src/HOL/Prod.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Prod.thy	Fri Mar 03 12:02:25 1995 +0100
@@ -0,0 +1,66 @@
+(*  Title:      HOL/Prod.thy
+    ID:         Prod.thy,v 1.5 1994/08/19 09:04:27 lcp Exp
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1992  University of Cambridge
+
+Ordered Pairs and the Cartesian product type.
+The unit type.
+*)
+
+Prod = Fun +
+
+(** Products **)
+
+(* type definition *)
+
+consts
+  Pair_Rep      :: "['a, 'b] => ['a, 'b] => bool"
+
+defs
+  Pair_Rep_def  "Pair_Rep == (%a b. %x y. x=a & y=b)"
+
+subtype (Prod)
+  ('a, 'b) "*"          (infixr 20)
+    = "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}"
+
+
+(* abstract constants and syntax *)
+
+consts
+  fst           :: "'a * 'b => 'a"
+  snd           :: "'a * 'b => 'b"
+  split         :: "[['a, 'b] => 'c, 'a * 'b] => 'c"
+  prod_fun      :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd"
+  Pair          :: "['a, 'b] => 'a * 'b"
+  Sigma         :: "['a set, 'a => 'b set] => ('a * 'b) set"
+
+syntax
+  "@Tuple"      :: "args => 'a * 'b"            ("(1<_>)")
+
+translations
+  "<x, y, z>"   == "<x, <y, z>>"
+  "<x, y>"      == "Pair x y"
+  "<x>"         => "x"
+
+defs
+  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 c p == c (fst p) (snd p)"
+  prod_fun_def  "prod_fun f g == split(%x y.<f(x), g(y)>)"
+  Sigma_def     "Sigma A B == UN x:A. UN y:B(x). {<x, y>}"
+
+
+
+(** Unit **)
+
+subtype (Unit)
+  unit = "{p. p = True}"
+
+consts
+  Unity         :: "unit"                       ("<>")
+
+defs
+  Unity_def     "Unity == Abs_Unit(True)"
+
+end