Re: [Haskell-cafe] Polyvariadic functions operating with a monoid

On Sun, Oct 3, 2010 at 1:26 PM, Luke Palmer wrote:

On Sun, Oct 3, 2010 at 1:24 AM, Kevin Jardine wrote:

...

I had a situation where I had some related types that all had toString functions.

Of course in Haskell, lists all have to be composed of values of exactly the same type, so instead of passing around lists of values with these related types, I created a polyvariadic function polyToString so that I could write:

(polyToString value1 value2 value3 ... valueN)

which would then become a list of strings:

[toString value1, toString value2, ... , toString valueN]

First of all, you are not using the monoidal structure of String at all.  This trick ought to work for any type whatsoever -- you're just throwing them in a list.

Oops, sorry for not reading your message more closely. You were indeed talking about the monoidal structure of list. So... nevermind about this comment. :-P

Other than a few brackets, commas, and a repeated identifier (which you can let-bind to shorten), what benefit is it giving you?  I strongly recommend against polyvariadic functions.  While you get a little bit of notational convenience, you lose composability.  There are pains when you try to write a function that takes a polyvariadic function as an argument, or when you try to feed the function values from a list, etc.  The mechanisms to create polyvariadic functions are brittle and hacky (eg. you cannot have a polymorphic return type, as you want in this case).

Since all your values are known statically, I would recommend biting the bullet and doing it the way you were doing it.

   [ s value1, s value2, s value3, ... ]       where       s x = toString x

(I had to eta expand s so that I didn't hit the monomorphism restriction)

When you want to be passing around "heterogeneous lists", it usually works to convert them before you put them in the list, like you were doing.

...

I finally figured out how to do this, but it was a bit harder to figure this out than I expected, and I was wondering if it might be possible to create a small utility library to help other developers do this.

It seems to me that in the general case, we would be dealing with a Monoid rather than a list of strings. We could have a toMonoid function and then return

polyToMonoid value1 value2 ... valueN =

(toMonoid value1) `mappend` (toMonoid value2) 'mappend' ... (toMonoid valueN)

So anyone who wanted to convert a bunch of values of different types to a Monoid  could easily pass them around using polyToMonoid so long as they defined the appropriate toMonoid function.

Basically, a generalised list.

So I tried writing the following code but GHC said it had undecidable instances.

Has this ever been done successfully?

class Monoidable a where    toMonoid :: Monoid r => a -> r

polyToMonoid :: (Monoidable a, Monoid r) => a -> r polyToMonoid k = polyToMonoid' k mempty

class PolyVariadic p where    polyToMonoid' :: (Monoidable a, Monoid r) => a -> r -> p

instance Monoid r => PolyVariadic r where    polyToMonoid' k ss = (toMonoid k) `mappend` ss

instance (Monoidable a, Monoid r) => PolyVariadic (a -> r) where    polyToMonoid' k ss = (\a -> polyToMonoid' k (toMonoid a) `mappend` ss)

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