing-2018}
|
||||
}
|
||||
|
||||
|
||||
@InCollection{ brucker.ea:interactive:2005,
|
||||
keywords = {symbolic test case generations, black box testing, white
|
||||
box testing, theorem proving, interactive testing},
|
||||
abstract = {HOL-TestGen is a test environment for specification-based
|
||||
unit testing build upon the proof assistant Isabelle/HOL\@.
|
||||
While there is considerable skepticism with regard to
|
||||
interactive theorem provers in testing communities, we
|
||||
argue that they are a natural choice for (automated)
|
||||
symbolic computations underlying systematic tests. This
|
||||
holds in particular for the development on non-trivial
|
||||
formal test plans of complex software, where some parts of
|
||||
the overall activity require inherently guidance by a test
|
||||
engineer. In this paper, we present the underlying methods
|
||||
for both black box and white box testing in interactive
|
||||
unit test scenarios. HOL-TestGen can also be understood as
|
||||
a unifying technical and conceptual framework for
|
||||
presenting and investigating the variety of unit test
|
||||
techniques in a logically consistent way. },
|
||||
location = {Edinburgh},
|
||||
author = {Achim D. Brucker and Burkhart Wolff},
|
||||
booktitle = {Formal Approaches to Testing of Software},
|
||||
language = {USenglish},
|
||||
publisher = pub-springer,
|
||||
address = pub-springer:adr,
|
||||
series = s-lncs,
|
||||
number = 3997,
|
||||
doi = {10.1007/11759744_7},
|
||||
isbn = {3-540-25109-X},
|
||||
editor = {Wolfgang Grieskamp and Carsten Weise},
|
||||
pdf = {http://www.brucker.ch/bibliography/download/2005/brucker.ea-interactive-2005.pdf},
|
||||
project = {CSFMDOS},
|
||||
title = {Interactive Testing using {HOL}-{TestGen}},
|
||||
classification= {workshop},
|
||||
areas = {formal methods, software},
|
||||
categories = {holtestgen},
|
||||
year = 2005,
|
||||
public = {yes},
|
||||
url = {http://www.brucker.ch/bibliography/abstract/brucker.ea-interactive-2005}
|
||||
}
|
||||
|
||||
|
||||
@Article{ brucker.ea:theorem-prover:2012,
|
||||
author = {Achim D. Brucker and Burkhart Wolff},
|
||||
journal = j-fac,
|
||||
publisher = pub-springer,
|
||||
address = pub-springer:adr,
|
||||
language = {USenglish},
|
||||
categories = {holtestgen},
|
||||
title = {On Theorem Prover-based Testing},
|
||||
year = 2013,
|
||||
issn = {0934-5043},
|
||||
pages = {683--721},
|
||||
volume = 25,
|
||||
number = 5,
|
||||
classification= {journal},
|
||||
areas = {formal methods, software},
|
||||
public = {yes},
|
||||
doi = {10.1007/s00165-012-0222-y},
|
||||
keywords = {test case generation, domain partitioning, test sequence,
|
||||
theorem proving, HOL-TestGen},
|
||||
abstract = {HOL-TestGen is a specification and test case generation
|
||||
environment extending the interactive theorem prover
|
||||
Isabelle/HOL. As such, HOL-TestGen allows for an integrated
|
||||
workflow supporting interactive theorem proving, test case
|
||||
generation, and test data generation.
|
||||
|
||||
The HOL-TestGen method is two-staged: first, the original
|
||||
formula is partitioned into test cases by transformation
|
||||
into a normal form called test theorem. Second, the test
|
||||
cases are analyzed for ground instances (the test data)
|
||||
satisfying the constraints of the test cases. Particular
|
||||
emphasis is put on the control of explicit test-hypotheses
|
||||
which can be proven over concrete programs.
|
||||
|
||||
Due to the generality of the underlying framework, our
|
||||
system can be used for black-box unit, sequence, reactive
|
||||
sequence and white-box test scenarios. Although based on
|
||||
particularly clean theoretical foundations, the system can
|
||||
be applied for substantial case-studies. },
|
||||
pdf = {http://www.brucker.ch/bibliography/download/2012/brucker.ea-theorem-prover-2012.pdf},
|
||||
url = {http://www.brucker.ch/bibliography/abstract/brucker.ea-theorem-prover-2012}
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
|
@ -1,261 +0,0 @@
|
|||
\documentclass[10pt,DIV16,a4paper,abstract=true,twoside=semi,openright]
|
||||
{scrreprt}
|
||||
\usepackage[USenglish]{babel}
|
||||
\usepackage[numbers, sort&compress]{natbib}
|
||||
\usepackage{isabelle,isabellesym}
|
||||
\usepackage{booktabs}
|
||||
\usepackage{paralist}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{xspace}
|
||||
\usepackage{xcolor}
|
||||
\usepackage{listings}
|
||||
\lstloadlanguages{HTML}
|
||||
\usepackage[]{mathtools}
|
||||
\usepackage[pdfpagelabels, pageanchor=false, plainpages=false]{hyperref}
|
||||
\lstdefinestyle{html}{language=XML,
|
||||
basicstyle=\ttfamily,
|
||||
commentstyle=\itshape,
|
||||
keywordstyle=\color{blue},
|
||||
ndkeywordstyle=\color{blue},
|
||||
}
|
||||
\lstdefinestyle{displayhtml}{style=html,
|
||||
floatplacement={tbp},
|
||||
captionpos=b,
|
||||
framexleftmargin=0pt,
|
||||
basicstyle=\ttfamily\scriptsize,
|
||||
backgroundcolor=\color{black!2},
|
||||
frame=lines,
|
||||
}
|
||||
\lstnewenvironment{html}[1][]{\lstset{style=displayhtml, #1}}{}
|
||||
\def\inlinehtml{\lstinline[style=html, columns=fullflexible]}
|
||||
|
||||
\pagestyle{headings}
|
||||
\isabellestyle{default}
|
||||
\setcounter{tocdepth}{1}
|
||||
\newcommand{\ie}{i.\,e.\xspace}
|
||||
\newcommand{\eg}{e.\,g.\xspace}
|
||||
\newcommand{\thy}{\isabellecontext}
|
||||
\renewcommand{\isamarkupsection}[1]{%
|
||||
\begingroup%
|
||||
\def\isacharunderscore{\textunderscore}%
|
||||
\section{#1 (\thy)}%
|
||||
\def\isacharunderscore{-}%
|
||||
\expandafter\label{sec:\isabellecontext}%
|
||||
\endgroup%
|
||||
}
|
||||
|
||||
\title{Core SC DOM\\\medskip \Large
|
||||
A Formal Model of the Document Object Model for Safe Components}%
|
||||
\author{%
|
||||
\href{https://www.brucker.ch/}{Achim~D.~Brucker}\footnotemark[1]
|
||||
\and
|
||||
\href{https://www.michael-herzberg.de/}{Michael Herzberg}\footnotemark[2]
|
||||
}
|
||||
|
||||
\publishers{
|
||||
\footnotemark[1]~Department of Computer Science, University of Exeter, Exeter, UK\texorpdfstring{\\}{, }
|
||||
\texttt{a.brucker@exeter.ac.uk}\\[2em]
|
||||
%
|
||||
\footnotemark[2]~ Department of Computer Science, The University of Sheffield, Sheffield, UK\texorpdfstring{\\}{, }
|
||||
\texttt{msherzberg1@sheffield.ac.uk}
|
||||
}
|
||||
\begin{document}
|
||||
\maketitle
|
||||
\begin{abstract}
|
||||
\begin{quote}
|
||||
In this AFP entry, we formalize the core of the Document Object
|
||||
Model (DOM). At its core, the DOM defines a tree-like data
|
||||
structure for representing documents in general and HTML documents
|
||||
in particular. It is the heart of any modern web browser.
|
||||
|
||||
Formalizing the key concepts of the DOM is a prerequisite for the
|
||||
formal reasoning over client-side JavaScript programs and for the
|
||||
analysis of security concepts in modern web browsers.
|
||||
|
||||
|
||||
We present a formalization of the core DOM, with focus on the
|
||||
\emph{node-tree} and the operations defined on node-trees, in
|
||||
Isabelle/HOL\@. We use the formalization to verify the functional
|
||||
correctness of the most important functions defined in the DOM
|
||||
standard. Moreover, our formalization is
|
||||
\begin{inparaenum}
|
||||
\item \emph{extensible}, i.e., can be extended without the need of
|
||||
re-proving already proven properties and
|
||||
\item \emph{executable}, i.e., we can generate executable code
|
||||
from our specification.
|
||||
\end{inparaenum}
|
||||
|
||||
\bigskip
|
||||
\noindent{\textbf{Keywords:}}
|
||||
Document Object Model, DOM, Formal Semantics, Isabelle/HOL
|
||||
\end{quote}
|
||||
\end{abstract}
|
||||
|
||||
|
||||
\tableofcontents
|
||||
\cleardoublepage
|
||||
|
||||
\chapter{Introduction}
|
||||
In a world in which more and more applications are offered as services
|
||||
on the internet, web browsers start to take on a similarly central
|
||||
role in our daily IT infrastructure as operating systems. Thus, web
|
||||
browsers should be developed as rigidly and formally as operating
|
||||
systems. While formal methods are a well-established technique in the
|
||||
development of operating systems (see,
|
||||
\eg,~\citet{klein:operating:2009} for an overview of formal
|
||||
verification of operating systems), there are few proposals for
|
||||
improving the development of web browsers using formal
|
||||
approaches~\cite{gardner.ea:dom:2008,raad.ea:dom:2016,jang.ea:establishing:2012,bohannon.ea:featherweight:2010}.
