Re: [Haskell-cafe] function arithmetic?
Might not be exactly what you're looking for, but Control.Arrow has a rich set of operators that can be used to combine functions. For instance, there's an example on http://en.wikibooks.org/wiki/Haskell/Understanding_arrows showing an addA function that can be used to apply two functions to the same argument and add the results: Prelude import Control.Arrow Prelude Control.Arrow let addA f g = f g arr (\ (y, z) - y + z) Prelude Control.Arrow addA (+2) (*5) 10 62 If you're set on using the + and * operators, I'm guessing it's not possible to define a (sane) instance of Num for (-), but it would probably be instructive to try. On Sat, Aug 31, 2013 at 10:01 PM, Christopher Howard christopher.how...@frigidcode.com wrote: Hi. I was just curious about something. In one of my math textbooks I see expressions like this f + g or (f + g)(a) where f and g are functions. What is meant is f(a) + g(a) Is there a way in Haskell you can make use of syntax like that (i.e., expressions like f + g and f * g to create a new function), perhaps by loading a module or something? __**_ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/**mailman/listinfo/haskell-cafehttp://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] function arithmetic?
Yes, you can do that, but you probably shouldn't. See also: http://www.haskell.org/haskellwiki/Num_instance_for_functions http://hackage.haskell.org/package/applicative-numbers On Sat, Aug 31, 2013 at 10:01 PM, Christopher Howard christopher.how...@frigidcode.com wrote: Hi. I was just curious about something. In one of my math textbooks I see expressions like this f + g or (f + g)(a) where f and g are functions. What is meant is f(a) + g(a) Is there a way in Haskell you can make use of syntax like that (i.e., expressions like f + g and f * g to create a new function), perhaps by loading a module or something? __**_ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/**mailman/listinfo/haskell-cafehttp://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] function arithmetic?
* Christopher Howard christopher.how...@frigidcode.com [2013-08-31 21:01:38-0800] Hi. I was just curious about something. In one of my math textbooks I see expressions like this f + g or (f + g)(a) where f and g are functions. What is meant is f(a) + g(a) Is there a way in Haskell you can make use of syntax like that (i.e., expressions like f + g and f * g to create a new function), perhaps by loading a module or something? Not the syntax, but the notion itself corresponds exactly to idiom brackets/applicative functors. In this case it's the Reader applicative. Roman signature.asc Description: Digital signature ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] function arithmetic?
To clarify in Bobs remark : while you're still learning Haskell and the
type system , things like lifted Num on functions can lead to some
potentially confusing type errors.
That said, it's absolutely doable, and can be a very nice / powerful tool
when used appropriately.
On Sunday, September 1, 2013, Bob Ippolito wrote:
Yes, you can do that, but you probably shouldn't.
See also:
http://www.haskell.org/haskellwiki/Num_instance_for_functions
http://hackage.haskell.org/package/applicative-numbers
On Sat, Aug 31, 2013 at 10:01 PM, Christopher Howard
christopher.how...@frigidcode.com javascript:_e({}, 'cvml',
'christopher.how...@frigidcode.com'); wrote:
Hi. I was just curious about something. In one of my math textbooks I see
expressions like this
f + g
or
(f + g)(a)
where f and g are functions. What is meant is
f(a) + g(a)
Is there a way in Haskell you can make use of syntax like that (i.e.,
expressions like f + g and f * g to create a new function), perhaps by
loading a module or something?
__**_
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Re: [Haskell-cafe] function arithmetic?
On 08/31/2013 09:27 PM, Charlie Paul wrote: I believe that this is what you want: http://www.haskell.org/haskellwiki/Num_instance_for_functions On Sat, Aug 31, 2013 at 10:01 PM, Christopher Howard christopher.how...@frigidcode.com wrote: The author seemed to be subtly mocking the idea. It seemed to be suggesting that a Num instance for functions would imply the need for constant number functions, which leads to difficulties. But I don't see why one would have to take it that far. In any case, I just tried the NumInstances package from Hackage and it seems to work great. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] function arithmetic?
On 1/09/2013, at 7:06 PM, Christopher Howard wrote: It seemed to be suggesting that a Num instance for functions would imply the need for constant number functions, which leads to difficulties. But I don't see why one would have to take it that far. You *cannot* make a type an instance of Num without saying how to map integer literals to that type. If you want (f+g)x = fx + gx then having 2x = 2 makes perfect sense, because then (f+2)x = fx + 2 just as an APL or S programmer would expect. The fact that 2(x+y) will then evaluate to 2 without evaluating x or y is unfortunate, but inevitable. I'm sure I could live with it. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] function arithmetic?
Hi. I was just curious about something. In one of my math textbooks I see expressions like this f + g or (f + g)(a) where f and g are functions. What is meant is f(a) + g(a) Is there a way in Haskell you can make use of syntax like that (i.e., expressions like f + g and f * g to create a new function), perhaps by loading a module or something? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
