--- a/src/HOLCF/Tr.ML Fri Apr 01 21:04:00 2005 +0200
+++ b/src/HOLCF/Tr.ML Fri Apr 01 23:44:41 2005 +0200
@@ -1,182 +1,34 @@
-(* Title: HOLCF/Tr.ML
- ID: $Id$
- Author: Franz Regensburger
-Introduce infix if_then_else_fi and boolean connectives andalso, orelse
-*)
-
-(* ------------------------------------------------------------------------ *)
-(* Exhaustion and Elimination for type one *)
-(* ------------------------------------------------------------------------ *)
-
-Goalw [FF_def,TT_def] "t=UU | t = TT | t = FF";
-by (induct_tac "t" 1);
-by (fast_tac HOL_cs 1);
-by (fast_tac (HOL_cs addss simpset()) 1);
-qed "Exh_tr";
-
-val prems = Goal "[| p=UU ==> Q; p = TT ==>Q; p = FF ==>Q|] ==>Q";
-by (rtac (Exh_tr RS disjE) 1);
-by (eresolve_tac prems 1);
-by (etac disjE 1);
-by (eresolve_tac prems 1);
-by (eresolve_tac prems 1);
-qed "trE";
-
-(* ------------------------------------------------------------------------ *)
-(* tactic for tr-thms with case split *)
-(* ------------------------------------------------------------------------ *)
-
-bind_thms ("tr_defs", [andalso_def,orelse_def,neg_def,ifte_def,TT_def,FF_def]);
-
-fun prover t = prove_goal thy t
- (fn prems =>
- [
- (res_inst_tac [("p","y")] trE 1),
- (REPEAT(asm_simp_tac (simpset() addsimps
- [o_def,flift1_def,flift2_def,inst_lift_po]@tr_defs) 1))
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* distinctness for type tr *)
-(* ------------------------------------------------------------------------ *)
-
-bind_thms ("dist_less_tr", map prover [
- "~TT << UU",
- "~FF << UU",
- "~TT << FF",
- "~FF << TT"
- ]);
-
-val dist_eq_tr = map prover ["TT~=UU","FF~=UU","TT~=FF"];
-bind_thms ("dist_eq_tr", dist_eq_tr @ (map (fn thm => (thm RS not_sym)) dist_eq_tr));
-
-(* ------------------------------------------------------------------------ *)
-(* lemmas about andalso, orelse, neg and if *)
-(* ------------------------------------------------------------------------ *)
-
-bind_thms ("andalso_thms", map prover [
- "(TT andalso y) = y",
- "(FF andalso y) = FF",
- "(UU andalso y) = UU",
- "(y andalso TT) = y",
- "(y andalso y) = y"
- ]);
-
-bind_thms ("orelse_thms", map prover [
- "(TT orelse y) = TT",
- "(FF orelse y) = y",
- "(UU orelse y) = UU",
- "(y orelse FF) = y",
- "(y orelse y) = y"]);
-
-bind_thms ("neg_thms", map prover [
- "neg$TT = FF",
- "neg$FF = TT",
- "neg$UU = UU"
- ]);
-
-bind_thms ("ifte_thms", map prover [
- "If UU then e1 else e2 fi = UU",
- "If FF then e1 else e2 fi = e2",
- "If TT then e1 else e2 fi = e1"]);
-
-Addsimps (dist_less_tr @ dist_eq_tr @ andalso_thms @
- orelse_thms @ neg_thms @ ifte_thms);
+(* legacy ML bindings *)
-(* ------------------------------------------------------------------- *)
-(* split-tac for If via If2 because the constant has to be a constant *)
-(* ------------------------------------------------------------------- *)
-
-Goalw [If2_def]
- "P (If2 Q x y ) = ((Q=UU --> P UU) & (Q=TT --> P x) & (Q=FF --> P y))";
-by (res_inst_tac [("p","Q")] trE 1);
-by (REPEAT (Asm_full_simp_tac 1));
-qed"split_If2";
-
-val split_If_tac =
- simp_tac (HOL_basic_ss addsimps [symmetric If2_def]) THEN' (split_tac [split_If2]);
-
-
-
-(* ----------------------------------------------------------------- *)
- section"Rewriting of HOLCF operations to HOL functions";
