Related papers: Type-two Iteration with Bounded Query Revision
We prove that omega^2 strictly bounds the iterations required for modal definable functions to reach a fixed point across all countable structures. The result corrects and extends the previously claimed result by the first and third authors…
We introduce a linear infinitary $\lambda$-calculus, called $\ell\Lambda_{\infty}$, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted…
The behavior of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the…
This paper provides foundations for strong (that is, possibly under abstraction) call-by-value evaluation for the lambda-calculus. Recently, Accattoli et al. proposed a form of call-by-value strong evaluation for the lambda-calculus, the…
Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped…
A system of session types is introduced as induced by a Curry Howard correspondence applied to Bounded Linear Logic, and then extending the thus obtained type system with probabilistic choices and ground types. The obtained system satisfies…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
We introduce a new, demand-driven variant of Spector's bar recursion in the spirit of the Berardi-Bezem-Coquand functional. The recursion takes place over finite partial functions $u$, where the control parameter $\varphi$, used in…
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
We consider answering queries on data available through access methods, that provide lookup access to the tuples matching a given binding. Such interfaces are common on the Web; further, they often have bounds on how many results they can…
Consider the problem of computing quantized linear functions with only a few queries. Formally, given $\mathbf{x}\in \mathbb{R}^k$, our goal is to encode $\mathbf{x}$ as $\mathbf{c} \in \mathbb{R}^n$, for $n > k$, so that for any…
In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous…
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
We investigate the interplay between a modality for controlling the behaviour of recursive functional programs on infinite structures which are completely silent in the syntax. The latter means that programs do not contain "marks" showing…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
This paper develops a new framework, \emph{simultaneous saturation}, designed to quantify the size of sets whose elements are simultaneously large. The framework establishes a correspondence between the magnitude of such sets and a system…