src/ZF/QPair.thy
author wenzelm
Tue Jan 12 15:17:37 1999 +0100 (1999-01-12 ago)
changeset 6093 87bf8c03b169
parent 3940 1d5bee4d047f
child 13220 62c899c77151
permissions -rw-r--r--
eliminated global/local names;
     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 +
    15 
    16 consts
    17   QPair     :: [i, i] => i                      ("<(_;/ _)>")
    18   qfst,qsnd :: i => i
    19   qsplit    :: [[i, i] => 'a, i] => 'a::logic  (*for pattern-matching*)
    20   qconverse :: i => i
    21   QSigma    :: [i, i => i] => i
    22 
    23   "<+>"     :: [i,i]=>i                         (infixr 65)
    24   QInl,QInr :: i=>i
    25   qcase     :: [i=>i, i=>i, i]=>i
    26 
    27 syntax
    28   "@QSUM"   :: [idt, i, i] => i               ("(3QSUM _:_./ _)" 10)
    29   "<*>"     :: [i, i] => i                      (infixr 80)
    30 
    31 translations
    32   "QSUM x:A. B"  => "QSigma(A, %x. B)"
    33   "A <*> B"      => "QSigma(A, _K(B))"
    34 
    35 
    36 defs
    37   QPair_def       "<a;b> == a+b"
    38   qfst_def        "qfst(p) == THE a. EX b. p=<a;b>"
    39   qsnd_def        "qsnd(p) == THE b. EX a. p=<a;b>"
    40   qsplit_def      "qsplit(c,p) == c(qfst(p), qsnd(p))"
    41 
    42   qconverse_def   "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}"
    43   QSigma_def      "QSigma(A,B)  ==  UN x:A. UN y:B(x). {<x;y>}"
    44 
    45   qsum_def        "A <+> B      == ({0} <*> A) Un ({1} <*> B)"
    46   QInl_def        "QInl(a)      == <0;a>"
    47   QInr_def        "QInr(b)      == <1;b>"
    48   qcase_def       "qcase(c,d)   == qsplit(%y z. cond(y, d(z), c(z)))"
    49 end
    50 
    51 ML
    52 
    53 val print_translation =
    54   [("QSigma", dependent_tr' ("@QSUM", "op <*>"))];