# HG changeset patch
# User huffman
# Date 1112391881 -7200
# Node ID f8345ee4f60759a9d77628084af6775a78dafdd6
# Parent  f6da795ee27abc93bb13ed24680beec18028ec52
convert to new-style theory

diff -r f6da795ee27a -r f8345ee4f607 src/HOLCF/Tr.ML
--- 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];
diff -r f6da795ee27a -r f8345ee4f607 src/HOLCF/Tr.thy
--- a/src/HOLCF/Tr.thy	Fri Apr 01 21:04:00 2005 +0200
+++ b/src/HOLCF/Tr.thy	Fri Apr 01 23:44:41 2005 +0200
@@ -1,11 +1,16 @@
 (*  Title:      HOLCF/Tr.thy
     ID:         $Id$
     Author:     Franz Regensburger
+    License:    GPL (GNU GENERAL PUBLIC LICENSE)
 
 Introduce infix if_then_else_fi and boolean connectives andalso, orelse
 *)
 
-Tr = Lift + Fix +
+header {* The type of lifted booleans *}
+
+theory Tr
+imports Lift Fix
+begin
 
 types
   tr = "bool lift"
@@ -14,7 +19,8 @@
   "tr" <= (type) "bool lift" 
 
 consts
-	TT,FF           :: "tr"
+	TT              :: "tr"
+	FF              :: "tr"
         Icifte          :: "tr -> 'c -> 'c -> 'c"
         trand           :: "tr -> tr -> tr"
         tror            :: "tr -> tr -> tr"
@@ -30,13 +36,164 @@
              "x orelse y"  == "tror$x$y"
              "If b then e1 else e2 fi" == "Icifte$b$e1$e2"
 defs
-  TT_def      "TT==Def True"
-  FF_def      "FF==Def False"
-  neg_def     "neg == flift2 Not"
-  ifte_def    "Icifte == (LAM b t e. flift1(%b. if b then t else e)$b)"
-  andalso_def "trand == (LAM x y. If x then y else FF fi)"
-  orelse_def  "tror == (LAM x y. If x then TT else y fi)"
-  If2_def     "If2 Q x y == If Q then x else y fi"
+  TT_def:      "TT==Def True"
+  FF_def:      "FF==Def False"
+  neg_def:     "neg == flift2 Not"
+  ifte_def:    "Icifte == (LAM b t e. flift1(%b. if b then t else e)$b)"
+  andalso_def: "trand == (LAM x y. If x then y else FF fi)"
+  orelse_def:  "tror == (LAM x y. If x then TT else y fi)"
+  If2_def:     "If2 Q x y == If Q then x else y fi"
+
+text {* Exhaustion and Elimination for type @{typ tr} *}
+
+lemma Exh_tr: "t=UU | t = TT | t = FF"
+apply (unfold FF_def TT_def)
+apply (induct_tac "t")
+apply fast
+apply fast
+done
+
+lemma trE: "[| p=UU ==> Q; p = TT ==>Q; p = FF ==>Q|] ==>Q"
+apply (rule Exh_tr [THEN disjE])
+apply fast
+apply (erule disjE)
+apply fast
+apply fast
+done
+
+text {* tactic for tr-thms with case split *}
+
+lemmas tr_defs = andalso_def orelse_def neg_def ifte_def TT_def FF_def
+(*
+fun prover t =  prove_goal thy t
+ (fn prems =>
+        [
+        (res_inst_tac [("p","y")] trE 1),
+	(REPEAT(asm_simp_tac (simpset() addsimps 
+		[o_def,flift1_def,flift2_def,inst_lift_po]@tr_defs) 1))
+	])
+*)
+text {* distinctness for type @{typ tr} *}
+
+lemma dist_less_tr [simp]: "~TT << UU" "~FF << UU" "~TT << FF" "~FF << TT"
+by (simp_all add: tr_defs)
+
+lemma dist_eq_tr [simp]: "TT~=UU" "FF~=UU" "TT~=FF" "UU~=TT" "UU~=FF" "FF~=TT"
