Applicative

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

• 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 = (id <$ u)
  <*> v

• u <* v = liftA2 const u v

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

• fmap f x = pure f <*> x

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2
  >>= (\x2 -> return (x1 x2)))

• (*>) = (>>)

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

This module describes a structure intermediate between a functor and a monad (technically, a strong lax monoidal functor). Compared with monads, this interface lacks the full power of the binding operation >>=, but

• it has more instances.
• it is sufficient for many uses, e.g. context-free parsing, or the Traversable class.
• instances can perform analysis of computations before they are executed, and thus produce shared optimizations.

This interface was introduced for parsers by Niklas Röjemo, because it admits more sharing than the monadic interface. The names here are mostly based on parsing work by Doaitse Swierstra. For more details, see Applicative Programming with Effects, by Conor McBride and Ross Paterson.

Applicative Argument

ApplicativeStmt represents an applicative expression built with <$> and <*>. It is generated by the renamer, and is desugared into the appropriate applicative expression by the desugarer, but it is intended to be invisible in error messages. For full details, see Note [ApplicativeDo] in GHC.Rename.Expr

Not on Stackage, so not searched. Instances for Applicative

Not on Stackage, so not searched. Applicative functor and monad which collects all your fails

Not on Stackage, so not searched. Applicative-based numeric instances

Not on Stackage, so not searched. An applicative parser combinator library

Not on Stackage, so not searched. Write applicative programs in direct style (generalizes idiom brackets).

Not on Stackage, so not searched. Generalized logic operations for Applicative and Alternative functors

Not on Stackage, so not searched. Quasiquoters for idiom brackets and an applicative do-notation

Not on Stackage, so not searched. Utilities and combinators for parsing command line options