author | wenzelm |
Fri, 03 Dec 2010 20:38:58 +0100 | |
changeset 40945 | b8703f63bfb2 |
parent 40774 | 0437dbc127b3 |
child 42151 | 4da4fc77664b |
permissions | -rw-r--r-- |
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(* Title: HOL/IOA/example/Correctness.thy |
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Author: Olaf Müller |
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*) |
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header {* Correctness Proof *} |
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theory Correctness |
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imports SimCorrectness Spec Impl |
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begin |
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default_sort type |
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definition |
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sim_relation :: "((nat * bool) * (nat set * bool)) set" where |
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"sim_relation = {qua. let c = fst qua; a = snd qua ; |
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k = fst c; b = snd c; |
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used = fst a; c = snd a |
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in |
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(! l:used. l < k) & b=c}" |
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declare split_paired_Ex [simp del] |
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(* Idea: instead of impl_con_lemma do not rewrite impl_ioa, but derive |
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simple lemmas asig_of impl_ioa = impl_sig, trans_of impl_ioa = impl_trans |
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Idea: ?ex. move .. should be generally replaced by a step via a subst tac if desired, |
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as this can be done globally *) |
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lemma issimulation: |
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"is_simulation sim_relation impl_ioa spec_ioa" |
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apply (simp (no_asm) add: is_simulation_def) |
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apply (rule conjI) |
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txt {* start states *} |
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apply (auto)[1] |
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apply (rule_tac x = " ({},False) " in exI) |
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apply (simp add: sim_relation_def starts_of_def spec_ioa_def impl_ioa_def) |
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txt {* main-part *} |
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apply (rule allI)+ |
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apply (rule imp_conj_lemma) |
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apply (rename_tac k b used c k' b' a) |
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apply (induct_tac "a") |
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apply (simp_all (no_asm) add: sim_relation_def impl_ioa_def impl_trans_def trans_of_def) |
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apply auto |
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txt {* NEW *} |
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apply (rule_tac x = "(used,True)" in exI) |
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apply simp |
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apply (rule transition_is_ex) |
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apply (simp (no_asm) add: spec_ioa_def spec_trans_def trans_of_def) |
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txt {* LOC *} |
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apply (rule_tac x = " (used Un {k},False) " in exI) |
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apply (simp add: less_SucI) |
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apply (rule transition_is_ex) |
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apply (simp (no_asm) add: spec_ioa_def spec_trans_def trans_of_def) |
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apply fast |
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txt {* FREE *} |
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apply (rule_tac x = " (used - {nat},c) " in exI) |
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apply simp |
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apply (rule transition_is_ex) |
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apply (simp (no_asm) add: spec_ioa_def spec_trans_def trans_of_def) |
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done |
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lemma implementation: |
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"impl_ioa =<| spec_ioa" |
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apply (unfold ioa_implements_def) |
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apply (rule conjI) |
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apply (simp (no_asm) add: impl_sig_def spec_sig_def impl_ioa_def spec_ioa_def |
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asig_outputs_def asig_of_def asig_inputs_def) |
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apply (rule trace_inclusion_for_simulations) |
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apply (simp (no_asm) add: impl_sig_def spec_sig_def impl_ioa_def spec_ioa_def |
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externals_def asig_outputs_def asig_of_def asig_inputs_def) |
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apply (rule issimulation) |
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done |
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end |