Adding modular predicates to first-order fragments

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which successfully covers the quantifier alternation hierarchy of first order logic and some of its fragments. We obtain that deciding this problem for each level of the alternation hierarchy of both first order logic and its two-variable fragment when equipped with all regular numerical predicates is not harder than deciding it for the corresponding level equipped with only the linear order and the successor. For two-variable fragments we also treat the case of the signature containing only the order and modular predicates.Relying on some recent results, this proves the decidability for each level of the alternation hierarchy of the two-variable first order fragmentwhile in the case of the first order logic the question remains open for levels greater than two.The main ingredients of the proofs are syntactic transformations of first order formulas as well as the algebraic framework of finite categories

Incremental and Modular Context-sensitive Analysis

Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few components, and it is desirable to reuse as much as possible previous analysis results. This has been achieved to date through incremental global analysis fixpoint algorithms that achieve cost reductions at fine levels of granularity, such as changes in program lines. However, these fine-grained techniques are not directly applicable to modular programs, nor are they designed to take advantage of modular structures. This paper describes, implements, and evaluates an algorithm that performs efficient context-sensitive analysis incrementally on modular partitions of programs. The experimental results show that the proposed modular algorithm shows significant improvements, in both time and memory consumption, when compared to existing non-modular, fine-grain incremental analysis techniques. Furthermore, thanks to the proposed inter-modular propagation of analysis information, our algorithm also outperforms traditional modular analysis even when analyzing from scratch.Comment: 56 pages, 27 figures. To be published in Theory and Practice of Logic Programming. v3 corresponds to the extended version of the ICLP2018 Technical Communication. v4 is the revised version submitted to Theory and Practice of Logic Programming. v5 (this one) is the final author version to be published in TPL

A new module system for prolog

It is now widely accepted that separating programs into modules has proven very useful in program development and maintenance. While many Prolog implementations include useful module systems, we feel that these systems can be improved in a number of ways, such as, for example, being more amenable to effective global analysis and allowing sepárate compilation or sensible creation of standalone executables. We discuss a number of issues related to the design of such an improved module system for Prolog. Based on this, we present the choices made in the Ciao module system, which has been designed to meet a number of objectives: allowing sepárate compilation, extensibility in features and in syntax, amenability to modular global analysis, etc

TOR: modular search with hookable disjunction

Horn Clause Programs have a natural exhaustive depth-first procedural semantics. However, for many programs this semantics is ineffective. In order to compute useful solutions, one needs the ability to modify the search method that explores the alternative execution branches. Tor, a well-defined hook into Prolog disjunction, provides this ability. It is light-weight thanks to its library approach and efficient because it is based on program transformation. Tor is general enough to mimic search-modifying predicates like ECLiPSe's search/6. Moreover, Tor supports modular composition of search methods and other hooks. The Tor library is already provided and used as an add-on to SWI-Prolog.publisher: Elsevier articletitle: Tor: Modular search with hookable disjunction journaltitle: Science of Computer Programming articlelink: http://dx.doi.org/10.1016/j.scico.2013.05.008 content_type: article copyright: Copyright © 2013 Elsevier B.V. All rights reserved.status: publishe

Monadic Second-Order Logic with Arbitrary Monadic Predicates

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent characterizations. We consider the regularity question: given a language in this class, when is it regular? To answer this, we show a substitution property and the existence of a syntactical predicate. We give three applications. The first two are to give very simple proofs that the Straubing Conjecture holds for all fragments of MSO with monadic predicates, and that the Crane Beach Conjecture holds for MSO with monadic predicates. The third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.Comment: Conference version: MFCS'14, Mathematical Foundations of Computer Science Journal version: ToCL'17, Transactions on Computational Logi