103 lines
3.1 KiB
Plaintext
103 lines
3.1 KiB
Plaintext
(*
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* Copyright 2014, NICTA
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*
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* This software may be distributed and modified according to the terms of
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* the BSD 2-Clause license. Note that NO WARRANTY is provided.
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* See "LICENSE_BSD2.txt" for details.
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*
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* @TAG(NICTA_BSD)
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*)
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theory Generic_Separation_Algebras
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imports Sep_Algebra_L4v
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begin
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instantiation "prod" :: (stronger_sep_algebra,stronger_sep_algebra) zero
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begin
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definition "zero_prod \<equiv> (0,0)"
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instance ..
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end
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instantiation "prod" :: (stronger_sep_algebra,stronger_sep_algebra) stronger_sep_algebra
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begin
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definition "sep_disj_prod x y \<equiv> sep_disj (fst x) (fst y) \<and> sep_disj (snd x) (snd y)"
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definition "plus_prod x y \<equiv> ( (fst x) + (fst y) , (snd x) + (snd y))"
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instance
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apply intro_classes
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apply (metis fst_conv sep_disj_prod_def sep_disj_zero snd_conv zero_prod_def)
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apply (metis (full_types) sep_disj_commuteI sep_disj_prod_def)
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apply (clarsimp simp: plus_prod_def zero_prod_def)
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apply (clarsimp simp: plus_prod_def sep_disj_prod_def)
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apply safe
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apply (metis sep_add_commute)
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apply (metis sep_add_commute)
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apply (clarsimp simp: plus_prod_def sep_disj_prod_def)
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apply (metis sep_add_assoc)
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apply (clarsimp simp: plus_prod_def sep_disj_prod_def)
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apply (clarsimp simp: plus_prod_def sep_disj_prod_def)
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apply (clarsimp simp: plus_prod_def sep_disj_prod_def)
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done
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end
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instantiation "option" :: (type) zero
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begin
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definition "zero_option \<equiv> None"
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instance ..
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end
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definition
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orelse :: "'a option \<Rightarrow> 'a option \<Rightarrow> 'a option"
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where
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"orelse x y \<equiv> case x of Some x' => Some x' | None => y"
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definition
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onlyone :: "'a option => 'a option => bool"
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where
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"onlyone x y \<equiv> case x of
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Some x' => (case y of Some y' => False | _ => True)
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| None => True"
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instantiation "option" :: (type) stronger_sep_algebra
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begin
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definition "sep_disj_option \<equiv> onlyone "
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definition "plus_option \<equiv> orelse"
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instance
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by intro_classes
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(clarsimp simp: sep_disj_option_def zero_option_def plus_option_def onlyone_def orelse_def
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split: option.splits)+
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end
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record 'a generic_heap_record =
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heap :: "'a "
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instantiation "generic_heap_record_ext" :: (stronger_sep_algebra, stronger_sep_algebra) stronger_sep_algebra
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begin
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definition "zero_generic_heap_record_ext \<equiv> Abs_generic_heap_record_ext 0"
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definition "plus_generic_heap_record_ext h1 h2 \<equiv>
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Abs_generic_heap_record_ext (Rep_generic_heap_record_ext h1 + Rep_generic_heap_record_ext h2)"
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definition "sep_disj_generic_heap_record_ext h1 h2 \<equiv> Rep_generic_heap_record_ext h1 ## Rep_generic_heap_record_ext h2"
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instance
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apply intro_classes
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apply (fastforce simp: sep_add_left_commute sep_disj_commute Rep_generic_heap_record_ext_inverse
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sep_disj_commuteI sep_add_assoc sep_add_commute Abs_generic_heap_record_ext_inverse
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zero_generic_heap_record_ext_def sep_disj_generic_heap_record_ext_def
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plus_generic_heap_record_ext_def)+
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done
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end
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end
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