src/HOL/Sum.thy
 author berghofe Tue, 30 May 2000 18:02:49 +0200 changeset 9001 93af64f54bf2 parent 7293 959e060f4a2f child 9311 ab5b24cbaa16 permissions -rw-r--r--
the is now defined using primrec, avoiding explicit use of arbitrary.
```
(*  Title:      HOL/Sum.thy
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

The disjoint sum of two types.
*)

Sum = mono + Prod +

(* type definition *)

constdefs
Inl_Rep       :: ['a, 'a, 'b, bool] => bool
"Inl_Rep == (%a. %x y p. x=a & p)"

Inr_Rep       :: ['b, 'a, 'b, bool] => bool
"Inr_Rep == (%b. %x y p. y=b & ~p)"

global

typedef (Sum)
('a, 'b) "+"          (infixr 10)
= "{f. (? a. f = Inl_Rep(a::'a)) | (? b. f = Inr_Rep(b::'b))}"

(* abstract constants and syntax *)

consts
Inl            :: "'a => 'a + 'b"
Inr            :: "'b => 'a + 'b"

(*disjoint sum for sets; the operator + is overloaded with wrong type!*)
Plus          :: "['a set, 'b set] => ('a + 'b) set"        (infixr 65)
Part          :: ['a set, 'b => 'a] => 'a set

local

defs
Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
Inr_def       "Inr == (%b. Abs_Sum(Inr_Rep(b)))"

sum_def       "A Plus B == (Inl``A) Un (Inr``B)"

(*for selecting out the components of a mutually recursive definition*)
Part_def      "Part A h == A Int {x. ? z. x = h(z)}"

end
```