--- a/src/CCL/CCL.thy Fri Oct 10 16:29:41 1997 +0200
+++ b/src/CCL/CCL.thy Fri Oct 10 17:10:12 1997 +0200
@@ -56,18 +56,18 @@
trueV "true ---> true"
falseV "false ---> false"
pairV "<a,b> ---> <a,b>"
- lamV "lam x.b(x) ---> lam x.b(x)"
+ lamV "lam x. b(x) ---> lam x. b(x)"
caseVtrue "[| t ---> true; d ---> c |] ==> case(t,d,e,f,g) ---> c"
caseVfalse "[| t ---> false; e ---> c |] ==> case(t,d,e,f,g) ---> c"
caseVpair "[| t ---> <a,b>; f(a,b) ---> c |] ==> case(t,d,e,f,g) ---> c"
- caseVlam "[| t ---> lam x.b(x); g(b) ---> c |] ==> case(t,d,e,f,g) ---> c"
+ caseVlam "[| t ---> lam x. b(x); g(b) ---> c |] ==> case(t,d,e,f,g) ---> c"
(*** Properties of evaluation: note that "t ---> c" impies that c is canonical ***)
canonical "[| t ---> c; c==true ==> u--->v;
c==false ==> u--->v;
- !!a b.c==<a,b> ==> u--->v;
- !!f.c==lam x.f(x) ==> u--->v |] ==>
+ !!a b. c==<a,b> ==> u--->v;
+ !!f. c==lam x. f(x) ==> u--->v |] ==>
u--->v"
(* Should be derivable - but probably a bitch! *)
@@ -77,9 +77,9 @@
(*** Definitions used in the following rules ***)
- apply_def "f ` t == case(f,bot,bot,%x y.bot,%u.u(t))"
- bot_def "bot == (lam x.x`x)`(lam x.x`x)"
- fix_def "fix(f) == (lam x.f(x`x))`(lam x.f(x`x))"
+ apply_def "f ` t == case(f,bot,bot,%x y. bot,%u. u(t))"
+ bot_def "bot == (lam x. x`x)`(lam x. x`x)"
+ fix_def "fix(f) == (lam x. f(x`x))`(lam x. f(x`x))"
(* The pre-order ([=) is defined as a simulation, and behavioural equivalence (=) *)
(* as a bisimulation. They can both be expressed as (bi)simulations up to *)
@@ -87,8 +87,8 @@
SIM_def
"SIM(t,t',R) == (t=true & t'=true) | (t=false & t'=false) |
- (EX a a' b b'.t=<a,b> & t'=<a',b'> & <a,a'> : R & <b,b'> : R) |
- (EX f f'.t=lam x.f(x) & t'=lam x.f'(x) & (ALL x.<f(x),f'(x)> : R))"
+ (EX a a' b b'. t=<a,b> & t'=<a',b'> & <a,a'> : R & <b,b'> : R) |
+ (EX f f'. t=lam x. f(x) & t'=lam x. f'(x) & (ALL x.<f(x),f'(x)> : R))"
POgen_def "POgen(R) == {p. EX t t'. p=<t,t'> & (t = bot | SIM(t,t',R))}"
EQgen_def "EQgen(R) == {p. EX t t'. p=<t,t'> & (t = bot & t' = bot | SIM(t,t',R))}"
@@ -105,7 +105,7 @@
po_cong "a [= b ==> f(a) [= f(b)"
(* Extend definition of [= to program fragments of higher type *)
- po_abstractn "(!!x. f(x) [= g(x)) ==> (%x.f(x)) [= (%x.g(x))"
+ po_abstractn "(!!x. f(x) [= g(x)) ==> (%x. f(x)) [= (%x. g(x))"
(** Equality - equivalence axioms inherited from FOL.thy **)
(** - congruence of "=" is axiomatised implicitly **)
@@ -122,11 +122,11 @@
caseBtrue "case(true,d,e,f,g) = d"
caseBfalse "case(false,d,e,f,g) = e"
caseBpair "case(<a,b>,d,e,f,g) = f(a,b)"
- caseBlam "case(lam x.b(x),d,e,f,g) = g(b)"
+ caseBlam "case(lam x. b(x),d,e,f,g) = g(b)"
caseBbot "case(bot,d,e,f,g) = bot" (* strictness *)
(** The theory is non-trivial **)
- distinctness "~ lam x.b(x) = bot"
+ distinctness "~ lam x. b(x) = bot"
(*** Definitions of Termination and Divergence ***)