Related papers: Rewriting Calculus: Foundations and Applications
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal categories, based on the observation that, under reasonable…
SQL query rewriting aims to reformulate a query into a more efficient form while preserving equivalence. Most existing methods rely on predefined rewrite rules. However, such rule-based approaches face fundamental limitations: (1) fixed…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the…
Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of…
We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we…
We positively answer the question A.1.6 in J. Klop's "Ustica Notes": "Is there a recursive normalizing one-step reduction strategy for micro $\lambda$-calculus?" Micro $\lambda$-calculus refers to an implementation of the $\lambda$-calculus…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…
Catalytic computing concerns space bounded computation which starts with memory full of data that have to be restored by the end of the computation. Lossy catalytic computing, defined by Gupta et al. (2024) and fully characterized by…
Embedding-based code retrieval often suffers when encoders overfit to surface syntax. Prior work mitigates this by using LLMs to rephrase queries and corpora into a normalized style, but leaves two questions open: how much representational…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a…
Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics. This paper is the first to apply…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…