src/HOL/Product_Type.thy
author wenzelm
Mon Oct 23 11:14:00 2000 +0200 (2000-10-23)
changeset 10289 475ea668c67d
parent 10213 01c2744a3786
child 11025 a70b796d9af8
permissions -rw-r--r--
tuned deps;
     1 (*  Title:      HOL/Product_Type.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 Product_Type = Fun +
    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   tuple_args patterns
    49 
    50 syntax
    51   "_tuple"      :: "'a => tuple_args => 'a * 'b"        ("(1'(_,/ _'))")
    52   "_tuple_arg"  :: "'a => tuple_args"                   ("_")
    53   "_tuple_args" :: "'a => tuple_args => tuple_args"     ("_,/ _")
    54   "_pattern"    :: [pttrn, patterns] => pttrn           ("'(_,/ _')")
    55   ""            :: pttrn => patterns                    ("_")
    56   "_patterns"   :: [pttrn, patterns] => patterns        ("_,/ _")
    57   "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3SIGMA _:_./ _)" 10)
    58   "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    (infixr "<*>" 80)
    59 
    60 translations
    61   "(x, y)"       == "Pair x y"
    62   "_tuple x (_tuple_args y z)" == "_tuple x (_tuple_arg (_tuple y z))"
    63   "%(x,y,zs).b"  == "split(%x (y,zs).b)"
    64   "%(x,y).b"     == "split(%x y. b)"
    65   "_abs (Pair x y) t" => "%(x,y).t"
    66   (* The last rule accommodates tuples in `case C ... (x,y) ... => ...'
    67      The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *)
    68 
    69   "SIGMA x:A. B" => "Sigma A (%x. B)"
    70   "A <*> B"      => "Sigma A (_K B)"
    71 
    72 syntax (symbols)
    73   "@Sigma"      :: "[pttrn, 'a set, 'b set] => ('a * 'b) set"   ("(3\\<Sigma> _\\<in>_./ _)" 10)
    74   "@Times"      :: "['a set, 'a => 'b set] => ('a * 'b) set"    ("_ \\<times> _" [81, 80] 80)
    75 
    76 
    77 (* definitions *)
    78 
    79 local
    80 
    81 defs
    82   Pair_def      "Pair a b == Abs_Prod(Pair_Rep a b)"
    83   fst_def       "fst p == @a. ? b. p = (a, b)"
    84   snd_def       "snd p == @b. ? a. p = (a, b)"
    85   split_def     "split == (%c p. c (fst p) (snd p))"
    86   prod_fun_def  "prod_fun f g == split(%x y.(f(x), g(y)))"
    87   Sigma_def     "Sigma A B == UN x:A. UN y:B(x). {(x, y)}"
    88 
    89 
    90 
    91 (** unit **)
    92 
    93 global
    94 
    95 typedef  unit = "{True}"
    96 
    97 consts
    98   "()"          :: unit                           ("'(')")
    99 
   100 local
   101 
   102 defs
   103   Unity_def     "() == Abs_unit True"
   104 
   105 end
   106 
   107 ML
   108 
   109 val print_translation = [("Sigma", dependent_tr' ("@Sigma", "@Times"))];