author | paulson |
Thu, 15 Oct 1998 11:35:07 +0200 | |
changeset 5648 | fe887910e32e |
parent 5639 | 29d8e53a4920 |
child 5804 | 8e0a4c4fd67b |
permissions | -rw-r--r-- |
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(* Title: HOL/UNITY/SubstAx |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1998 University of Cambridge |
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LeadsTo relation, restricted to the set of reachable states. |
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*) |
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overload_1st_set "SubstAx.LeadsTo"; |
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(*** Specialized laws for handling invariants ***) |
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(** Conjoining a safety property **) |
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Goal "[| reachable F <= C; F : LeadsTo (C Int A) A' |] \ |
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\ ==> F : LeadsTo A A'"; |
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by (asm_full_simp_tac |
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(simpset() addsimps [LeadsTo_def, Int_absorb2, Int_assoc RS sym]) 1); |
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qed "reachable_LeadsToI"; |
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Goal "[| reachable F <= C; F : LeadsTo A A' |] \ |
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\ ==> F : LeadsTo A (C Int A')"; |
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by (asm_full_simp_tac |
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(simpset() addsimps [LeadsTo_def, Int_absorb2, |
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Int_assoc RS sym]) 1); |
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qed "reachable_LeadsToD"; |
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(** Conjoining an invariant **) |
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(* [| Invariant F C; F : LeadsTo (C Int A) A' |] ==> F : LeadsTo A A' *) |
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bind_thm ("Invariant_LeadsToI", |
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Invariant_includes_reachable RS reachable_LeadsToI); |
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(* [| Invariant F C; F : LeadsTo A A' |] ==> F : LeadsTo A (C Int A') *) |
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bind_thm ("Invariant_LeadsToD", |
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Invariant_includes_reachable RS reachable_LeadsToD); |
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(*** Introduction rules: Basis, Trans, Union ***) |
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Goal "F : leadsTo A B ==> F : LeadsTo A B"; |
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by (simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (blast_tac (claset() addIs [psp_stable2, stable_reachable]) 1); |
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qed "leadsTo_imp_LeadsTo"; |
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Goal "[| F : LeadsTo A B; F : LeadsTo B C |] ==> F : LeadsTo A C"; |
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by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (blast_tac (claset() addIs [leadsTo_Trans]) 1); |
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qed "LeadsTo_Trans"; |
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val prems = Goalw [LeadsTo_def] |
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"(!!A. A : S ==> F : LeadsTo A B) ==> F : LeadsTo (Union S) B"; |
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by (Simp_tac 1); |
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by (stac Int_Union 1); |
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by (blast_tac (claset() addIs [leadsTo_UN] addDs prems) 1); |
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qed "LeadsTo_Union"; |
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(*** Derived rules ***) |
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Goal "F : LeadsTo A UNIV"; |
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by (asm_simp_tac |
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(simpset() addsimps [LeadsTo_def, Int_lower1 RS subset_imp_leadsTo]) 1); |
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qed "LeadsTo_UNIV"; |
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Addsimps [LeadsTo_UNIV]; |
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(*Useful with cancellation, disjunction*) |
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Goal "F : LeadsTo A (A' Un A') ==> F : LeadsTo A A'"; |
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by (asm_full_simp_tac (simpset() addsimps Un_ac) 1); |
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qed "LeadsTo_Un_duplicate"; |
