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

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.