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Apply.md

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Apply

A data structure admits an Apply instance if allows lifting a function of any arity.

Equivalently, an Apply instance allows applying a function to a value where both are wrapped in the data structure.

Parent

The Apply typeclass extends the Functor typeclass.

API

The Apply typeclass adds a single method to the Functor one, which allows to apply a wrapped function to a wrapped value.

interface Apply extends Functor
{
    /**
     * @param F<callable(A): B> $f
     * @param F<A> $a
     * @return F<B>
     */
    public function apply($f, $a);
}

Its simplified signature is

apply :: (F<callable(A): B>, F<A>) -> F<B>

Extra

The ExtraApply class exposes a series of methods to lift functions of higher arity. For example lift2 allows to lift functions of arity 2.

final class ExtraApply
{
    /**
     * @param callable(A, B): C $f
     * @param F<A> $a
     * @param F<B> $b
     * @return F<C>
     */
    public function lift2(callable $f, $a, $b)

It simplified signature is

lift2 :: (callable(A): B, F<A>, F<B>) -> F<C>

Laws

Instances of the Apply typeclass need to satisfy one law in addition to the Functor laws, which states that application is associative

$apply->apply($apply->apply($apply->map(fn ($f, $g) => fn ($x) => $f($g($x)), $a), $b), $c) == $apply->apply($a, $apply->apply($b, $c))

Implemented instances

  • EitherApply
  • ValidationApply
  • IdentityApply
  • IOApply
  • LinkedListApply
  • MaybeApply
  • PairApply
  • ReaderApply
  • StateApply