src/HOLCF/Fix.thy

added Induct/Binary_Trees.thy, Induct/Tree_Forest (converted from
former ex/TF.ML ex/TF.thy ex/Term.ML ex/Term.thy);

(*  Title:      HOLCF/Fix.thy
    ID:         $Id$
    Author:     Franz Regensburger
    License:    GPL (GNU GENERAL PUBLIC LICENSE)

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