Re: [racket-dev] feature request: gcd, lcm for rationals
What does divides even mean in Q? I think we need David to explain what his extension of GCD and LCM means here, in that divisors and multiples are fairly trivial things in Q. Carl Eastlund On Fri, Dec 9, 2011 at 3:08 PM, J. Ian Johnson i...@ccs.neu.edu wrote: What? The greatest common divisor would definitely not divide 1, unless it truly were 1. -Ian - Original Message - From: Jens Axel Søgaard jensa...@soegaard.net To: David Van Horn dvanh...@ccs.neu.edu Cc: Racket Dev List dev@racket-lang.org Sent: Friday, December 9, 2011 2:04:46 PM GMT -05:00 US/Canada Eastern Subject: Re: [racket-dev] feature request: gcd, lcm for rationals One definition of greatest common divisor in a ring R is: d is a greatest common divisor of x and y when: i) d divides both x and y ii) If e is a divisor of both x and y, then d divides e Now let's consider the ring Q. Since Q is a field, 1 divides all elements. This implies that 1 is a greatest common divisor of any non-zero x and y. ( ad i) 1 is a divisor of both x and y ad ii) 1 is a divisor of e ) It is therefore not obvious that gcd should be extendend as you suggest. But maybe we can finde another name for the operation? /Jens Axel 2011/12/7 David Van Horn dvanh...@ccs.neu.edu It would be nice if gcd and lcm were extended to rational numbers, which seems in-line with Scheme's philosophy (but not standards) on numbers. (define (gcd-rational . rs) (/ (apply gcd (map numerator rs)) (apply lcm (map denominator rs (define (lcm-rational . rs) (/ (abs (apply * rs)) (apply gcd-rational rs))) David _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] feature request: gcd, lcm for rationals
On Fri, Dec 9, 2011 at 15:27, Carl Eastlund c...@ccs.neu.edu wrote: What does divides even mean in Q? I think we need David to explain what his extension of GCD and LCM means here, in that divisors and multiples are fairly trivial things in Q. I don't suppose to understand all the math on this page, but I think it uses the same definition that dvh is using. http://mathworld.wolfram.com/GreatestCommonDivisor.html -- Dan King College of Computer and Information Science Northeastern University _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] [racket-bug] all/12434: match fails to signal type error?
This is now the fourth time I've seen people ask about this. Why can't Typed Racket be a little different than Racket and have another match form that does this or a notion of disjoint unions? You've said many times that TR is for converting Racket programs, but clearly some of us want to write quasi-ML in TR, but we can't without hacks like this. Jay On Fri, Dec 9, 2011 at 1:29 PM, Sam Tobin-Hochstadt sa...@ccs.neu.eduwrote: I think what you're asking for is static errors for coverage failures in `match' when used in Typed Racket. There are two reasons this isn't something I'm planning on doing in general: 1. It would be a significant change from the semantics of `match' in Racket, which as you note raises a runtime error. 2. It's unlikely to be precise enough in enough cases to be useful. `match' is just too flexible, and TR insufficiently smart, for this to be the right default. However, for this purpose, Typed Racket provides the `typecheck-fail' form [1], for raising explicit type errors. Rewrite your match expression to: (match f [(list s) #true] [_ (typecheck-fail #'here #:covered-id f)]) and you get the error message: Type Checker: Incomplete case coverage; missing coverage of Foo [1] http://pre.racket-lang.org/docs/html/ts-reference/Utilities.html?q=type-e#%28form._%28%28lib._typed-racket/base-env/prims..rkt%29._typecheck-fail%29%29 On Fri, Dec 9, 2011 at 3:20 PM, cleme...@brinckerhoff.org wrote: *** Description: Code using match to take apart opaque types signal runtime match failure rather than a type-checking failure. -- sam th sa...@ccs.neu.edu -- Jay McCarthy j...@cs.byu.edu Assistant Professor / Brigham Young University http://faculty.cs.byu.edu/~jay The glory of God is Intelligence - DC 93 _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
[racket-dev] error using local-expand
Say I have the following program: #lang racket (define-for-syntax (loc-expand stx) (local-expand stx 'expression '())) (define-syntax (my-begin stx) (syntax-case stx () [(_ e ...) (with-syntax ([(x ...) (map loc-expand (syntax-list #'(e ...)))]) #'(begin x ...))])) (define-syntax (my-lambda1 stx) (syntax-case stx () [(_ args body ...) #'(lambda args (my-begin body ...))])) (define-syntax (my-lambda2 stx) (syntax-case stx () [(_ args body ...) (with-syntax ([(x ...) (map loc-expand (syntax-list #'(body ...)))]) #'(lambda args (begin x ...)))])) An expression (my-lambda1 (y) (+ y 1)) works fine but (my-lambda2 (y) (+ y 1)) produces the error: expand: unbound identifier in module in: y I can't figure out why this is the case. Anyone know? _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] error using local-expand
On Fri, Dec 9, 2011 at 4:53 PM, Stephen Chang stch...@ccs.neu.edu wrote: Say I have the following program: #lang racket (define-for-syntax (loc-expand stx) (local-expand stx 'expression '())) (define-syntax (my-begin stx) (syntax-case stx () [(_ e ...) (with-syntax ([(x ...) (map loc-expand (syntax-list #'(e ...)))]) #'(begin x ...))])) (define-syntax (my-lambda1 stx) (syntax-case stx () [(_ args body ...) #'(lambda args (my-begin body ...))])) `my-lambda1' does the local expansion after the `lambda' form introduces the bindings from `args' into the environment. (define-syntax (my-lambda2 stx) (syntax-case stx () [(_ args body ...) (with-syntax ([(x ...) (map loc-expand (syntax-list #'(body ...)))]) #'(lambda args (begin x ...)))])) `my-lambda2' does the local expansion before the `lambda' form introduces the bindings from `args' into the environment, meaning that there's no binding yet for any of the arguments. An expression (my-lambda1 (y) (+ y 1)) works fine but (my-lambda2 (y) (+ y 1)) produces the error: expand: unbound identifier in module in: y I can't figure out why this is the case. Anyone know? _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev -- sam th sa...@ccs.neu.edu _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] [racket-bug] all/12434: match fails to signal type error?
On Dec 9, 2011, at 3:32 PM, Jay McCarthy wrote: but clearly some of us want to write quasi-ML in TR, but we can't without hacks like this. ML's match plays a very different role in the process of type inference. We would have to change the language in HUGE way. If you really want quasi-ML, consider implementing the 17th version of parenthesized ML. Everyone who did abandoned it eventually. Perhaps that's a hint. _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
Re: [racket-dev] feature request: gcd, lcm for rationals
On Dec 9, 2011, at 3:31 PM, Daniel King wrote: On Fri, Dec 9, 2011 at 15:27, Carl Eastlund c...@ccs.neu.edu wrote: What does divides even mean in Q? I think we need David to explain what his extension of GCD and LCM means here, in that divisors and multiples are fairly trivial things in Q. I don't suppose to understand all the math on this page, but I think it uses the same definition that dvh is using. http://mathworld.wolfram.com/GreatestCommonDivisor.html Interesting: the Mathematica people have extended the gcd function from the integers to the rationals, not by applying the usual definition of gcd to Q (which would indeed be silly, as everything except 0 divides everything else), but by coming up with a different definition which, when restricted to integers, happens to coincide with the usual definition of gcd. I would wonder: is this the ONLY reasonable function on rationals which, when restricted to integers, coincides with the usual definition of gcd? Stephen Bloch sbl...@adelphi.edu _ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
