src/HOLCF/ssum0.thy

Addition of cardinals and order types, various tidying

(*  Title: 	HOLCF/ssum0.thy
    ID:         $Id$
    Author: 	Franz Regensburger
    Copyright   1993  Technische Universitaet Muenchen

Strict sum
*)

Ssum0 = Cfun3 +

(* new type for strict sum *)

types "++" 2        (infixr 10)

arities "++" :: (pcpo,pcpo)term	

consts
  Ssum		:: "(['a,'b,bool]=>bool)set"
  Sinl_Rep	:: "['a,'a,'b,bool]=>bool"
  Sinr_Rep	:: "['b,'a,'b,bool]=>bool"
  Rep_Ssum	:: "('a ++ 'b) => (['a,'b,bool]=>bool)"
  Abs_Ssum	:: "(['a,'b,bool]=>bool) => ('a ++ 'b)"
  Isinl		:: "'a => ('a ++ 'b)"
  Isinr		:: "'b => ('a ++ 'b)"
  Iwhen		:: "('a->'c)=>('b->'c)=>('a ++ 'b)=> 'c"

rules

  Sinl_Rep_def		"Sinl_Rep == (%a.%x y p.\
\				(~a=UU --> x=a  & p))"

  Sinr_Rep_def		"Sinr_Rep == (%b.%x y p.\
\				(~b=UU --> y=b  & ~p))"

  Ssum_def		"Ssum =={f.(? a.f=Sinl_Rep(a))|(? b.f=Sinr_Rep(b))}"

  (*faking a type definition... *)
  (* "++" is isomorphic to Ssum *)

  Rep_Ssum		"Rep_Ssum(p):Ssum"		
  Rep_Ssum_inverse	"Abs_Ssum(Rep_Ssum(p)) = p"	
  Abs_Ssum_inverse	"f:Ssum ==> Rep_Ssum(Abs_Ssum(f)) = f"

   (*defining the abstract constants*)
  Isinl_def	"Isinl(a) == Abs_Ssum(Sinl_Rep(a))"
  Isinr_def	"Isinr(b) == Abs_Ssum(Sinr_Rep(b))"

  Iwhen_def	"Iwhen(f)(g)(s) == @z.\
\				    (s=Isinl(UU) --> z=UU)\
\			&(!a. ~a=UU & s=Isinl(a) --> z=f[a])\  
\			&(!b. ~b=UU & s=Isinr(b) --> z=g[b])"  

end