--- a/src/ZF/IsaMakefile Fri May 24 13:15:37 2002 +0200
+++ b/src/ZF/IsaMakefile Fri May 24 15:24:29 2002 +0200
@@ -43,7 +43,7 @@
Sum.thy Tools/cartprod.ML Tools/datatype_package.ML \
Tools/ind_cases.ML Tools/induct_tacs.ML Tools/inductive_package.ML \
Tools/numeral_syntax.ML Tools/primrec_package.ML Tools/typechk.ML \
- Trancl.ML Trancl.thy Univ.thy Update.ML Update.thy \
+ Trancl.ML Trancl.thy Univ.thy Update.thy \
WF.thy ZF.ML ZF.thy Zorn.thy arith_data.ML equalities.thy func.thy \
ind_syntax.ML mono.ML mono.thy pair.ML pair.thy simpdata.ML \
subset.ML subset.thy thy_syntax.ML upair.ML upair.thy
--- a/src/ZF/Update.ML Fri May 24 13:15:37 2002 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,39 +0,0 @@
-(* Title: ZF/Update.ML
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1998 University of Cambridge
-
-Function updates: like theory Map, but for ordinary functions
-*)
-
-Goal "f(x:=y) ` z = (if z=x then y else f`z)";
-by (simp_tac (simpset() addsimps [update_def]) 1);
-by (case_tac "z : domain(f)" 1);
-by (Asm_simp_tac 1);
-by (asm_simp_tac (simpset() addsimps [apply_0]) 1);
-qed "update_apply";
-Addsimps [update_apply];
-
-Goalw [update_def] "[| f`x = y; f: Pi(A,B); x: A |] ==> f(x:=y) = f";
-by (asm_simp_tac (simpset() addsimps [domain_of_fun, cons_absorb]) 1);
-by (rtac fun_extension 1);
-by (best_tac (claset() addIs [apply_type, if_type, lam_type]) 1);
-by (assume_tac 1);
-by (Asm_simp_tac 1);
-qed "update_idem";
-
-
-(* [| f: Pi(A, B); x:A |] ==> f(x := f`x) = f *)
-Addsimps [refl RS update_idem];
-
-Goalw [update_def] "domain(f(x:=y)) = cons(x, domain(f))";
-by (Asm_simp_tac 1);
-qed "domain_update";
-Addsimps [domain_update];
-
-Goalw [update_def] "[| f: A -> B; x : A; y: B |] ==> f(x:=y) : A -> B";
-by (asm_simp_tac (simpset() addsimps [domain_of_fun, cons_absorb,
- apply_funtype, lam_type]) 1);
-qed "update_type";
-
-
--- a/src/ZF/Update.thy Fri May 24 13:15:37 2002 +0200
+++ b/src/ZF/Update.thy Fri May 24 15:24:29 2002 +0200
@@ -6,10 +6,11 @@
Function updates: like theory Map, but for ordinary functions
*)
-Update = func +
+theory Update = func:
-consts
+constdefs
update :: "[i,i,i] => i"
+ "update(f,a,b) == lam x: cons(a, domain(f)). if(x=a, b, f`x)"
nonterminals
updbinds updbind
@@ -18,16 +19,50 @@
(* Let expressions *)
- "_updbind" :: [i, i] => updbind ("(2_ :=/ _)")
- "" :: updbind => updbinds ("_")
- "_updbinds" :: [updbind, updbinds] => updbinds ("_,/ _")
- "_Update" :: [i, updbinds] => i ("_/'((_)')" [900,0] 900)
+ "_updbind" :: "[i, i] => updbind" ("(2_ :=/ _)")
+ "" :: "updbind => updbinds" ("_")
+ "_updbinds" :: "[updbind, updbinds] => updbinds" ("_,/ _")
+ "_Update" :: "[i, updbinds] => i" ("_/'((_)')" [900,0] 900)
translations
"_Update (f, _updbinds(b,bs))" == "_Update (_Update(f,b), bs)"
- "f(x:=y)" == "update(f,x,y)"
+ "f(x:=y)" == "update(f,x,y)"
+
+
+lemma update_apply [simp]: "f(x:=y) ` z = (if z=x then y else f`z)"
+apply (simp add: update_def)
+apply (rule_tac P="z \<in> domain(f)" in case_split_thm)
+apply (simp_all add: apply_0)
+done
+
+lemma update_idem: "[| f`x = y; f: Pi(A,B); x: A |] ==> f(x:=y) = f"
+apply (unfold update_def)
+apply (simp add: domain_of_fun cons_absorb)
+apply (rule fun_extension)
+apply (best intro: apply_type if_type lam_type, assumption)
+apply simp
+done
+
-defs
- update_def "f(a:=b) == lam x: cons(a, domain(f)). if(x=a, b, f`x)"
+(* [| f: Pi(A, B); x:A |] ==> f(x := f`x) = f *)
+declare refl [THEN update_idem, simp]
+
+lemma domain_update [simp]: "domain(f(x:=y)) = cons(x, domain(f))"
+by (unfold update_def, simp)
+
+lemma update_type: "[| f: A -> B; x : A; y: B |] ==> f(x:=y) : A -> B"
+apply (unfold update_def)
+apply (simp add: domain_of_fun cons_absorb apply_funtype lam_type)
+done
+
+ML
+{*
+val update_def = thm "update_def";
+val update_apply = thm "update_apply";
+val update_idem = thm "update_idem";
+val domain_update = thm "domain_update";
+val update_type = thm "update_type";
+*}
+
end