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Goal "F : LeadsTo A (A' Un C Un C) ==> F : LeadsTo A (A' Un C)"; |
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by (asm_full_simp_tac (simpset() addsimps Un_ac) 1); |
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qed "LeadsTo_Un_duplicate2"; |
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val prems = |
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Goal "(!!i. i : I ==> F : LeadsTo (A i) B) ==> F : LeadsTo (UN i:I. A i) B"; |
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by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1); |
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by (blast_tac (claset() addIs (LeadsTo_Union::prems)) 1); |
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qed "LeadsTo_UN"; |
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(*Binary union introduction rule*) |
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Goal "[| F : LeadsTo A C; F : LeadsTo B C |] ==> F : LeadsTo (A Un B) C"; |
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by (stac Un_eq_Union 1); |
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by (blast_tac (claset() addIs [LeadsTo_Union]) 1); |
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qed "LeadsTo_Un"; |
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Goal "A <= B ==> F : LeadsTo A B"; |
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by (simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (blast_tac (claset() addIs [subset_imp_leadsTo]) 1); |
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qed "subset_imp_LeadsTo"; |
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bind_thm ("empty_LeadsTo", empty_subsetI RS subset_imp_LeadsTo); |
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Addsimps [empty_LeadsTo]; |
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Goal "[| F : LeadsTo A A'; A' <= B' |] ==> F : LeadsTo A B'"; |
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by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (blast_tac (claset() addIs [leadsTo_weaken_R]) 1); |
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qed_spec_mp "LeadsTo_weaken_R"; |
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Goal "[| F : LeadsTo A A'; B <= A |] \ |
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\ ==> F : LeadsTo B A'"; |
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by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (blast_tac (claset() addIs [leadsTo_weaken_L]) 1); |
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qed_spec_mp "LeadsTo_weaken_L"; |
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Goal "[| F : LeadsTo A A'; \ |
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\ B <= A; A' <= B' |] \ |
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\ ==> F : LeadsTo B B'"; |
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by (blast_tac (claset() addIs [LeadsTo_weaken_R, LeadsTo_weaken_L, |
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LeadsTo_Trans]) 1); |
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qed "LeadsTo_weaken"; |
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Goal "[| reachable F <= C; F : LeadsTo A A'; \ |
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\ C Int B <= A; C Int A' <= B' |] \ |
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\ ==> F : LeadsTo B B'"; |
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by (blast_tac (claset() addDs [reachable_LeadsToI] addIs[LeadsTo_weaken] |
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addIs [reachable_LeadsToD]) 1); |
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qed "reachable_LeadsTo_weaken"; |
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(** Two theorems for "proof lattices" **) |
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Goal "[| F : LeadsTo A B |] ==> F : LeadsTo (A Un B) B"; |
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by (blast_tac (claset() addIs [LeadsTo_Un, subset_imp_LeadsTo]) 1); |
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qed "LeadsTo_Un_post"; |
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Goal "[| F : LeadsTo A B; F : LeadsTo B C |] \ |
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\ ==> F : LeadsTo (A Un B) C"; |
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by (blast_tac (claset() addIs [LeadsTo_Un, subset_imp_LeadsTo, |
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LeadsTo_weaken_L, LeadsTo_Trans]) 1); |
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qed "LeadsTo_Trans_Un"; |
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(** Distributive laws **) |
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Goal "(F : LeadsTo (A Un B) C) = (F : LeadsTo A C & F : LeadsTo B C)"; |
