src/HOL/Prod.thy
author clasohm
Fri Mar 08 13:11:09 1996 +0100 (1996-03-08)
changeset 1558 9c6ebfab4e05
parent 1475 7f5a4cd08209
child 1636 e18416e3e1d4
permissions -rw-r--r--
added constdefs section
     1 (*  Title:      HOL/Prod.thy
     2     ID:         Prod.thy,v 1.5 1994/08/19 09:04:27 lcp Exp
     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 +
    11 
    12 (** Products **)
    13 
    14 (* type definition *)
    15 
    16 constdefs
    17   Pair_Rep      :: ['a, 'b] => ['a, 'b] => bool
    18   "Pair_Rep == (%a b. %x y. x=a & y=b)"
    19 
    20 typedef (Prod)
    21   ('a, 'b) "*"          (infixr 20)
    22     = "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}"
    23 
    24 
    25 (* abstract constants and syntax *)
    26 
    27 consts
    28   fst           :: "'a * 'b => 'a"
    29   snd           :: "'a * 'b => 'b"
    30   split         :: "[['a, 'b] => 'c, 'a * 'b] => 'c"
    31   prod_fun      :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd"
    32   Pair          :: "['a, 'b] => 'a * 'b"
    33   Sigma         :: "['a set, 'a => 'b set] => ('a * 'b) set"
    34 
    35 (** Patterns -- extends pre-defined type "pttrn" used in abstractions **)
    36 types pttrns
    37 
    38 syntax
    39   "@Tuple"      :: "['a, args] => 'a * 'b"            ("(1'(_,/ _'))")
    40 
    41   "@pttrn"  :: [pttrn,pttrns] => pttrn              ("'(_,/_')")
    42   ""        ::  pttrn         => pttrns             ("_")
    43   "@pttrns" :: [pttrn,pttrns] => pttrns             ("_,/_")
    44 
    45 translations
    46   "(x, y, z)"   == "(x, (y, z))"
    47   "(x, y)"      == "Pair x y"
    48 
    49   "%(x,y,zs).b"   == "split(%x (y,zs).b)"
    50   "%(x,y).b"      == "split(%x y.b)"
    51 
    52 defs
    53   Pair_def      "Pair a b == Abs_Prod(Pair_Rep a b)"
    54   fst_def       "fst(p) == @a. ? b. p = (a, b)"
    55   snd_def       "snd(p) == @b. ? a. p = (a, b)"
    56   split_def     "split c p == c (fst p) (snd p)"
    57   prod_fun_def  "prod_fun f g == split(%x y.(f(x), g(y)))"
    58   Sigma_def     "Sigma A B == UN x:A. UN y:B(x). {(x, y)}"
    59 
    60 (** Unit **)
    61 
    62 typedef (Unit)
    63   unit = "{p. p = True}"
    64 
    65 consts
    66   "()"          :: unit                           ("'(')")
    67 
    68 defs
    69   Unity_def     "() == Abs_Unit(True)"
    70 
    71 (* start 8bit 1 *)
    72 (* end 8bit 1 *)
    73 
    74 end