forked from afp-mirror/Core_DOM
532 lines
40 KiB
Plaintext
532 lines
40 KiB
Plaintext
(***********************************************************************************
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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
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* 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
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* 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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section\<open>CharacterData\<close>
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text\<open>In this theory, we introduce the monadic method setup for the CharacterData class.\<close>
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theory CharacterDataMonad
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imports
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ElementMonad
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"../classes/CharacterDataClass"
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begin
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type_synonym ('object_ptr, 'node_ptr, 'element_ptr, 'character_data_ptr, 'document_ptr,
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'shadow_root_ptr, 'Object, 'Node, 'Element, 'CharacterData, 'result) dom_prog
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= "((_) heap, exception, 'result) prog"
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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, 'CharacterData, 'result) dom_prog"
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global_interpretation l_ptr_kinds_M character_data_ptr_kinds
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defines character_data_ptr_kinds_M = a_ptr_kinds_M .
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lemmas character_data_ptr_kinds_M_defs = a_ptr_kinds_M_def
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lemma character_data_ptr_kinds_M_eq:
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assumes "|h \<turnstile> node_ptr_kinds_M|\<^sub>r = |h' \<turnstile> node_ptr_kinds_M|\<^sub>r"
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shows "|h \<turnstile> character_data_ptr_kinds_M|\<^sub>r = |h' \<turnstile> character_data_ptr_kinds_M|\<^sub>r"
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using assms
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by(auto simp add: character_data_ptr_kinds_M_defs node_ptr_kinds_M_defs
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character_data_ptr_kinds_def)
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lemma character_data_ptr_kinds_M_reads:
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"reads (\<Union>node_ptr. {preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t node_ptr RObject.nothing)}) character_data_ptr_kinds_M h h'"
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using node_ptr_kinds_M_reads
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apply(simp add: reads_def node_ptr_kinds_M_defs character_data_ptr_kinds_M_defs
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character_data_ptr_kinds_def preserved_def)
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by (smt node_ptr_kinds_small preserved_def unit_all_impI)
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global_interpretation l_dummy defines get_M\<^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 = "l_get_M.a_get_M 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" .
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lemma get_M_is_l_get_M: "l_get_M 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 type_wf character_data_ptr_kinds"
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apply(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_type_wf l_get_M_def)
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by (metis (no_types, hide_lams) NodeMonad.get_M_is_l_get_M bind_eq_Some_conv
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character_data_ptr_kinds_commutes 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_get_M_def option.distinct(1))
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lemmas get_M_defs = get_M\<^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[unfolded l_get_M.a_get_M_def[OF get_M_is_l_get_M]]
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adhoc_overloading get_M get_M\<^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
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locale l_get_M\<^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 = 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
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begin
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sublocale l_get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas by unfold_locales
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interpretation l_get_M 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 type_wf character_data_ptr_kinds
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apply(unfold_locales)
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apply (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_type_wf local.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)
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by (meson CharacterDataMonad.get_M_is_l_get_M l_get_M_def)
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lemmas get_M\<^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_ok = get_M_ok[folded get_M\<^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]
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end
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global_interpretation l_get_M\<^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 by unfold_locales
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global_interpretation l_put_M type_wf character_data_ptr_kinds 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 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
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rewrites "a_get_M = get_M\<^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" defines put_M\<^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_put_M
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apply (simp add: get_M_is_l_get_M l_put_M_def)
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by (simp add: get_M\<^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)
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lemmas put_M_defs = a_put_M_def
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adhoc_overloading put_M put_M\<^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
