Related papers: A typed parallel {\lambda}-calculus via 1-depth in…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…
The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
Motivated by potential applications to theoretical computer science, in particular those areas where the Curry-Howard correspondence plays an important role, as well as by the ongoing search in pure mathematics for feasible approaches to…
Multi types---aka non-idempotent intersection types---have been used to obtain quantitative bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the same time the number of evaluation steps and the size of…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
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…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
We give an elementary and purely arithmetical proof of the strong normalization of Parigot's simply typed $\lambda\mu$-calculus.
The aim of this work is to characterize three fundamental normalization proprieties in lambda-calculus trough the Taylor expansion of $ \lambda$-terms. The general proof strategy consists in stating the dependence of ordinary reduction…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Session types are a typed approach to message-passing concurrency, where types describe sequences of intended exchanges over channels. Session type systems have been given strong logical foundations via Curry-Howard correspondences with…
We present $\lambda_B$, a quantum-control $\lambda$-calculus that refines previous basis-sensitive systems by allowing abstractions to be expressed with respect to arbitrary -- possibly entangled -- bases. Each abstraction and let construct…
The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions.…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
While transistor density is still increasing, clock speeds are not, motivating the search for new parallel architectures. One approach is to completely abandon the concept of CPU -- and thus serial imperative programming -- and instead to…
Formal mathematics and computer science proofs are formalized using Hilbert-Russell-style logical systems which are designed to not admit paradoxes and self-refencing reasoning. These logical systems are natural way to describe and reason…