(* Title: HOLCF/IOA/meta_theory/RefMappings.ML ID: $Id: RefMappings.ML,v 1.19 2005/09/02 15:24:01 wenzelm Exp $ Author: Olaf Müller *) (* ---------------------------------------------------------------------------- *) section "transitions and moves"; Goal "s -a--A-> t ==> ? ex. move A ex s a t"; by (res_inst_tac [("x","(a,t)>>nil")] exI 1); by (asm_full_simp_tac (simpset() addsimps [move_def]) 1); qed"transition_is_ex"; Goal "(~a:ext A) & s=t ==> ? ex. move A ex s a t"; by (res_inst_tac [("x","nil")] exI 1); by (asm_full_simp_tac (simpset() addsimps [move_def]) 1); qed"nothing_is_ex"; Goal "(s -a--A-> s') & (s' -a'--A-> s'') & (~a':ext A) \ \ ==> ? ex. move A ex s a s''"; by (res_inst_tac [("x","(a,s')>>(a',s'')>>nil")] exI 1); by (asm_full_simp_tac (simpset() addsimps [move_def]) 1); qed"ei_transitions_are_ex"; Goal "(s1 -a1--A-> s2) & (s2 -a2--A-> s3) & (s3 -a3--A-> s4) &\ \ (~a2:ext A) & (~a3:ext A) ==> \ \ ? ex. move A ex s1 a1 s4"; by (res_inst_tac [("x","(a1,s2)>>(a2,s3)>>(a3,s4)>>nil")] exI 1); by (asm_full_simp_tac (simpset() addsimps [move_def]) 1); qed"eii_transitions_are_ex"; (* ---------------------------------------------------------------------------- *) section "weak_ref_map and ref_map"; Goalw [is_weak_ref_map_def,is_ref_map_def] "[| ext C = ext A; \ \ is_weak_ref_map f C A |] ==> is_ref_map f C A"; by (safe_tac set_cs); by (case_tac "a:ext A" 1); by (rtac transition_is_ex 1); by (Asm_simp_tac 1); by (rtac nothing_is_ex 1); by (Asm_simp_tac 1); qed"weak_ref_map2ref_map"; val prems = Goal "(P ==> Q-->R) ==> P&Q --> R"; by (fast_tac (claset() addDs prems) 1); qed "imp_conj_lemma"; Delsplits [split_if]; Delcongs [if_weak_cong]; Goal "[| is_weak_ref_map f C A |] \ \ ==> (is_weak_ref_map f (rename C g) (rename A g))"; by (asm_full_simp_tac (simpset() addsimps [is_weak_ref_map_def]) 1); by (rtac conjI 1); (* 1: start states *) by (asm_full_simp_tac (simpset() addsimps [rename_def,rename_set_def,starts_of_def]) 1); (* 2: reachable transitions *) by (REPEAT (rtac allI 1)); by (rtac imp_conj_lemma 1); by (simp_tac (simpset() addsimps [rename_def,rename_set_def]) 1); by (asm_full_simp_tac (simpset() addsimps [externals_def,asig_inputs_def, asig_outputs_def,asig_of_def,trans_of_def]) 1); by Safe_tac; by (stac split_if 1); by (rtac conjI 1); by (rtac impI 1); by (etac disjE 1); by (etac exE 1); by (etac conjE 1); (* x is input *) by (dtac sym 1); by (dtac sym 1); by (Asm_full_simp_tac 1); by (REPEAT (hyp_subst_tac 1)); by (ftac reachable_rename 1); by (Asm_full_simp_tac 1); (* x is output *) by (etac exE 1); by (etac conjE 1); by (dtac sym 1); by (dtac sym 1); by (Asm_full_simp_tac 1); by (REPEAT (hyp_subst_tac 1)); by (ftac reachable_rename 1); by (Asm_full_simp_tac 1); (* x is internal *) by (ftac reachable_rename 1); by Auto_tac; qed"rename_through_pmap"; Addsplits [split_if]; Addcongs [if_weak_cong];