author  berghofe 
Tue, 30 May 2000 18:02:49 +0200  
changeset 9001  93af64f54bf2 
parent 8703  816d8f6513be 
child 9341  40bab6613000 
permissions  rwrr 
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(* Title: HOL/Prod.thy 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
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Copyright 1992 University of Cambridge 

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Ordered Pairs and the Cartesian product type. 

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The unit type. 

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*) 

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Prod = Fun + equalities + 
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(** products **) 

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(* type definition *) 

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constdefs 
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Pair_Rep :: ['a, 'b] => ['a, 'b] => bool 
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"Pair_Rep == (%a b. %x y. x=a & y=b)" 
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global 
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typedef (Prod) 
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('a, 'b) "*" (infixr 20) 
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= "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}" 

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syntax (symbols) 
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"*" :: [type, type] => type ("(_ \\<times>/ _)" [21, 20] 20) 

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syntax (HTML output) 
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"*" :: [type, type] => type ("(_ \\<times>/ _)" [21, 20] 20) 

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(* abstract constants and syntax *) 

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consts 

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fst :: "'a * 'b => 'a" 

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snd :: "'a * 'b => 'b" 

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split :: "[['a, 'b] => 'c, 'a * 'b] => 'c" 

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prod_fun :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd" 

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Pair :: "['a, 'b] => 'a * 'b" 

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Sigma :: "['a set, 'a => 'b set] => ('a * 'b) set" 

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(* patterns  extends predefined type "pttrn" used in abstractions *) 

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nonterminals 
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patterns 

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syntax 
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"@Tuple" :: "['a, args] => 'a * 'b" ("(1'(_,/ _'))") 
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"_pattern" :: [pttrn, patterns] => pttrn ("'(_,/_')") 
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"" :: pttrn => patterns ("_") 

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"_patterns" :: [pttrn, patterns] => patterns ("_,/_") 

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"@Sigma" :: "[pttrn, 'a set, 'b set] => ('a * 'b) set" ("(3SIGMA _:_./ _)" 10) 
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"@Times" :: "['a set, 'a => 'b set] => ('a * 'b) set" (infixr "<*>" 80) 
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translations 
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"(x, y, z)" == "(x, (y, z))" 
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"(x, y)" == "Pair x y" 

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"%(x,y,zs).b" == "split(%x (y,zs).b)" 
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"%(x,y).b" == "split(%x y. b)" 

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"_abs (Pair x y) t" => "%(x,y).t" 
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(* The last rule accommodates tuples in `case C ... (x,y) ... => ...' 
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The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *) 
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"SIGMA x:A. B" => "Sigma A (%x. B)" 
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"A <*> B" => "Sigma A (_K B)" 
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syntax (symbols) 
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"@Sigma" :: "[pttrn, 'a set, 'b set] => ('a * 'b) set" ("(3\\<Sigma> _\\<in>_./ _)" 10) 
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"@Times" :: "['a set, 'a => 'b set] => ('a * 'b) set" ("_ \\<times> _" [81, 80] 80) 
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(* definitions *) 

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local 
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defs 
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Pair_def "Pair a b == Abs_Prod(Pair_Rep a b)" 

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fst_def "fst p == @a. ? b. p = (a, b)" 
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snd_def "snd p == @b. ? a. p = (a, b)" 

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split_def "split == (%c p. c (fst p) (snd p))" 
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prod_fun_def "prod_fun f g == split(%x y.(f(x), g(y)))" 
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Sigma_def "Sigma A B == UN x:A. UN y:B(x). {(x, y)}" 
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(** unit **) 

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global 
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typedef unit = "{True}" 
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consts 

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"()" :: unit ("'(')") 
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local 
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defs 
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Unity_def "() == Abs_unit True" 
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end 
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ML 

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val print_translation = [("Sigma", dependent_tr' ("@Sigma", "@Times"))]; 