|
||||
|
||||
As a first step towards a verified client-side web application stack,
|
||||
we model and formally verify the Document Object Model (DOM) in
|
||||
Isabelle/HOL\@. The DOM~\cite{whatwg:dom:2017,w3c:dom:2015} is
|
||||
\emph{the} central data structure of all modern web browsers. At its
|
||||
core, the Document Object Model (DOM), defines a tree-like data
|
||||
structure for representing documents in general and HTML documents in
|
||||
particular. Thus, the correctness of a DOM implementation is crucial
|
||||
for ensuring that a web browser displays web pages correctly.
|
||||
Moreover, the DOM is the core data structure underlying client-side
|
||||
JavaScript programs, \ie, client-side JavaScript programs are mostly
|
||||
programs that read, write, and update the DOM.
|
||||
|
||||
In more detail, we formalize the core DOM as a shallow
|
||||
embedding~\cite{joyce.ea:higher:1994} in Isabelle/HOL\@. Our
|
||||
formalization is based on a typed data model for the \emph{node-tree},
|
||||
\ie, a data structure for representing XML-like documents in a tree
|
||||
structure. Furthermore, we formalize a typed heap for storing
|
||||
(partial) node-trees together with the necessary consistency
|
||||
constraints. Finally, we formalize the operations (as described in the
|
||||
DOM standard~\cite{whatwg:dom:2017}) on this heap that allow
|
||||
manipulating node-trees.
|
||||
|
||||
Our machine-checked formalization of the DOM node
|
||||
tree~\cite{whatwg:dom:2017} has the following desirable properties:
|
||||
\begin{itemize}
|
||||
\item It provides a \emph{consistency guarantee.} Since all
|
||||
definitions in our formal semantics are conservative and all rules
|
||||
are derived, the logical consistency of the DOM node-tree is reduced
|
||||
to the consistency of HOL.
|
||||
\item It serves as a \emph{technical basis for a proof system.} Based
|
||||
on the derived rules and specific setup of proof tactics over
|
||||
node-trees, our formalization provides a generic proof environment
|
||||
for the verification of programs manipulating node-trees.
|
||||
\item It is \emph{executable}, which allows to validate its compliance
|
||||
to the standard by evaluating the compliance test suite on the
|
||||
formal model and
|
||||
\item It is \emph{extensible} in the sense
|
||||
of~\cite{brucker.ea:extensible:2008-b,brucker:interactive:2007},
|
||||
\ie, properties proven over the core DOM do not need to be re-proven
|
||||
for object-oriented extensions such as the HTML document model.
|
||||
\end{itemize}
|
||||
|
||||
The rest of this document is automatically generated from the
|
||||
formalization in Isabelle/HOL, i.e., all content is checked by
|
||||
Isabelle.\footnote{For a brief overview of the work, we refer the
|
||||
reader to~\cite{brucker.ea:core-dom:2018}.} The structure follows
|
||||
the theory dependencies (see \autoref{fig:session-graph}): we start
|
||||
with introducing the technical preliminaries of our formalization
|
||||
(\autoref{cha:perliminaries}). Next, we introduce the concepts of
|
||||
pointers (\autoref{cha:pointers}) and classes (\autoref{cha:classes}),
|
||||
i.e., the core object-oriented datatypes of the DOM. On top of this
|
||||
data model, we define the functional behavior of the DOM classes,
|
||||
i.e., their methods (\autoref{cha:monads}). In \autoref{cha:dom}, we
|
||||
introduce the formalization of the functionality of the core DOM,
|
||||
i.e., the \emph{main entry point for users} that want to use this AFP
|
||||
entry. Finally, we formalize the relevant compliance test cases in
|
||||
\autoref{cha:tests}.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=.8\textwidth]{session_graph}
|
||||
\caption{The Dependency Graph of the Isabelle Theories.\label{fig:session-graph}}
|
||||
\end{figure}
|
||||
|
||||
\clearpage
|
||||
|
||||
\chapter{Preliminaries}
|
||||
\label{cha:perliminaries}
|
||||
In this chapter, we introduce the technical preliminaries of our
|
||||
formalization of the core DOM, namely a mechanism for hiding type
|
||||
variables and the heap error monad.
|
||||
\input{Hiding_Type_Variables}
|
||||
\input{Heap_Error_Monad}
|
||||
|
||||
\chapter{References and Pointers}
|
||||
\label{cha:pointers}
|
||||
In this chapter, we introduce a generic type for object-oriented
|
||||
references and typed pointers for each class type defined in the DOM
|
||||
standard.
|
||||
\input{Ref}
|
||||
\input{ObjectPointer}
|
||||
\input{NodePointer}
|
||||
\input{ElementPointer}
|
||||
\input{CharacterDataPointer}
|
||||
\input{DocumentPointer}
|
||||
\input{ShadowRootPointer}
|
||||
|
||||
\chapter{Classes}
|
||||
\label{cha:classes}
|
||||
In this chapter, we introduce the classes of our DOM model.
|
||||
The definition of the class types follows closely the one of the
|
||||
pointer types. Instead of datatypes, we use records for our classes.
|
||||
a generic type for object-oriented references and typed pointers for
|
||||
each class type defined in the DOM standard.
|
||||
\input{BaseClass}
|
||||
\input{ObjectClass}
|
||||
\input{NodeClass}
|
||||
\input{ElementClass}
|
||||
\input{CharacterDataClass}
|
||||
\input{DocumentClass}
|
||||
|
||||
\chapter{Monadic Object Constructors and Accessors}
|
||||
\label{cha:monads}
|
||||
In this chapter, we introduce the moandic method definitions for the
|
||||
classes of our DOM formalization. Again the overall structure follows
|
||||
the same structure as for the class types and the pointer types.
|
||||
\input{BaseMonad}
|
||||
\input{ObjectMonad}
|
||||
\input{NodeMonad}
|
||||
\input{ElementMonad}
|
||||
\input{CharacterDataMonad}
|
||||
\input{DocumentMonad}
|
||||
|
||||
\chapter{The Core DOM}
|
||||
\label{cha:dom}
|
||||
In this chapter, we introduce the formalization of the core DOM, i.e.,
|
||||
the most important algorithms for querying or modifying the DOM, as
|
||||
defined in the standard. For more details, we refer the reader to
|
||||
\cite{brucker.ea:core-dom:2018}.
|
||||
\input{Core_DOM_Basic_Datatypes}
|
||||
\input{Core_DOM_Functions}
|
||||
\input{Core_DOM_Heap_WF}
|
||||
\input{Core_DOM}
|
||||
|
||||
\chapter{Test Suite}
|
||||
\label{cha:tests}
|
||||
In this chapter, we present the formalized compliance test cases for
|
||||
the core DOM. As our formalization is executable, we can
|
||||
(symbolically) execute the test cases on top of our model. Executing
|
||||
these test cases successfully shows that our model is compliant to the
|
||||
official DOM standard. As future work, we plan to generate test cases
|
||||
from our formal model (e.g.,
|
||||
using~\cite{brucker.ea:interactive:2005,brucker.ea:theorem-prover:2012})
|
||||
to improve the quality of the official compliance test suite. For more
|
||||
details on the relation of test and proof in the context of web
|
||||
standards, we refer the reader to
|
||||
\cite{brucker.ea:standard-compliance-testing:2018}.
