author  lcp 
Tue, 07 Mar 1995 13:18:48 +0100  
changeset 929  137035296ad6 
parent 753  ec86863e87c8 
child 1097  01379c46ad2d 
permissions  rwrr 
0  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 
Quineinspired ordered pairs and disjoint sums, for nonwellfounded 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 

124  14 
QPair = Sum + "simpdata" + 
0  15 
consts 
16 
QPair :: "[i, i] => i" ("<(_;/ _)>") 

17 
qsplit :: "[[i,i] => i, i] => i" 

18 
qfsplit :: "[[i,i] => o, i] => o" 

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 

929
137035296ad6
Moved declarations of @QSUM and <*> to a syntax section.
lcp
parents:
753
diff
changeset

26 
syntax 
137035296ad6
Moved declarations of @QSUM and <*> to a syntax section.
lcp
parents:
753
diff
changeset

27 
"@QSUM" :: "[idt, i, i] => i" ("(3QSUM _:_./ _)" 10) 
137035296ad6
Moved declarations of @QSUM and <*> to a syntax section.
lcp
parents:
753
diff
changeset

28 
"<*>" :: "[i, i] => i" (infixr 80) 
137035296ad6
Moved declarations of @QSUM and <*> to a syntax section.
lcp
parents:
753
diff
changeset

29 

0  30 
translations 
31 
"QSUM x:A. B" => "QSigma(A, %x. B)" 

44  32 
"A <*> B" => "QSigma(A, _K(B))" 
0  33 

753  34 
defs 
0  35 
QPair_def "<a;b> == a+b" 
120  36 
qsplit_def "qsplit(c,p) == THE y. EX a b. p=<a;b> & y=c(a,b)" 
0  37 
qfsplit_def "qfsplit(R,z) == EX x y. z=<x;y> & R(x,y)" 
38 
qconverse_def "qconverse(r) == {z. w:r, EX x y. w=<x;y> & z=<y;x>}" 

39 
QSigma_def "QSigma(A,B) == UN x:A. UN y:B(x). {<x;y>}" 

40 

120  41 
qsum_def "A <+> B == ({0} <*> A) Un ({1} <*> B)" 
0  42 
QInl_def "QInl(a) == <0;a>" 
43 
QInr_def "QInr(b) == <1;b>" 

44 
qcase_def "qcase(c,d) == qsplit(%y z. cond(y, d(z), c(z)))" 

45 
end 

46 

47 
ML 

48 

49 
val print_translation = 

929
137035296ad6
Moved declarations of @QSUM and <*> to a syntax section.
lcp
parents:
753
diff
changeset

50 
[("QSigma", dependent_tr' ("@QSUM", "op <*>"))]; 