Re: [Haskell-cafe] N and R are categories, no?
On 3/15/07, Steve Downey [EMAIL PROTECTED] wrote: EOk, i'm trying to write down, not another monad tutorial, because I don't know that much yet, but an explication of my current understanding of monads. But before I write down something that is just flat worng, I thought I'd get a cross check. (and I can't get to #haskell) Monads are Functors. Functors are projections from one category to another such that structure is preserved. One example I have in mind is the embedding of the natural numbers into the real numbers. The mapping is so good, that we don't flinch at saying 1 == 1.0. Monads are endofunctors (functors from one category to itself). This is easy to see from the type of join: join : m (m a) - m a For Haskell monads the category is the category of Haskell types and Haskell functions. In this category N and R are objects, so you'll get the wrong idea trying to see them as categories. / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Logic programming using lazy evaluation
On 2/27/07, Henning Thielemann [EMAIL PROTECTED] wrote: I suspect that someone has already done this: A Haskell library which solves a system of simple equations, where it is only necessary to derive a value from an equation where all but one variables are determined. Say You might want to check out the following paper: http://www.cs.chalmers.se/~koen/pubs/entry-haskell00-typedlp.html / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Happy outputs parE - ideas on what to change in my .y file?
On Jan 27, 2007, at 11:11 AM, Mark Wassell wrote:
Sometimes happy outputs 'parE' when I run it on my .y file? I
believe it is coming from a part of Grammer.lhs which has the
comment line
This bit is a real mess, mainly because of the error message
support.
Are there any suggestions on what to change in my .y file to get
over this?
I've run into this problem as well (and submitted a bug report). You
get the problem when there are undefined productions in your grammar.
For instance:
%name parser Foo
%%
Foo : Bar { () }
/ Ulf
___
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Article review: Category Theory
On Jan 18, 2007, at 10:09 PM, Yitzchak Gale wrote: I wrote: Will (id :: A - A $!) do the trick? Ulf Norell wrote: The problem is not with id, it's with composition. For any f and g we have f . g = \x - f (g x) So _|_ . g = \x - _|_ for any g. OK, so then how about f .! g = ((.) $! f) $! g That should probably do the trick. / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Article review: Category Theory
On Jan 19, 2007, at 1:06 PM, Yitzchak Gale wrote: Hmm. I wrote: for simplicity, we will ignore these distinctions But do we really want to do that? Are the monads that we use every day in Haskell really monads if we check the axioms using (.!) instead of (.) as we should? I'm not so sure anymore... Personally I think that the distinction between _|_ and \x - _|_ is a mistake and should be ignored whenever possible. / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Article review: Category Theory
On Jan 16, 2007, at 7:22 PM, David House wrote: Hey all, I've written a chapter for the Wikibook that attempts to teach some basic Category Theory in a Haskell hacker-friendly fashion. http://en.wikibooks.org/wiki/Haskell/Category_theory In the section on the category laws you say that the identity morphism should satisfy f . idA = idB . f This is not strong enough. You need f . idA = f = idB . f Unfortunately, fixing this means that the category Hask is no longer a category since _|_ . id = \x - _|_ ≠ _|_ Also it's a bit strange to state that morphisms are closed under composition after the associativity law. Wouldn't it be nicer to introduce composition as a total operation off the bat? / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: Reversing a string of words: C# v Perl V Ruby v Haskell
On Dec 13, 2006, at 3:54 AM, Yitz Gale wrote: Nice. Here is something similar: reverseWords = concat . reverse . groupBy eqsp where eqsp x y = isSpace x == isSpace y This can be made even nicer using the 'on' function [1]: reverseWords = concat . reverse . groupBy ((==) `on` isSpace) [1] http://www.haskell.org/pipermail/libraries/2006-November/006156.html / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Simple GADT parser for the eval example
On Oct 31, 2006, at 2:19 AM, Dimitrios Vytiniotis wrote: -- Give a GADT for representation types data R a where Rint :: R Int Rbool :: R Bool Rpair :: R a - R b - R (a,b) -- Give an existential type with a type representation data TermEx where MkTerm :: R a - Term a - TermEx -- we use Weirich's higher-order type-safe cast to avoid deep traversals -- one can replace the type_cast with a more simple traversal-based -- version. ...complicated higher order stuff... For instance: data a :==: b where Refl :: a :==: a (===) :: Monad m = R a - R b - m (a :==: b) Rint === Rint = return Refl Rbool === Rbool = return Refl Rpair a b === Rpair c d = do Refl - a === c Refl - b === d return Refl a === b = fail $ show a ++ =/= ++ show b cast :: a :==: b - c a - c b cast Refl x = x In particular one wants to extract the Term part of a TermEx: getTerm :: Monad m = TermEx - R a - m (Term a) getTerm (MkTerm r' t) r = do Refl - r === r' return t / Ulf ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Last statement in 'do' must be an expression error.
On Aug 17, 2006, at 10:18 AM, Szymon Ząbkiewicz wrote:
Hi.
When trying to compilke this code:
{...}
8.if (a == 0) (b == 0)
9. then do
10. nr1 - read (prompt enter 1. number: )
11. nr2 - read (prompt enter 2. number: )
12. else do
13.let nr1 = a
14.nr2 = b
{...}
The compiler tells me thats there's an error on line 10:
The last statement in a 'do' construct mesy be an expression
Could you tell me how to change it so that the declaration of the
first nr1 and nr2 is still in the then block.
The problem is that variables defined in the branch of an if are
local to the branch. If you want to use them outside you have to
return them from the branch:
do
(nr1, nr2) -
if (a == 0) (b == 0)
then do
nr1 - read (prompt enter 1. number: )
nr2 - read (prompt enter 2. number: )
return (nr1, nr2)
else do
let nr1 = a
nr2 = b
return (nr1, nr2)
/ Ulf___
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
