src/ZF/qpair.thy
 author wenzelm Fri, 08 Oct 1993 14:16:29 +0100 changeset 44 00597b21a6a9 parent 0 a5a9c433f639 child 120 09287f26bfb8 permissions -rw-r--r--
added parse rule for "<*>"; removed ndependent_tr;
```
(*  Title: 	ZF/qpair.thy
ID:         \$Id\$
Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory

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 +
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      == QSigma({0}, %x.A) Un QSigma({1}, %x.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", " <*>"))];
```