(* Title: HOLCF/cont.thy
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Results about continuity and monotonicity
*)
Cont = Fun3 +
(*
Now we change the default class! Form now on all untyped typevariables are
of default class pcpo
*)
default pcpo
consts
monofun :: "('a::po => 'b::po) => bool" (* monotonicity *)
contlub :: "('a => 'b) => bool" (* first cont. def *)
cont :: "('a => 'b) => bool" (* secnd cont. def *)
defs
monofun "monofun(f) == ! x y. x << y --> f(x) << f(y)"
contlub "contlub(f) == ! Y. is_chain(Y) -->
f(lub(range(Y))) = lub(range(% i.f(Y(i))))"
cont "cont(f) == ! Y. is_chain(Y) -->
range(% i.f(Y(i))) <<| f(lub(range(Y)))"
(* ------------------------------------------------------------------------ *)
(* the main purpose of cont.thy is to show: *)
(* monofun(f) & contlub(f) <==> cont(f) *)
(* ------------------------------------------------------------------------ *)
end