inversetype

Inversetype is a theoretical construct in computer science used to formalize bidirectional transformations between related data types. It represents a pairing of a forward function with a means to reconstruct the input from the output, under conditions that guarantee invertibility in practice.

Formally, an inversetype for types A and B consists of a forward function f: A -> B and an inverse candidate g: B -> A, with a guarantee that g(f(a)) = a for all a in A, and, when appropriate, f(g(b)) = b for b in the image of f. In practice, inverses may be partial or require extra context such as provenance or additional state to ensure reconstructability.

Common examples arise in reversible or bidirectional programming, data serialization formats with lossless encoding, and user interface syncing where edits can be undone by applying the inverse operation. A straightforward instance is a pair of inverse encoding and decoding functions, provided no information is lost in the process.

Applications include reversible computing, debuggability, round-trip data editing, and data provenance tracking. Limitations include that many real-world transformations are not inherently invertible, allowing loss of information or requiring extra metadata, which can complicate type systems and incur runtime overhead.

Related topics include bidirectional programming, reversible computing, and type isomorphisms.