src/ZF/QPair.thy
 author paulson Fri, 16 Feb 1996 18:00:47 +0100 changeset 1512 ce37c64244c0 parent 1478 2b8c2a7547ab child 2469 b50b8c0eec01 permissions -rw-r--r--
Elimination of fully-functorial style. Type tactic changed to a type abbrevation (from a datatype). Constructor tactic and function apply deleted.
```
(*  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 + "simpdata" +
consts
QPair     :: [i, i] => i                      ("<(_;/ _)>")
qfst,qsnd :: i => i
qsplit    :: [[i, i] => 'a, i] => 'a::logic  (*for pattern-matching*)
qconverse :: i => i
QSigma    :: [i, i => i] => i

"<+>"     :: [i,i]=>i                         (infixr 65)
QInl,QInr :: i=>i
qcase     :: [i=>i, i=>i, i]=>i

syntax
"@QSUM"   :: [idt, i, i] => i               ("(3QSUM _:_./ _)" 10)
"<*>"     :: [i, i] => i                      (infixr 80)

translations
"QSUM x:A. B"  => "QSigma(A, %x. B)"
"A <*> B"      => "QSigma(A, _K(B))"

defs
QPair_def       "<a;b> == a+b"
qfst_def        "qfst(p) == THE a. EX b. p=<a;b>"
qsnd_def        "qsnd(p) == THE b. EX a. p=<a;b>"
qsplit_def      "qsplit(c,p) == c(qfst(p), qsnd(p))"

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      == ({0} <*> A) Un ({1} <*> 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", "op <*>"))];
```