Appl -package:ghc

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")

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)

This module corresponds to section 3.8.15 (Texture Application) of the OpenGL 2.1 specs.

Phantom type indicating application traffic secrets.

Handshake information generated for traffic at application level.

Type level function application

An "internal" definition used primary in the Apply instance for TyCon. Note that this only defined on GHC 8.6 or later.

An "internal" defunctionalization symbol used primarily in the definition of ApplyTyCon, as well as the SingI instances for TyCon1, TyCon2, etc. Note that this is only defined on GHC 8.6 or later.