ghc-validation

A data-type like Either but with an accumulating Applicative

<<http://i.imgur.com/Ns5hntl.jpg>>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`. * `Validation'` 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.

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