|
||||
\input{Core_DOM_BaseTest} \input{Document_adoptNode}
|
||||
\input{Document_getElementById} \input{Node_insertBefore}
|
||||
\input{Node_removeChild} \input{Core_DOM_Tests}
|
||||
|
||||
{\small
|
||||
\bibliographystyle{abbrvnat}
|
||||
\bibliography{root}
|
||||
}
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: t
|
||||
%%% End:
|
||||
|
|
@ -0,0 +1,10 @@
|
|||
chapter AFP
|
||||
|
||||
session "Core_DOM" (AFP) = "HOL-Library" +
|
||||
options [timeout = 600]
|
||||
theories
|
||||
Core_DOM
|
||||
Core_DOM_Tests
|
||||
document_files
|
||||
"root.tex"
|
||||
"root.bib"
|
||||
|
|
@ -1,2 +0,0 @@
|
|||
Core_DOM
|
||||
Core_SC_DOM
|
||||
|
|
@ -164,8 +164,7 @@ lemma get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>
|
|||
\<longleftrightarrow> get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr h \<noteq> None"
|
||||
using l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_axioms assms
|
||||
apply(simp add: type_wf_defs get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def l_type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def)
|
||||
by (metis assms bind.bind_lzero character_data_ptr_kinds_commutes fmember.rep_eq
|
||||
local.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf option.exhaust option.simps(3))
|
||||
by (metis assms bind.bind_lzero character_data_ptr_kinds_commutes fmember.rep_eq local.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf option.exhaust option.simps(3))
|
||||
end
|
||||
|
||||
global_interpretation l_get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_lemmas type_wf
|
||||
|
|
@ -259,16 +258,14 @@ lemma new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>
|
|||
lemma new_character_data_ptr_new:
|
||||
"character_data_ptr.Ref (Suc (fMax (finsert 0 (character_data_ptr.the_ref |`| character_data_ptrs h))))
|
||||
|\<notin>| character_data_ptrs h"
|
||||
by (metis Suc_n_not_le_n character_data_ptr.sel(1) fMax_ge fimage_finsert finsertI1
|
||||
finsertI2 set_finsert)
|
||||
by (metis Suc_n_not_le_n character_data_ptr.sel(1) fMax_ge fimage_finsert finsertI1 finsertI2 set_finsert)
|
||||
|
||||
lemma new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_ptr_not_in_heap:
|
||||
assumes "new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a h = (new_character_data_ptr, h')"
|
||||
shows "new_character_data_ptr |\<notin>| character_data_ptr_kinds h"
|
||||
using assms
|
||||
unfolding new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def
|
||||
by (metis Pair_inject character_data_ptrs_def fMax_finsert fempty_iff ffmember_filter
|
||||
fimage_is_fempty is_character_data_ptr_ref max_0L new_character_data_ptr_new)
|
||||
by (metis Pair_inject character_data_ptrs_def fMax_finsert fempty_iff ffmember_filter fimage_is_fempty is_character_data_ptr_ref max_0L new_character_data_ptr_new)
|
||||
|
||||
lemma new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_new_ptr:
|
||||
assumes "new\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a h = (new_character_data_ptr, h')"
|
||||
|
|
@ -340,9 +337,7 @@ lemma known_ptrs_preserved:
|
|||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a known_ptr defines known_ptrs = a_known_ptrs .
|
||||
|
|
@ -136,8 +136,7 @@ lemma get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_type_w
|
|||
shows "document_ptr |\<in>| document_ptr_kinds h \<longleftrightarrow> get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr h \<noteq> None"
|
||||
using l_type_wf\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_axioms assms
|
||||
apply(simp add: type_wf_defs get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
by (metis document_ptr_kinds_commutes fmember.rep_eq is_none_bind is_none_simps(1)
|
||||
is_none_simps(2) local.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf)
|
||||
by (metis document_ptr_kinds_commutes fmember.rep_eq is_none_bind is_none_simps(1) is_none_simps(2) local.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf)
|
||||
end
|
||||
|
||||
global_interpretation l_get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas type_wf by unfold_locales
|
||||
|
|
@ -196,14 +195,12 @@ lemma get_document_ptr_simp2 [simp]:
|
|||
lemma get_document_ptr_simp3 [simp]:
|
||||
"get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr (put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr f h) = get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr h"
|
||||
by(auto simp add: get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
lemma get_document_ptr_simp4 [simp]:
|
||||
"get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr (put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr f h) = get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr h"
|
||||
lemma get_document_ptr_simp4 [simp]: "get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr (put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr f h) = get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr h"
|
||||
by(auto simp add: get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def)
|
||||
lemma get_document_ptr_simp5 [simp]:
|
||||
"get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr (put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr f h) = get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr h"
|
||||
by(auto simp add: get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
lemma get_document_ptr_simp6 [simp]:
|
||||
"get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr (put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr f h) = get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr h"
|
||||
lemma get_document_ptr_simp6 [simp]: "get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr (put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a character_data_ptr f h) = get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t document_ptr h"
|
||||
by(auto simp add: get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def)
|
||||
|
||||
lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t [simp]:
|
||||
|
|
@ -330,9 +327,7 @@ lemma known_ptrs_preserved:
|
|||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
|
|
@ -31,18 +31,18 @@ section\<open>Element\<close>
|
|||
text\<open>In this theory, we introduce the types for the Element class.\<close>
|
||||
theory ElementClass
|
||||
imports
|
||||
"NodeClass"
|
||||
"ShadowRootPointer"
|
||||
NodeClass
|
||||
"../pointers/ShadowRootPointer"
|
||||
begin
|
||||
text\<open>The type @{type "DOMString"} is a type synonym for @{type "string"}, define
|
||||
in \autoref{sec:Core_DOM_Basic_Datatypes}.\<close>
|
||||
type_synonym attr_key = DOMString
|
||||
type_synonym attr_value = DOMString
|
||||
type_synonym attrs = "(attr_key, attr_value) fmap"
|
||||
type_synonym tag_name = DOMString
|
||||
type_synonym tag_type = DOMString
|
||||
record ('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr) RElement = RNode +
|
||||
nothing :: unit
|
||||
tag_name :: tag_name
|
||||
tag_type :: tag_type
|
||||
child_nodes :: "('node_ptr, 'element_ptr, 'character_data_ptr) node_ptr list"
|
||||
attrs :: attrs
|
||||
shadow_root_opt :: "'shadow_root_ptr shadow_root_ptr option"
|
||||
|
|
@ -58,31 +58,24 @@ register_default_tvars
|
|||
"('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Node, 'Element) Node"
|
||||
type_synonym
|
||||
('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) Object
|
||||
= "('Object, ('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option)
|
||||
RElement_ext + 'Node) Object"
|
||||
= "('Object, ('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option) RElement_ext + 'Node) Object"
|
||||
register_default_tvars
|
||||
"('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) Object"
|
||||
|
||||
type_synonym
|
||||
('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr,
|
||||
'Object, 'Node, 'Element) heap
|
||||
= "(('document_ptr, 'shadow_root_ptr) document_ptr + 'object_ptr, 'element_ptr element_ptr +
|
||||
'character_data_ptr character_data_ptr + 'node_ptr, 'Object,
|
||||
('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option)
|
||||
RElement_ext + 'Node) heap"
|
||||
('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) heap
|
||||
= "(('document_ptr, 'shadow_root_ptr) document_ptr + 'object_ptr, 'element_ptr element_ptr + 'character_data_ptr character_data_ptr + 'node_ptr, 'Object,
|
||||
('node_ptr, 'element_ptr, 'character_data_ptr, 'shadow_root_ptr, 'Element option) RElement_ext + 'Node) heap"
|
||||
register_default_tvars
|
||||
"('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr,
|
||||
'Object, 'Node, 'Element) heap"
|
||||
"('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr, 'shadow_root_ptr, 'Object, 'Node, 'Element) heap"
|
||||
type_synonym heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l = "(unit, unit, unit, unit, unit, unit, unit, unit, unit) heap"
|
||||
|
||||
definition element_ptr_kinds :: "(_) heap \<Rightarrow> (_) element_ptr fset"
|
||||
where
|
||||
"element_ptr_kinds heap = the |`| (cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r |`|
|
||||
(ffilter is_element_ptr_kind (node_ptr_kinds heap)))"
|
||||
"element_ptr_kinds heap = the |`| (cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r |`| (ffilter is_element_ptr_kind (node_ptr_kinds heap)))"
|
||||
|
||||
lemma element_ptr_kinds_simp [simp]:
