src/ZF/QPair.thy
author clasohm
Tue, 06 Feb 1996 12:27:17 +0100
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(*  Title:      ZF/qpair.thy
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Quine-inspired ordered pairs and disjoint sums, for non-well-founded data
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structures in ZF.  Does not precisely follow Quine's construction.  Thanks
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to Thomas Forster for suggesting this approach!
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W. V. Quine, On Ordered Pairs and Relations, in Selected Logic Papers,
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1966.
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*)
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QPair = Sum + "simpdata" +
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consts
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  QPair     :: [i, i] => i                      ("<(_;/ _)>")
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  qfst,qsnd :: i => i
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  qsplit    :: [[i, i] => 'a, i] => 'a::logic  (*for pattern-matching*)
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  qconverse :: i => i
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  QSigma    :: [i, i => i] => i
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  "<+>"     :: [i,i]=>i                         (infixr 65)
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  QInl,QInr :: i=>i
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  qcase     :: [i=>i, i=>i, i]=>i
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syntax
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  "@QSUM"   :: [idt, i, i] => i               ("(3QSUM _:_./ _)" 10)
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  "<*>"     :: [i, i] => i                      (infixr 80)
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translations
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  "QSUM x:A. B"  => "QSigma(A, %x. B)"
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  "A <*> B"      => "QSigma(A, _K(B))"
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defs
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  QPair_def       "<a;b> == a+b"
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  qfst_def        "qfst(p) == THE a. EX b. p=<a;b>"
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  qsnd_def        "qsnd(p) == THE b. EX a. p=<a;b>"
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  qsplit_def      "qsplit(c,p) == c(qfst(p), qsnd(p))"
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  qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
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  QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"
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  qsum_def        "A <+> B      == ({0} <*> A) Un ({1} <*> B)"
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  QInl_def        "QInl(a)      == <0;a>"
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  QInr_def        "QInr(b)      == <1;b>"
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  qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
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end
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ML
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val print_translation =
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  [("QSigma", dependent_tr' ("@QSUM", "op <*>"))];