Related papers: A static higher-order dependency pair framework

Algorithms having uniform convergence with respect to their initial condition (i.e., with fixed-time stability) are receiving increasing attention for solving control and observer design problems under time constraints. However, we still…

Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…

On the one hand, checking specific termination proofs by hand, say using a particular collection of matrix interpretations, can be an arduous and error-prone task. On the other hand, automation of such checks would save time and help to…

Modern processors deploy a variety of weak memory models, which for efficiency reasons may (appear to) execute instructions in an order different to that specified by the program text. The consequences of instruction reordering can be…

We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…

Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to…

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

Despite the impressive growth of the abilities of multilingual language models, such as XLM-R and mT5, it has been shown that they still face difficulties when tackling typologically-distant languages, particularly in the low-resource…

We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…

In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…

We generalise the termination method of higher-order polynomial interpretations to a setting with impredicative polymorphism. Instead of using weakly monotonic functionals, we interpret terms in a suitable extension of System F-omega. This…

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…

We present a new modular proof method of termination for second-order computation, and report its implementation SOL. The proof method is useful for proving termination of higher-order foundational calculi. To establish the method, we use a…

In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…

Component substitution has numerous practical applications and constitutes an active research topic. This paper proposes to enrich an existing component-based framework--a model with dynamic reconfigurations making the system evolve--with a…

Session types are used to describe and structure interactions between independent processes in distributed systems. Higher-order types are needed in order to properly structure delegation of responsibility between processes. In this paper…

Efficient pattern matching is fundamental for practical term rewrite engines. By preprocessing the given patterns into a finite deterministic automaton the matching patterns can be decided in a single traversal of the relevant parts of the…

We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…

This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair…