src/ZF/QPair.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 2469 b50b8c0eec01
permissions -rw-r--r--
expanded tabs
     1 (*  Title:      ZF/qpair.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1993  University of Cambridge
     5 
     6 Quine-inspired ordered pairs and disjoint sums, for non-well-founded data
     7 structures in ZF.  Does not precisely follow Quine's construction.  Thanks
     8 to Thomas Forster for suggesting this approach!
     9 
    10 W. V. Quine, On Ordered Pairs and Relations, in Selected Logic Papers,
    11 1966.
    12 *)
    13 
    14 QPair = Sum + "simpdata" +
    15 consts
    16   QPair     :: [i, i] => i                      ("<(_;/ _)>")
    17   qfst,qsnd :: i => i
    18   qsplit    :: [[i, i] => 'a, i] => 'a::logic  (*for pattern-matching*)
    19   qconverse :: i => i
    20   QSigma    :: [i, i => i] => i
    21 
    22   "<+>"     :: [i,i]=>i                         (infixr 65)
    23   QInl,QInr :: i=>i
    24   qcase     :: [i=>i, i=>i, i]=>i
    25 
    26 syntax
    27   "@QSUM"   :: [idt, i, i] => i               ("(3QSUM _:_./ _)" 10)
    28   "<*>"     :: [i, i] => i                      (infixr 80)
    29 
    30 translations
    31   "QSUM x:A. B"  => "QSigma(A, %x. B)"
    32   "A <*> B"      => "QSigma(A, _K(B))"
    33 
    34 defs
    35   QPair_def       "<a;b> == a+b"
    36   qfst_def        "qfst(p) == THE a. EX b. p=<a;b>"
    37   qsnd_def        "qsnd(p) == THE b. EX a. p=<a;b>"
    38   qsplit_def      "qsplit(c,p) == c(qfst(p), qsnd(p))"
    39 
    40   qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
    41   QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"
    42 
    43   qsum_def        "A <+> B      == ({0} <*> A) Un ({1} <*> B)"
    44   QInl_def        "QInl(a)      == <0;a>"
    45   QInr_def        "QInr(b)      == <1;b>"
    46   qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
    47 end
    48 
    49 ML
    50 
    51 val print_translation =
    52   [("QSigma", dependent_tr' ("@QSUM", "op <*>"))];