(* Title: HOLCF/cfun1.thy
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Definition of the type -> of continuous functions
*)
Cfun1 = Cont +
(* new type of continuous functions *)
types "->" 2 (infixr 5)
arities "->" :: (pcpo,pcpo)term (* No properties for ->'s range *)
consts
Cfun :: "('a => 'b)set"
fapp :: "('a -> 'b)=>('a => 'b)" ("(_[_])" [11,0] 1000)
(* usually Rep_Cfun *)
(* application *)
fabs :: "('a => 'b)=>('a -> 'b)" (binder "LAM " 10)
(* usually Abs_Cfun *)
(* abstraction *)
less_cfun :: "[('a -> 'b),('a -> 'b)]=>bool"
rules
Cfun_def "Cfun == {f. contX(f)}"
(*faking a type definition... *)
(* -> is isomorphic to Cfun *)
Rep_Cfun "fapp(fo):Cfun"
Rep_Cfun_inverse "fabs(fapp(fo)) = fo"
Abs_Cfun_inverse "f:Cfun ==> fapp(fabs(f))=f"
(*defining the abstract constants*)
less_cfun_def "less_cfun(fo1,fo2) == ( fapp(fo1) << fapp(fo2) )"
end