--- a/src/HOL/IMP/Expr.ML Tue May 07 18:15:51 1996 +0200
+++ b/src/HOL/IMP/Expr.ML Tue May 07 18:17:52 1996 +0200
@@ -10,36 +10,36 @@
open Expr;
val evala_elim_cases = map (evala.mk_cases aexp.simps)
- ["<N(n),sigma> -a-> i", "<X(x),sigma> -a-> i",
- "<Op1 f e,sigma> -a-> i", "<Op2 f a1 a2,sigma> -a-> i"
+ ["(N(n),sigma) -a-> i", "(X(x),sigma) -a-> i",
+ "(Op1 f e,sigma) -a-> i", "(Op2 f a1 a2,sigma) -a-> i"
];
val evalb_elim_cases = map (evalb.mk_cases bexp.simps)
- ["<true,sigma> -b-> x", "<false,sigma> -b-> x",
- "<ROp f a0 a1,sigma> -b-> x", "<noti(b),sigma> -b-> x",
- "<b0 andi b1,sigma> -b-> x", "<b0 ori b1,sigma> -b-> x"
+ ["(true,sigma) -b-> x", "(false,sigma) -b-> x",
+ "(ROp f a0 a1,sigma) -b-> x", "(noti(b),sigma) -b-> x",
+ "(b0 andi b1,sigma) -b-> x", "(b0 ori b1,sigma) -b-> x"
];
val evalb_simps = map (fn s => prove_goal Expr.thy s
(fn _ => [fast_tac (HOL_cs addSIs evalb.intrs addSEs evalb_elim_cases) 1]))
- ["(<true,sigma> -b-> w) = (w=True)",
- "(<false,sigma> -b-> w) = (w=False)",
- "(<ROp f a0 a1,sigma> -b-> w) = \
-\ (? m. <a0,sigma> -a-> m & (? n. <a1,sigma> -a-> n & w = f m n))",
- "(<noti(b),sigma> -b-> w) = (? x. <b,sigma> -b-> x & w = (~x))",
- "(<b0 andi b1,sigma> -b-> w) = \
-\ (? x. <b0,sigma> -b-> x & (? y. <b1,sigma> -b-> y & w = (x&y)))",
- "(<b0 ori b1,sigma> -b-> w) = \
-\ (? x. <b0,sigma> -b-> x & (? y. <b1,sigma> -b-> y & w = (x|y)))"];
+ ["((true,sigma) -b-> w) = (w=True)",
+ "((false,sigma) -b-> w) = (w=False)",
+ "((ROp f a0 a1,sigma) -b-> w) = \
+\ (? m. (a0,sigma) -a-> m & (? n. (a1,sigma) -a-> n & w = f m n))",
+ "((noti(b),sigma) -b-> w) = (? x. (b,sigma) -b-> x & w = (~x))",
+ "((b0 andi b1,sigma) -b-> w) = \
+\ (? x. (b0,sigma) -b-> x & (? y. (b1,sigma) -b-> y & w = (x&y)))",
+ "((b0 ori b1,sigma) -b-> w) = \
+\ (? x. (b0,sigma) -b-> x & (? y. (b1,sigma) -b-> y & w = (x|y)))"];
-goal Expr.thy "!n. (<a,s> -a-> n) = (n = A a s)";
+goal Expr.thy "!n. ((a,s) -a-> n) = (n = A a s)";
by (aexp.induct_tac "a" 1); (* struct. ind. *)
by (ALLGOALS Simp_tac); (* rewr. Den. *)
by (TRYALL (fast_tac (set_cs addSIs (evala.intrs@prems)
addSEs evala_elim_cases)));
qed_spec_mp "aexp_iff";
-goal Expr.thy "!w. (<b,s> -b-> w) = (w = B b s)";
+goal Expr.thy "!w. ((b,s) -b-> w) = (w = B b s)";
by (bexp.induct_tac "b" 1);
by (ALLGOALS(asm_simp_tac (!simpset addcongs [conj_cong]
addsimps (aexp_iff::evalb_simps))));
--- a/src/HOL/IMP/Expr.thy Tue May 07 18:15:51 1996 +0200
+++ b/src/HOL/IMP/Expr.thy Tue May 07 18:17:52 1996 +0200
@@ -24,17 +24,17 @@
| Op2 n2n2n aexp aexp
(** Evaluation of arithmetic expressions **)
-consts evala :: "(aexp*state*nat)set"
- "@evala" :: [aexp,state,nat] => bool ("<_,_>/ -a-> _" [0,0,50] 50)
+consts evala :: "((aexp*state) * nat) set"
+ "-a->" :: "[aexp*state,nat] => bool" (infixl 50)
translations
- "<ae,sig> -a-> n" == "(ae,sig,n) : evala"
+ "aesig -a-> n" == "(aesig,n) : evala"
inductive "evala"
intrs
- N "<N(n),s> -a-> n"
- X "<X(x),s> -a-> s(x)"
- Op1 "<e,s> -a-> n ==> <Op1 f e,s> -a-> f(n)"
- Op2 "[| <e0,s> -a-> n0; <e1,s> -a-> n1 |]
- ==> <Op2 f e0 e1,s> -a-> f n0 n1"
+ N "(N(n),s) -a-> n"
+ X "(X(x),s) -a-> s(x)"
+ Op1 "(e,s) -a-> n ==> (Op1 f e,s) -a-> f(n)"
+ Op2 "[| (e0,s) -a-> n0; (e1,s) -a-> n1 |]
+ ==> (Op2 f e0 e1,s) -a-> f n0 n1"
types n2n2b = "[nat,nat] => bool"
@@ -49,23 +49,23 @@
| ori bexp bexp (infixl 60)
(** Evaluation of boolean expressions **)
-consts evalb :: "(bexp*state*bool)set"
- "@evalb" :: [bexp,state,bool] => bool ("<_,_>/ -b-> _" [0,0,50] 50)
+consts evalb :: "((bexp*state) * bool)set"
+ "-b->" :: "[bexp*state,bool] => bool" (infixl 50)
translations
- "<be,sig> -b-> b" == "(be,sig,b) : evalb"
+ "besig -b-> b" == "(besig,b) : evalb"
inductive "evalb"
intrs (*avoid clash with ML constructors true, false*)
- tru "<true,s> -b-> True"
- fls "<false,s> -b-> False"
- ROp "[| <a0,s> -a-> n0; <a1,s> -a-> n1 |]
- ==> <ROp f a0 a1,s> -b-> f n0 n1"
- noti "<b,s> -b-> w ==> <noti(b),s> -b-> (~w)"
- andi "[| <b0,s> -b-> w0; <b1,s> -b-> w1 |]
- ==> <b0 andi b1,s> -b-> (w0 & w1)"
- ori "[| <b0,s> -b-> w0; <b1,s> -b-> w1 |]
- ==> <b0 ori b1,s> -b-> (w0 | w1)"
+ tru "(true,s) -b-> True"
+ fls "(false,s) -b-> False"
+ ROp "[| (a0,s) -a-> n0; (a1,s) -a-> n1 |]
+ ==> (ROp f a0 a1,s) -b-> f n0 n1"
+ noti "(b,s) -b-> w ==> (noti(b),s) -b-> (~w)"
+ andi "[| (b0,s) -b-> w0; (b1,s) -b-> w1 |]
+ ==> (b0 andi b1,s) -b-> (w0 & w1)"
+ ori "[| (b0,s) -b-> w0; (b1,s) -b-> w1 |]
+ ==> (b0 ori b1,s) -b-> (w0 | w1)"
(** Denotational semantics of arithemtic and boolean expressions **)
consts