-(* ----------------------------------------------------------------- *)
-
-
-Goal
-"!!t.[|t~=UU|]==> ((t andalso s)=FF)=(t=FF | s=FF)";
-by (rtac iffI 1);
-by (res_inst_tac [("p","t")] trE 1);
-by Auto_tac;
-by (res_inst_tac [("p","t")] trE 1);
-by Auto_tac;
-qed"andalso_or";
-
-Goal "[|t~=UU|]==> ((t andalso s)~=FF)=(t~=FF & s~=FF)";
-by (rtac iffI 1);
-by (res_inst_tac [("p","t")] trE 1);
-by Auto_tac;
-by (res_inst_tac [("p","t")] trE 1);
-by Auto_tac;
-qed"andalso_and";
-
-Goal "(Def x ~=FF)= x";
-by (simp_tac (simpset() addsimps [FF_def]) 1);
-qed"Def_bool1";
-
-Goal "(Def x = FF) = (~x)";
-by (simp_tac (simpset() addsimps [FF_def]) 1);
-qed"Def_bool2";
+val TT_def = thm "TT_def";
+val FF_def = thm "FF_def";
+val neg_def = thm "neg_def";
+val ifte_def = thm "ifte_def";
+val andalso_def = thm "andalso_def";
+val orelse_def = thm "orelse_def";
+val If2_def = thm "If2_def";
+val Exh_tr = thm "Exh_tr";
+val trE = thm "trE";
+val tr_defs = thms "tr_defs";
+val dist_less_tr = thms "dist_less_tr";
+val dist_eq_tr = thms "dist_eq_tr";
+val ifte_simp = thm "ifte_simp";
+val ifte_thms = thms "ifte_thms";
+val andalso_thms = thms "andalso_thms";
+val orelse_thms = thms "orelse_thms";
+val neg_thms = thms "neg_thms";
+val split_If2 = thm "split_If2";
+val andalso_or = thm "andalso_or";
+val andalso_and = thm "andalso_and";
+val Def_bool1 = thm "Def_bool1";
+val Def_bool2 = thm "Def_bool2";
+val Def_bool3 = thm "Def_bool3";
+val Def_bool4 = thm "Def_bool4";
+val If_and_if = thm "If_and_if";
+val adm_trick_1 = thm "adm_trick_1";
+val adm_trick_2 = thm "adm_trick_2";
+val adm_tricks = thms "adm_tricks";
+val adm_nTT = thm "adm_nTT";
+val adm_nFF = thm "adm_nFF";
-Goal "(Def x = TT) = x";
-by (simp_tac (simpset() addsimps [TT_def]) 1);
-qed"Def_bool3";
-
-Goal "(Def x ~= TT) = (~x)";
-by (simp_tac (simpset() addsimps [TT_def]) 1);
-qed"Def_bool4";
-
-Goal
- "(If Def P then A else B fi)= (if P then A else B)";
-by (res_inst_tac [("p","Def P")] trE 1);
-by (Asm_full_simp_tac 1);
-by (asm_full_simp_tac (simpset() addsimps tr_defs@[flift1_def,o_def]) 1);
-by (asm_full_simp_tac (simpset() addsimps tr_defs@[flift1_def,o_def]) 1);
-qed"If_and_if";
-
-Addsimps [Def_bool1,Def_bool2,Def_bool3,Def_bool4];
-
-(* ----------------------------------------------------------------- *)
- section"admissibility";
-(* ----------------------------------------------------------------- *)
-
-
-(* The following rewrite rules for admissibility should in the future be
- replaced by a more general admissibility test that also checks
- chain-finiteness, of which these lemmata are specific examples *)
-
-Goal "(x~=FF) = (x=TT|x=UU)";
-by (res_inst_tac [("p","x")] trE 1);
-by (TRYALL (Asm_full_simp_tac));
-qed"adm_trick_1";
-
-Goal "(x~=TT) = (x=FF|x=UU)";
-by (res_inst_tac [("p","x")] trE 1);
-by (TRYALL (Asm_full_simp_tac));
-qed"adm_trick_2";
-
-bind_thms ("adm_tricks", [adm_trick_1,adm_trick_2]);
-
-
-Goal "cont(f) ==> adm (%x. (f x)~=TT)";
-by (simp_tac (HOL_basic_ss addsimps adm_tricks) 1);
-by (REPEAT ((resolve_tac (adm_lemmas@cont_lemmas1) 1) ORELSE atac 1));
-qed"adm_nTT";
-
-Goal "cont(f) ==> adm (%x. (f x)~=FF)";
-by (simp_tac (HOL_basic_ss addsimps adm_tricks) 1);
-by (REPEAT ((resolve_tac (adm_lemmas@cont_lemmas1) 1) ORELSE atac 1));
-qed"adm_nFF";
-
-Addsimps [adm_nTT,adm_nFF];