Creates polyvariadic functions that map their parameters into a given monoid.

Haskell lists contain an indefinite number of elements of a single type. It is sometimes useful to create list-like functions that accept an indefinite number of parameters of multiple types.

PolyToMonoid provides two such functions, ptm and ctm, as well as a typeclass Monoidable. The only precondition is that the parameters of ptm and ctm can be mapped to an underlying monoid using the toMonoid function provided by Monoidable.

To understand how the polyToMonoid functions work, consider a function list that maps its parameters to a list:

 list p1 p2 ... pN =
    [p1] ++ [p2] ++ ... ++ [pN]

(which is the same as [p1,p2, ..., pN] )

list can be generalised to any monoid conceptually as:

 polyToMonoid p1 p2 ... pN =
    (toMonoid p1) `mappend` (toMonoid p2) `mappend` ... `mappend` (toMonoid pN)

Remember that a monoid, defined in Data.Monoid, is any set of elements with an identity element mempty and an associative operator mappend .

As any list type is automatically a monoid with mempty = [] and mappend = (++), the list function defined above is just a specific version of polyToMonoid.

The main difficulty with defining a polyToMonoid function is communicating to Haskell what underlying monoid to use.

Through Haskell type magic, this can be done with a simple type annotation.

Specifically, you can pass mempty as the first element of the function and annotate it with the type of the monoid it belongs to. Think of the mempty value as like the initial value of a fold.

This library provides two variants of a polyToMonoid function. The first, ptm, simply takes a list of arguments starting with mempty and returns the monoid result.

The second variant, ctm, is composible. In effect, it returns a function that consumes the next parameter. You can feed the ctm result to a second termination function trm to get the actual result.

We can first tell Haskell how to map a set of types to a list of strings using Monoidable:

 instance Show a => Monoidable a [String] where
    toMonoid a = [show a]

and then tell ptm to use the [String] monoid:

 ptm (mempty :: [String]) True "alpha" [(5 :: Int)]

The result returned would be:

 ["True","\"alpha]\"","[5]"]

In this case, Monoidable tells the ptm function to accept a wide variety of types (anything with a show function) when using the [String] monoid.

The first parameter of ptm, (mempty :: [String]) tells it to map its parameters into the [String] monoid.

Unlike ptm, the ctm function in effect returns a partial function ready to consume the next parameter rather than a monoid result.

It is therefore more composable, at the cost of requiring a second termination function trm to return the actual monoid result.

 ctmfirstbit = ctm mempty :: [String]) True "alpha"
 ctmsecondbit = ctmfirstbit [(5 :: Int)]
 finalresult = trm ctmsecondbit

The result returned would be the same as above:

 ["True","\"alpha]\"","[5]"]

Monoids, of course, do not have to be lists.

Here's a second example which multiplies together numbers of several types:

 instance Monoid Double where
     mappend = (*)
     mempty = (1.0) :: Double

 instance Monoidable Int Double where
     toMonoid = fromIntegral

 instance Monoidable Double Double where
     toMonoid = id

 ptm (mempty :: Double) (5 :: Int) (2.3 :: Double) (3 :: Int)

In this case, ptm accepts parameters that are either ints or doubles, converts them to doubles, and then multiplies them together.

You can use the composibility of ctm to define a productOf function:

 productOf = ctm (mempty :: Double)
 trm $ productOf (5 :: Int) (2.3 :: Double) (3 :: Int)

As before the trm function is required to terminate the ctm calculation and deliver the final result.

Note that since ptm returns its result immediately, it is not possible to use it to define other functions using Haskell. You can use it in CPP defines, however. For example:

 #define productOf ptm (mempty :: Double)
 productOf (5 :: Int) (2.3 :: Double) (3 :: Int)

You will probably need to enable the following extensions to use this library:

 TypeSynonymInstances, FlexibleInstances, MultiParamTypeClasses