validation: A data-type like Either but with an accumulating Applicative

Several data-types like Either but with differing properties and type-class instances.

Library support is provided for those different representations, include lens-related functions for converting between each and abstracting over their similarities.

• AccValidation

The AccValidation data type is isomorphic to Either, but has an instance of Applicative that accumulates on the error side. That is to say, if two (or more) errors are encountered, they are appended using a Semigroup operation.

As a consequence of this Applicative instance, there is no corresponding Bind or Monad instance. AccValidation is an example of, "An applicative functor that is not a monad."

• Validation

The Validation data type is isomorphic to Either and has a Monad instance that does the same as Either. The only difference to Either is the constructor names and surrounding library support.

• ValidationT

The ValidationT data type is the monad transformer for Validation. An instance of MonadTrans is provided for `(ValidationT err)`. Due to the arrangement of the ValidationT type constructor, which permits a `MonadTrans instance, there is no possible Bifunctor instance. Consequently, the ValidationB data type provides a Bifunctor instance (but not a MonadTrans instance). Library support is provided to exploit the isomorphism to ValidationB.

Note that since AccValidation is not a monad, there is also no corresponding monad transformer for this data type.

• ValidationB

The ValidationB data type is similar to the monad transformer for Validation (ValidationT), however, due to the arrangement of the ValidationB type constructor, which permits a Bifunctor instance, there is no possible MonadTrans instance. Consequently, the ValidationT data type provides a MonadTrans instance (but not a Bifunctor instance). Library support is provided to exploit the isomorphism to ValidationT.

• Data
  • Data.Validation