Programming in Scala”

Chapter notes 38
Notes on chapter 12: Applicative and traversable
functors
The cost of power
There is a tradeoff between applicative APIs and monadic ones. Monadic APIs are strictly more
powerful and flexible, but the cost is a certain loss of algebraic reasoning.
The difference is easy to demonstrate in theory, but takes some experience to fully appreciate in
practice.
Consider composition in a monad, via compose (Kleisli composition):
val foo: A => F[B] = ???
val bar: B => F[C] = ???
val baz: A => F[C] = bar compose foo
There is no way that the implementation of the compose function in the Monad[F] instance can
inspect the values foo and bar. They are functions, so the only way to “see inside” them is to
give them arguments. The values of type F[B] and F[C] respectively are not determined until the
composite function runs.
Contrast this with combining values with map2:
val quux: F[A] = ???
val corge: F[B] = ???
val grault: F[C] = map2(quux, corge)(f)
Here the implementation of map2 can actually look at the values quux and corge, and take different
paths depending on what they are. For instance, it might rewrite them to a normal form for improved
efficiency. If F is something like Future, it might decide to start immediately evaluating them on
different threads. If the data type F is applicative but not a monad, then the implementation has this
flexibility universally. There is then never any chance that an expression in F is going to involve
functions of the form A => F[B] that it can’t see inside of.
The lesson here is that power and flexibility in the interface often restricts power and flexibility in
the implementation. And a more restricted interface often gives the implementation more options.
See this StackOverflow question¹⁶⁴ for a discussion of the issue with regard to parsers.
See also the end of the note below on “Applicative laws”, for an example of the loss of algebraic
reasoning that comes with making an API monadic rather than applicative.
¹⁶⁴http://stackoverflow.com/questions/7861903/what-are-the-benefits-of-applicative-parsing-over-monadic-parsing