Related papers: A type-based termination criterion for dependently…

We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…

We study the derivational complexity of rewrite systems whose termination is provable in the dependency pair framework using the processors for reduction pairs, dependency graphs, or the subterm criterion. We show that the derivational…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

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 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…

Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean…

We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through pattern-based blocking. Previous approaches to related…

We define a type system with intersection types for an extension of lambda-calculus with unbind and rebind operators. In this calculus, a term with free variables, representing open code, can be packed into an "unbound" term, and passed…

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system 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…

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…

We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…

This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. We enrich this calculus with a type discipline to guarantee the soundness of reduction rules with respect…

Systems that are based on recursive Bayesian updates for classification limit the cost of evidence collection through certain stopping/termination criteria and accordingly enforce decision making. Conventionally, two termination criteria…

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…

There are many evaluation strategies for term rewrite systems, but automatically proving termination or analyzing complexity is usually easiest for innermost rewriting. Several syntactic criteria exist when innermost termination implies…

In this short paper, we consider a form of higher-order rewriting with a call-by-value evaluation strategy so as to model call-by-value programs. We briefly present a cost-size semantics to call-by-value rewriting: a class of algebraic…