src/ZF/qpair.thy
author clasohm
Tue, 24 Oct 1995 13:53:09 +0100
changeset 1291 e173be970d27
parent 124 858ab9a9b047
permissions -rw-r--r--
added generation of HTML files to thy_read.ML; removed old HTML package

(*  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"
  "@QSUM"   :: "[idt, i, i] => i"               ("(3QSUM _:_./ _)" 10)
  " <*>"    :: "[i, i] => i"         		("(_ <*>/ _)" [81, 80] 80)
  QSigma    :: "[i, i => i] => i"

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

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

rules
  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", " <*>"))];