src/ZF/QPair.thy
author lcp
Tue, 25 Apr 1995 11:14:03 +0200
changeset 1072 0140ff702b23
parent 929 137035296ad6
child 1097 01379c46ad2d
permissions -rw-r--r--
updated version

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

Quine-inspired ordered pairs and disjoint sums, for non-well-founded data
structures in ZF.  Does not precisely follow Quine's construction.  Thanks
to Thomas Forster for suggesting this approach!

W. V. Quine, On Ordered Pairs and Relations, in Selected Logic Papers,
1966.
*)

QPair = Sum + "simpdata" +
consts
  QPair     :: "[i, i] => i"               	("<(_;/ _)>")
  qsplit    :: "[[i,i] => i, i] => i"
  qfsplit   :: "[[i,i] => o, i] => o"
  qconverse :: "i => i"
  QSigma    :: "[i, i => i] => i"

  "<+>"     :: "[i,i]=>i"      			(infixr 65)
  QInl,QInr :: "i=>i"
  qcase     :: "[i=>i, i=>i, i]=>i"

syntax
  "@QSUM"   :: "[idt, i, i] => i"               ("(3QSUM _:_./ _)" 10)
  "<*>"     :: "[i, i] => i"         		(infixr 80)

translations
  "QSUM x:A. B"  => "QSigma(A, %x. B)"
  "A <*> B"      => "QSigma(A, _K(B))"

defs
  QPair_def       "<a;b> == a+b"
  qsplit_def      "qsplit(c,p)  == THE y. EX a b. p=<a;b> & y=c(a,b)"
  qfsplit_def     "qfsplit(R,z) == EX x y. z=<x;y> & R(x,y)"
  qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
  QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"

  qsum_def        "A <+> B      == ({0} <*> A) Un ({1} <*> B)"
  QInl_def        "QInl(a)      == <0;a>"
  QInr_def        "QInr(b)      == <1;b>"
  qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
end

ML

val print_translation =
  [("QSigma", dependent_tr' ("@QSUM", "op <*>"))];