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

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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