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locale l_put_M\<^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 = 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
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begin
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sublocale l_put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_lemmas by unfold_locales
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interpretation l_put_M type_wf character_data_ptr_kinds 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 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
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apply(unfold_locales)
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using 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_type_wf 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.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 local.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
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apply blast
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by (meson CharacterDataMonad.get_M_is_l_get_M l_get_M_def)
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lemmas put_M\<^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_ok = put_M_ok[folded put_M\<^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]
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end
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global_interpretation l_put_M\<^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 by unfold_locales
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lemma CharacterData_simp1 [simp]:
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"(\<And>x. getter (setter (\<lambda>_. v) x) = v) \<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> h' \<turnstile> get_M\<^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 getter \<rightarrow>\<^sub>r v"
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by(auto simp add: put_M_defs get_M_defs split: option.splits)
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lemma CharacterData_simp2 [simp]:
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"character_data_ptr \<noteq> character_data_ptr'
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^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' getter) h h'"
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by(auto simp add: put_M_defs get_M_defs preserved_def split: option.splits dest: get_heap_E)
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lemma CharacterData_simp3 [simp]: "
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(\<And>x. getter (setter (\<lambda>_. v) x) = getter x)
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^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' getter) h h'"
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apply(cases "character_data_ptr = character_data_ptr'")
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by(auto simp add: put_M_defs get_M_defs preserved_def split: option.splits dest: get_heap_E)
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lemma CharacterData_simp4 [simp]:
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"h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr getter) h h'"
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by(auto simp add: put_M_defs ElementMonad.get_M_defs preserved_def
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split: option.splits dest: get_heap_E)
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lemma CharacterData_simp5 [simp]:
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"h \<turnstile> put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^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 getter) h h'"
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by(auto simp add: ElementMonad.put_M_defs get_M_defs preserved_def
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split: option.splits dest: get_heap_E)
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lemma CharacterData_simp6 [simp]:
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"(\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
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apply (cases "cast character_data_ptr = object_ptr")
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by(auto simp add: put_M_defs get_M_defs ObjectMonad.get_M_defs NodeMonad.get_M_defs
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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 preserved_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
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bind_eq_Some_conv split: option.splits)
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lemma CharacterData_simp7 [simp]:
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"(\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
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apply(cases "cast character_data_ptr = node_ptr")
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by(auto simp add: put_M_defs get_M_defs ObjectMonad.get_M_defs NodeMonad.get_M_defs
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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 preserved_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
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bind_eq_Some_conv split: option.splits)
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lemma CharacterData_simp8 [simp]:
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"cast character_data_ptr \<noteq> node_ptr
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
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by(auto simp add: put_M_defs get_M_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 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 NodeMonad.get_M_defs
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preserved_def split: option.splits dest: get_heap_E)
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lemma CharacterData_simp9 [simp]:
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"h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> (\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
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\<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr getter) h h'"
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apply(cases "cast character_data_ptr \<noteq> node_ptr")
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by(auto simp add: put_M_defs get_M_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 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
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NodeMonad.get_M_defs preserved_def split: option.splits bind_splits
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dest: get_heap_E)
