相关论文: Rewriting Calculus: Foundations and Applications

We present a new version of ReLoC: a relational separation logic for proving refinements of programs with higher-order state, fine-grained concurrency, polymorphism and recursive types. The core of ReLoC is its refinement judgment $e…

Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…

Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…

Automatic query reformulation refers to rewriting a user's original query in order to improve the ranking of retrieval results compared to the original query. We present a general framework for automatic query reformulation based on…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…

Undo and redo functionality is ubiquitous in collaboration software. In single user settings, undo and redo are well understood. However, when multiple users edit a document, concurrency may arise, leading to a non-linear operation history.…

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…

This paper addresses the problem of creating simplifiers for logic formulas based on conditional term rewriting. In particular, the paper focuses on a program synthesis application where formula simplifications have been shown to have a…

First, we extend Leifer-Milner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching. Moreover, we study the weak variant…

We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…

Reinforcement learning (RL) has proven remarkably effective at improving the accuracy of language models in verifiable and deterministic domains like mathematics. Here, we examine if current RL methods are also effective at optimizing…

Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the…

The existing call-by-need lambda calculi describe lazy evaluation via equational logics. A programmer can use these logics to safely ascertain whether one term is behaviorally equivalent to another or to determine the value of a lazy…

We propose a general framework for first-order functional logic programming, supporting lazy functions, non-determinism and polymorphic datatypes whose data constructors obey a set C of equational axioms. On top of a given C, we specify a…

Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for…

Term rewriting is a Turing complete model of computation. When taught to students of computer science, key properties of computation as well as techniques to analyze programs on an abstract level are conveyed. This paper gives a swift…

Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…

Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…

All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…