Related papers: On stratified regions

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…

Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the…

This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…

Functional languages with strong static type systems have beneficial properties to help ensure program correctness and reliability. Surprisingly, their practical significance in applications is low relative to other languages lacking in…

Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…

Strategy-proof mechanisms are widely used in market design. In an abstract allocation framework where outside options are available to agents, we obtain two results for strategy-proof mechanisms. They provide a unified foundation for…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

In this paper we first show that every non-zero $\tau$-rigid $A$-module induces at least one stratifying system in the module category of $A$. Moreover, we show that each of these stratifying systems can be seen as a signed…

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…

In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and…

Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…

We study a classical realizability model (in the sense of J.-L. Krivine) arising from a model of untyped lambda calculus in coherence spaces. We show that this model validates countable choice using bar recursion and bar induction.

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…

We present a novel approach to termination analysis. In a first step, the analysis uses a program as a black-box which exhibits only a finite set of sample traces. Each sample trace is infinite but can be represented by a finite lasso. The…

Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…

Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…

In type-and-coeffect systems, contexts are enriched by coeffects modeling how they are actually used, typically through annotations on single variables. Coeffects are computed bottom-up, combining, for each term, the coeffects of its…