相关论文: Rewriting Calculus: Foundations and Applications
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…
Rewriting Induction (RI) is a principle to prove that an equation over terms is an inductive theorem of a rewrite system, i.e., that any ground instance of the equation is a theorem of the rewrite system. RI has been adapted to several…
Binary rewriting is a rapidly-maturing technique for modifying software for instrumentation, customization, optimization, and hardening without access to source code. Unfortunately, the practical applications of binary rewriting tools are…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
Refactoring is a practice widely adopted during software maintenance and evolution. Due to its importance, there is extensive work on the effectiveness of refactoring in achieving code quality. However, developer's intentions are usually…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Feature attribution has gained prominence as a tool for explaining model decisions, yet evaluating explanation quality remains challenging due to the absence of ground-truth explanations. To circumvent this, explanation-guided input…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notion…
The Lasso has attracted the attention of many authors these last years. While many efforts have been made to prove that the Lasso behaves like a variable selection procedure at the price of strong (though unavoidable) assumptions on the…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
In this work, we address the problem of determining reliable policies in reinforcement learning (RL), with a focus on optimization under uncertainty and the need for performance guarantees. While classical RL algorithms aim at maximizing…
Abstraction is an important and useful concept in the field of artificial intelligence. To the best of our knowledge, there is no syntactic method to compute a sound and complete abstraction from a given low-level basic action theory and a…
We present and formalize h, a core (or "plank") calculus that can serve as the foundation for several compiler specification languages, notably CRSX (Combinatory Reductions Systems with eXtensions), HACS (Higher-order Attribute Contraction…
In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…