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by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken_L]) 1); |
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qed "LeadsTo_Un_distrib"; |
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Goal "(F : LeadsTo (UN i:I. A i) B) = (ALL i : I. F : LeadsTo (A i) B)"; |
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by (blast_tac (claset() addIs [LeadsTo_UN, LeadsTo_weaken_L]) 1); |
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qed "LeadsTo_UN_distrib"; |
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Goal "(F : LeadsTo (Union S) B) = (ALL A : S. F : LeadsTo A B)"; |
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by (blast_tac (claset() addIs [LeadsTo_Union, LeadsTo_weaken_L]) 1); |
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qed "LeadsTo_Union_distrib"; |
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(** More rules using the premise "Invariant F" **) |
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Goal "[| F : Constrains (A-A') (A Un A'); F : transient (A-A') |] \ |
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\ ==> F : LeadsTo A A'"; |
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by (asm_full_simp_tac (simpset() addsimps [LeadsTo_def, Constrains_def]) 1); |
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by (rtac (ensuresI RS leadsTo_Basis) 1); |
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by (blast_tac (claset() addIs [transient_strengthen]) 2); |
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by (blast_tac (claset() addIs [constrains_weaken]) 1); |
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qed "LeadsTo_Basis"; |
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Goal "[| F : Invariant INV; \ |
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\ F : Constrains (INV Int (A-A')) (A Un A'); \ |
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\ F : transient (INV Int (A-A')) |] \ |
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\ ==> F : LeadsTo A A'"; |
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by (rtac Invariant_LeadsToI 1); |
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by (assume_tac 1); |
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by (rtac LeadsTo_Basis 1); |
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by (blast_tac (claset() addIs [transient_strengthen]) 2); |
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by (blast_tac (claset() addIs [Invariant_ConstrainsD RS Constrains_weaken]) 1); |
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qed "Invariant_LeadsTo_Basis"; |
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Goal "[| F : Invariant INV; \ |
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\ F : LeadsTo A A'; INV Int B <= A; INV Int A' <= B' |] \ |
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\ ==> F : LeadsTo B B'"; |
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by (REPEAT (ares_tac [Invariant_includes_reachable, |
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reachable_LeadsTo_weaken] 1)); |
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qed "Invariant_LeadsTo_weaken"; |
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(*Set difference: maybe combine with leadsTo_weaken_L?? |
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This is the most useful form of the "disjunction" rule*) |
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Goal "[| F : LeadsTo (A-B) C; F : LeadsTo (A Int B) C |] \ |
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\ ==> F : LeadsTo A C"; |
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by (blast_tac (claset() addIs [LeadsTo_Un, LeadsTo_weaken]) 1); |
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qed "LeadsTo_Diff"; |
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val prems = |
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Goal "(!! i. i:I ==> F : LeadsTo (A i) (A' i)) \ |
192 |
\ ==> F : LeadsTo (UN i:I. A i) (UN i:I. A' i)"; |
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by (simp_tac (simpset() addsimps [Union_image_eq RS sym]) 1); |
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by (blast_tac (claset() addIs [LeadsTo_Union, LeadsTo_weaken_R] |
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addIs prems) 1); |
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qed "LeadsTo_UN_UN"; |
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(*Version with no index set*) |
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val prems = |
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Goal "(!! i. F : LeadsTo (A i) (A' i)) \ |
202 |
\ ==> F : LeadsTo (UN i. A i) (UN i. A' i)"; |
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by (blast_tac (claset() addIs [LeadsTo_UN_UN] |
204 |
addIs prems) 1); |
