Related papers: Expansion for Universal Quantifiers
We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
Abbreviation expansion is a strategy used to speed up communication by limiting the amount of typing and using a language model to suggest expansions. Here we look at personalizing a Large Language Model's (LLM) suggestions based on prior…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
Python's typing system has evolved pragmatically into a powerful but theoretically fragmented system, with scattered specifications. This paper proposes a formalization to address this fragmentation. The central contribution is a formal…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
We extend the semantics and type system of a lambda calculus equipped with common constructs to be "resource-aware". That is, the semantics keeps track of the usage of resources, and is stuck, besides in case of type errors, if either a…
Fine-grained entity typing is the task of assigning fine-grained semantic types to entity mentions. We propose a neural architecture which learns a distributional semantic representation that leverages a greater amount of semantic context…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
The vocabulary mismatch problem is one of the important challenges facing traditional keyword-based Information Retrieval Systems. The aim of query expansion (QE) is to reduce this query-document mismatch by adding related or synonymous…
In the pure Calculus of Constructions (CC) one can define data types and function over these, and there is a powerful higher order logic to reason over these functions and data types. This is due to the combination of impredicativity and…
Modern information retrieval must reconcile short, ambiguous queries with increasingly diverse and dynamic corpora. Query expansion (QE) remains a core technique for mitigating vocabulary mismatch, but its design space has been reshaped by…
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…