Program verification and Prolog

TL;DR: The directional type that the author derives from a logic program P is uniformly at least as precise as any discriminative directional type of P, i.e., any directional type out of the class for which the type checking algorithm of Aiken and Lakshman is sound and complete.

TL;DR: It is seen that when working over a fixed but arbitrary preinterpretation, a method can be provided for obtaining both a suitable model and a canonical level mapping which are sufficient for this purpose.

TL;DR: In this article, it was shown that directional-type checking for logic programs wrt. general regular types is Dexptime-complete and fixed-parameter linear, and that despite the exponential lower bound, the type system might be usable in practice.

TL;DR: This paper proposes a fourth semantics that associates with a “correctly typed” program the “well-typed” subset of its least Herbrand model, which is used to reason about partial correctness and absence of failures of correctly typed programs.