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qed "LeadsTo_UN_UN_noindex"; |
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(*Version with no index set*) |
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Goal "ALL i. F : LeadsTo (A i) (A' i) \ |
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\ ==> F : LeadsTo (UN i. A i) (UN i. A' i)"; |
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by (blast_tac (claset() addIs [LeadsTo_UN_UN]) 1); |
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qed "all_LeadsTo_UN_UN"; |
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(*Binary union version*) |
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Goal "[| F : LeadsTo A A'; F : LeadsTo B B' |] \ |
216 |
\ ==> F : LeadsTo (A Un B) (A' Un B')"; |
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by (blast_tac (claset() addIs [LeadsTo_Un, |
218 |
LeadsTo_weaken_R]) 1); |
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qed "LeadsTo_Un_Un"; |
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(** The cancellation law **) |
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Goal "[| F : LeadsTo A (A' Un B); F : LeadsTo B B' |] \ |
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\ ==> F : LeadsTo A (A' Un B')"; |
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by (blast_tac (claset() addIs [LeadsTo_Un_Un, |
227 |
subset_imp_LeadsTo, LeadsTo_Trans]) 1); |
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qed "LeadsTo_cancel2"; |
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Goal "[| F : LeadsTo A (A' Un B); F : LeadsTo (B-A') B' |] \ |
231 |
\ ==> F : LeadsTo A (A' Un B')"; |
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by (rtac LeadsTo_cancel2 1); |
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by (assume_tac 2); |
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by (ALLGOALS Asm_simp_tac); |
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qed "LeadsTo_cancel_Diff2"; |
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Goal "[| F : LeadsTo A (B Un A'); F : LeadsTo B B' |] \ |
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\ ==> F : LeadsTo A (B' Un A')"; |
|
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by (asm_full_simp_tac (simpset() addsimps [Un_commute]) 1); |
240 |
by (blast_tac (claset() addSIs [LeadsTo_cancel2]) 1); |
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241 |
qed "LeadsTo_cancel1"; |
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Goal "[| F : LeadsTo A (B Un A'); F : LeadsTo (B-A') B' |] \ |
244 |
\ ==> F : LeadsTo A (B' Un A')"; |
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by (rtac LeadsTo_cancel1 1); |
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by (assume_tac 2); |
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by (ALLGOALS Asm_simp_tac); |
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qed "LeadsTo_cancel_Diff1"; |
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(** The impossibility law **) |
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(*The set "A" may be non-empty, but it contains no reachable states*) |
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Goal "F : LeadsTo A {} ==> reachable F Int A = {}"; |
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by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
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by (etac leadsTo_empty 1); |
257 |
qed "LeadsTo_empty"; |
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(** PSP: Progress-Safety-Progress **) |
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(*Special case of PSP: Misra's "stable conjunction"*) |
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Goal "[| F : LeadsTo A A'; F : Stable B |] \ |
264 |
\ ==> F : LeadsTo (A Int B) (A' Int B)"; |
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by (full_simp_tac (simpset() addsimps [LeadsTo_def, Stable_eq_stable]) 1); |
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by (dtac psp_stable 1); |
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by (assume_tac 1); |
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by (asm_full_simp_tac (simpset() addsimps Int_ac) 1); |
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qed "PSP_stable"; |
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Goal "[| F : LeadsTo A A'; F : Stable B |] \ |
272 |
\ ==> F : LeadsTo (B Int A) (B Int A')"; |
|
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by (asm_simp_tac (simpset() addsimps PSP_stable::Int_ac) 1); |
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qed "PSP_stable2"; |
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276 |
Goalw [LeadsTo_def, Constrains_def] |
5648 | 277 |
"[| F : LeadsTo A A'; F : Constrains B B' |] \ |
278 |
\ ==> F : LeadsTo (A Int B) ((A' Int B) Un (B' - B))"; |
