# HG changeset patch # User nipkow # Date 785705469 -3600 # Node ID 12dd5d2e266b1fbb273826ed2b5eb8f850c294ad # Parent 768d3504d7cdec30395c93473e03b7daa0610bc7 rules -> defs diff -r 768d3504d7cd -r 12dd5d2e266b Gfp.thy --- a/Gfp.thy Thu Nov 24 20:11:40 1994 +0100 +++ b/Gfp.thy Thu Nov 24 20:31:09 1994 +0100 @@ -8,7 +8,7 @@ Gfp = Lfp + consts gfp :: "['a set=>'a set] => 'a set" -rules +defs (*greatest fixed point*) gfp_def "gfp(f) == Union({u. u <= f(u)})" end diff -r 768d3504d7cd -r 12dd5d2e266b Lfp.thy --- a/Lfp.thy Thu Nov 24 20:11:40 1994 +0100 +++ b/Lfp.thy Thu Nov 24 20:31:09 1994 +0100 @@ -8,7 +8,7 @@ Lfp = mono + consts lfp :: "['a set=>'a set] => 'a set" -rules +defs (*least fixed point*) lfp_def "lfp(f) == Inter({u. f(u) <= u})" end diff -r 768d3504d7cd -r 12dd5d2e266b Sexp.thy --- a/Sexp.thy Thu Nov 24 20:11:40 1994 +0100 +++ b/Sexp.thy Thu Nov 24 20:31:09 1994 +0100 @@ -24,7 +24,7 @@ NumbI "Numb(a): sexp" SconsI "[| M: sexp; N: sexp |] ==> M$N : sexp" -rules +defs sexp_case_def "sexp_case(c,d,e,M) == @ z. (? x. M=Leaf(x) & z=c(x)) \ @@ -38,4 +38,3 @@ "sexp_rec(M,c,d,e) == wfrec(pred_sexp, M, \ \ %M g. sexp_case(c, d, %N1 N2. e(N1, N2, g(N1), g(N2)), M))" end - diff -r 768d3504d7cd -r 12dd5d2e266b Trancl.thy --- a/Trancl.thy Thu Nov 24 20:11:40 1994 +0100 +++ b/Trancl.thy Thu Nov 24 20:31:09 1994 +0100 @@ -15,7 +15,7 @@ rtrancl :: "('a * 'a)set => ('a * 'a)set" ("(_^*)" [100] 100) trancl :: "('a * 'a)set => ('a * 'a)set" ("(_^+)" [100] 100) O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60) -rules +defs trans_def "trans(r) == (!x y z. :r --> :r --> :r)" comp_def (*composition of relations*) "r O s == {xz. ? x y z. xz = & :s & :r}" diff -r 768d3504d7cd -r 12dd5d2e266b WF.thy --- a/WF.thy Thu Nov 24 20:11:40 1994 +0100 +++ b/WF.thy Thu Nov 24 20:31:09 1994 +0100 @@ -14,7 +14,7 @@ is_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b, 'a=>'b] => bool" the_recfun :: "[('a * 'a)set, 'a, ['a,'a=>'b]=>'b] => 'a=>'b" -rules +defs wf_def "wf(r) == (!P. (!x. (!y. :r --> P(y)) --> P(x)) --> (!x.P(x)))" cut_def "cut(f,r,x) == (%y. if(:r, f(y), @z.True))"