--- a/src/HOL/Prod.thy Thu Oct 12 18:38:23 2000 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,109 +0,0 @@
-(* Title: HOL/Prod.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.
-*)
-
-Prod = 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"))];