Re: [Haskell-cafe] How odd...
On 8/4/07, Dan Piponi [EMAIL PROTECTED] wrote: On 8/4/07, Albert Y. C. Lai [EMAIL PROTECTED] wrote: There is no reason to expect complex ** to agree with real **. There's every reason. It is standard mathematical practice to embed the integers in the rationals in the reals in the complex numbers and it is nice to have as many functions as possible respect that embedding. A example I have seen before that illustrates some the difficulties with preserving such behaviour is (-1)^(1/3). Of course, taking the nth root is multi-valued, so if you're to return a single value, you must choose a convention. Many implementations I have seen choose the solution with lowest argument (i.e. the first solution encounted by a counterclockwise sweep through the plane starting at (1,0).) With this interpretation, (-1)^(1/3) = 0.5 + sqrt(3)/2 * i. If you go with the real solution (-1) you might need to do so carefully in order to preserve other useful properties of ^, like continuity. Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Clearly, Haskell is ill-founded
On 7/9/07, Daniel McAllansmith [EMAIL PROTECTED] wrote: I wouldn't want to comment on the validity of his claim, maybe he's wrong, or maybe he's... well, anyway... what I will say is I got a chuckle out of the 'Citations' that Amazon lists. As amusing as that thought is, it seems that this is regrettably an error on Amazon's part. After looking at the actual page images where the alleged citations occur, there is nowhere any mention of this book. (How could there be? It was just published.) It looks like Amazon's citation database is mistakenly using the index for the book _Beating Depression_ by John Rush (Toronto: John Wiley Sons, Canada Ltd., 1983). Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Just curios
On 6/10/07, Brandon S. Allbery KF8NH [EMAIL PROTECTED] wrote: You're pretty close, actually :) Names derived from Hebrew were fairly common in the Bible belt back when he was born. (Haskell from השקל, wisdom. I half suspect Curry has a Biblical origin as well, from קרי.) Bible belt? Curry was born in Millis, Massachusetts, and grew up in Boston. The word Haskell seems to occur much more frequently as a surname, originating in the British Isles. It seems more plausible that he got the name Haskell from some relative or family friend somewhere than ascribing a Hebrew origin for his name. Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Prime finding
On 2/22/07, Ruben Zilibowitz [EMAIL PROTECTED] wrote: I see that there has been some discussion on the list about prime finding algorithms recently. I just wanted to contribute my own humble algorithm: [snip] Comparing it to some of the algorithms in: http://www.haskell.org/pipermail/haskell-cafe/2007-February/022765.html It seems to perform reasonably well. It also has the advantage of being quite short. It has the advantage of conciseness, and for small enough examples will give reasonable results, though computing O(n/log(n)) gcds can be very expensive. One suggestion I would make is to build the list in reverse order. Since the test proceeds through the list from left to right, and an arbitrary positive integer is more likely to be divisible by a small primes than a larger one, this ought to produce a faster result when the input is composite. Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: Justification for Ord inheriting from Eq?
On 4/7/06, Jared Updike [EMAIL PROTECTED] wrote: given an Ord instance (for a type T) a corresponding Eq instance can be given by: instance Eq T where a == b = compare a b == EQ where did this second -^ == come from? (I guess if if Ordering derives Eq :-) I think you meant I think another poster essentially already said this, but the second == comes from the Eq instance for type Ordering, which is in the Prelude. So this we can actually rely on. Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Justification for Ord inheriting from Eq?
On 4/6/06, Brian Hulley [EMAIL PROTECTED] wrote: What about: class Eq a where (==), (/=) :: ... class PartialOrd a where (), () :: a-a-Bool x y = y x class (PartialOrd a) = TotalOrd a where x = y = not (y x) -- = not meaning inheritance but just a restriction on a for use of TotalOrd A partial order can be defined in either of two ways, both of which require some notion of equality. If it is a weak partial order, you need to require reflexivity, i.e. x=y implies R(x,y). If it is a strong partial order, you need to require irreflexivity. So some notion of equality is necessary in either case. (I think the same is true of preorders, if we want to generalize to that.) So, if such a PartialOrd existed, it really should be between Eq and Ord in the class hierarchy. Steve ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