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lemma CharacterData_simp10 [simp]:
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"cast character_data_ptr \<noteq> node_ptr
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\<Longrightarrow> h \<turnstile> put_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr setter v \<rightarrow>\<^sub>h h'
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\<Longrightarrow> preserved (get_M\<^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 getter) h h'"
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by(auto simp add: NodeMonad.put_M_defs get_M_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 NodeMonad.get_M_defs
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preserved_def split: option.splits dest: get_heap_E)
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lemma CharacterData_simp11 [simp]:
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"cast character_data_ptr \<noteq> object_ptr
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\<Longrightarrow> h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
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|
\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
|
|
by(auto simp add: put_M_defs get_M_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 get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_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
|
|
ObjectMonad.get_M_defs preserved_def
|
|
split: option.splits dest: get_heap_E)
|
|
|
|
lemma CharacterData_simp12 [simp]:
|
|
"h \<turnstile> put_M\<^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 setter v \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> (\<And>x. getter (cast (setter (\<lambda>_. v) x)) = getter (cast x))
|
|
\<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr getter) h h'"
|
|
apply(cases "cast character_data_ptr \<noteq> object_ptr")
|
|
apply(auto simp add: put_M_defs get_M_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 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
|
|
get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def ObjectMonad.get_M_defs preserved_def
|
|
split: option.splits bind_splits dest: get_heap_E)[1]
|
|
by(auto simp add: put_M_defs get_M_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 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
|
|
get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def ObjectMonad.get_M_defs preserved_def
|
|
split: option.splits bind_splits dest: get_heap_E)[1]
|
|
|
|
lemma CharacterData_simp13 [simp]:
|
|
"cast character_data_ptr \<noteq> object_ptr \<Longrightarrow> h \<turnstile> put_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr setter v \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> preserved (get_M\<^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 getter) h h'"
|
|
by(auto simp add: ObjectMonad.put_M_defs get_M_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 get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def
|
|
ObjectMonad.get_M_defs preserved_def split: option.splits dest: get_heap_E)
|
|
|
|
lemma new_element_get_M\<^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 \<turnstile> new_element \<rightarrow>\<^sub>h h' \<Longrightarrow> preserved (get_M\<^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 getter) h h'"
|
|
by(auto simp add: new_element_def get_M_defs preserved_def split: prod.splits option.splits
|
|
elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
|
|
subsection\<open>Creating CharacterData\<close>
|
|
|
|
definition new_character_data :: "(_, (_) character_data_ptr) dom_prog"
|
|
where
|
|
"new_character_data = do {
|
|
h \<leftarrow> get_heap;
|
|
(new_ptr, h') \<leftarrow> return (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);
|
|
return_heap h';
|
|
return new_ptr
|
|
}"
|
|
|
|
lemma new_character_data_ok [simp]:
|
|
"h \<turnstile> ok new_character_data"
|
|
by(auto simp add: new_character_data_def split: prod.splits)
|
|
|
|
lemma new_character_data_ptr_in_heap:
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
|
|
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
|
|
shows "new_character_data_ptr |\<in>| character_data_ptr_kinds h'"
|
|
using assms
|
|
unfolding new_character_data_def
|
|
by(auto simp add: new_character_data_def 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 Let_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_ptr_in_heap
|
|
is_OK_returns_result_I
|
|
elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
lemma new_character_data_ptr_not_in_heap:
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
|
|
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
|
|
shows "new_character_data_ptr |\<notin>| character_data_ptr_kinds h"
|
|
using assms 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
|
|
by(auto simp add: new_character_data_def split: prod.splits
|
|
elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
lemma new_character_data_new_ptr:
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
|
|
and "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
|
|
shows "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|cast new_character_data_ptr|}"
|
|
using assms 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
|
|
by(auto simp add: new_character_data_def split: prod.splits
|
|
elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
lemma new_character_data_is_character_data_ptr:
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
|
|
shows "is_character_data_ptr new_character_data_ptr"
|
|
using assms 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_is_character_data_ptr
|
|
by(auto simp add: new_character_data_def elim!: bind_returns_result_E split: prod.splits)
|
|
|
|
lemma new_character_data_child_nodes:
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h'"
|
|
assumes "h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr"
|
|
shows "h' \<turnstile> get_M new_character_data_ptr val \<rightarrow>\<^sub>r ''''"
|
|
using assms
|
|
by(auto simp add: get_M_defs new_character_data_def 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 Let_def
|
|
split: option.splits prod.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
lemma new_character_data_get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t:
|
|
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
|
|
\<Longrightarrow> ptr \<noteq> cast new_character_data_ptr \<Longrightarrow> preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr getter) h h'"
|
|
by(auto simp add: new_character_data_def ObjectMonad.get_M_defs preserved_def
|
|
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
|
lemma new_character_data_get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e:
|
