Copatternbased

Copatternbased refers to programming and formal methods that rely on copatterns as the primary means of defining data and corecursive computations, especially for coinductive or potentially infinite structures. A copattern is a pattern that matches over a value's observations rather than its constructors; for streams, this means specifying how to observe the next element (head) and how to obtain the rest (tail) rather than how to build a stream.

This approach is dual to the traditional inductive definitions that use algebraic data types and constructors. It emphasizes productivity and guarded corecursion, ensuring that infinite structures can be defined safely by observing their outputs rather than constructing them all at once. In theory, copatternbased relates to coalgebras and the categorical dual of algebras, providing a natural model for processes and ongoing behavior.

Practically, it appears in some languages and proof tools where copattern-like constructs or libraries exist; common use cases include streams, reactive systems, and other coinductive data types. The approach can improve modularity and clarity when defining observable behavior, but it can also introduce reasoning complexity and require tooling support to enforce productivity and termination conditions. As with any coinductive style, careful design is needed to avoid non-terminating definitions or hidden dependencies.