a package:selective

A lifted version of all. Retains the short-circuiting behaviour.

Accumulate the Right values, or return the first Left.

A lifted version of any. Retains the short-circuiting behaviour.

Recover the application operator <*> from select. Rigid selective functors satisfy the law <*> = apS and furthermore, the resulting applicative functor satisfies all laws of Applicative:

• Identity:

  pure id <*> v = v

• Homomorphism:

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

• Interchange:

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

• Composition:

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

Recover the application operator <*> from matchOne.

Recover the application operator <*> from match.

Update a generalised sum given a generalised product that takes care of all possible cases.

An alternative definition of applicative functors, as witnessed by ap and matchOne. This class is almost like Selective but has a strict constraint on t.

A list of values, equipped with a fast membership test.

Composition of a selective functor f and an applicative traversable functor g.

Any applicative functor can be given a Selective instance by defining select = selectA. This data type captures this pattern, so you can use it in combination with the DerivingVia extension as follows:

newtype Over m a = Over m
deriving (Functor, Applicative, Selective) via SelectA (Const m)

Selective instance for the standard applicative functor Validation. This is a good example of a non-trivial selective functor which is not a monad.

The branch function is a natural generalisation of select: instead of skipping an unnecessary effect, it chooses which of the two given effectful functions to apply to a given argument; the other effect is unnecessary. It is possible to implement branch in terms of select, which is a good puzzle (give it a try!). We can also implement select via branch:

selectB :: Selective f => f (Either a b) -> f (a -> b) -> f b
selectB x y = branch x y (pure id)

Embed a list of values into Cases using the trivial but slow membership test based on elem.

The list of all possible values of an enumerable data type.

A lifted version of fromMaybe.

Eliminate all specified values a from f (Either a b) by replacing each of them with a given f a.

Eliminate all specified values a from f (Either a b) by replacing each of them with a given f a.

We can write a function with the type signature of select using the Applicative type class, but it will always execute the effects associated with the second argument, hence being potentially less efficient.

Swap Left and Right.