Realization of Coinductive Types

Realization of Coinductive Types

We give an explicit combinatorial construction of final coalgebras for a modest generalization of polynomial functors on Set. Type signatures are modeled as directed multigraphs instead of endofunctors. The final coalgebra for a type signature F involves the notion of Brzozowski derivative on sets of paths in F .

CoCaml: Programming with Coinductive Types

We present CoCaml, a functional programming language extending OCaml, which allows us to define functions on coinductive datatypes parameterized by an equation solver. We provide numerous examples that attest to the usefulness of the new programming constructs, including operations on infinite lists, infinitary λ-terms and p-adic numbers. keywords: coalgebraic types, functional programming, rec...

General recursion via coinductive types

A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of domain theory, and inductive definition of domain predicates. Here, a different solution is proposed: exploiti...

Coinductive Intersection Types are Completely Unsound

Guarded Dependent Type Theory with Coinductive Types

We present guarded dependent type theory, gDTT, an extensional dependent type theory with a ‘later’ modality and clock quantifiers for programming and proving with guarded recursive and coinductive types. The later modality is used to ensure the productivity of recursive definitions in a modular, type based, way. Clock quantifiers are used for controlled elimination of the later modality and fo...