|
||||
"element_ptr_kinds (Heap (fmupd (cast element_ptr) element (the_heap h))) =
|
||||
{|element_ptr|} |\<union>| element_ptr_kinds h"
|
||||
"element_ptr_kinds (Heap (fmupd (cast element_ptr) element (the_heap h))) = {|element_ptr|} |\<union>| element_ptr_kinds h"
|
||||
apply(auto simp add: element_ptr_kinds_def)[1]
|
||||
by force
|
||||
|
||||
|
|
@ -92,8 +85,7 @@ definition element_ptrs :: "(_) heap \<Rightarrow> (_) element_ptr fset"
|
|||
|
||||
definition cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) Node \<Rightarrow> (_) Element option"
|
||||
where
|
||||
"cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node = (case RNode.more node of Inl element \<Rightarrow>
|
||||
Some (RNode.extend (RNode.truncate node) element) | _ \<Rightarrow> None)"
|
||||
"cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t node = (case RNode.more node of Inl element \<Rightarrow> Some (RNode.extend (RNode.truncate node) element) | _ \<Rightarrow> None)"
|
||||
adhoc_overloading cast cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
|
||||
abbreviation cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) Object \<Rightarrow> (_) Element option"
|
||||
|
|
@ -218,9 +210,9 @@ lemma get_elment_ptr_simp2 [simp]:
|
|||
by(auto simp add: get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
||||
|
||||
|
||||
abbreviation "create_element_obj tag_name_arg child_nodes_arg attrs_arg shadow_root_opt_arg
|
||||
abbreviation "create_element_obj tag_type_arg child_nodes_arg attrs_arg shadow_root_opt_arg
|
||||
\<equiv> \<lparr> RObject.nothing = (), RNode.nothing = (), RElement.nothing = (),
|
||||
tag_name = tag_name_arg, Element.child_nodes = child_nodes_arg, attrs = attrs_arg,
|
||||
tag_type = tag_type_arg, Element.child_nodes = child_nodes_arg, attrs = attrs_arg,
|
||||
shadow_root_opt = shadow_root_opt_arg, \<dots> = None \<rparr>"
|
||||
|
||||
definition new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t :: "(_) heap \<Rightarrow> ((_) element_ptr \<times> (_) heap)"
|
||||
|
|
@ -306,22 +298,17 @@ lemma known_ptrs_known_ptr:
|
|||
apply(simp add: a_known_ptrs_def)
|
||||
using notin_fset by fastforce
|
||||
|
||||
lemma known_ptrs_preserved:
|
||||
"object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved known_ptrs_subset known_ptrs_new_ptr l_known_ptrs_def
|
||||
by blast
|
||||
using known_ptrs_known_ptr known_ptrs_preserved known_ptrs_subset known_ptrs_new_ptr l_known_ptrs_def by blast
|
||||
|
||||
end
|
||||
|
|
@ -181,23 +181,18 @@ definition a_known_ptrs :: "(_) heap \<Rightarrow> bool"
|
|||
lemma known_ptrs_known_ptr: "a_known_ptrs h \<Longrightarrow> ptr |\<in>| object_ptr_kinds h \<Longrightarrow> known_ptr ptr"
|
||||
apply(simp add: a_known_ptrs_def)
|
||||
using notin_fset by fastforce
|
||||
lemma known_ptrs_preserved:
|
||||
"object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>N\<^sub>o\<^sub>d\<^sub>e known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset
|
||||
known_ptrs_new_ptr
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset known_ptrs_new_ptr
|
||||
by blast
|
||||
|
||||
lemma get_node_ptr_simp1 [simp]: "get\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr (put\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr node h) = Some node"
|
||||
|
|
@ -127,13 +127,9 @@ lemmas known_ptr_defs = a_known_ptr_def
|
|||
locale l_known_ptrs = l_known_ptr known_ptr for known_ptr :: "(_) object_ptr \<Rightarrow> bool" +
|
||||
fixes known_ptrs :: "(_) heap \<Rightarrow> bool"
|
||||
assumes known_ptrs_known_ptr: "known_ptrs h \<Longrightarrow> ptr |\<in>| object_ptr_kinds h \<Longrightarrow> known_ptr ptr"
|
||||
assumes known_ptrs_preserved:
|
||||
"object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> known_ptrs h = known_ptrs h'"
|
||||
assumes known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
assumes known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
assumes known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> known_ptrs h = known_ptrs h'"
|
||||
assumes known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
assumes known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
|
||||
locale l_known_ptrs\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t = l_known_ptr known_ptr for known_ptr :: "(_) object_ptr \<Rightarrow> bool"
|
||||
begin
|
||||
|
|
@ -146,15 +142,11 @@ lemma known_ptrs_known_ptr:
|
|||
apply(simp add: a_known_ptrs_def)
|
||||
using notin_fset by fastforce
|
||||
|
||||
lemma known_ptrs_preserved:
|
||||
"object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> a_known_ptrs h = a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset:
|
||||
"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def less_eq_fset.rep_eq subsetD)
|
||||
lemma known_ptrs_new_ptr:
|
||||
"object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow>
|
||||
a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
|
|
@ -36,8 +36,8 @@ theory BaseMonad
|
|||
begin
|
||||
subsection\<open>Datatypes\<close>
|
||||
|
||||
datatype exception = NotFoundError | HierarchyRequestError | NotSupportedError | SegmentationFault
|
||||
| AssertException | NonTerminationException | InvokeError | TypeError
|
||||
datatype exception = NotFoundError | SegmentationFault | HierarchyRequestError | AssertException
|
||||
| NonTerminationException | InvokeError | TypeError | DebugException nat
|
||||
|
||||
lemma finite_set_in [simp]: "x \<in> fset FS \<longleftrightarrow> x |\<in>| FS"
|
||||
by (meson notin_fset)
|
||||
|
|
@ -308,7 +308,7 @@ lemma type_wf_put_ptr_not_in_heap_E:
|
|||
shows "type_wf h"
|
||||
using assms
|
||||
apply(auto simp add: type_wf_defs elim!: ElementMonad.type_wf_put_ptr_not_in_heap_E
|
||||
split: option.splits if_splits)[1]
|
||||
split: option.splits if_splits)
|
||||
using assms(2) node_ptr_kinds_commutes by blast
|
||||
|
||||
lemma type_wf_put_ptr_in_heap_E:
|
||||
|
|
@ -319,8 +319,7 @@ lemma type_wf_put_ptr_in_heap_E:
|
|||
shows "type_wf h"
|
||||
using assms
|
||||
apply(auto simp add: type_wf_defs split: option.splits if_splits)[1]
|
||||
by (metis (no_types, lifting) ElementClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf assms(2) bind.bind_lunit
|
||||
cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_inv cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_inv get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def notin_fset option.collapse)
|
||||
by (metis (no_types, lifting) ElementClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf assms(2) bind.bind_lunit cast\<^sub>N\<^sub>o\<^sub>d\<^sub>e\<^sub>2\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_inv cast\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>2\<^sub>N\<^sub>o\<^sub>d\<^sub>e_inv get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def notin_fset option.collapse)
|
||||
|
||||
subsection\<open>Preserving Types\<close>
|
||||
|
||||
|
|
@ -341,8 +340,8 @@ lemma new_element_is_l_new_element: "l_new_element type_wf"
|
|||
using l_new_element.intro new_element_type_wf_preserved
|
||||
by blast
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_name_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_name_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_type_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_type_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
|
||||
dest!: get_heap_E
|
||||
elim!: bind_returns_heap_E2
|
||||
|
|
@ -527,8 +526,6 @@ lemma type_wf_drop: "type_wf h \<Longrightarrow> type_wf (Heap (fmdrop ptr (the_
|
|||
apply(auto simp add: type_wf_def ElementMonad.type_wf_drop
|
||||
l_type_wf_def\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a.a_type_wf_def)[1]
|
||||
using type_wf_drop
|
||||
by (metis (no_types, lifting) ElementClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ObjectClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf
|
||||
character_data_ptr_kinds_commutes finite_set_in fmlookup_drop get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
|
||||
get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def node_ptr_kinds_commutes object_ptr_kinds_code5)
|
||||
by (metis (no_types, lifting) ElementClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ObjectClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf character_data_ptr_kinds_commutes finite_set_in fmlookup_drop get\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def node_ptr_kinds_commutes object_ptr_kinds_code5)
|
||||
|
||||
end
|
||||
|
|
@ -55,10 +55,10 @@ lemma document_ptr_kinds_M_eq:
|
|||
lemma document_ptr_kinds_M_reads:
|
||||
"reads (\<Union>object_ptr. {preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing)}) document_ptr_kinds_M h h'"
|
||||
using object_ptr_kinds_M_reads
|
||||
|
||||
apply(simp add: reads_def object_ptr_kinds_M_defs document_ptr_kinds_M_defs
|
||||
document_ptr_kinds_def preserved_def cong del: image_cong_simp)
|
||||
apply (metis (mono_tags, hide_lams) object_ptr_kinds_preserved_small old.unit.exhaust preserved_def)
|
||||
done
|
||||
document_ptr_kinds_def preserved_def)
|
||||
by (smt object_ptr_kinds_preserved_small preserved_def unit_all_impI)
|
||||
|
||||
global_interpretation l_dummy defines get_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t = "l_get_M.a_get_M get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t" .
