src/HOL/Product_Type.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Product_Type.thy	Thu Oct 12 18:44:35 2000 +0200
@@ -0,0 +1,109 @@
+(*  Title:      HOL/Product_Type.thy
+    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.
+*)
+
+Product_Type = Fun + equalities +
+
+
+(** products **)
+
+(* type definition *)
+
+constdefs
+  Pair_Rep      :: ['a, 'b] => ['a, 'b] => bool
+  "Pair_Rep == (%a b. %x y. x=a & y=b)"
+
+global
+
+typedef (Prod)
+  ('a, 'b) "*"          (infixr 20)
+    = "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}"
+
+syntax (symbols)
+  "*"           :: [type, type] => type         ("(_ \\<times>/ _)" [21, 20] 20)
+
+syntax (HTML output)
+  "*"           :: [type, type] => type         ("(_ \\<times>/ _)" [21, 20] 20)
+
+
+(* 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"
+
+
+(* patterns -- extends pre-defined type "pttrn" used in abstractions *)
+
+nonterminals
+  tuple_args patterns
+
+syntax
+  "_tuple"      :: "'a => tuple_args => 'a * 'b"        ("(1'(_,/ _'))")
+  "_tuple_arg"  :: "'a => tuple_args"                   ("_")
+  "_tuple_args" :: "'a => tuple_args => tuple_args"     ("_,/ _")
+  "_pattern"    :: [pttrn, patterns] => pttrn           ("'(_,/ _')")
+  ""            :: pttrn => patterns                    ("_")
+  "_patterns"   :: [pttrn, patterns] => patterns        ("_,/ _")
+  "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3SIGMA _:_./ _)" 10)
+  "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    (infixr "<*>" 80)
+
+translations
+  "(x, y)"       == "Pair x y"
+  "_tuple x (_tuple_args y z)" == "_tuple x (_tuple_arg (_tuple y z))"
+  "%(x,y,zs).b"  == "split(%x (y,zs).b)"
+  "%(x,y).b"     == "split(%x y. b)"
+  "_abs (Pair x y) t" => "%(x,y).t"
+  (* The last rule accommodates tuples in `case C ... (x,y) ... => ...'
+     The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *)
+
+  "SIGMA x:A. B" => "Sigma A (%x. B)"
+  "A <*> B"      => "Sigma A (_K B)"
+
+syntax (symbols)
+  "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3\\<Sigma> _\\<in>_./ _)" 10)
+  "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    ("_ \\<times> _" [81, 80] 80)
+
+
+(* definitions *)
+
+local
+
+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 **)
+
+global
+
+typedef  unit = "{True}"
+
+consts
+  "()"          :: unit                           ("'(')")
+
+local
+
+defs
+  Unity_def     "() == Abs_unit True"
+
+end
+
+ML
+
+val print_translation = [("Sigma", dependent_tr' ("@Sigma", "@Times"))];