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`include Base.Applicative.Basic`

`val return : 'a -> 'a t`

The following identities ought to hold for every Applicative (for some value of =):

- identity:
`return Fn.id <*> t = t`

- composition:
`return Fn.compose <*> tf <*> tg <*> tx = tf <*> (tg <*> tx)`

- homomorphism:
`return f <*> return x = return (f x)`

- interchange:
`tf <*> return x = return (fun f -> f x) <*> tf`

Note: <*> is the infix notation for apply.

The `map`

argument to `Applicative.Make`

says how to implement the applicative's `map`

function. ``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.

`val select : ('a, 'b) Base.Either.t t -> ('a -> 'b) t -> 'b t`

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 `b`

from `Second b`

.

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 `>>=`

, and indeed a selective functor is in some sense a composition of an applicative functor and the `Either`

monad.

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