diff -r 196ca0973a6d -r ff1574a81019 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 + "" == ">" + "" == "Pair x y" + "" => "x" + +defs + Pair_def "Pair a b == Abs_Prod(Pair_Rep a b)" + fst_def "fst(p) == @a. ? b. p = " + snd_def "snd(p) == @b. ? a. p = " + split_def "split c p == c (fst p) (snd p)" + prod_fun_def "prod_fun f g == split(%x y.)" + Sigma_def "Sigma A B == UN x:A. UN y:B(x). {}" + + + +(** Unit **) + +subtype (Unit) + unit = "{p. p = True}" + +consts + Unity :: "unit" ("<>") + +defs + Unity_def "Unity == Abs_Unit(True)" + +end