Confluence of Prefix-Constrained Rewrite Systems

Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L: l -> r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix\u27s critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one

SAT Competition 2020

The SAT Competitions constitute a well-established series of yearly open international algorithm implementation competitions, focusing on the Boolean satisfiability (or propositional satisfiability, SAT) problem. In this article, we provide a detailed account on the 2020 instantiation of the SAT Competition, including the new competition tracks and benchmark selection procedures, overview of solving strategies implemented in top-performing solvers, and a detailed analysis of the empirical data obtained from running the competition

SAT Competition 2020

The SAT Competitions constitute a well-established series of yearly open international algorithm implementation competitions, focusing on the Boolean satisfiability (or propositional satisfiability, SAT) problem. In this article, we provide a detailed account on the 2020 instantiation of the SAT Competition, including the new competition tracks and benchmark selection procedures, overview of solving strategies implemented in top-performing solvers, and a detailed analysis of the empirical data obtained from running the competition. (C) 2021 The Authors. Published by Elsevier B.V.Peer reviewe

Applications and extensions of context-sensitive rewriting

[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312

Natural type inference

Recently, dynamic language users have started to recognize the value of types in their code. To fulfil this need, many popular dynamic languages have adopted extensions that support type annotations. A prominent example is that of TypeScript which offers a module system, classes, interfaces, and an optional type system on top of JavaScript. However, providing usable (not too verbose, or complex) types via traditional type inference is more challenging in optional type systems. Motivated by this, we redefine the goal of type inference for optionally typed languages as: infer the maximally natural and sound type, instead of the most general one. By the maximally natural and sound, we refer to a type that (1) is derivable in the type system, and (2) maximally reflects the intention of the programmer with respect to a learnt model. We formally devise a type inference problem that aids the inference of the maximally natural type. Towards this goal, our problem asks to combine information derived from two sources: (1) from algorithmic type systems using deductive logic-based techniques; and (2) from the source code text using inductive machine learning techniques. To tackle our formulated problem, we develop two frameworks that combine the two sources of information using mathematical optimization. In the first framework, we formulate the inference problem as a problem in numerical optimization. In the second framework, we map the inference problem into popular problems in discrete optimization: maximum satisfiability (MaxSAT) and Integer Linear Programming (ILP). Both frameworks are built to be consistent with information derived from the different sources. Moreover, through formal proofs, we validate the soundness and completeness of the developed framework for a core lambda-calculus with named types. To assess the efficacy of the developed frameworks, we implement them in a tool named Optyper that realizes natural type inference for TypeScript. We evaluate Optyperon TypeSript programs obtained from real world projects. By evaluating our theoretical frameworks we show that, in practice, the combination of logical and natural constraints yields a large improvement in performance over either kind of information individually. Further, we demonstrate that our frameworks out-perform state-of-the-art techniques in type inference to produce natural and sound types