src/HOL/Sum.thy
author paulson
Thu Dec 28 11:54:15 1995 +0100 (1995-12-28)
changeset 1423 5726a8243d3f
parent 1370 7361ac9b024d
child 1475 7f5a4cd08209
permissions -rw-r--r--
fixed indentation
     1 (*  Title:      HOL/Sum.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1992  University of Cambridge
     5 
     6 The disjoint sum of two types.
     7 *)
     8 
     9 Sum = Prod +
    10 
    11 (* type definition *)
    12 
    13 consts
    14   Inl_Rep       :: ['a, 'a, 'b, bool] => bool
    15   Inr_Rep       :: ['b, 'a, 'b, bool] => bool
    16 
    17 defs
    18   Inl_Rep_def   "Inl_Rep == (%a. %x y p. x=a & p)"
    19   Inr_Rep_def   "Inr_Rep == (%b. %x y p. y=b & ~p)"
    20 
    21 subtype (Sum)
    22   ('a, 'b) "+"          (infixr 10)
    23     = "{f. (? a. f = Inl_Rep(a::'a)) | (? b. f = Inr_Rep(b::'b))}"
    24 
    25 
    26 (* abstract constants and syntax *)
    27 
    28 consts
    29   Inl           :: "'a => 'a + 'b"
    30   Inr           :: "'b => 'a + 'b"
    31   sum_case      :: "['a => 'c, 'b => 'c, 'a + 'b] => 'c"
    32 
    33   (*disjoint sum for sets; the operator + is overloaded with wrong type!*)
    34   "plus"        :: "['a set, 'b set] => ('a + 'b) set"        (infixr 65)
    35   Part          :: ['a set, 'b => 'a] => 'a set
    36 
    37 translations
    38   "case p of Inl(x) => a | Inr(y) => b" == "sum_case (%x.a) (%y.b) p"
    39 
    40 defs
    41   Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
    42   Inr_def       "Inr == (%b. Abs_Sum(Inr_Rep(b)))"
    43   sum_case_def  "sum_case f g p == @z.  (!x. p=Inl(x) --> z=f(x))      
    44                                       & (!y. p=Inr(y) --> z=g(y))"
    45 
    46   sum_def       "A plus B == (Inl``A) Un (Inr``B)"
    47 
    48   (*for selecting out the components of a mutually recursive definition*)
    49   Part_def      "Part A h == A Int {x. ? z. x = h(z)}"
    50 
    51 end