If (implies a b ... z) is equivalent to (implies a (implies b ... z)), then it is also equivalent to (implies (and a b ...) z). In which case, the 1-ary case should be clear: just return z. In truth, it is not really necessary to have n-ary implies if you're willing to nest the (and ...) explicitly. Given that Scheme/Racket n-ary operators tend to have the "..." last, with occasional exceptions like list* and apply, restricting implies to 2 arguments might avoid cases where (implies a b c d e) is confusing to read. (implies (and a b c d) e) is clearer. Carl Eastlund <div class="gmail_quote">On Sun, Feb 19, 2012 at 8:16 PM, Robby Findler <<a href="mailto:robby@eecs.northwestern.edu">robby@eecs.northwestern.edu</a>> wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"> <div class="HOEnZb"><div class="h5">On Sun, Feb 19, 2012 at 7:10 PM, Neil Toronto <<a href="mailto:neil.toronto@gmail.com">neil.toronto@gmail.com</a>> wrote: > On 02/19/2012 06:05 AM, Robby Findler wrote: >> >> On Sun, Feb 19, 2012 at 12:30 AM, Gary Baumgartner<<a href="mailto:gfb@cs.toronto.edu">gfb@cs.toronto.edu</a>> >> wrote: >>> >>> On a more productive note: in Racket code I define and use 'implies' a >>> lot, >>> often conjoined, for predicates. It's mainly of declarative value, which >>> is >>> perhaps why it's uncommon in implementation despite how common it is in >>> specification. And for boolean expressions in general I also use >>> 'neither'. >>> Are these something that others [would] use and so could be added to >>> Racket's >>> library? >> >> >> Seems to me adding implies, nand, and nor to racket/bool is a good idea. >> >> Let me know if you disagree (and if you disagree after I've already >> committed, it is a simple thing to drop the commit or change it). > > > I've occasionally written my own `implies', but never make it shortcut like > `and' and `or'. Speaking of which, would it handle more than two arguments? > One? Zero? What kind of associativity would be appropriate? </div></div>The version I checked in shortcuts in an implication-appropriate way (if the first argument is #f). I think the convention (due to functions and currying) is pretty well established that it associates to the right. So that's what the version I checked in does for the 3+ argument case. I didn't see something reasonable for the 0 or 2-ary case so it doesn't handle them. > Bwahaha. :) I'm still pondering those questions for xor. :) Robby <div class="HOEnZb"><div class="h5"> ____________________ Racket Users list: <a href="http://lists.racket-lang.org/users" target="_blank">http://lists.racket-lang.org/users</a> </div></div></blockquote></div>