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.