
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.
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."
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.
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.
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.
The Validation err a` type-alias is equivalent to
`ValidationT err Identity a` and so is isomorphic to Either and others.
Libraries are supplied accordingly.