Related papers: Argument filterings and usable rules in higher-ord…
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…
Dependency pairs (DPs) are one of the most powerful techniques for automated termination analysis of term rewrite systems. Recently, we adapted the DP framework to the probabilistic setting to prove almost-sure termination (AST) via…
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…
Rewriting is a framework for reasoning about functional programming. The dependency pair criterion is a well-known mechanism to analyze termination of term rewriting systems. Functional specifications with an operational semantics based on…
In this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of $\beta$-reduction in the polymorphic $\lambda$-calculus, to prove the termination of various kinds of rewrite relations on…
We introduce a new formulation of the axiom of dependent choice that can be viewed as an abstract termination principle, which generalises the recursive path orderings used to establish termination of rewrite systems. We consider several…
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…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
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…
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…
We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
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…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Under current policy decision making paradigm, we make or evaluate a policy decision by intervening different socio-economic parameters and analyzing the impact of those interventions. This process involves identifying the causal relation…
In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like…