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Comment by cousin_it | Hacker News Reader

It seems to me that Collector a b is isomorphic to [a] -> b, so not clear why you need existentials or GADTs.

    iso1 :: Collector a b -> ([a] -> b)
    iso1 (MakeCollector f x g) = g . foldl f x

    iso2 :: ([a] -> b) -> Collector a b
    iso2 f = MakeCollector (flip (:)) [] (f . reverse)

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It's not isomorphic to [a] -> b, because you are not restricted to feed a Collector with a preexisting list, you can feed it with lines read incrementally from stdin for example.

Another difference is that you can combine a "Collector a b" and a "Collector a c" into a "Collector a (b,c)" that, like its components, only requires a single pass of the data. (This would be the Applicative instance for collectors.) Combining functions [a] -> b and [a] -> c doesn't necessarily "stream".

Also, I didn't use GADTs, only GADT "syntax" in which data constructors are provided as functions with signatures (MakeCollector :: ...)

Personally, I find this syntax much clearer for existential types. It amounts to having a type variable in a parameter which doesn't appear in the return type of the constructor.

Since Haskell is lazy you can feed final list to its construction (like the prime sieve examples). Combination in a single-pass is optimisable by loop-fusion. Though optimisations are famous for 'flaking out' at the worst moment.

With [a] -> b, when production of the input elements requires I/O and you don't want to read the entire list beforehand, you are forced to use lazy I/O, which is notoriously flaky and doesn't handle errors well.

Meanwhile, with a Collector, you can read the inputs with standard IO actions just fine, and feed them as they are produced.

Because of non-functional properties of programming code. Of course the archetype of a Collector can be used as a backing data structure. But maybe, if you want an accumulator you're better of calculating the sum without constructing a list (or relying on fusion).

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