--- a/src/LCF/lcf.thy Sat Apr 05 16:24:20 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,110 +0,0 @@
-(* Title: LCF/lcf.thy
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1992 University of Cambridge
-
-Natural Deduction Rules for LCF
-*)
-
-LCF = FOL +
-
-classes cpo < term
-
-default cpo
-
-types
- tr
- void
- ('a,'b) "*" (infixl 6)
- ('a,'b) "+" (infixl 5)
-
-arities
- fun, "*", "+" :: (cpo,cpo)cpo
- tr,void :: cpo
-
-consts
- UU :: "'a"
- TT,FF :: "tr"
- FIX :: "('a => 'a) => 'a"
- FST :: "'a*'b => 'a"
- SND :: "'a*'b => 'b"
- INL :: "'a => 'a+'b"
- INR :: "'b => 'a+'b"
- WHEN :: "['a=>'c, 'b=>'c, 'a+'b] => 'c"
- adm :: "('a => o) => o"
- VOID :: "void" ("()")
- PAIR :: "['a,'b] => 'a*'b" ("(1<_,/_>)" [0,0] 100)
- COND :: "[tr,'a,'a] => 'a" ("(_ =>/ (_ |/ _))" [60,60,60] 60)
- "<<" :: "['a,'a] => o" (infixl 50)
-rules
- (** DOMAIN THEORY **)
-
- eq_def "x=y == x << y & y << x"
-
- less_trans "[| x << y; y << z |] ==> x << z"
-
- less_ext "(ALL x. f(x) << g(x)) ==> f << g"
-
- mono "[| f << g; x << y |] ==> f(x) << g(y)"
-
- minimal "UU << x"
-
- FIX_eq "f(FIX(f)) = FIX(f)"
-
- (** TR **)
-
- tr_cases "p=UU | p=TT | p=FF"
-
- not_TT_less_FF "~ TT << FF"
- not_FF_less_TT "~ FF << TT"
- not_TT_less_UU "~ TT << UU"
- not_FF_less_UU "~ FF << UU"
-
- COND_UU "UU => x | y = UU"
- COND_TT "TT => x | y = x"
- COND_FF "FF => x | y = y"
-
- (** PAIRS **)
-
- surj_pairing "<FST(z),SND(z)> = z"
-
- FST "FST(<x,y>) = x"
- SND "SND(<x,y>) = y"
-
- (*** STRICT SUM ***)
-
- INL_DEF "~x=UU ==> ~INL(x)=UU"
- INR_DEF "~x=UU ==> ~INR(x)=UU"
-
- INL_STRICT "INL(UU) = UU"
- INR_STRICT "INR(UU) = UU"
-
- WHEN_UU "WHEN(f,g,UU) = UU"
- WHEN_INL "~x=UU ==> WHEN(f,g,INL(x)) = f(x)"
- WHEN_INR "~x=UU ==> WHEN(f,g,INR(x)) = g(x)"
-
- SUM_EXHAUSTION
- "z = UU | (EX x. ~x=UU & z = INL(x)) | (EX y. ~y=UU & z = INR(y))"
-
- (** VOID **)
-
- void_cases "(x::void) = UU"
-
- (** INDUCTION **)
-
- induct "[| adm(P); P(UU); ALL x. P(x) --> P(f(x)) |] ==> P(FIX(f))"
-
- (** Admissibility / Chain Completeness **)
- (* All rules can be found on pages 199--200 of Larry's LCF book.
- Note that "easiness" of types is not taken into account
- because it cannot be expressed schematically; flatness could be. *)
-
- adm_less "adm(%x.t(x) << u(x))"
- adm_not_less "adm(%x.~ t(x) << u)"
- adm_not_free "adm(%x.A)"
- adm_subst "adm(P) ==> adm(%x.P(t(x)))"
- adm_conj "[| adm(P); adm(Q) |] ==> adm(%x.P(x)&Q(x))"
- adm_disj "[| adm(P); adm(Q) |] ==> adm(%x.P(x)|Q(x))"
- adm_imp "[| adm(%x.~P(x)); adm(Q) |] ==> adm(%x.P(x)-->Q(x))"
- adm_all "(!!y.adm(P(y))) ==> adm(%x.ALL y.P(y,x))"
-end