Since list is a monad then we know that join can be specialized to
join :: [[a]] -> [a]
which is just `concat` then. Now Transducers are a bit of an elaboration over functions like
Transducer in out === in -> [out]
and so we might compose them a little like
comp t1 t2 in = concat (map t2 (t1 in))
which if you follow in types ends up working out. Finally, that concat/map business is just monadic bind in the list monad. We could also write
comp t1 t2 in = t1 in >>= t2
= (concatMap t1 t2)
= bind t2 (t1 in)
depending on what syntax is most familiar. That's why they're (an elaboration of) "monad composition", i.e. a Kleisli category.
The only thing left is just that Hickey did a transformation called "Church Encoding" or "Continuation Passing Style" to the regular list functions. This eliminates the need to generate concrete lists and turns this fancy composition into reverse normal function composition. It's a clever trick.
The only thing left is just that Hickey did a transformation called "Church Encoding" or "Continuation Passing Style" to the regular list functions. This eliminates the need to generate concrete lists and turns this fancy composition into reverse normal function composition. It's a clever trick.