
diff -r 2c38796b33b9 -r ee4dfce170a0 src/HOLCF/Sprod0.thy
--- a/src/HOLCF/Sprod0.thy	Sat Feb 15 18:24:05 1997 +0100
+++ b/src/HOLCF/Sprod0.thy	Mon Feb 17 10:57:11 1997 +0100
@@ -1,57 +1,36 @@
-(*  Title:      HOLCF/sprod0.thy
+(*  Title:      HOLCF/Sprod0.thy
     ID:         $Id$
     Author:     Franz Regensburger
     Copyright   1993  Technische Universitaet Muenchen
 
-Strict product
+Strict product with typedef
 *)
 
 Sprod0 = Cfun3 +
 
-(* new type for strict product *)
+constdefs
+  Spair_Rep     :: ['a,'b] => ['a,'b] => bool
+ "Spair_Rep == (%a b. %x y.(~a=UU & ~b=UU --> x=a  & y=b ))"
 
-types "**" 2        (infixr 20)
-
-arities "**" :: (pcpo,pcpo)term 
+typedef (Sprod)  ('a, 'b) "**" (infixr 20) = "{f. ? a b. f = Spair_Rep a b}"
 
 syntax (symbols)
- 
-  "**"		:: [type, type] => type		("(_ \\<otimes>/ _)" [21,20] 20)
+  "**"		:: [type, type] => type	 ("(_ \\<otimes>/ _)" [21,20] 20)
 
 consts
-  Sprod         :: "('a => 'b => bool)set"
-  Spair_Rep     :: "['a,'b] => ['a,'b] => bool"
-  Rep_Sprod     :: "('a ** 'b) => ('a => 'b => bool)"
-  Abs_Sprod     :: "('a => 'b => bool) => ('a ** 'b)"
   Ispair        :: "['a,'b] => ('a ** 'b)"
   Isfst         :: "('a ** 'b) => 'a"
   Issnd         :: "('a ** 'b) => 'b"  
 
 defs
-  Spair_Rep_def         "Spair_Rep == (%a b. %x y.
-                                (~a=UU & ~b=UU --> x=a  & y=b ))"
-
-  Sprod_def             "Sprod == {f. ? a b. f = Spair_Rep a b}"
-
-rules
-  (*faking a type definition... *)
-  (* "**" is isomorphic to Sprod *)
-
-  Rep_Sprod             "Rep_Sprod(p):Sprod"            
-  Rep_Sprod_inverse     "Abs_Sprod(Rep_Sprod(p)) = p"   
-  Abs_Sprod_inverse     "f:Sprod ==> Rep_Sprod(Abs_Sprod(f)) = f"
-
-defs
    (*defining the abstract constants*)
 
   Ispair_def    "Ispair a b == Abs_Sprod(Spair_Rep a b)"
 
-  Isfst_def     "Isfst(p) == @z.
-                                        (p=Ispair UU UU --> z=UU)
+  Isfst_def     "Isfst(p) == @z.        (p=Ispair UU UU --> z=UU)
                 &(! a b. ~a=UU & ~b=UU & p=Ispair a b   --> z=a)"  
 
-  Issnd_def     "Issnd(p) == @z.
-                                        (p=Ispair UU UU  --> z=UU)
+  Issnd_def     "Issnd(p) == @z.        (p=Ispair UU UU  --> z=UU)
                 &(! a b. ~a=UU & ~b=UU & p=Ispair a b    --> z=b)"  
 
 




