val return : 'a -> 'a t
The following identities ought to hold for every Applicative (for some value of =):
return Fn.id <*> t = t
return Fn.compose <*> tf <*> tg <*> tx = tf <*> (tg <*> tx)
return f <*> return x = return (f x)
tf <*> return x = return (fun f -> f x) <*> tf
Note: <*> is the infix notation for apply.
map argument to
Applicative.Make says how to implement the applicative's
`Define_using_apply means to define
map t ~f = return f <*> t.
`Custom overrides the default implementation, presumably with something more efficient.
Some other functions returned by
Applicative.Make are defined in terms of
map, so passing in a more efficient
map will improve their efficiency as well.
Selective applicative functors. You can think of
select as a selective function application: you apply a function only when given a value
First a. Otherwise, you can skip the function and associted effects and return the
Note that it is not a requirement for selective functors to skip unnecessary effects. It may be counterintuitive, but this makes them more useful. Why? Typically, when executing a selective computation, you would want to skip the effects (saving work); but on the other hand, if your goal is to statically analyse a given selective computation and extract the set of all possible effects (without actually executing them), then you do not want to skip any effects, because that defeats the purpose of static analysis.
The type signature of
select is reminiscent of both
>>=, and indeed a selective functor is in some sense a composition of an applicative functor and the