36 research outputs found
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
Exploiting parallelism in coalgebraic logic programming
We present a parallel implementation of Coalgebraic Logic Programming (CoALP)
in the programming language Go. CoALP was initially introduced to reflect
coalgebraic semantics of logic programming, with coalgebraic derivation
algorithm featuring both corecursion and parallelism. Here, we discuss how the
coalgebraic semantics influenced our parallel implementation of logic
programming
Sound Regular Corecursion in coFJ
The aim of the paper is to provide solid foundations for a programming paradigm natively supporting the creation and manipulation of cyclic data structures. To this end, we describe coFJ, a Java-like calculus where objects can be infinite and methods are equipped with a codefinition (an alternative body). We provide an abstract semantics of the calculus based on the framework of inference systems with corules. In coFJ with this semantics, FJ recursive methods on finite objects can be extended to infinite objects as well, and behave as desired by the programmer, by specifying a codefinition. We also describe an operational semantics which can be directly implemented in a programming language, and prove the soundness of such semantics with respect to the abstract one
Corecursive featherweight Java revisited
We describe a Java-like calculus which supports cyclic data structures, and offers a mechanism of flexible regular corecursion for their manipulation. The calculus enhances an earlier proposal by a more sophisticated reduction semantics, which filters out, by an additional check, some spurious results which were obtained in the previous model
Enhancing Expressivity of Checked Corecursive Streams
We propose a novel approach to stream definition and manipulation. Our solution is based on two key ideas. Regular corecursion, which avoids non termination by detecting cyclic calls, is enhanced, by allowing in equations defining streams other operators besides the stream constructor. In this way, some non-regular streams are definable. Furthermore, execution includes a runtime check to ensure that the stream generated by a function call is well-defined, in the sense that access to an arbitrary index always succeeds. We extend the technique beyond the simple stream operators considered in previous work, notably by adding an interleaving combinator which has a non-trivial recursion scheme
Structural Resolution with Co-inductive Loop Detection
A way to combine co-SLD style loop detection with structural resolution was
found and is introduced in this work, to extend structural resolution with
co-induction. In particular, we present the operational semantics, called
co-inductive structural resolution, of this novel combination and prove its
soundness with respect to the greatest complete Herbrand model.Comment: In Proceedings CoALP-Ty'16, arXiv:1709.0419
Enhancing Regular Corecursion
Nowadays, data structures which are conceptually infinite, such as streams or infinite trees, are very common in computer science. When it comes to their manipulation, one major problem to face is how to finitely represent and deal with them without incurring in non-terminating behaviours. Regular corecursion is a solution relying on finite representation of regular data structures, and detection of cyclic calls. The topics in the thesis revolve around two enhancements of regular corecursion in different directions. In the first part, we present Corecursive Featherweight Java (coFJ), an object-oriented calculus which supports flexible regular corecursion, that is, allows the programmer to specify the behaviour when a cyclic call is found. In the second part, instead, we extend regular corecursion beyond regular terms, focusing on the significant case of stream definitions