src/HOLCF/fix.thy

+(*  Title: 	HOLCF/fix.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993  Technische Universitaet Muenchen
+
+
+definitions for fixed point operator and admissibility
+
+*)
+
+Fix = Cfun3 +
+
+consts
+
+iterate :: "nat=>('a->'a)=>'a=>'a"
+Ifix    :: "('a->'a)=>'a"
+fix     :: "('a->'a)->'a"
+adm          :: "('a=>bool)=>bool"
+admw         :: "('a=>bool)=>bool"
+chain_finite :: "'a=>bool"
+flat         :: "'a=>bool"
+
+rules
+
+iterate_def   "iterate(n,F,c) == nat_rec(n,c,%n x.F[x])"
+Ifix_def      "Ifix(F) == lub(range(%i.iterate(i,F,UU)))"
+fix_def       "fix == (LAM f. Ifix(f))"
+
+adm_def       "adm(P) == !Y. is_chain(Y) --> \
+\                        (!i.P(Y(i))) --> P(lub(range(Y)))"
+
+admw_def      "admw(P)== (!F.((!n.P(iterate(n,F,UU)))-->\
+\			 P(lub(range(%i.iterate(i,F,UU))))))" 
+
+chain_finite_def  "chain_finite(x::'a)==\
+\                        !Y. is_chain(Y::nat=>'a) --> (? n.max_in_chain(n,Y))"
+
+flat_def          "flat(x::'a) ==\
+\                        ! x y. x::'a << y --> (x = UU) | (x=y)"
+
+end
+