Appl

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.

(name)

The WAI application. Note that, since WAI 3.0, this type is structured in continuation passing style to allow for proper safe resource handling. This was handled in the past via other means (e.g., ResourceT). As a demonstration:

app :: Application
app req respond = bracket_
(putStrLn "Allocating scarce resource")
(putStrLn "Cleaning up")
(respond $ responseLBS status200 [] "Hello World")

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

Application

Application

Application

Application

Module that deals with expression application in JavaScript. In some cases we rely on pre-generated functions that are bundled with the RTS (see rtsApply).

Apply the monomorphism restriction, never quantifying over any constraints

The WAI application. Note that, since WAI 3.0, this type is structured in continuation passing style to allow for proper safe resource handling. This was handled in the past via other means (e.g., ResourceT). As a demonstration:

app :: Application
app req respond = bracket_
(putStrLn "Allocating scarce resource")
(putStrLn "Cleaning up")
(respond $ responseLBS status200 [] "Hello World")

A strong lax semi-monoidal endofunctor. This is equivalent to an Applicative without pure. Laws:

(.) <$> u <.> v <.> w = u <.> (v <.> w)
x <.> (f <$> y) = (. f) <$> x <.> y
f <$> (x <.> y) = (f .) <$> x <.> y

The laws imply that .> and <. really ignore their left and right results, respectively, and really return their right and left results, respectively. Specifically,

(mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
(mf <$> m) <. (nf <$> n) = mf <$> (m <. n)