|
||||
lemma get_M_is_l_get_M: "l_get_M get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t type_wf document_ptr_kinds"
|
||||
|
|
@ -322,8 +322,7 @@ lemma type_wf_put_ptr_in_heap_E:
|
|||
using assms
|
||||
apply(auto simp add: type_wf_defs elim!: CharacterDataMonad.type_wf_put_ptr_in_heap_E
|
||||
split: option.splits if_splits)[1]
|
||||
by (metis (no_types, lifting) CharacterDataClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf bind.bind_lunit get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def
|
||||
is_document_kind_def notin_fset option.exhaust_sel)
|
||||
by (metis (no_types, lifting) CharacterDataClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf bind.bind_lunit get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def is_document_kind_def notin_fset option.exhaust_sel)
|
||||
|
||||
|
||||
|
||||
|
|
@ -348,8 +347,8 @@ lemma new_element_is_l_new_element [instances]:
|
|||
using l_new_element.intro new_element_type_wf_preserved
|
||||
by blast
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_name_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_name_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_type_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_type_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
apply(auto simp add: ElementMonad.put_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
|
||||
DocumentClass.type_wf\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a DocumentClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
DocumentClass.type_wf\<^sub>N\<^sub>o\<^sub>d\<^sub>e DocumentClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t
|
||||
|
|
@ -361,9 +360,7 @@ lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_name_typ
|
|||
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
||||
ElementMonad.get_M_defs ObjectClass.type_wf_defs
|
||||
CharacterDataClass.type_wf_defs split: option.splits)[1]
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def
|
||||
bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse
|
||||
option.distinct(1) option.simps(3))
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse option.distinct(1) option.simps(3))
|
||||
by (metis fmember.rep_eq)
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_child_nodes_type_wf_preserved [simp]:
|
||||
|
|
@ -379,9 +376,7 @@ lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_child_nodes_
|
|||
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
||||
NodeClass.type_wf_defs ElementMonad.get_M_defs ObjectClass.type_wf_defs
|
||||
CharacterDataClass.type_wf_defs split: option.splits)[1]
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def
|
||||
bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse
|
||||
option.distinct(1) option.simps(3))
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse option.distinct(1) option.simps(3))
|
||||
by (metis fmember.rep_eq)
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_attrs_type_wf_preserved [simp]:
|
||||
|
|
@ -397,9 +392,7 @@ lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_attrs_type_w
|
|||
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
||||
NodeClass.type_wf_defs ElementMonad.get_M_defs ObjectClass.type_wf_defs
|
||||
CharacterDataClass.type_wf_defs split: option.splits)[1]
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def
|
||||
bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse
|
||||
option.distinct(1) option.simps(3))
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse option.distinct(1) option.simps(3))
|
||||
by (metis fmember.rep_eq)
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_shadow_root_opt_type_wf_preserved [simp]:
|
||||
|
|
@ -415,9 +408,7 @@ lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_shadow_root_
|
|||
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
||||
NodeClass.type_wf_defs ElementMonad.get_M_defs ObjectClass.type_wf_defs
|
||||
CharacterDataClass.type_wf_defs split: option.splits)[1]
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def
|
||||
bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse
|
||||
option.distinct(1) option.simps(3))
|
||||
apply (metis NodeClass.a_type_wf_def NodeClass.get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_type_wf ObjectClass.a_type_wf_def bind.bind_lzero finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def l_type_wf_def\<^sub>N\<^sub>o\<^sub>d\<^sub>e.a_type_wf_def option.collapse option.distinct(1) option.simps(3))
|
||||
by (metis fmember.rep_eq)
|
||||
|
||||
lemma new_character_data_type_wf_preserved [simp]:
|
||||
|
|
@ -467,8 +458,7 @@ lemma new_document_type_wf_preserved [simp]: "h \<turnstile> new_document \<righ
|
|||
split: option.splits)[1]
|
||||
using document_ptrs_def apply fastforce
|
||||
apply (simp add: is_document_kind_def)
|
||||
apply (metis Suc_n_not_le_n document_ptr.sel(1) document_ptrs_def fMax_ge ffmember_filter
|
||||
fimage_eqI is_document_ptr_ref)
|
||||
apply (metis Suc_n_not_le_n document_ptr.sel(1) document_ptrs_def fMax_ge ffmember_filter fimage_eqI is_document_ptr_ref)
|
||||
done
|
||||
|
||||
locale l_new_document = l_type_wf +
|
||||
|
|
@ -508,7 +498,7 @@ lemma put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_doct
|
|||
apply(auto simp add: is_document_kind_def type_wf_defs ElementClass.type_wf_defs
|
||||
NodeClass.type_wf_defs ElementMonad.get_M_defs ObjectClass.type_wf_defs
|
||||
CharacterDataClass.type_wf_defs split: option.splits)[1]
|
||||
apply(auto simp add: get_M_defs)[1]
|
||||
apply(auto simp add: get_M_defs)
|
||||
by (metis (mono_tags) error_returns_result finite_set_in option.exhaust_sel option.simps(4))
|
||||
|
||||
lemma put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_document_element_type_wf_preserved [simp]:
|
||||
|
|
@ -609,6 +599,5 @@ lemma type_wf_drop: "type_wf h \<Longrightarrow> type_wf (Heap (fmdrop ptr (the_
|
|||
apply(auto simp add: type_wf_defs)[1]
|
||||
using type_wf_drop
|
||||
apply blast
|
||||
by (metis (no_types, lifting) CharacterDataClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf CharacterDataMonad.type_wf_drop
|
||||
document_ptr_kinds_commutes finite_set_in fmlookup_drop get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def heap.sel)
|
||||
by (metis (no_types, lifting) CharacterDataClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf CharacterDataMonad.type_wf_drop document_ptr_kinds_commutes finite_set_in fmlookup_drop get\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def heap.sel)
|
||||
end
|
||||
|
|
@ -32,7 +32,7 @@ text\<open>In this theory, we introduce the monadic method setup for the Element
|
|||
theory ElementMonad
|
||||
imports
|
||||
NodeMonad
|
||||
"ElementClass"
|
||||
"../classes/ElementClass"
|
||||
begin
|
||||
|
||||
type_synonym ('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr,
|
||||
|
|
@ -55,9 +55,8 @@ lemma element_ptr_kinds_M_eq:
|
|||
lemma element_ptr_kinds_M_reads:
|
||||
"reads (\<Union>element_ptr. {preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t element_ptr RObject.nothing)}) element_ptr_kinds_M h h'"
|
||||
apply(simp add: reads_def node_ptr_kinds_M_defs element_ptr_kinds_M_defs element_ptr_kinds_def
|
||||
node_ptr_kinds_M_reads preserved_def cong del: image_cong_simp)
|
||||
apply (metis (mono_tags, hide_lams) node_ptr_kinds_small old.unit.exhaust preserved_def)
|
||||
done
|
||||
node_ptr_kinds_M_reads preserved_def)
|
||||
by (smt filter_fset node_ptr_kinds_small preserved_def unit_all_impI)
|
||||
|
||||
global_interpretation l_dummy defines get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t = "l_get_M.a_get_M get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t" .
|
||||
lemma get_M_is_l_get_M: "l_get_M get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t type_wf element_ptr_kinds"
|
||||
|
|
@ -233,10 +232,10 @@ lemma new_element_child_nodes:
|
|||
by(auto simp add: get_M_defs new_element_def new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def
|
||||
split: option.splits prod.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
||||
|
||||
lemma new_element_tag_name:
|
||||
lemma new_element_tag_type:
|
||||
assumes "h \<turnstile> new_element \<rightarrow>\<^sub>h h'"
|
||||
assumes "h \<turnstile> new_element \<rightarrow>\<^sub>r new_element_ptr"
|
||||
shows "h' \<turnstile> get_M new_element_ptr tag_name \<rightarrow>\<^sub>r ''''"
|
||||
shows "h' \<turnstile> get_M new_element_ptr tag_type \<rightarrow>\<^sub>r ''''"
|
||||
using assms
|
||||
by(auto simp add: get_M_defs new_element_def new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def
|
||||
split: option.splits prod.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
||||
|
|
@ -300,7 +299,7 @@ lemma type_wf_put_ptr_not_in_heap_E:
|
|||
shows "type_wf h"
|
||||
using assms
|
||||
apply(auto simp add: type_wf_defs elim!: NodeMonad.type_wf_put_ptr_not_in_heap_E