|
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
|
|
\<Longrightarrow> ptr \<noteq> cast new_character_data_ptr \<Longrightarrow> preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e ptr getter) h h'"
|
|
by(auto simp add: new_character_data_def NodeMonad.get_M_defs preserved_def
|
|
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
|
lemma new_character_data_get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t:
|
|
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
|
|
\<Longrightarrow> preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t ptr getter) h h'"
|
|
by(auto simp add: new_character_data_def ElementMonad.get_M_defs preserved_def
|
|
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
|
lemma new_character_data_get_M\<^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 \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> h \<turnstile> new_character_data \<rightarrow>\<^sub>r new_character_data_ptr
|
|
\<Longrightarrow> ptr \<noteq> new_character_data_ptr \<Longrightarrow> preserved (get_M\<^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 getter) h h'"
|
|
by(auto simp add: new_character_data_def get_M_defs preserved_def
|
|
split: prod.splits option.splits elim!: bind_returns_result_E bind_returns_heap_E)
|
|
|
|
|
|
|
|
subsection\<open>Modified Heaps\<close>
|
|
|
|
lemma get_CharacterData_ptr_simp [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>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)
|
|
= (if ptr = cast character_data_ptr then cast obj else get 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 split: option.splits Option.bind_splits)
|
|
|
|
lemma Character_data_ptr_kinds_simp [simp]:
|
|
"character_data_ptr_kinds (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h) = character_data_ptr_kinds h |\<union>|
|
|
(if is_character_data_ptr_kind ptr then {|the (cast ptr)|} else {||})"
|
|
by(auto simp add: character_data_ptr_kinds_def is_node_ptr_kind_def split: option.splits)
|
|
|
|
lemma type_wf_put_I:
|
|
assumes "type_wf h"
|
|
assumes "ElementClass.type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
|
|
assumes "is_character_data_ptr_kind ptr \<Longrightarrow> is_character_data_kind obj"
|
|
shows "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
|
|
using assms
|
|
by(auto simp add: type_wf_defs split: option.splits)
|
|
|
|
lemma type_wf_put_ptr_not_in_heap_E:
|
|
assumes "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
|
|
assumes "ptr |\<notin>| object_ptr_kinds h"
|
|
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)
|
|
using assms(2) node_ptr_kinds_commutes by blast
|
|
|
|
lemma type_wf_put_ptr_in_heap_E:
|
|
assumes "type_wf (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t ptr obj h)"
|
|
assumes "ptr |\<in>| object_ptr_kinds h"
|
|
assumes "ElementClass.type_wf h"
|
|
assumes "is_character_data_ptr_kind ptr \<Longrightarrow> is_character_data_kind (the (get ptr h))"
|
|
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)
|
|
|
|
subsection\<open>Preserving Types\<close>
|
|
|
|
lemma new_element_type_wf_preserved [simp]:
|
|
assumes "h \<turnstile> new_element \<rightarrow>\<^sub>h h'"
|
|
shows "type_wf h = type_wf h'"
|
|
using assms
|
|
apply(auto simp add: new_element_def 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
|
|
elim!: bind_returns_heap_E type_wf_put_ptr_not_in_heap_E
|
|
intro!: type_wf_put_I split: if_splits)[1]
|
|
using CharacterDataClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t assms new_element_type_wf_preserved apply blast
|
|
using element_ptrs_def apply fastforce
|
|
using CharacterDataClass.type_wf\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t assms new_element_type_wf_preserved apply blast
|
|
by (metis Suc_n_not_le_n element_ptr.sel(1) element_ptrs_def fMax_ge ffmember_filter
|
|
fimage_eqI is_element_ptr_ref)
|
|
|
|
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_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
|
|
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
|
|
ObjectMonad.type_wf_put_I)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs split: option.splits)[1]
|
|
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
|
|
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
|
apply (metis finite_set_in)
|
|
done
|
|
|
|
|
|
lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_child_nodes_type_wf_preserved [simp]:
|
|
"h \<turnstile> put_M element_ptr child_nodes_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
|
|
intro!: type_wf_put_I ElementMonad.type_wf_put_I
|
|
NodeMonad.type_wf_put_I ObjectMonad.type_wf_put_I)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs ElementMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
|
|
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
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apply (metis finite_set_in)
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done
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lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_attrs_type_wf_preserved [simp]:
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"h \<turnstile> put_M element_ptr attrs_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
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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
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dest!: get_heap_E
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elim!: bind_returns_heap_E2
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intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
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ObjectMonad.type_wf_put_I)[1]
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apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
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ElementMonad.get_M_defs split: option.splits)[1]
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apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
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ElementMonad.get_M_defs split: option.splits)[1]
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apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
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ElementMonad.get_M_defs split: option.splits)[1]
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apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
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ElementMonad.get_M_defs split: option.splits)[1]
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apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
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ElementMonad.get_M_defs split: option.splits)[1]
