<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; charset=iso-8859-1"> <META content="MSHTML 6.00.6000.16587" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face="Courier New" size=2>For who likes it.</FONT></DIV> <DIV><FONT face="Courier New" size=2>A probably useless but funny applicative-order Y-combinator for arbitrary numbers of mutual dependent procedures of arbitrary arities:</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT face="Courier New" size=2>(lambda ms<BR> (apply values<BR>  ((lambda (c)<BR>    ((lambda (e) (map e ms))<BR>     (lambda (m) (apply (c m) (map c ms)))))<BR>   (lambda (m)<BR>    (lambda fs<BR>     (apply m<BR>      (map<BR>       (lambda (f)<BR>        (lambda xs (apply (apply f fs) xs)))<BR>       fs)))))))</FONT></DIV> <DIV><FONT face="Courier New" size=2></FONT> </DIV> <DIV><FONT><FONT face="Courier New" size=2> <DIV><FONT size=+0><FONT face="Courier New" size=2>It took me some labour to concoct this thing.</FONT></FONT></DIV> <DIV><FONT size=+0><FONT face="Courier New" size=2>A useless e</FONT></FONT>xample:</FONT></FONT></DIV></DIV> <DIV><FONT><FONT face="Courier New" size=2></FONT></FONT> </DIV> <DIV><FONT><FONT face="Courier New" size=2>(let-values<BR> (((triple? triple+1? triple+2?)<BR>   (y ; insert the above procedure<BR>    (lambda (triple? triple+1? triple+2?)<BR>     (lambda (x)<BR>      (or (zero? x) (triple+2? (sub1 x) 'ignored)))) ; multiple of 3 + 0<BR>    (lambda (triple? triple+1? triple+2?)<BR>     (lambda (x)<BR>      (and (not (zero? x)) (triple? (sub1 x))))) ; multiple of 3 + 1<BR>    (lambda (triple? triple+1? triple+2?)<BR>     (lambda (x ignored)<BR>      (and (not (zero? x)) (triple+1? (sub1 x))))))))<BR>  (triple? 100002)) ;--> #t</FONT></DIV> <DIV><FONT size=2><BR><FONT face="Courier New"></FONT></FONT></DIV></FONT> <DIV><FONT face="Courier New" size=2>Jos koot</FONT></DIV></BODY></HTML>