Identityeither

Identityeither is a conceptual wrapper that combines the Identity functor with the Either sum type to model computations that may fail with an error or succeed with a value, while preserving an identity context. The term is not part of a single canonical standard; it appears in some library sketches and discussions as a lightweight alias around a value of type Either e a wrapped in an Identity-like container.

In a Haskell-like pseudocode, IdentityEither can be defined as a newtype: newtype IdentityEither e a = IdentityEither { runIdentityEither :: Either e a }. The behavior is that fmap maps over the Right case, while the Left case propagates unchanged. For example, fmap f (IdentityEither (Right a)) yields IdentityEither (Right (f a)), and fmap f (IdentityEither (Left e)) yields IdentityEither (Left e). The Applicative and Monad interfaces align with the corresponding Either instances, so the monadic or applicative structure is governed by the Either semantics, with the Identity wrapper acting as a no-op in terms of computational effects.

A key property is that IdentityEither e a is isomorphic to Either e a. The Identity wrapper does not add computational context beyond what Either already provides, so many operations behave identically to working directly with Either. This makes IdentityEither useful as a signaling device in type signatures or as a building block in type-level design, where the intent is to emphasize the preservation of an identity context alongside potential failure.

Relation to transformers: in monad transformer patterns, developers often use EitherT e m a to embed error handling in a base monad. IdentityEither can serve as a non-transformer, straightforward wrapper when an identity context needs explicit representation in types, or as a convenient stepping stone within more complex compositions.

See also: Either, Identity, Maybe, EitherT, IdentityT.