Confluence of Conditional Term Rewrite Systems via Transformations

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems. Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with certain syntactic properties like weak left-linearity. These syntactic properties imply that the transformations are sound for the given CTRS. This paper shows how to use transformations to prove confluence of operationally terminating, right-stable deterministic conditional term rewrite systems without the necessity of soundness restrictions. For this purpose, it is shown that certain rewrite strategies, in particular almost U-eagerness and innermost rewriting, always imply soundness

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

Verifying procedural programs via constrained rewriting induction

This paper aims to develop a verification method for procedural programs via a transformation into Logically Constrained Term Rewriting Systems (LCTRSs). To this end, we extend transformation methods based on integer TRSs to handle arbitrary data types, global variables, function calls and arrays, as well as encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations, so in contrast to other works, we do not require an explicit specification in a separate specification language

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field

Deduction-Based Software Component Retrieval

Deduction-based software component retrieval is a software reuse technique that uses formal specifications as component descriptors and as search keys; matching components are identified using an automated theorem prover. This dissertation contains a detailed theoretical investigation of the concept as well as the first substantial experimental evaluation of its technical feasibility.Deduktionsbasiertes Kompenentenretrieval ist eine Softwarereusetechnik, in der formale Spezifikationen zur Beschreibung von Komponenten sowie als Anfragen verwendet werden; passende Komponenten werden mit Hilfe eines automatischen Theorembeweisers ermittelt. Diese Arbeit enthält eine detaillierte theoretische Untersuchung dieses Konzeptes und die erste ausführliche experimentelle Evaluierung seiner technischen Realisierbarkeit

Structural theories of modelling token causation.

This thesis deals with the most prominent accounts of analyzing singular event causation by employing counterfactuals or counterfactual information. The classic counterfactual account of token event causation was proposed in 1973 by the philosopher David Lewis and ruled that an event c is a cause of event e, if and only if there is a chain of counterfactually dependent events between c and e. Apart from facing conceptual problems due to its metaphysical claim to analyze causation 'as such' and to reduce it to counterfactual dependency, this account also produced implausible results: first, it stipulated that token causation is a transitive relation, and second, it could not analyze situations in which an effect is over-determined by various causes, either symmetrically or by one cause pre-empting another one. In 2000, almost three decades later, Judea Pearl, formerly an engineer, formulated a new and highly influential theory of modeling causal dependencies using counterfactual information that, as I argue, neither faces these conceptual problems nor produces these undesired results. This formal theory analyzes causal relationships between token events in a given situation in two steps: first, a causal model describing the relevant mechanisms at work in the situation is constructed, and second, causal relationships between the events featured in the situation are determined relatively to this model. Pearl's definition of causation according to a model is technically complicated, but its underlying rationale is that the decisive property of a cause is to sustain its effect via a certain causal process against possible contingencies, this notion of sustenance embodying an aspect of production and an aspect of counterfactual dependency. This theory of Pearl's was received with great interest in the philosophical community, most importantly by Christopher Hitchcock and James Woodward, who tried to simplify this account while preserving the basic intuition that a cause is linked to its effect by a causal process, in essence a concatenation of the mechanisms at work in the situation, just defining a causal process in a formally simpler way. I describe and employ this simplified account by Hitchcock and Woodward as a graphic introduction to Pearl's theory, because the same basic notions, like the one of a causal model, are defined in a formally more accessible way and the basic problems, like the generation of a causal model, become obvious. I mainly discuss Hitchcock's account, since this is the earlier one, since it is more elaborate, and mainly since it is conceptually in need of clarification. Woodward's account is in essence equivalent to Hitchcock's, given a slightly changed terminology. The core of my thesis consists of a comparison of Pearl's theory with Hitchcock's account. I present four paradigmatic examples, three of which are judged differently by these two theories. In each of these three examples our causal intuition is in accord with the judgment delivered by Pearl's account but contradicts the verdict of Hitchcock's. I draw the conclusion that Hitchcock's project of simplifying Pearl's theory fails in the second step of causal analysis, i.e. in defining causation according to a given model. Building on the lessons learned from this comparison, I offer a slight generalization of Pearl's definition of token causation according to a model, since Pearl's original account has the shortcoming that token causes cannot be exogenous in a model