Related papers: Dependency Pairs Termination in Dependent Type The…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
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…
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…
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…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
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 study the derivational complexity induced by the dependency pair method, enhanced with standard refinements. We obtain upper bounds on the derivational complexity induced by the dependency pair method in terms of the derivational…
We present two methods for proving confluence of left-linear term rewrite systems. One is hot-decreasingness, combining the parallel/development closedness theorems with rule labelling based on a terminating subsystem. The other is…
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…
We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…
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…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
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…
This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
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…
In the dependency pair framework for proving termination of rewriting systems, polynomial interpretations are used to transform dependency chains into bounded decreasing sequences of integers, and they play an important role for the success…
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…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…