src/HOLCF/Fix.thy

Added "discrete" CPOs and modified IMP to use those rather than "lift"

(*  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::cpo=>bool)=>bool"
admw		:: "('a=>bool)=>bool"
chain_finite	:: "'a::cpo=>bool"
flat		:: "'a=>bool"

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::cpo)==
                   !Y. is_chain (Y::nat=>'a::cpo) --> (? 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