Applicative package:basic-prelude

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

• identity

  pure id <*>
  v = v

• composition

  pure (.) <*> u
  <*> v <*> w = u <*> (v
  <*> w)

• homomorphism

  pure f <*>
  pure x = pure (f x)

• interchange

  u <*> pure y =
  pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

• u *> v = pure (const id)
  <*> u <*> v

• u <* v = pure const <*>
  u <*> v

As a consequence of these laws, the Functor instance for f will satisfy

• fmap f x = pure f <*> x

If f is also a Monad, it should satisfy

• pure = return

• (<*>) = ap

(which implies that pure and <*> satisfy the applicative functor laws).