tag:blogger.com,1999:blog-5894839.post3926774904222000648..comments2014-09-07T02:00:56.971+02:00Comments on Kazimir Majorinc's Lisp Programming Blog.: Conflation of Subtraction and Additive Inverse in Lisp.Kazimir Majorincnoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5894839.post-49591318184538327492011-05-21T01:19:06.782+02:002011-05-21T01:19:06.782+02:002011-05-20
hi kaz,
very interesting post.
at fi...2011-05-20<br /><br />hi kaz,<br /><br />very interesting post.<br /><br />at first, when reading the first paragraph, i don't agree or i didn't find the way you expressed it being correct. Anyhow, i find the main point of your article interesting.<br /><br />i think, in some respect, mathematically there's no such thing as substraction, but only addictive inverse. So, if we take this view, then when we write 「a-b」 that “-” operator is really a sugar syntax for 「+(-b)」. If we take this attitude to lisp syntax, then, the expression 「(- a b)」 would be illegal. The function “-” would only allow one argument. This would be alternative way to resolve the syntax problem in your article.<br /><br />however, forcing the modern algebra foundation view of treating substractions as addition with inverse elements is really too much. The idea of substraction of taking n things out of m is perfectly fine by itself.<br /><br />so, overall, am not sure what to make of this.<br /><br />i've put my thought out similarly, here<br />〈What's Function, What's Operator?〉<br />http://xahlee.org/math/function_and_operators.html<br />(in the section “Implicit Operators”.)Xah Leehttp://www.blogger.com/profile/11896508961236679878noreply@blogger.comtag:blogger.com,1999:blog-5894839.post-5144495890629084302011-05-03T20:54:20.907+02:002011-05-03T20:54:20.907+02:00If (- 5) means something *different* from negation...If (- 5) means something *different* from negation of 5, that would be error-prone because of what humans who write or read it might expect it to mean; hence, for Kernel I require applicative - to have at least two arguments.John Shutthttp://www.blogger.com/profile/00041398073010099077noreply@blogger.com