src/HOL/Sum_Type.thy
author nipkow
Thu Oct 12 18:44:35 2000 +0200 (2000-10-12)
changeset 10213 01c2744a3786
child 10832 e33b47e4246d
permissions -rw-r--r--
*** empty log message ***
     1 (*  Title:      HOL/Sum_Type.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_Type = mono + Product_Type +
    10 
    11 (* type definition *)
    12 
    13 constdefs
    14   Inl_Rep       :: ['a, 'a, 'b, bool] => bool
    15   "Inl_Rep == (%a. %x y p. x=a & p)"
    16 
    17   Inr_Rep       :: ['b, 'a, 'b, bool] => bool
    18   "Inr_Rep == (%b. %x y p. y=b & ~p)"
    19 
    20 global
    21 
    22 typedef (Sum)
    23   ('a, 'b) "+"          (infixr 10)
    24     = "{f. (? a. f = Inl_Rep(a::'a)) | (? b. f = Inr_Rep(b::'b))}"
    25 
    26 
    27 (* abstract constants and syntax *)
    28 
    29 consts
    30   Inl            :: "'a => 'a + 'b"
    31   Inr            :: "'b => 'a + 'b"
    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 local
    38 
    39 defs
    40   Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
    41   Inr_def       "Inr == (%b. Abs_Sum(Inr_Rep(b)))"
    42 
    43   sum_def       "A <+> B == (Inl``A) Un (Inr``B)"
    44 
    45   (*for selecting out the components of a mutually recursive definition*)
    46   Part_def      "Part A h == A Int {x. ? z. x = h(z)}"
    47 
    48 end