Related papers: The unified higher-order dependency pair framework
We revisit the static dependency pair method for proving termination of higher-order term rewriting and extend it in a number of ways: (1) We introduce a new rewrite formalism designed for general applicability in termination proving of…
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
We extend the higher-order termination method of dynamic dependency pairs to Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms with algebraic reduction and separate {\beta}-steps are considered. For left-linear…
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…
Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the…
Dependency pairs constitute a series of very effective techniques for the termination analysis of term rewriting systems. In this paper, we adapt the static dependency pair framework to logically constrained simply-typed term rewriting…
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…
Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems automatically. We adapt dependency pairs to the probabilistic setting and develop an annotated dependency pair framework for…
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…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…
We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the…
Dependency pairs are one of the most powerful techniques for proving termination of term rewrite systems (TRSs), and they are used in almost all tools for termination analysis of TRSs. Problem #106 of the RTA List of Open Problems asks for…
Arts and Giesl proved that the termination of a first-order rewrite system can be reduced to the study of its "dependency pairs". We extend these results to rewrite systems on simply typed lambda-terms by using Tait's computability…
In this paper we present a combination framework for polynomial complexity analysis of term rewrite systems. The framework covers both derivational and runtime complexity analysis. We present generalisations of powerful complexity…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
This article is concerned with automated complexity analysis of term rewrite systems. Since these systems underlie much of declarative programming, time complexity of functions defined by rewrite systems is of particular interest. Among…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
The dependency pair (DP) framework is one of the most powerful techniques for automatic termination and complexity analysis of term rewrite systems. While DPs were extended to prove almost-sure termination of probabilistic term rewrite…