
diff -r 000000000000 -r 7949f97df77a Prod.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Prod.thy	Thu Sep 16 12:21:07 1993 +0200
@@ -0,0 +1,66 @@
+(*  Title: 	HOL/prod
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Ordered Pairs and the Cartesian product type
+The unit type
+
+The type definition admits the following unused axiom:
+  Abs_Unit_inverse 	"f: Unit ==> Rep_Unit(Abs_Unit(f)) = f"
+*)
+
+Prod = Set +
+types   
+	"*"  2        (infixr 20)
+        unit 0
+arities 
+   "*"      :: (term,term)term
+   unit     :: term
+consts
+   Pair_Rep :: "['a,'b] => ['a,'b] => bool"
+   Prod	    :: "('a => 'b => bool)set"
+   Rep_Prod :: "'a * 'b => ('a => 'b => bool)"
+   Abs_Prod :: "('a => 'b => bool) => 'a * 'b"
+   fst	    :: "'a * 'b => 'a"
+   snd	    :: "'a * 'b => 'b"
+   split    :: "['a * 'b, ['a,'b]=>'c] => 'c"
+   prod_fun :: "['a=>'b, 'c=>'d, 'a*'c] => 'b*'d"
+   Pair	    :: "['a,'b] => 'a * 'b"
+   "@Tuple" :: "args => 'a*'b"			("(1<_>)")
+   Sigma    :: "['a set, 'a => 'b set] => ('a*'b)set"
+
+   Unit	    :: "bool set"
+   Rep_Unit :: "unit => bool"
+   Abs_Unit :: "bool => unit"
+   Unity    :: "unit"					("<>")
+
+translations
+
+  "<x,y,z>" == "<x,<y,z>>"
+  "<x,y>"   == "Pair(x,y)"
+  "<x>"     => "x"
+
+rules
+
+  Pair_Rep_def     "Pair_Rep == (%a b. %x y. x=a & y=b)"
+  Prod_def         "Prod == {f. ? a b. f = Pair_Rep(a,b)}"
+    (*faking a type definition...*)
+  Rep_Prod         "Rep_Prod(p): Prod"
+  Rep_Prod_inverse "Abs_Prod(Rep_Prod(p)) = p"
+  Abs_Prod_inverse "f: Prod ==> Rep_Prod(Abs_Prod(f)) = f"
+    (*defining the abstract constants*)
+  Pair_def         "Pair(a,b) == Abs_Prod(Pair_Rep(a,b))"
+  fst_def          "fst(p) == @a. ? b. p = <a,b>"
+  snd_def          "snd(p) == @b. ? a. p = <a,b>"
+  split_def        "split(p,c) == c(fst(p),snd(p))"
+  prod_fun_def     "prod_fun(f,g) == (%z.split(z, %x y.<f(x), g(y)>))"
+  Sigma_def        "Sigma(A,B) == UN x:A. UN y:B(x). {<x,y>}"
+
+  Unit_def         "Unit == {p. p=True}"
+    (*faking a type definition...*)
+  Rep_Unit         "Rep_Unit(u): Unit"
+  Rep_Unit_inverse "Abs_Unit(Rep_Unit(u)) = u"
+    (*defining the abstract constants*)
+  Unity_def        "Unity == Abs_Unit(True)"
+end