|
||||
split: option.splits if_splits)[1]
|
||||
split: option.splits if_splits)
|
||||
using assms(2) node_ptr_kinds_commutes by blast
|
||||
|
||||
lemma type_wf_put_ptr_in_heap_E:
|
||||
|
|
@ -338,8 +337,8 @@ lemma new_element_is_l_new_element: "l_new_element type_wf"
|
|||
using l_new_element.intro new_element_type_wf_preserved
|
||||
by blast
|
||||
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_name_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_name_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_tag_type_type_wf_preserved [simp]:
|
||||
"h \<turnstile> put_M element_ptr tag_type_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
||||
apply(auto simp add: type_wf_defs NodeClass.type_wf_defs ObjectClass.type_wf_defs
|
||||
Let_def put_M_defs get_M_defs put\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def
|
||||
get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_def
|
||||
|
|
@ -165,7 +165,7 @@ lemma type_wf_put_ptr_in_heap_E:
|
|||
assumes "is_node_ptr_kind ptr \<Longrightarrow> is_node_kind (the (get ptr h))"
|
||||
shows "type_wf h"
|
||||
using assms
|
||||
apply(auto simp add: type_wf_defs split: option.splits if_splits)[1]
|
||||
apply(auto simp add: type_wf_defs split: option.splits if_splits)
|
||||
by (metis ObjectClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf bind.bind_lunit finite_set_in get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def is_node_kind_def option.exhaust_sel)
|
||||
|
||||
|
||||
|
|
@ -192,7 +192,7 @@ lemma type_wf_preserved_small:
|
|||
assumes "\<And>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
|
||||
shows "type_wf h = type_wf h'"
|
||||
using type_wf_preserved allI[OF assms(2), of id, simplified]
|
||||
apply(auto simp add: type_wf_defs)[1]
|
||||
apply(auto simp add: type_wf_defs)
|
||||
apply(auto simp add: preserved_def get_M_defs node_ptr_kinds_small[OF assms(1)]
|
||||
split: option.splits)[1]
|
||||
apply (metis notin_fset option.simps(3))
|
||||
|
|
@ -34,7 +34,7 @@ We only include them here, as they are required for future work and they cannot
|
|||
following the object-oriented extensibility of our data model.\<close>
|
||||
theory ShadowRootPointer
|
||||
imports
|
||||
"DocumentPointer"
|
||||
DocumentPointer
|
||||
begin
|
||||
|
||||
datatype 'shadow_root_ptr shadow_root_ptr = Ref (the_ref: ref) | Ext 'shadow_root_ptr
|
||||
|
|
@ -79,8 +79,7 @@ adhoc_overloading cast cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^su
|
|||
consts is_shadow_root_ptr_kind :: 'a
|
||||
definition is_shadow_root_ptr_kind\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) document_ptr \<Rightarrow> bool"
|
||||
where
|
||||
"is_shadow_root_ptr_kind\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr =
|
||||
(case cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of Some _ \<Rightarrow> True | _ \<Rightarrow> False)"
|
||||
"is_shadow_root_ptr_kind\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr = (case cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of Some _ \<Rightarrow> True | _ \<Rightarrow> False)"
|
||||
|
||||
abbreviation is_shadow_root_ptr_kind\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r :: "(_) object_ptr \<Rightarrow> bool"
|
||||
where
|
||||
|
|
@ -108,18 +107,15 @@ abbreviation is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\
|
|||
Some document_ptr \<Rightarrow> is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr
|
||||
| None \<Rightarrow> False)"
|
||||
|
||||
adhoc_overloading is_shadow_root_ptr is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
adhoc_overloading is_shadow_root_ptr is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
lemmas is_shadow_root_ptr_def = is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
|
||||
consts is_shadow_root_ptr_ext :: 'a
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> \<not> is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr"
|
||||
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv>
|
||||
is_shadow_root_ptr_kind ptr \<and> (\<not> is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr)"
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> is_shadow_root_ptr_kind ptr \<and> (\<not> is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr)"
|
||||
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv>
|
||||
is_shadow_root_ptr_kind ptr \<and> (\<not> is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr)"
|
||||
abbreviation "is_shadow_root_ptr_ext\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<equiv> is_shadow_root_ptr_kind ptr \<and> (\<not> is_shadow_root_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr)"
|
||||
adhoc_overloading is_shadow_root_ptr_ext is_shadow_root_ptr_ext\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r is_shadow_root_ptr_ext\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r
|
||||
|
||||
|
||||
|
|
@ -143,8 +139,7 @@ lemma is_shadow_root_ptr_ref [simp]: "is_shadow_root_ptr (shadow_root_ptr.Ref n)
|
|||
by(simp add: is_shadow_root_ptr\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma shadow_root_ptr_casts_commute [simp]:
|
||||
"cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr =
|
||||
Some shadow_root_ptr \<longleftrightarrow> cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr = document_ptr"
|
||||
"cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr = Some shadow_root_ptr \<longleftrightarrow> cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r shadow_root_ptr = document_ptr"
|
||||
unfolding cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def cast\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def
|
||||
by(auto split: document_ptr.splits sum.splits)
|
||||
|
||||
|
|
@ -183,8 +178,7 @@ lemma cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub
|
|||
"cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r (document_ptr.Ext (Inr (Inr document_ext_ptr))) = None"
|
||||
by(simp add: cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>s\<^sub>h\<^sub>a\<^sub>d\<^sub>o\<^sub>w\<^sub>_\<^sub>r\<^sub>o\<^sub>o\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
|
||||
|
||||
lemma is_shadow_root_ptr_implies_kind [dest]:
|
||||
"is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<Longrightarrow> is_shadow_root_ptr_kind\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr"
|
||||
lemma is_shadow_root_ptr_implies_kind [dest]: "is_shadow_root_ptr\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr \<Longrightarrow> is_shadow_root_ptr_kind\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr"
|
||||
by(auto split: option.splits)
|
||||
|
||||
lemma is_shadow_root_ptr_kind_not_document_ptr [simp]: "\<not>is_shadow_root_ptr_kind (document_ptr.Ref x)"
|
||||
|
|
@ -93,8 +93,7 @@ definition
|
|||
where
|
||||
"returns_result_heap h p r h' \<longleftrightarrow> h \<turnstile> p \<rightarrow>\<^sub>r r \<and> h \<turnstile> p \<rightarrow>\<^sub>h h'"
|
||||
|
||||
lemma return_result_heap_code [code]:
|
||||
"returns_result_heap h p r h' \<longleftrightarrow> (case h \<turnstile> p of Inr (r', h'') \<Rightarrow> r = r' \<and> h' = h'' | Inl _ \<Rightarrow> False)"
|
||||
lemma [code]: "returns_result_heap h p r h' \<longleftrightarrow> (case h \<turnstile> p of Inr (r', h'') \<Rightarrow> r = r' \<and> h' = h'' | Inl _ \<Rightarrow> False)"
|
||||
by(auto simp add: returns_result_heap_def returns_result_def returns_heap_def split: sum.splits)
|
||||
|
||||
fun select_result_heap ("|(_)|\<^sub>r\<^sub>h")
|
||||
|
|
@ -453,10 +452,32 @@ fun forall_M :: "('y \<Rightarrow> ('heap, 'e, 'result) prog) \<Rightarrow> 'y l
|
|||
P x;
|
||||
forall_M P xs
|
||||
}"
|
||||
(*
|
||||
lemma forall_M_elim:
|
||||
assumes "h \<turnstile> forall_M P xs \<rightarrow>\<^sub>r True" and "\<And>x h. x \<in> set xs \<Longrightarrow> pure (P x) h"
|
||||
shows "\<forall>x \<in> set xs. h \<turnstile> P x \<rightarrow>\<^sub>r True"
|
||||
apply(insert assms, induct xs)
|
||||
apply(simp)
|
||||
apply(auto elim!: bind_returns_result_E)[1]
|
||||
by (metis (full_types) pure_returns_heap_eq) *)
|
||||
|
||||
lemma pure_forall_M_I: "(\<And>x. x \<in> set xs \<Longrightarrow> pure (P x) h) \<Longrightarrow> pure (forall_M P xs) h"
|
||||
apply(induct xs)
|
||||
by(auto intro!: bind_pure_I)
|
||||
(*
|
||||
lemma forall_M_pure_I:
|
||||
assumes "\<And>x. x \<in> set xs \<Longrightarrow> h \<turnstile> P x \<rightarrow>\<^sub>r True" and "\<And>x h. x \<in> set xs \<Longrightarrow> pure (P x)h"
|
||||
shows "h \<turnstile> forall_M P xs \<rightarrow>\<^sub>r True"
|
||||
apply(insert assms, induct xs)
|
||||
apply(simp)
|
||||
by(fastforce)
|
||||
|
||||
lemma forall_M_pure_eq:
|
||||
assumes "\<And>x. x \<in> set xs \<Longrightarrow> h \<turnstile> P x \<rightarrow>\<^sub>r True \<longleftrightarrow> h' \<turnstile> P x \<rightarrow>\<^sub>r True"
