src/ZF/Sum.thy

New unified treatment of sequent calculi by Sara Kalvala
combines the old LK and Modal with the new ILL (Int. Linear Logic)

(*  Title:      ZF/sum.thy
    ID:         $Id$
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge

Disjoint sums in Zermelo-Fraenkel Set Theory 
"Part" primitive for simultaneous recursive type definitions
*)

Sum = Bool + "simpdata" +
consts
    "+"         :: [i,i]=>i                     (infixr 65)
    Inl,Inr     :: i=>i
    case        :: [i=>i, i=>i, i]=>i
    Part        :: [i,i=>i] => i

defs
    sum_def     "A+B == {0}*A Un {1}*B"
    Inl_def     "Inl(a) == <0,a>"
    Inr_def     "Inr(b) == <1,b>"
    case_def    "case(c,d) == (%<y,z>. cond(y, d(z), c(z)))"

  (*operator for selecting out the various summands*)
    Part_def    "Part(A,h) == {x: A. EX z. x = h(z)}"
end