src/HOL/Prod.thy
author clasohm
Wed Nov 29 16:44:59 1995 +0100 (1995-11-29)
changeset 1370 7361ac9b024d
parent 1273 6960ec882bca
child 1454 d0266c81a85e
permissions -rw-r--r--
removed quotes from types in consts and syntax sections
     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 consts
    17   Pair_Rep      :: ['a, 'b] => ['a, 'b] => bool
    18 
    19 defs
    20   Pair_Rep_def  "Pair_Rep == (%a b. %x y. x=a & y=b)"
    21 
    22 subtype (Prod)
    23   ('a, 'b) "*"          (infixr 20)
    24     = "{f. ? a b. f = Pair_Rep (a::'a) (b::'b)}"
    25 
    26 
    27 (* abstract constants and syntax *)
    28 
    29 consts
    30   fst           :: "'a * 'b => 'a"
    31   snd           :: "'a * 'b => 'b"
    32   split         :: "[['a, 'b] => 'c, 'a * 'b] => 'c"
    33   prod_fun      :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd"
    34   Pair          :: "['a, 'b] => 'a * 'b"
    35   Sigma         :: "['a set, 'a => 'b set] => ('a * 'b) set"
    36 
    37 (** Patterns -- extends pre-defined type "pttrn" used in abstractions **)
    38 types pttrns
    39 
    40 syntax
    41   "@Tuple"      :: "['a, args] => 'a * 'b"            ("(1'(_,/ _'))")
    42 
    43   "@pttrn"  :: [pttrn,pttrns] => pttrn              ("'(_,/_')")
    44   ""        ::  pttrn         => pttrns             ("_")
    45   "@pttrns" :: [pttrn,pttrns] => pttrns             ("_,/_")
    46 
    47 translations
    48   "(x, y, z)"   == "(x, (y, z))"
    49   "(x, y)"      == "Pair x y"
    50 
    51   "%(x,y,zs).b"   == "split(%x (y,zs).b)"
    52   "%(x,y).b"      == "split(%x y.b)"
    53 (* The <= direction fails if split has more than one argument because
    54    ast-matching fails. Otherwise it would work fine *)
    55 
    56 defs
    57   Pair_def      "Pair a b == Abs_Prod(Pair_Rep a b)"
    58   fst_def       "fst(p) == @a. ? b. p = (a, b)"
    59   snd_def       "snd(p) == @b. ? a. p = (a, b)"
    60   split_def     "split c p == c (fst p) (snd p)"
    61   prod_fun_def  "prod_fun f g == split(%x y.(f(x), g(y)))"
    62   Sigma_def     "Sigma A B == UN x:A. UN y:B(x). {(x, y)}"
    63 
    64 
    65 
    66 (** Unit **)
    67 
    68 subtype (Unit)
    69   unit = "{p. p = True}"
    70 
    71 consts
    72   "()"          :: unit                           ("'(')")
    73 
    74 defs
    75   Unity_def     "() == Abs_Unit(True)"
    76 
    77 (* start 8bit 1 *)
    78 (* end 8bit 1 *)
    79 
    80 end
    81 (*
    82 ML
    83 
    84 local open Syntax
    85 
    86 fun pttrn(_ $ s $ t) = const"@pttrn" $ s $ t;
    87 fun pttrns s t = const"@pttrns" $ s $ t;
    88 
    89 fun split2(Abs(x,T,t)) =
    90       let val (pats,u) = split1 t
    91       in (pttrns (Free(x,T)) pats, subst_bounds([free x],u)) end
    92   | split2(Const("split",_) $ r) =
    93       let val (pats,s) = split2(r)
    94           val (pats2,t) = split1(s)
    95       in (pttrns (pttrn pats) pats2, t) end
    96 and split1(Abs(x,T,t)) =  (Free(x,T), subst_bounds([free x],t))
    97   | split1(Const("split",_)$t) = split2(t);
    98 
    99 fun split_tr'(t::args) =
   100   let val (pats,ft) = split2(t)
   101   in list_comb(const"_lambda" $ pttrn pats $ ft, args) end;
   102 
   103 in
   104 
   105 val print_translation = [("split", split_tr')];
   106 
   107 end;
   108 *)