|
||||
and "\<And>x h. x \<in> set xs \<Longrightarrow> pure (P x) h"
|
||||
shows "(h \<turnstile> forall_M P xs \<rightarrow>\<^sub>r True) \<longleftrightarrow> h' \<turnstile> forall_M P xs \<rightarrow>\<^sub>r True"
|
||||
using assms
|
||||
by(auto intro!: forall_M_pure_I dest!: forall_M_elim) *)
|
||||
|
||||
subsection \<open>Fold\<close>
|
||||
|
||||
|
|
@ -485,8 +506,7 @@ lemma filter_M_pure_I [intro]: "(\<And>x. x \<in> set xs \<Longrightarrow> pure
|
|||
apply(induct xs)
|
||||
by(auto intro!: bind_pure_I)
|
||||
|
||||
lemma filter_M_is_OK_I [intro]:
|
||||
"(\<And>x. x \<in> set xs \<Longrightarrow> h \<turnstile> ok (P x)) \<Longrightarrow> (\<And>x. x \<in> set xs \<Longrightarrow> pure (P x) h) \<Longrightarrow> h \<turnstile> ok (filter_M P xs)"
|
||||
lemma filter_M_is_OK_I [intro]: "(\<And>x. x \<in> set xs \<Longrightarrow> h \<turnstile> ok (P x)) \<Longrightarrow> (\<And>x. x \<in> set xs \<Longrightarrow> pure (P x) h) \<Longrightarrow> h \<turnstile> ok (filter_M P xs)"
|
||||
apply(induct xs)
|
||||
apply(simp)
|
||||
by(auto intro!: bind_is_OK_pure_I)
|
||||
|
|
@ -498,8 +518,7 @@ lemma filter_M_not_more_elements:
|
|||
by(auto elim!: bind_returns_result_E2 split: if_splits intro!: set_ConsD)
|
||||
|
||||
lemma filter_M_in_result_if_ok:
|
||||
assumes "h \<turnstile> filter_M P xs \<rightarrow>\<^sub>r ys" and "\<And>h x. x \<in> set xs \<Longrightarrow> pure (P x) h" and "x \<in> set xs" and
|
||||
"h \<turnstile> P x \<rightarrow>\<^sub>r True"
|
||||
assumes "h \<turnstile> filter_M P xs \<rightarrow>\<^sub>r ys" and "\<And>h x. x \<in> set xs \<Longrightarrow> pure (P x) h" and "x \<in> set xs" and "h \<turnstile> P x \<rightarrow>\<^sub>r True"
|
||||
shows "x \<in> set ys"
|
||||
apply(insert assms, induct xs arbitrary: ys)
|
||||
apply(simp)
|
||||
|
|
@ -711,9 +730,8 @@ definition preserved :: "('heap, 'e, 'result) prog \<Rightarrow> 'heap \<Rightar
|
|||
where
|
||||
"preserved f h h' \<longleftrightarrow> (\<forall>x. h \<turnstile> f \<rightarrow>\<^sub>r x \<longleftrightarrow> h' \<turnstile> f \<rightarrow>\<^sub>r x)"
|
||||
|
||||
lemma preserved_code [code]:
|
||||
"preserved f h h' = (((h \<turnstile> ok f) \<and> (h' \<turnstile> ok f) \<and> |h \<turnstile> f|\<^sub>r = |h' \<turnstile> f|\<^sub>r) \<or> ((\<not>h \<turnstile> ok f) \<and> (\<not>h' \<turnstile> ok f)))"
|
||||
apply(auto simp add: preserved_def)[1]
|
||||
lemma preserved_code [code]: "preserved f h h' = (((h \<turnstile> ok f) \<and> (h' \<turnstile> ok f) \<and> |h \<turnstile> f|\<^sub>r = |h' \<turnstile> f|\<^sub>r) \<or> ((\<not>h \<turnstile> ok f) \<and> (\<not>h' \<turnstile> ok f)))"
|
||||
apply(auto simp add: preserved_def)
|
||||
apply (meson is_OK_returns_result_E is_OK_returns_result_I)+
|
||||
done
|
||||
|
||||
|
|
@ -750,16 +768,13 @@ lemma reads_bind_pure:
|
|||
dest: pure_returns_heap_eq
|
||||
elim!: bind_returns_result_E)
|
||||
|
||||
lemma reads_insert_writes_set_left:
|
||||
"\<forall>P \<in> S. reflp P \<and> transp P \<Longrightarrow> reads {getter} f h h' \<Longrightarrow> reads (insert getter S) f h h'"
|
||||
lemma reads_insert_writes_set_left: "\<forall>P \<in> S. reflp P \<and> transp P \<Longrightarrow> reads {getter} f h h' \<Longrightarrow> reads (insert getter S) f h h'"
|
||||
unfolding reads_def by simp
|
||||
|
||||
lemma reads_insert_writes_set_right:
|
||||
"reflp getter \<Longrightarrow> transp getter \<Longrightarrow> reads S f h h' \<Longrightarrow> reads (insert getter S) f h h'"
|
||||
lemma reads_insert_writes_set_right: "reflp getter \<Longrightarrow> transp getter \<Longrightarrow> reads S f h h' \<Longrightarrow> reads (insert getter S) f h h'"
|
||||
unfolding reads_def by blast
|
||||
|
||||
lemma reads_subset:
|
||||
"reads S f h h' \<Longrightarrow> \<forall>P \<in> S' - S. reflp P \<and> transp P \<Longrightarrow> S \<subseteq> S' \<Longrightarrow> reads S' f h h'"
|
||||
lemma reads_subset: "reads S f h h' \<Longrightarrow> \<forall>P \<in> S' - S. reflp P \<and> transp P \<Longrightarrow> S \<subseteq> S' \<Longrightarrow> reads S' f h h'"
|
||||
by(auto simp add: reads_def)
|
||||
|
||||
lemma return_reads [simp]: "reads {} (return x) h h'"
|
||||
|
|
@ -276,8 +276,7 @@ structure Hide_Tvar : HIDE_TVAR = struct
|
|||
val thy = Proof_Context.theory_of ctx
|
||||
|
||||
fun parse_ast ((Ast.Constant const)::[]) = (const,NONE)
|
||||
| parse_ast ((Ast.Constant sort)::(Ast.Constant const)::[])
|
||||
= (const,SOME sort)
|
||||
| parse_ast (sort::(Ast.Constant const)::[]) = (const,SOME sort)
|
||||
| parse_ast _ = error("AST type not supported.")
|
||||
|
||||
val (decorated_name, decorated_sort) = parse_ast ast
|
||||
|
|
@ -297,7 +296,7 @@ structure Hide_Tvar : HIDE_TVAR = struct
|
|||
NONE => Ast.Variable(name_of_tvar n)
|
||||
| SOME sort => Ast.Appl([Ast.Constant("_ofsort"),
|
||||
Ast.Variable(name_of_tvar n),
|
||||
Ast.Constant(sort)])
|
||||
sort])
|
||||
in
|
||||
map mk_tvar (#tvars default_info)
|
||||
end
|
||||
|
|
@ -0,0 +1,39 @@
|
|||
(***********************************************************************************
|
||||
* Copyright (c) 2016-2018 The University of Sheffield, UK
|
||||
*
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions are met:
|
||||
*
|
||||
* * Redistributions of source code must retain the above copyright notice, this
|
||||
* list of conditions and the following disclaimer.
|
||||
*
|
||||
* * Redistributions in binary form must reproduce the above copyright notice,
|
||||
* this list of conditions and the following disclaimer in the documentation
|
||||
* and/or other materials provided with the distribution.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
||||
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
||||
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
||||
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
* SPDX-License-Identifier: BSD-2-Clause
|
||||
***********************************************************************************)
|
||||
|
||||
theory Testing_Utils
|
||||
imports Main
|
||||
begin
|
||||
ML \<open>
|
||||
val _ = Theory.setup
|
||||
(Method.setup @{binding timed_code_simp}
|
||||
(Scan.succeed (SIMPLE_METHOD' o (CHANGED_PROP oo (fn a => fn b => Timeout.apply (seconds 3600.0) (Code_Simp.dynamic_tac a b)))))
|
||||
"simplification with code equations, aborts after 1 hour");
|
||||
\<close>
|
||||
end
|
||||
|
|
@ -142,23 +142,19 @@ fun get_element_by_id_with_null :: "((_::linorder) object_ptr option) \<Rightarr
|
|||
| "get_element_by_id_with_null _ _ = error SegmentationFault"
|
||||
notation get_element_by_id_with_null ("_ . getElementById'(_')")
|
||||
|
||||
fun get_elements_by_class_name_with_null ::
|
||||
"((_::linorder) object_ptr option) \<Rightarrow> string \<Rightarrow> (_, ((_) object_ptr option) list) dom_prog"
|
||||
fun get_elements_by_class_name_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> string \<Rightarrow> (_, ((_) object_ptr option) list) dom_prog"
|
||||
where
|
||||
"get_elements_by_class_name_with_null (Some ptr) class_name =
|
||||
get_elements_by_class_name ptr class_name \<bind> map_M (return \<circ> Some \<circ> cast\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r)"
|
||||
notation get_elements_by_class_name_with_null ("_ . getElementsByClassName'(_')")
|
||||
|
||||
fun get_elements_by_tag_name_with_null ::
|
||||
"((_::linorder) object_ptr option) \<Rightarrow> string \<Rightarrow> (_, ((_) object_ptr option) list) dom_prog"
|
||||
fun get_elements_by_tag_name_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> string \<Rightarrow> (_, ((_) object_ptr option) list) dom_prog"
|
||||
where
|
||||
"get_elements_by_tag_name_with_null (Some ptr) tag =
|
||||
get_elements_by_tag_name ptr tag \<bind> map_M (return \<circ> Some \<circ> cast\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r)"
|
||||
"get_elements_by_tag_name_with_null (Some ptr) tag_name =
|
||||
get_elements_by_tag_name ptr tag_name \<bind> map_M (return \<circ> Some \<circ> cast\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r)"
|
||||
notation get_elements_by_tag_name_with_null ("_ . getElementsByTagName'(_')")
|
||||
|
||||
fun insert_before_with_null ::
|
||||
"((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow>
|
||||
(_, ((_) object_ptr option)) dom_prog"
|
||||
fun insert_before_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"insert_before_with_null (Some ptr) (Some child_obj) ref_child_obj_opt = (case cast child_obj of
|
||||
Some child \<Rightarrow> do {
|
||||
|
|
@ -169,8 +165,7 @@ fun insert_before_with_null ::
|
|||
| None \<Rightarrow> error HierarchyRequestError)"
|
||||
notation insert_before_with_null ("_ . insertBefore'(_, _')")
|
||||
|
||||
fun append_child_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow>
|
||||
