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 equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property -- of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no figure

Structural Resolution for Automated Verification

We pose a research question: Can the newly-developed structural resolution be used to extend co-inductive methods in automated theorem proving

Static Single Information Form for Abstract Compilation

In previous work we have shown that more precise type analysis can be achieved by exploiting union types and static single assignment (SSA) intermediate representation (IR) of code. In this paper we exploit static single information (SSI), an extension of SSA proposed in literature and adopted by some compilers, to allow assignments of more precise types to variables in conditional branches. In particular, SSI can be exploited rather easily and effectively to infer more precise types in dynamic object-oriented languages, where explicit runtime typechecking is frequently used. We show how the use of SSI form can be smoothly integrated with abstract compilation, our approach to static type analysis. In particular, we define abstract compilation based on union and nominal types for a simple dynamic object-oriented language in SSI form with a runtime typechecking operator, to show how precise type inference can be