validation

A data type like Either but with an accumulating Applicative instance.

The Validation 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. Validation is an example of, "An applicative functor that is not a monad."

The library provides:

Classy optics (GetValidation, HasValidation, ReviewValidation, AsValidation) following the conventions of makeClassy and makeClassyPrisms from lens. Polymorphic prisms (__Failure, __Success) for type-changing operations. Isomorphisms to Either and (Bool, a).

ValidationMonadT err m a is a monad transformer wrapping m (Validation err a). Unlike Validation, it has short-circuiting Applicative, Bind, Monad, and MonadError instances.

Four validator newtypes wrap a validation function with different type parameter orders, enabling different class instances:

Validator x err a — Bifunctor, accumulating Applicative, Either-like Alt ValidatorProfunctor err x a — Profunctor, accumulating Applicative ValidatorMonadT x err f a — Monad, MonadTrans, BindTrans ValidatorMonadProfunctorT err f x a — Profunctor, Monad, Category, Arrow

All four are isomorphic and have cross-type optics instances.

Validator is the odd one out in its Alt instance. For the other three validators, <!> accumulates errors when both sides fail. For Validator, <!> behaves like Either: the first success wins, otherwise the second failure is returned. Validator has no Plus or Alternative instance, and its <> still accumulates errors.