forked from afp-mirror/Core_DOM
63 lines
2.6 KiB
Plaintext
63 lines
2.6 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>References\<close>
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text\<open>
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This theory, we introduce a generic reference. All our typed pointers include such
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a reference, which allows us to distinguish pointers of the same type, but also to
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iterate over all pointers in a set.\<close>
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theory
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Ref
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imports
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"HOL-Library.Adhoc_Overloading"
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"../preliminaries/Hiding_Type_Variables"
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begin
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instantiation sum :: (linorder, linorder) linorder
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begin
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definition less_eq_sum :: "'a + 'b \<Rightarrow> 'a + 'b \<Rightarrow> bool"
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where
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"less_eq_sum t t' = (case t of
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Inl l \<Rightarrow> (case t' of
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Inl l' \<Rightarrow> l \<le> l'
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| Inr r' \<Rightarrow> True)
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| Inr r \<Rightarrow> (case t' of
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Inl l' \<Rightarrow> False
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| Inr r' \<Rightarrow> r \<le> r'))"
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definition less_sum :: "'a + 'b \<Rightarrow> 'a + 'b \<Rightarrow> bool"
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where
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"less_sum t t' \<equiv> t \<le> t' \<and> \<not> t' \<le> t"
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instance by(standard) (auto simp add: less_eq_sum_def less_sum_def split: sum.splits)
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end
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type_synonym ref = nat
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consts cast :: 'a
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end
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