src/HOL/Sum_Type.thy
 author wenzelm Thu Sep 27 22:28:16 2001 +0200 (2001-09-27) changeset 11609 3f3d1add4d94 parent 10832 e33b47e4246d child 15391 797ed46d724b permissions -rw-r--r--
eliminated theories "equalities" and "mono" (made part of "Typedef",
which supercedes "subset");
1 (*  Title:      HOL/Sum_Type.thy
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1992  University of Cambridge
6 The disjoint sum of two types.
7 *)
9 Sum_Type = Product_Type +
11 (* type definition *)
13 constdefs
14   Inl_Rep       :: ['a, 'a, 'b, bool] => bool
15   "Inl_Rep == (%a. %x y p. x=a & p)"
17   Inr_Rep       :: ['b, 'a, 'b, bool] => bool
18   "Inr_Rep == (%b. %x y p. y=b & ~p)"
20 global
22 typedef (Sum)
23   ('a, 'b) "+"          (infixr 10)
24     = "{f. (? a. f = Inl_Rep(a::'a)) | (? b. f = Inr_Rep(b::'b))}"
27 (* abstract constants and syntax *)
29 consts
30   Inl            :: "'a => 'a + 'b"
31   Inr            :: "'b => 'a + 'b"
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
37 local
39 defs
40   Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
41   Inr_def       "Inr == (%b. Abs_Sum(Inr_Rep(b)))"
43   sum_def       "A <+> B == (Inl`A) Un (Inr`B)"
45   (*for selecting out the components of a mutually recursive definition*)
46   Part_def      "Part A h == A Int {x. ? z. x = h(z)}"
48 end