src/HOL/Prod.thy
author wenzelm
Thu Mar 11 13:20:35 1999 +0100 (1999-03-11)
changeset 6349 f7750d816c21
parent 6340 7d5cbd5819a0
child 8703 816d8f6513be
permissions -rw-r--r--
removed foo_build_completed -- now handled by session management (via usedir);
     1 (*  Title:      HOL/Prod.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 Ordered Pairs and the Cartesian product type.
     7 The unit type.
     8 *)
     9 
    10 Prod = Fun + equalities +
    11 
    12 
    13 (** products **)
    14 
    15 (* type definition *)
    16 
    17 constdefs
    18   Pair_Rep      :: ['a, 'b] => ['a, 'b] => bool
    19   "Pair_Rep == (%a b. %x y. x=a & y=b)"
    20 
    21 global
    22 
    23 typedef (Prod)
    24   ('a, 'b) "*"          (infixr 20)
    25     = "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}"
    26 
    27 syntax (symbols)
    28   "*"           :: [type, type] => type         ("(_ \\<times>/ _)" [21, 20] 20)
    29 
    30 syntax (HTML output)
    31   "*"           :: [type, type] => type         ("(_ \\<times>/ _)" [21, 20] 20)
    32 
    33 
    34 (* abstract constants and syntax *)
    35 
    36 consts
    37   fst           :: "'a * 'b => 'a"
    38   snd           :: "'a * 'b => 'b"
    39   split         :: "[['a, 'b] => 'c, 'a * 'b] => 'c"
    40   prod_fun      :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd"
    41   Pair          :: "['a, 'b] => 'a * 'b"
    42   Sigma         :: "['a set, 'a => 'b set] => ('a * 'b) set"
    43 
    44 
    45 (* patterns -- extends pre-defined type "pttrn" used in abstractions *)
    46 
    47 nonterminals
    48   patterns
    49 
    50 syntax
    51   "@Tuple"      :: "['a, args] => 'a * 'b"       ("(1'(_,/ _'))")
    52 
    53   "_pattern"    :: [pttrn, patterns] => pttrn    ("'(_,/_')")
    54   ""            :: pttrn => patterns             ("_")
    55   "_patterns"   :: [pttrn, patterns] => patterns ("_,/_")
    56 
    57   "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3SIGMA _:_./ _)" 10)
    58   "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    ("_ Times _" [81, 80] 80)
    59 
    60 translations
    61   "(x, y, z)"    == "(x, (y, z))"
    62   "(x, y)"       == "Pair x y"
    63 
    64   "%(x,y,zs).b"  == "split(%x (y,zs).b)"
    65   "%(x,y).b"     == "split(%x y. b)"
    66   "_abs (Pair x y) t" => "%(x,y).t"
    67   (* The last rule accommodates tuples in `case C ... (x,y) ... => ...'
    68      The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *)
    69 
    70   "SIGMA x:A. B" => "Sigma A (%x. B)"
    71   "A Times B"    => "Sigma A (_K B)"
    72 
    73 syntax (symbols)
    74   "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3\\<Sigma> _\\<in>_./ _)" 10)
    75   "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    ("_ \\<times> _" [81, 80] 80)
    76 
    77 
    78 (* definitions *)
    79 
    80 local
    81 
    82 defs
    83   Pair_def      "Pair a b == Abs_Prod(Pair_Rep a b)"
    84   fst_def       "fst p == @a. ? b. p = (a, b)"
    85   snd_def       "snd p == @b. ? a. p = (a, b)"
    86   split_def     "split == (%c p. c (fst p) (snd p))"
    87   prod_fun_def  "prod_fun f g == split(%x y.(f(x), g(y)))"
    88   Sigma_def     "Sigma A B == UN x:A. UN y:B(x). {(x, y)}"
    89 
    90 
    91 
    92 (** unit **)
    93 
    94 global
    95 
    96 typedef  unit = "{True}"
    97 
    98 consts
    99   "()"          :: unit                           ("'(')")
   100 
   101 local
   102 
   103 defs
   104   Unity_def     "() == Abs_unit True"
   105 
   106 end
   107 
   108 ML
   109 
   110 val print_translation = [("Sigma", dependent_tr' ("@Sigma", "@Times"))];