Re: [Haskell-cafe] Are there arithmetic composition of functions?

Oh man, I came late to this party. I'll throw what little weight I have here behind Jerry's argument. Yes, this change to base is not Haskell2010 compatible, but it's still a good change and I hope that Haskell2012 or 2013 or whatever the next version of the standard that comes out incorporates it. As to why it's a good change: (1) People were doing it anyways with bogus Eq instances; the syntactic benefit of being able to use integer literals is huge; using the standard +/-/* etc functions is a nice bonus. For an example, see http://twanvl.nl/blog/haskell/simple-reflection-of-expressions (2) Pattern matching on numeric literals is what requires Eq, and combined with (1) leads to fragile code. Now, for example, fac 0 = 1 fac n = n * fac (n-1) Now the type of fac explicitly states that it requires Eq to work; with the 'hack' version of Eq in the expressions above, "fac x" doesn't terminate and instead gives x * (x-1) * (x-1-1) * ... forever. Other versions (like the version in this thread with Num (e -> a)) turn fac into a function that always returns bottom. -- ryan On Tue, Mar 20, 2012 at 12:02 PM, Ryan Ingram wrote:

This instance can be made more general without changing the code; change the first line to

instance Num a => Num (e -> a) where

I think this version doesn't even require FlexibleInstances.

This lets you do

f x = if x then 2 else 3 g x = if x then 5 else 10

-- f + g = \x -> if x then 7 else 13

-- ryan

On Mon, Mar 19, 2012 at 10:38 AM, Ozgur Akgun wrote:

...

Hi,

If you are feeling adventurous enough, you can define a num instance for functions:

{-# LANGUAGE FlexibleInstances #-}

instance Num a => Num (a -> a) where f + g = \ x -> f x + g x f - g = \ x -> f x - g x f * g = \ x -> f x * g x abs f = abs . f signum f = signum . f fromInteger = const . fromInteger

ghci> let f x = x * 2 ghci> let g x = x * 3 ghci> (f + g) 3 15 ghci> (f+g+2) 2 17

HTH, Ozgur

On 19 March 2012 16:57, wrote:

...

By arithmetic I mean the everyday arithmetic operations used in engineering. In signal processing for example, we write a lot of expressions like f(t)=g(t)+h(t)+g'(t) or f(t)=g(t)*h(t). I feel it would be very natural to have in haskell something like g::Float->Float --define g here h::Float->Float --define h here f::Float->Float f = g+h --instead of f t = g t+h t --Of course, f = g+h is defined as f t = g t+h t

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