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The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension…
The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication…
We compare mechanisms for compensation handling and dynamic update in calculi for concurrency. These mechanisms are increasingly relevant in the specification of reliable communicating systems. Compensations and updates are intuitively…
We introduce the task of cross-lingual semantic parsing: mapping content provided in a source language into a meaning representation based on a target language. We present: (1) a meaning representation designed to allow systems to target…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
Pre-trained text encoders have drawn sustaining attention in natural language processing (NLP) and shown their capability in obtaining promising results in different tasks. Recent studies illustrated that external self-supervised signals…
Foundation models have achieved great advances in multi-task learning with a unified interface of unimodal and multimodal tasks. However, the potential of such multi-task learners has not been exploited during transfer learning. In this…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
We derive and discuss a technique for manipulating power series which is complementary to standard procedures. We begin with the translation operator, but we express the operator as an infinite product instead of expanding it as a series…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
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…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, $\lambda_\rho$, follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide…
Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…
Continuous prompts, or "soft prompts", are a widely-adopted parameter-efficient tuning strategy for large language models, but are often less favorable due to their opaque nature. Prior attempts to interpret continuous prompts relied on…
This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
We develop and investigate several cross-lingual alignment approaches for neural sentence embedding models, such as the supervised inference classifier, InferSent, and sequential encoder-decoder models. We evaluate three alignment…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…