Related papers: Type theory and rewriting
Several authors devised type-based termination criteria for ML-like languages allowing non-structural recursive calls. We extend these works to general rewriting and dependent types, hence providing a powerful termination criterion for the…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
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…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure…
The Size-Change Termination principle was first introduced to study the termination of first-order functional programs. In this work, we show that it can also be used to study the termination of higher-order rewriting in a system of…
Since Val Tannen's pioneer work on the combination of simply-typed lambda-calculus and first-order rewriting (LICS'88), many authors have contributed to this subject by extending it to richer typed lambda-calculi and rewriting paradigms,…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
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…
This paper shows how a recently developed view of typing as small-step abstract reduction, due to Kuan, MacQueen, and Findler, can be used to recast the development of simple type theory from a rewriting perspective. We show how standard…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
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…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
We study the termination problem for probabilistic term rewrite systems. We prove that the interpretation method is sound and complete for a strengthening of positive almost sure termination, when abstract reduction systems and term rewrite…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
We provide a general and modular criterion for the termination of simply-typed $\lambda$ -calculus extended with function symbols defined by user-defined rewrite rules. Following a work of Hughes, Pareto and Sabry for functions defined with…
This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed…