Related papers: Characterisation of Approximation and (Head) Norma…
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,…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
We characterize in simple terms the Pak-Stanley labels $\lambda(R)$ of the regions $R$ of the $m$-Catalan arrangement. We also propose a simple algorithm that returns $R$ from $\lambda(R)$. Finally, we characterize in close terms the labels…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
A polarized version of Girard, Scedrov and Scott's Bounded Linear Logic is introduced and its normalization properties studied. Following Laurent, the logic naturally gives rise to a type system for the lambda-mu-calculus, whose derivations…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
We introduce the notion of $\lambda$-equivalence and $\lambda$-embeddings of objects in suitable categories. This notion specializes to $L_{\infty\lambda}$-equivalence and $L_{\infty\lambda}$-elementary embedding for categories of…
We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no…
We introduce a Curry-Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The…
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for approximating elements, approximation of individual elements,…
A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common…
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…
Identifying texts with a given semantics is central for many information seeking scenarios. Similarity search over vector embeddings appear to be central to this ability, yet the similarity reflected in current text embeddings is…
We present a quantitative, statistical analysis of random lambda terms in the de Bruijn notation. Following an analytic approach using multivariate generating functions, we investigate the distribution of various combinatorial parameters of…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…
We survey several methods of generating large random lambda-terms, focusing on their closed and simply-typed variants. We discuss methods of exact- and approximate-size generation, as well as methods of achieving size-uniform and…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonalities in polysemy patterns---how languages package up meanings into words. Recent computational research has enabled…