(_, unit) dom_prog"
|
||||
fun append_child_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> (_, unit) dom_prog"
|
||||
where
|
||||
"append_child_with_null (Some ptr) (Some child_obj) = (case cast child_obj of
|
||||
Some child \<Rightarrow> append_child ptr child
|
||||
|
|
@ -185,8 +180,7 @@ fun get_body :: "((_::linorder) object_ptr option) \<Rightarrow> (_, ((_) object
|
|||
}"
|
||||
notation get_body ("_ . body")
|
||||
|
||||
fun get_document_element_with_null :: "((_::linorder) object_ptr option) \<Rightarrow>
|
||||
(_, ((_) object_ptr option)) dom_prog"
|
||||
fun get_document_element_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"get_document_element_with_null (Some ptr) = (case cast\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr of
|
||||
Some document_ptr \<Rightarrow> do {
|
||||
|
|
@ -196,16 +190,14 @@ fun get_document_element_with_null :: "((_::linorder) object_ptr option) \<Right
|
|||
| None \<Rightarrow> None)})"
|
||||
notation get_document_element_with_null ("_ . documentElement")
|
||||
|
||||
fun get_owner_document_with_null :: "((_::linorder) object_ptr option) \<Rightarrow>
|
||||
(_, ((_) object_ptr option)) dom_prog"
|
||||
fun get_owner_document_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"get_owner_document_with_null (Some ptr) = (do {
|
||||
document_ptr \<leftarrow> get_owner_document ptr;
|
||||
return (Some (cast\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r document_ptr))})"
|
||||
notation get_owner_document_with_null ("_ . ownerDocument")
|
||||
|
||||
fun remove_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow>
|
||||
(_, ((_) object_ptr option)) dom_prog"
|
||||
fun remove_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"remove_with_null (Some ptr) (Some child) = (case cast child of
|
||||
Some child_node \<Rightarrow> do {
|
||||
|
|
@ -216,8 +208,7 @@ fun remove_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) ob
|
|||
| "remove_with_null _ None = error TypeError"
|
||||
notation remove_with_null ("_ . remove'(')")
|
||||
|
||||
fun remove_child_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow>
|
||||
(_, ((_) object_ptr option)) dom_prog"
|
||||
fun remove_child_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"remove_child_with_null (Some ptr) (Some child) = (case cast child of
|
||||
Some child_node \<Rightarrow> do {
|
||||
|
|
@ -231,7 +222,7 @@ notation remove_child_with_null ("_ . removeChild")
|
|||
fun get_tag_name_with_null :: "((_) object_ptr option) \<Rightarrow> (_, attr_value) dom_prog"
|
||||
where
|
||||
"get_tag_name_with_null (Some ptr) = (case cast ptr of
|
||||
Some element_ptr \<Rightarrow> get_M element_ptr tag_name)"
|
||||
Some element_ptr \<Rightarrow> get_M element_ptr tag_type)"
|
||||
notation get_tag_name_with_null ("_ . tagName")
|
||||
|
||||
abbreviation "remove_attribute_with_null ptr k \<equiv> set_attribute_with_null2 ptr k None"
|
||||
|
|
@ -265,8 +256,7 @@ fun first_child_with_null :: "((_) object_ptr option) \<Rightarrow> (_, ((_) obj
|
|||
| None \<Rightarrow> None)}"
|
||||
notation first_child_with_null ("_ . firstChild")
|
||||
|
||||
fun adopt_node_with_null ::
|
||||
"((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow>(_, ((_) object_ptr option)) dom_prog"
|
||||
fun adopt_node_with_null :: "((_::linorder) object_ptr option) \<Rightarrow> ((_) object_ptr option) \<Rightarrow> (_, ((_) object_ptr option)) dom_prog"
|
||||
where
|
||||
"adopt_node_with_null (Some ptr) (Some child) = (case cast ptr of
|
||||
Some document_ptr \<Rightarrow> (case cast child of
|
||||
|
|
@ -276,8 +266,7 @@ fun adopt_node_with_null ::
|
|||
notation adopt_node_with_null ("_ . adoptNode'(_')")
|
||||
|
||||
|
||||
definition createTestTree ::
|
||||
"((_::linorder) object_ptr option) \<Rightarrow> (_, (string \<Rightarrow> (_, ((_) object_ptr option)) dom_prog)) dom_prog"
|
||||
definition createTestTree :: "((_::linorder) object_ptr option) \<Rightarrow> (_, (string \<Rightarrow> (_, ((_) object_ptr option)) dom_prog)) dom_prog"
|
||||
where
|
||||
"createTestTree ref = return (\<lambda>id. get_element_by_id_with_null ref id)"
|
||||
|
||||
|
|
@ -29,15 +29,15 @@
|
|||
|
||||
(* This file is automatically generated, please do not modify! *)
|
||||
|
||||
section\<open>Testing Document\_adoptNode\<close>
|
||||
text\<open>This theory contains the test cases for Document\_adoptNode.\<close>
|
||||
section\<open>Testing Document_adoptNode\<close>
|
||||
text\<open>This theory contains the test cases for Document_adoptNode.\<close>
|
||||
|
||||
theory Document_adoptNode
|
||||
imports
|
||||
"Core_DOM_BaseTest"
|
||||
begin
|
||||
|
||||
definition Document_adoptNode_heap :: heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l where
|
||||
definition Document_adoptNode_heap :: heap⇩f⇩i⇩n⇩a⇩l where
|
||||
"Document_adoptNode_heap = create_heap [(cast (document_ptr.Ref 1), cast (create_document_obj html (Some (cast (element_ptr.Ref 1))) [])),
|
||||
(cast (element_ptr.Ref 1), cast (create_element_obj ''html'' [cast (element_ptr.Ref 2), cast (element_ptr.Ref 8)] fmempty None)),
|
||||
(cast (element_ptr.Ref 2), cast (create_element_obj ''head'' [cast (element_ptr.Ref 3), cast (element_ptr.Ref 4), cast (element_ptr.Ref 5), cast (element_ptr.Ref 6), cast (element_ptr.Ref 7)] fmempty None)),
|
||||
|
|
@ -29,15 +29,15 @@
|
|||
|
||||
(* This file is automatically generated, please do not modify! *)
|
||||
|
||||
section\<open>Testing Document\_getElementById\<close>
|
||||
text\<open>This theory contains the test cases for Document\_getElementById.\<close>
|
||||
section\<open>Testing Document_getElementById\<close>
|
||||
text\<open>This theory contains the test cases for Document_getElementById.\<close>
|
||||
|
||||
theory Document_getElementById
|
||||
imports
|
||||
"Core_DOM_BaseTest"
|
||||
begin
|
||||
|
||||
definition Document_getElementById_heap :: heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l where
|
||||
definition Document_getElementById_heap :: heap⇩f⇩i⇩n⇩a⇩l where
|
||||
"Document_getElementById_heap = create_heap [(cast (document_ptr.Ref 1), cast (create_document_obj html (Some (cast (element_ptr.Ref 1))) [])),
|
||||
(cast (element_ptr.Ref 1), cast (create_element_obj ''html'' [cast (element_ptr.Ref 2), cast (element_ptr.Ref 9)] fmempty None)),
|
||||
(cast (element_ptr.Ref 2), cast (create_element_obj ''head'' [cast (element_ptr.Ref 3), cast (element_ptr.Ref 4), cast (element_ptr.Ref 5), cast (element_ptr.Ref 6), cast (element_ptr.Ref 7), cast (element_ptr.Ref 8)] fmempty None)),
|
||||
|
|
@ -29,15 +29,15 @@
|
|||
|
||||
(* This file is automatically generated, please do not modify! *)
|
||||
|
||||
section\<open>Testing Node\_insertBefore\<close>
|
||||
text\<open>This theory contains the test cases for Node\_insertBefore.\<close>
|
||||
section\<open>Testing Node_insertBefore\<close>
|
||||
text\<open>This theory contains the test cases for Node_insertBefore.\<close>
|
||||
|
||||
theory Node_insertBefore
|
||||
imports
|
||||
"Core_DOM_BaseTest"
|
||||
begin
|
||||
|
||||
definition Node_insertBefore_heap :: heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l where
|
||||
definition Node_insertBefore_heap :: heap⇩f⇩i⇩n⇩a⇩l where
|
||||
"Node_insertBefore_heap = create_heap [(cast (document_ptr.Ref 1), cast (create_document_obj html (Some (cast (element_ptr.Ref 1))) [])),
|
||||
(cast (element_ptr.Ref 1), cast (create_element_obj ''html'' [cast (element_ptr.Ref 2), cast (element_ptr.Ref 6)] fmempty None)),
|
||||
(cast (element_ptr.Ref 2), cast (create_element_obj ''head'' [cast (element_ptr.Ref 3), cast (element_ptr.Ref 4), cast (element_ptr.Ref 5)] fmempty None)),
|
||||
|
|
@ -29,15 +29,15 @@
|
|||
|
||||
(* This file is automatically generated, please do not modify! *)
|
||||
|
||||
section\<open>Testing Node\_removeChild\<close>
|
||||
text\<open>This theory contains the test cases for Node\_removeChild.\<close>
|
||||
section\<open>Testing Node_removeChild\<close>
|
||||
text\<open>This theory contains the test cases for Node_removeChild.\<close>
|
||||
|
||||
theory Node_removeChild
|
||||
imports
|
||||
"Core_DOM_BaseTest"
|
||||
begin
|
||||
|
||||
definition Node_removeChild_heap :: heap\<^sub>f\<^sub>i\<^sub>n\<^sub>a\<^sub>l where
|
||||
definition Node_removeChild_heap :: heap⇩f⇩i⇩n⇩a⇩l where
|
||||
"Node_removeChild_heap = create_heap [(cast (document_ptr.Ref 1), cast (create_document_obj html (Some (cast (element_ptr.Ref 1))) [])),
|
||||
(cast (element_ptr.Ref 1), cast (create_element_obj ''html'' [cast (element_ptr.Ref 2), cast (element_ptr.Ref 7)] fmempty None)),
|
||||
(cast (element_ptr.Ref 2), cast (create_element_obj ''head'' [cast (element_ptr.Ref 3), cast (element_ptr.Ref 4), cast (element_ptr.Ref 5), cast (element_ptr.Ref 6)] fmempty None)),
|
||||
Reference in New Issue