Remember the exercise in the online Haskell course that had several tests to filter out weak passwords, all of which had to pass for the fictitious system to allow a String value to be used as a password? I wanted to make it easy to change, so I wanted to take a [String -> Bool] and get a [Bool] I could apply and to for the final thumbs up/thumbs down decision.
The first step: roll my own, which has a pleasing symmetry with map if you write it as a list comprehension:
wonkyMap fs x = [f x | f <- fs]
Then I stumbled across Derek Wyatt's blog post about using sequence for the purpose. Life was good... and then I got Haskell Programming from first principles, and life got better, because its authors do a very good job of explaining the Applicative type class. Applicative defines two functions, pure and (<*>):
class Functor f => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
Here f is a unary type constructor like Maybe or [] (both of which happen to be in Applicative). Being a Functor is a prerequisite for being an Applicative, as you can see from that first line. pure, given a value of type a, gives you back one of type f a. (<*>) is intended to act like function application, letting you take plain old a -> b values and apply some number of them (possibly zero--an empty list is a list, and Nothing is a Maybe (a -> b)) to some number of a values in an f a and get back an f b.
For our purposes, f is [], and if you think about it there's not much choice for what pure and (<*>) can be:
instance Applicative [] where
pure x = [x]
fs <*> xs = [f x | f <- fs, x <- xs]
That's almost exactly what we want--the only thing we have to do is put our candidate password in a list (purify it?), like so:
s `satisfies` cs = and $ cs <*> [s]
So, for this exercise, Haskell is kind of Perl-like: TMTOWDI (there's more than one way to do it). Some would say this shows Haskell is Perl-like in a worse way, namely having weird unintelligible operators. I won't take a position, save to say that ghci makes it a lot easier than Perl (or APL, the original "WTF does this do?" language). :t is your friend!
Prelude> :t (<*>)
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
Now, are all three ways we've come up with equally good? Rolling your own function is a way to start, but why reinvent the wheel? sequence works, but
Prelude> :t sequence
sequence :: (Monad m, Traversable t) => t (m a) -> m (t a)
is far more general than (<*>), so that it takes more thought to realize it can be used this way. (<*>) more directly and specifically says it has to do with what we want, so I would argue that it is clearer.
One more thing: type classes don't just have functions; they have rules that those functions must follow. I urge you to track down the rules for Applicative and persuade yourself that [] satisfies them.
