[Haskell-cafe] Increasing number of parameters

[Jacek Generowicz]

On 2010 Oct 15, at 11:38, Jacek Generowicz wrote:

> [...]
> So I'm trying to get to grips with a simpler variation on the same  
> theme, and I'm still failing. I'm trying to write something along  
> the lines of
>
> addArg :: nArgFn -> a -> nPlus1ArgFn
> addArg fn a = (a+) <---- fn where
>    <---- = something which applies its right parameter to however  
> many arguments it needs and feeds the result to the left parameter
>
> in order to allow me to say
>
> sum2 = (+)
> sum3 = addArg sum2
> sum4 = addArg sum3
>
> etc.


-- OK, I've understood.

-- You use an accumulator to keep track of what has been done with the
-- arguments that have been seen so far, and addArg takes one more
-- argument, each time, and mixes it in with what is already there.

-- I smell a monad.

addArgSum :: (Num a) => (a -> t) -> a -> a -> t
addArgSum fn acc arg = fn (acc + arg)

sum1' = id
sum2' = addArgSum sum1'
sum3' = addArgSum sum2'

-- And here's a more general version.

addArg combine fn acc arg = fn (combine arg acc)

sum1 = id
sum2 = addArg (+) sum1
sum3 = addArg (+) sum2
sum4 = addArg (+) sum3

-- But I don't really get why the following leads to complaints about
-- infinite types.

-- sumN n = iterate (addArg (+)) id