Coalgebraic logic programming: from Semantics to Implementation

Abstract

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 questions of lazy corecursive derivations 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, developing coalgebra to characterise naturally arising trees, and proceeding towards implementation of a new dialect, CoALP, of logic programming, characterised by guarded lazy corecursion and parallelism.

Structural Resolution with Co-inductive Loop Detection

“…For more details on structural resolution, see [13,11,15]. Next we introduce the combination of structural resolution and co-SLD style loop detection.…”

“…Co-inductive logic programming extends traditional logic programming by enabling co-inductive reasoning to deal with infinite SLD-derivation, which has practical implication in different fields of computing such as model checking, planning as well as type inference [21,20,2,15].…”

“…One operational semantics of co-inductive logic programming is co-inductive SLD resolution (co-SLD) [21,20], which combines loop detection with traditional SLD resolution, so that it can be used to reason co-inductively about infinite rational terms. An alternative operational semantics for coinductive logic programming is co-algebraic logic programming [15,13], which adopts a more general co-induction rule and uses structural resolution instead of SLD resolution as its induction rule.…”

Structural Resolution for Abstract Compilation of Object-Oriented Languages

“…S-resolution [19,16,11] stratifies the SLD-derivation steps into those done by term-matching and those requiring full unification. Term-matching in this case plays a role that pattern-matching on constructors of data structures plays in functional programming.…”

Logic programming: Laxness and saturation

“…[4]. That fact has formed the basis for our work on lax semantics [1,10,11,12,13] and for Bonchi and Zanasi's work on saturation semantics [14,2].…”