+by (simp_all add: tr_defs)
+
+text {* lemmas about andalso, orelse, neg and if *}
+
+lemma ifte_simp:
+  "If x then e1 else e2 fi =
+    flift1 (%b. if b then e1 else e2)$x"
+apply (unfold ifte_def TT_def FF_def flift1_def)
+apply (simp add: cont_flift1_arg cont_if)
+done
+
+lemma ifte_thms [simp]:
+  "If UU then e1 else e2 fi = UU"
+  "If FF then e1 else e2 fi = e2"
+  "If TT then e1 else e2 fi = e1"
+by (simp_all add: ifte_simp TT_def FF_def)
+
+lemma andalso_thms [simp]:
+  "(TT andalso y) = y"
+  "(FF andalso y) = FF"
+  "(UU andalso y) = UU"
+  "(y andalso TT) = y"
+  "(y andalso y) = y"
+apply (unfold andalso_def, simp_all)
+apply (rule_tac p=y in trE, simp_all)
+apply (rule_tac p=y in trE, simp_all)
+done
+
+lemma orelse_thms [simp]:
+  "(TT orelse y) = TT"
+  "(FF orelse y) = y"
+  "(UU orelse y) = UU"
+  "(y orelse FF) = y"
+  "(y orelse y) = y"
+apply (unfold orelse_def, simp_all)
+apply (rule_tac p=y in trE, simp_all)
+apply (rule_tac p=y in trE, simp_all)
+done
+
+lemma neg_thms [simp]:
+  "neg$TT = FF"
+  "neg$FF = TT"
+  "neg$UU = UU"
+by (simp_all add: neg_def TT_def FF_def)
+
+text {* split-tac for If via If2 because the constant has to be a constant *}
+  
+lemma split_If2: 
+  "P (If2 Q x y ) = ((Q=UU --> P UU) & (Q=TT --> P x) & (Q=FF --> P y))"  
+apply (unfold If2_def)
+apply (rule_tac p = "Q" in trE)
+apply (simp_all)
+done
+
+ML_setup {*
+val split_If_tac =
+  simp_tac (HOL_basic_ss addsimps [symmetric (thm "If2_def")])
+    THEN' (split_tac [thm "split_If2"])
+*}
+
+subsection "Rewriting of HOLCF operations to HOL functions"
+
+lemma andalso_or: 
+"!!t.[|t~=UU|]==> ((t andalso s)=FF)=(t=FF | s=FF)"
+apply (rule_tac p = "t" in trE)
+apply simp_all
+done
+
+lemma andalso_and: "[|t~=UU|]==> ((t andalso s)~=FF)=(t~=FF & s~=FF)"
+apply (rule_tac p = "t" in trE)
+apply simp_all
+done
+
+lemma Def_bool1 [simp]: "(Def x ~= FF) = x"
+by (simp add: FF_def)
+
+lemma Def_bool2 [simp]: "(Def x = FF) = (~x)"
+by (simp add: FF_def)
+
+lemma Def_bool3 [simp]: "(Def x = TT) = x"
+by (simp add: TT_def)
+
+lemma Def_bool4 [simp]: "(Def x ~= TT) = (~x)"
+by (simp add: TT_def)
+
+lemma If_and_if: 
+  "(If Def P then A else B fi)= (if P then A else B)"
+apply (rule_tac p = "Def P" in trE)
+apply (auto simp add: TT_def[symmetric] FF_def[symmetric])
+done
+
+subsection "admissibility"
+
+text {*
+   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
+*}
+
+lemma adm_trick_1: "(x~=FF) = (x=TT|x=UU)"
+apply (rule_tac p = "x" in trE)
+apply (simp_all)
+done
+
+lemma adm_trick_2: "(x~=TT) = (x=FF|x=UU)"
+apply (rule_tac p = "x" in trE)
+apply (simp_all)
+done
+
+lemmas adm_tricks = adm_trick_1 adm_trick_2
+
+lemma adm_nTT [simp]: "cont(f) ==> adm (%x. (f x)~=TT)"
+by (simp add: adm_tricks)
+
+lemma adm_nFF [simp]: "cont(f) ==> adm (%x. (f x)~=FF)"
+by (simp add: adm_tricks)
 
 end
-