Coalgebraic Logic Programming: from Semantics to Implementation

Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops.  Such definitions give rise to complex questions of evaluation and parallelism, as execution of such 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 and developing coalgebra to characterise naturally arising trees. This has been used by Ekaterina Komendantskaya and her group (but I will not discuss it in this talk) to proceed towards implementation of a new dialect, CoALP, of logic programming, characterised by guarded lazy corecursion and parallelism.