--- a/src/CCL/coinduction.ML Mon Jul 17 18:42:38 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,108 +0,0 @@
-(* Title: CCL/Coinduction.ML
- ID: $Id$
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-Lemmas and tactics for using the rule coinduct3 on [= and =.
-*)
-
-val [mono,prem] = goal (the_context ()) "[| mono(f); a : f(lfp(f)) |] ==> a : lfp(f)";
-by (stac (mono RS lfp_Tarski) 1);
-by (rtac prem 1);
-qed "lfpI";
-
-val prems = goal (the_context ()) "[| a=a'; a' : A |] ==> a : A";
-by (simp_tac (term_ss addsimps prems) 1);
-qed "ssubst_single";
-
-val prems = goal (the_context ()) "[| a=a'; b=b'; <a',b'> : A |] ==> <a,b> : A";
-by (simp_tac (term_ss addsimps prems) 1);
-qed "ssubst_pair";
-
-(***)
-
-local
-fun mk_thm s = prove_goal (the_context ()) s (fn mono::prems =>
- [fast_tac (term_cs addIs ((mono RS coinduct3_mono_lemma RS lfpI)::prems)) 1]);
-in
-val ci3_RI = mk_thm "[| mono(Agen); a : R |] ==> a : lfp(%x. Agen(x) Un R Un A)";
-val ci3_AgenI = mk_thm "[| mono(Agen); a : Agen(lfp(%x. Agen(x) Un R Un A)) |] ==> \
-\ a : lfp(%x. Agen(x) Un R Un A)";
-val ci3_AI = mk_thm "[| mono(Agen); a : A |] ==> a : lfp(%x. Agen(x) Un R Un A)";
-end;
-
-fun mk_genIs thy defs genXH gen_mono s = prove_goalw thy defs s
- (fn prems => [rtac (genXH RS iffD2) 1,
- (simp_tac term_ss 1),
- TRY (fast_tac (term_cs addIs
- ([genXH RS iffD2,gen_mono RS coinduct3_mono_lemma RS lfpI]
- @ prems)) 1)]);
-
-(** POgen **)
-
-goal (the_context ()) "<a,a> : PO";
-by (rtac (po_refl RS (XH_to_D PO_iff)) 1);
-qed "PO_refl";
-
-val POgenIs = map (mk_genIs (the_context ()) data_defs POgenXH POgen_mono)
- ["<true,true> : POgen(R)",
- "<false,false> : POgen(R)",
- "[| <a,a'> : R; <b,b'> : R |] ==> <<a,b>,<a',b'>> : POgen(R)",
- "[|!!x. <b(x),b'(x)> : R |] ==><lam x. b(x),lam x. b'(x)> : POgen(R)",
- "<one,one> : POgen(R)",
- "<a,a'> : lfp(%x. POgen(x) Un R Un PO) ==> \
-\ <inl(a),inl(a')> : POgen(lfp(%x. POgen(x) Un R Un PO))",
- "<b,b'> : lfp(%x. POgen(x) Un R Un PO) ==> \
-\ <inr(b),inr(b')> : POgen(lfp(%x. POgen(x) Un R Un PO))",
- "<zero,zero> : POgen(lfp(%x. POgen(x) Un R Un PO))",
- "<n,n'> : lfp(%x. POgen(x) Un R Un PO) ==> \
-\ <succ(n),succ(n')> : POgen(lfp(%x. POgen(x) Un R Un PO))",
- "<[],[]> : POgen(lfp(%x. POgen(x) Un R Un PO))",
- "[| <h,h'> : lfp(%x. POgen(x) Un R Un PO); \
-\ <t,t'> : lfp(%x. POgen(x) Un R Un PO) |] ==> \
-\ <h$t,h'$t'> : POgen(lfp(%x. POgen(x) Un R Un PO))"];
-
-fun POgen_tac (rla,rlb) i =
- SELECT_GOAL (safe_tac ccl_cs) i THEN
- rtac (rlb RS (rla RS ssubst_pair)) i THEN
- (REPEAT (resolve_tac (POgenIs @ [PO_refl RS (POgen_mono RS ci3_AI)] @
- (POgenIs RL [POgen_mono RS ci3_AgenI]) @ [POgen_mono RS ci3_RI]) i));
-
-(** EQgen **)
-
-goal (the_context ()) "<a,a> : EQ";
-by (rtac (refl RS (EQ_iff RS iffD1)) 1);
-qed "EQ_refl";
-
-val EQgenIs = map (mk_genIs (the_context ()) data_defs EQgenXH EQgen_mono)
-["<true,true> : EQgen(R)",
- "<false,false> : EQgen(R)",
- "[| <a,a'> : R; <b,b'> : R |] ==> <<a,b>,<a',b'>> : EQgen(R)",
- "[|!!x. <b(x),b'(x)> : R |] ==> <lam x. b(x),lam x. b'(x)> : EQgen(R)",
- "<one,one> : EQgen(R)",
- "<a,a'> : lfp(%x. EQgen(x) Un R Un EQ) ==> \
-\ <inl(a),inl(a')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))",
- "<b,b'> : lfp(%x. EQgen(x) Un R Un EQ) ==> \
-\ <inr(b),inr(b')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))",
- "<zero,zero> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))",
- "<n,n'> : lfp(%x. EQgen(x) Un R Un EQ) ==> \
-\ <succ(n),succ(n')> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))",
- "<[],[]> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))",
- "[| <h,h'> : lfp(%x. EQgen(x) Un R Un EQ); \
-\ <t,t'> : lfp(%x. EQgen(x) Un R Un EQ) |] ==> \
-\ <h$t,h'$t'> : EQgen(lfp(%x. EQgen(x) Un R Un EQ))"];
-
-fun EQgen_raw_tac i =
- (REPEAT (resolve_tac (EQgenIs @ [EQ_refl RS (EQgen_mono RS ci3_AI)] @
- (EQgenIs RL [EQgen_mono RS ci3_AgenI]) @ [EQgen_mono RS ci3_RI]) i));
-
-(* Goals of the form R <= EQgen(R) - rewrite elements <a,b> : EQgen(R) using rews and *)
-(* then reduce this to a goal <a',b'> : R (hopefully?) *)
-(* rews are rewrite rules that would cause looping in the simpifier *)
-
-fun EQgen_tac simp_set rews i =
- SELECT_GOAL
- (TRY (safe_tac ccl_cs) THEN
- resolve_tac ((rews@[refl]) RL ((rews@[refl]) RL [ssubst_pair])) i THEN
- ALLGOALS (simp_tac simp_set) THEN
- ALLGOALS EQgen_raw_tac) i;