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using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
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apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
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apply (metis finite_set_in)
|
|
done
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lemma put_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_shadow_root_opt_type_wf_preserved [simp]:
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"h \<turnstile> put_M element_ptr shadow_root_opt_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
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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
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|
elim!: bind_returns_heap_E2
|
|
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
|
|
ObjectMonad.type_wf_put_I)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
|
ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
|
ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
|
ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
|
ElementMonad.get_M_defs split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs
|
|
ElementMonad.get_M_defs split: option.splits)[1]
|
|
using ObjectMonad.type_wf_put_ptr_in_heap_E ObjectMonad.type_wf_put_ptr_not_in_heap_E apply blast
|
|
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in get\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def)
|
|
apply (metis finite_set_in)
|
|
done
|
|
|
|
|
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lemma new_character_data_type_wf_preserved [simp]:
|
|
"h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
|
apply(auto simp add: new_character_data_def 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 Let_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
|
|
elim!: bind_returns_heap_E type_wf_put_ptr_not_in_heap_E
|
|
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I ObjectMonad.type_wf_put_I
|
|
split: if_splits)[1]
|
|
apply(simp_all add: type_wf_defs ElementClass.type_wf_defs NodeClass.type_wf_defs is_node_kind_def)
|
|
by (meson 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 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)
|
|
|
|
locale l_new_character_data = l_type_wf +
|
|
assumes new_character_data_types_preserved: "h \<turnstile> new_character_data \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
|
|
|
lemma new_character_data_is_l_new_character_data: "l_new_character_data type_wf"
|
|
using l_new_character_data.intro new_character_data_type_wf_preserved
|
|
by blast
|
|
|
|
lemma put_M\<^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_val_type_wf_preserved [simp]:
|
|
"h \<turnstile> put_M character_data_ptr val_update v \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
|
apply(auto simp add: CharacterDataMonad.put_M_defs 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
|
|
CharacterDataClass.type_wf\<^sub>N\<^sub>o\<^sub>d\<^sub>e CharacterDataClass.type_wf\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t
|
|
is_node_kind_def
|
|
dest!: get_heap_E
|
|
elim!: bind_returns_heap_E2
|
|
intro!: type_wf_put_I ElementMonad.type_wf_put_I NodeMonad.type_wf_put_I
|
|
ObjectMonad.type_wf_put_I)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs CharacterDataMonad.get_M_defs
|
|
split: option.splits)[1]
|
|
apply(auto simp add: is_node_kind_def type_wf_defs ElementClass.type_wf_defs
|
|
NodeClass.type_wf_defs CharacterDataMonad.get_M_defs
|
|
ObjectClass.a_type_wf_def
|
|
split: option.splits)[1]
|
|
apply (metis (no_types, lifting) bind_eq_Some_conv finite_set_in 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)
|
|
apply (metis finite_set_in)
|
|
done
|
|
|
|
lemma character_data_ptr_kinds_small:
|
|
assumes "\<And>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
|
|
shows "character_data_ptr_kinds h = character_data_ptr_kinds h'"
|
|
by(simp add: character_data_ptr_kinds_def node_ptr_kinds_def preserved_def
|
|
object_ptr_kinds_preserved_small[OF assms])
|
|
|
|
lemma character_data_ptr_kinds_preserved:
|
|
assumes "writes SW setter h h'"
|
|
assumes "h \<turnstile> setter \<rightarrow>\<^sub>h h'"
|
|
assumes "\<And>h h'. \<forall>w \<in> SW. h \<turnstile> w \<rightarrow>\<^sub>h h'
|
|
\<longrightarrow> (\<forall>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h')"
|
|
shows "character_data_ptr_kinds h = character_data_ptr_kinds h'"
|
|
using writes_small_big[OF assms]
|
|
apply(simp add: reflp_def transp_def preserved_def character_data_ptr_kinds_def)
|
|
by (metis assms node_ptr_kinds_preserved)
|
|
|
|
|
|
lemma type_wf_preserved_small:
|
|
assumes "\<And>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
|
|
assumes "\<And>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
|
|
assumes "\<And>element_ptr. preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr RElement.nothing) h h'"
|
|
assumes "\<And>character_data_ptr. preserved (get_M\<^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
|
|
RCharacterData.nothing) h h'"
|
|
shows "type_wf h = type_wf h'"
|
|
using type_wf_preserved_small[OF assms(1) assms(2) assms(3)]
|
|
allI[OF assms(4), of id, simplified] character_data_ptr_kinds_small[OF assms(1)]
|
|
apply(auto simp add: type_wf_defs preserved_def get_M_defs character_data_ptr_kinds_small[OF assms(1)]
|
|
split: option.splits)[1]
|
|
apply(force)
|
|
by force
|
|
|
|
lemma type_wf_preserved:
|
|
assumes "writes SW setter h h'"
|
|
assumes "h \<turnstile> setter \<rightarrow>\<^sub>h h'"
|
|
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> \<forall>object_ptr. preserved (get_M\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr RObject.nothing) h h'"
|
|
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> \<forall>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
|
|
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> \<forall>element_ptr. preserved (get_M\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t element_ptr RElement.nothing) h h'"
|
|
assumes "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h'
|
|
\<Longrightarrow> \<forall>character_data_ptr. preserved (get_M\<^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
|
|
RCharacterData.nothing) h h'"
|
|
shows "type_wf h = type_wf h'"
|
|
proof -
|
|
have "\<And>h h' w. w \<in> SW \<Longrightarrow> h \<turnstile> w \<rightarrow>\<^sub>h h' \<Longrightarrow> type_wf h = type_wf h'"
|
|
using assms type_wf_preserved_small by fast
|
|
with assms(1) assms(2) show ?thesis
|
|
apply(rule writes_small_big)
|
|
by(auto simp add: reflp_def transp_def)
|
|
qed
|
|
|
|
lemma type_wf_drop: "type_wf h \<Longrightarrow> type_wf (Heap (fmdrop ptr (the_heap h)))"
|
|
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)
|
|
|
|
end
|