generalized theorems and class instances for Cprod.
Now "*"::(cpo,cpo)cpo and "*"::(pcpo,pcpo)pcpo
(* 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" (* should be called flat, for consistency *)
defs
iterate_def "iterate n F c == nat_rec c (%n x.F`x) n"
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)"
(* further useful class for HOLCF *)
axclass chfin<pcpo
ax_chfin "!Y.is_chain Y-->(? n.max_in_chain n Y)"
axclass flat<pcpo
ax_flat "! x y.x << y --> (x = UU) | (x=y)"
end