Recursion and corecursion have the same equational logic

Recursion and corecursion have the same equational logic

This paper is concerned with the equational logic of corecursion, that is of definitions involving final coalgebra maps. The framework for our study is iteration theories (cf. e.g. Bloom and Ésik [?, ?]), recently re-introduced as models of the FLR0 fragment of the Formal Language of Recursion [?, ?, ?]. We present a new class of iteration theories derived from final coalgebras. This allows us ...

Ramified Structural Recursion and Corecursion

We investigate feasible computation over a fairly general notion of data and codata. Specifically, we present a direct Bellantoni-Cookstyle normal/safe typed programming formalism, RS1 , that expresses feasible structural recursions and corecursions over data and codata specified by polynomial functors. (Lists, streams, finite trees, infinite trees, etc. are all directly definable.) A novel asp...

Using Structural Recursion for Corecursion

We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq, AGDA, and other higher-order proof assistants. In this paper, we concentrate in particular on those nonguarded equations where recursive calls appear under f...

Productive corecursion in logic programming

Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but...

Equational Logic and Equational Theories of Algebras