Coalgebraic logic programming: from semantics to implementation

Corecursive definitions, such as that of a stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value while infinite SLD-derivations are of considerable value. Such definitions give rise to questions of parallelism, and logic programs can have both recursive and corecursive features at once. Observational and coalgebraic semantics have been used to study them abstractly. The programming developments have often occurred separately and have usually been implementation-led. Here, we give a coherent semantics-led account of the issues, starting with abstract category theoretic semantics, developing coalgebra to characterise naturally arising trees, and proceeding towards implementation of a new dialect, CoALP, of logic programming, characterised by guarded recursion and parallelism.