author  paulson 
Fri, 16 Feb 1996 18:00:47 +0100  
changeset 1512  ce37c64244c0 
parent 1478  2b8c2a7547ab 
child 2469  b50b8c0eec01 
permissions  rwrr 
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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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Quineinspired ordered pairs and disjoint sums, for nonwellfounded 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 patternmatching*) 

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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 <*>"))]; 