(* Title: HOLCF/Fix.thy
ID: $Id$
Author: Franz Regensburger
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::cpo=>bool)=>bool"
admw :: "('a=>bool)=>bool"
primrec
iterate_0 "iterate 0 F x = x"
iterate_Suc "iterate (Suc n) F x = F$(iterate n F x)"
defs
Ifix_def "Ifix F == lub(range(%i. iterate i F UU))"
fix_def "fix == (LAM f. Ifix f)"
adm_def "adm P == !Y. 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)))"
end