invartype

Invartype is a theoretical concept in programming language theory used to describe a class of types that represent the inverse of a given type's mapping under certain operations. The term combines inverse and type, and is used primarily in informal discussions and thought experiments about bidirectional type systems and reversible computation. In such a framework, an Invartype associated with a type T encodes the information needed to reconstruct inputs from outputs when a function f: X -> T is invertible, typically supplemented by a backward function g: T -> X with the property g(f(x)) = x for all x in X. Invartypes are discussed in relation to bidirectional type checking, type inference, and refinement typing, where the availability of an inverse operation can simplify type derivations and enable back-propagation of constraints from outputs to inputs.

In practice, Invartype is considered only when invertibility constraints hold and information is not lost, limiting applicability to bijective or lossless mappings. They are sometimes treated as a theoretical aid to reason about reversibility and provenance in data processing, or to model reversible computations where every step is invertible.

Criticism notes that Invartype demands stringent conditions such as bijectivity and may introduce overhead for maintaining inverse mappings, making it largely of academic interest rather than mainstream adoption. Nonetheless, it is cited as a conceptual tool for exploring the links between type theory, programming language design, and reversible computation.

See also: inverse function, bijection, reversible computing, bidirectional type checking, type inference.