Coherencefor

Coherencefor is a term used in theoretical computer science and category theory to denote a framework or property that ensures coherence conditions hold for a class of compositional structures. The phrase is often encountered in discussions of when different ways of composing operations yield the same result, up to specified isomorphisms. In practice, coherencefor refers to providing a set of coherence laws—diagrams that must commute—for a given structure, such as a monoidal category, operad, or type constructor. The goal is to guarantee that all higher-level constructions built from basic operations behave predictably.

In mathematical contexts, coherence for monoidal categories is a classic example: every diagram built from associators and unitors commutes, allowing one to ignore parenthesization or unit placement. The term coherencefor is sometimes used to describe either a particular formalization of these conditions or a programmable framework to verify them within a system.

In computer science, coherencefor appears in language design and formal verification as a method to ensure that optimizations, transformations, or rewrites preserve semantics. A coherencefor framework might include a language to declare coherence laws, a verification engine that checks diagram commutativity, and tooling to generate canonical representations from equivalent expressions.

Criticism notes that the term is not universally standardized and is sometimes used informally to discuss coherence phenomena rather than as a formal name. See also coherence theorem, monoidal categories, and Mac Lane’s coherence results.