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We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…
The capability of in-context learning (ICL) enables large language models (LLMs) to perform novel tasks without parameter updates by conditioning on a few input-output examples. However, collecting high-quality examples for new or…
Usage similarity estimation addresses the semantic proximity of word instances in different contexts. We apply contextualized (ELMo and BERT) word and sentence embeddings to this task, and propose supervised models that leverage these…
Integrating LLM powered operators in declarative query languages allows for the combination of cheap and interpretable functions with powerful, generalizable language model reasoning. However, in order to benefit from the optimized…
Dense retrieval calls for discriminative embeddings to represent the semantic relationship between query and document. It may benefit from the using of large language models (LLMs), given LLMs' strong capability on semantic understanding.…
Tool-augmented large language models (LLMs) leverage external functions to extend their capabilities, but inaccurate function calls can lead to inefficiencies and increased costs.Existing methods address this challenge by fine-tuning LLMs…
How data is represented and operationalized is critical for building computational solutions that are both effective and efficient. A common approach is to represent data objects as binary vectors, denoted \textit{hash codes}, which require…
The purpose of this paper is to identify programs with control operators whose reduction semantics are in exact correspondence. This is achieved by introducing a relation $\simeq$, defined over a revised presentation of Parigot's…
Building Information Modeling (BIM) is widely used in the Architecture, Engineering, and Construction (AEC) industry, but the complexity of Industry Foundation Classes (IFC) limits accessibility for non-expert users. To address this, we…
In this paper, we show how to interpret a language featuring concurrency, references and replication into proof nets, which correspond to a fragment of differential linear logic. We prove a simulation and adequacy theorem. A key element in…
Initiated by Abramsky [1994], the Proofs as Processes agenda is to establish a solid foundation for the study of concurrent languages, by researching the connection between linear logic and the $\pi$-calculus. To date, Proofs as Processes…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
Large language models (LLMs) are increasingly deployed for understanding large codebases, but whether they understand operational semantics of long code context or rely on pattern matching shortcuts remains unclear. We distinguish between…
This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…
Grounded claim factuality checking is important for large language model (LLM) applications such as retrieval-augmented generation, as it helps users assess the correctness of generated outputs. Existing metrics using entailment classifiers…
Linear typed $\lambda$-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
We present two rewriting systems that define labelled explicit substitution lambda-calculi. Our work is motivated by the close correspondence between Levy's labelled lambda-calculus and paths in proof-nets, which played an important role in…
In order to understand the relative expressive power of larger concurrent programming languages, we analyze translations of small process calculi which model the communication and synchronization of concurrent processes. The source language…