|
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279 |
by (blast_tac (claset() addDs [psp] addIs [leadsTo_weaken]) 1); |
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280 |
qed "PSP"; |
4776 | 281 |
|
5648 | 282 |
Goal "[| F : LeadsTo A A'; F : Constrains B B' |] \ |
283 |
\ ==> F : LeadsTo (B Int A) ((B Int A') Un (B' - B))"; |
|
5536 | 284 |
by (asm_simp_tac (simpset() addsimps PSP::Int_ac) 1); |
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285 |
qed "PSP2"; |
4776 | 286 |
|
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287 |
Goalw [Unless_def] |
5648 | 288 |
"[| F : LeadsTo A A'; F : Unless B B' |] \ |
289 |
\ ==> F : LeadsTo (A Int B) ((A' Int B) Un B')"; |
|
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290 |
by (dtac PSP 1); |
4776 | 291 |
by (assume_tac 1); |
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292 |
by (blast_tac (claset() addIs [LeadsTo_Diff, LeadsTo_weaken, |
5584 | 293 |
subset_imp_LeadsTo]) 1); |
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294 |
qed "PSP_Unless"; |
4776 | 295 |
|
296 |
||
297 |
(*** Induction rules ***) |
|
298 |
||
299 |
(** Meta or object quantifier ????? **) |
|
5232 | 300 |
Goal "[| wf r; \ |
5648 | 301 |
\ ALL m. F : LeadsTo (A Int f-``{m}) \ |
5584 | 302 |
\ ((A Int f-``(r^-1 ^^ {m})) Un B) |] \ |
5648 | 303 |
\ ==> F : LeadsTo A B"; |
5111 | 304 |
by (full_simp_tac (simpset() addsimps [LeadsTo_def]) 1); |
4776 | 305 |
by (etac leadsTo_wf_induct 1); |
306 |
by (blast_tac (claset() addIs [leadsTo_weaken]) 1); |
|
307 |
qed "LeadsTo_wf_induct"; |
|
308 |
||
309 |
||
5232 | 310 |
Goal "[| wf r; \ |
5648 | 311 |
\ ALL m:I. F : LeadsTo (A Int f-``{m}) \ |
5584 | 312 |
\ ((A Int f-``(r^-1 ^^ {m})) Un B) |] \ |
5648 | 313 |
\ ==> F : LeadsTo A ((A - (f-``I)) Un B)"; |
4776 | 314 |
by (etac LeadsTo_wf_induct 1); |
315 |
by Safe_tac; |
|
316 |
by (case_tac "m:I" 1); |
|
317 |
by (blast_tac (claset() addIs [LeadsTo_weaken]) 1); |
|
318 |
by (blast_tac (claset() addIs [subset_imp_LeadsTo]) 1); |
|
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319 |
qed "Bounded_induct"; |
4776 | 320 |
|
321 |
||
5648 | 322 |
Goal "[| ALL m. F : LeadsTo (A Int f-``{m}) \ |
5584 | 323 |
\ ((A Int f-``(lessThan m)) Un B) |] \ |
5648 | 324 |
\ ==> F : LeadsTo A B"; |
4776 | 325 |
by (rtac (wf_less_than RS LeadsTo_wf_induct) 1); |
326 |
by (Asm_simp_tac 1); |
|
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327 |
qed "LessThan_induct"; |
4776 | 328 |
|
5544 | 329 |
(*Integer version. Could generalize from #0 to any lower bound*) |
5584 | 330 |
val [reach, prem] = |
5620 | 331 |
Goal "[| reachable F <= {s. #0 <= f s}; \ |
5648 | 332 |
\ !! z. F : LeadsTo (A Int {s. f s = z}) \ |
5584 | 333 |
\ ((A Int {s. f s < z}) Un B) |] \ |
5648 | 334 |
\ ==> F : LeadsTo A B"; |
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|
335 |
by (res_inst_tac [("f", "nat o f")] (allI RS LessThan_induct) 1); |
5544 | 336 |
by (simp_tac (simpset() addsimps [vimage_def]) 1); |
5620 | 337 |
by (rtac ([reach, prem] MRS reachable_LeadsTo_weaken) 1); |
5584 | 338 |
by (auto_tac (claset(), simpset() addsimps [nat_eq_iff, nat_less_iff])); |
5544 | 339 |
qed "integ_0_le_induct"; |
340 |
||
5648 | 341 |
Goal "[| ALL m:(greaterThan l). F : LeadsTo (A Int f-``{m}) \ |
5584 | 342 |
\ ((A Int f-``(lessThan m)) Un B) |] \ |
5648 | 343 |
\ ==> F : LeadsTo A ((A Int (f-``(atMost l))) Un B)"; |
4776 | 344 |
by (simp_tac (HOL_ss addsimps [Diff_eq RS sym, vimage_Compl, Compl_greaterThan RS sym]) 1); |
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345 |
by (rtac (wf_less_than RS Bounded_induct) 1); |
4776 | 346 |
by (Asm_simp_tac 1); |
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347 |
qed "LessThan_bounded_induct"; |
4776 | 348 |
|
5648 | 349 |
Goal "[| ALL m:(lessThan l). F : LeadsTo (A Int f-``{m}) \ |
5584 | 350 |
\ ((A Int f-``(greaterThan m)) Un B) |] \ |
5648 | 351 |
\ ==> F : LeadsTo A ((A Int (f-``(atLeast l))) Un B)"; |
4776 | 352 |
by (res_inst_tac [("f","f"),("f1", "%k. l - k")] |
353 |
(wf_less_than RS wf_inv_image RS LeadsTo_wf_induct) 1); |
|
354 |
by (simp_tac (simpset() addsimps [inv_image_def, Image_singleton]) 1); |
|
355 |
by (Clarify_tac 1); |
|
356 |
by (case_tac "m<l" 1); |
|
357 |
by (blast_tac (claset() addIs [not_leE, subset_imp_LeadsTo]) 2); |
|
358 |
by (blast_tac (claset() addIs [LeadsTo_weaken_R, diff_less_mono2]) 1); |
|
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359 |
qed "GreaterThan_bounded_induct"; |
4776 | 360 |
|
361 |
||
362 |
(*** Completion: Binary and General Finite versions ***) |
|
363 |
||
5648 | 364 |
Goal "[| F : LeadsTo A A'; F : Stable A'; \ |
365 |
\ F : LeadsTo B B'; F : Stable B' |] \ |
|
366 |
\ ==> F : LeadsTo (A Int B) (A' Int B')"; |
|
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|
367 |
