Related papers: Termination Casts: A Flexible Approach to Terminat…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…

We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…

Let T be Goedel's system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of…

Teaching a computer to read and answer general questions pertaining to a document is a challenging yet unsolved problem. In this paper, we describe a novel neural network architecture called the Reasoning Network (ReasoNet) for machine…

Type-and-effect systems are a widely-used approach to program verification, verifying the result of a computation using types, and the behavior using effects. This paper extends an effect system for verifying temporal, value-dependent…

This paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear…

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

We propose an automated method for proving termination of $\pi$-calculus processes, based on a reduction to termination of sequential programs: we translate a $\pi$-calculus process to a sequential program, so that the termination of the…

We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…

We establish a calculus of differences for taut endofunctors of the category of sets, analogous to the classical calculus of finite differences for real valued functions. We study how the difference operator interacts with limits and…

We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…

There are many techniques and tools for termination of C programs, but up to now they were not very powerful for termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

This paper is a brief and informal presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility…

In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…

Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…

The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…