by (full_simp_tac (simpset() addsimps [LeadsTo_def, Stable_eq_stable]) 1); |
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|
368 |
by (blast_tac (claset() addIs [stable_completion, leadsTo_weaken]) 1); |
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|
369 |
qed "Stable_completion"; |
4776 | 370 |
|
371 |
||
5584 | 372 |
Goal "finite I \ |
5648 | 373 |
\ ==> (ALL i:I. F : LeadsTo (A i) (A' i)) --> \ |
374 |
\ (ALL i:I. F : Stable (A' i)) --> \ |
|
375 |
\ F : LeadsTo (INT i:I. A i) (INT i:I. A' i)"; |
|
4776 | 376 |
by (etac finite_induct 1); |
377 |
by (Asm_simp_tac 1); |
|
5313
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|
378 |
by (asm_simp_tac (simpset() addsimps [Stable_completion, ball_Stable_INT]) 1); |
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|
379 |
qed_spec_mp "Finite_stable_completion"; |
4776 | 380 |
|
381 |
||
5648 | 382 |
Goal "[| F : LeadsTo A (A' Un C); F : Constrains A' (A' Un C); \ |
383 |
\ F : LeadsTo B (B' Un C); F : Constrains B' (B' Un C) |] \ |
|
384 |
\ ==> F : LeadsTo (A Int B) ((A' Int B') Un C)"; |
|
5313
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5277
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|
385 |
by (full_simp_tac (simpset() addsimps [LeadsTo_def, Constrains_def, |
1861a564d7e2
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|
386 |
Int_Un_distrib]) 1); |
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
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|
387 |
by (blast_tac (claset() addIs [completion, leadsTo_weaken]) 1); |
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A higher-level treatment of LeadsTo, minimizing use of "reachable"
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|
388 |
qed "Completion"; |
4776 | 389 |
|
390 |
||
5584 | 391 |
Goal "[| finite I |] \ |
5648 | 392 |
\ ==> (ALL i:I. F : LeadsTo (A i) (A' i Un C)) --> \ |
393 |
\ (ALL i:I. F : Constrains (A' i) (A' i Un C)) --> \ |
|
394 |
\ F : LeadsTo (INT i:I. A i) ((INT i:I. A' i) Un C)"; |
|
4776 | 395 |
by (etac finite_induct 1); |
396 |
by (ALLGOALS Asm_simp_tac); |
|
397 |
by (Clarify_tac 1); |
|
5313
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Constrains, Stable, Invariant...more of the substitution axiom, but Union
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changeset
|
398 |
by (dtac ball_Constrains_INT 1); |
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A higher-level treatment of LeadsTo, minimizing use of "reachable"
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|
399 |
by (asm_full_simp_tac (simpset() addsimps [Completion]) 1); |
e4297d03e5d2
A higher-level treatment of LeadsTo, minimizing use of "reachable"
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|
400 |
qed "Finite_completion"; |
5232 | 401 |
|
402 |
||
5313
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|
403 |
(*proves "ensures/leadsTo" properties when the program is specified*) |
5426
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A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5422
diff
changeset
|
404 |
fun ensures_tac sact = |
5240
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
5232
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changeset
|
405 |
SELECT_GOAL |
5313
1861a564d7e2
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|
406 |
(EVERY [REPEAT (Invariant_Int_tac 1), |
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
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|
407 |
etac Invariant_LeadsTo_Basis 1 |
5240
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
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changeset
|
408 |
ORELSE (*subgoal may involve LeadsTo, leadsTo or ensures*) |
5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
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changeset
|
409 |
REPEAT (ares_tac [LeadsTo_Basis, ensuresI] 1), |
5648 | 410 |
(*now there are two subgoals: constrains & transient*) |
411 |
simp_tac (simpset() addsimps !program_defs_ref) 2, |
|
5240
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
5232
diff
changeset
|
412 |
res_inst_tac [("act", sact)] transient_mem 2, |
5340 | 413 |
(*simplify the command's domain*) |
5426
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5422
diff
changeset
|
414 |
simp_tac (simpset() addsimps [Domain_def]) 3, |
566f47250bd0
A new approach, using simp_of_act and simp_of_set to activate definitions when
paulson
parents:
5422
diff
changeset
|
415 |
constrains_tac 1, |
5240
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
5232
diff
changeset
|
416 |
ALLGOALS Clarify_tac, |
5422 | 417 |
ALLGOALS Asm_full_simp_tac]); |
5240
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
5232
diff
changeset
|
418 |
|
bbcd79ef7cf2
Constant "invariant" and new constrains_tac, ensures_tac
paulson
parents:
5232
diff
changeset
|
419 |