Related papers: Geometry of Resource Interaction - A Minimalist Ap…
The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…
In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and…
We give a geometry of interaction model for a typed lambda-calculus endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. The…
In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
Twenty years after its introduction by Ehrhard and Regnier, differentiation in $\lambda$-calculus and in linear logic is now a celebrated tool. In particular, it allows to establish a Taylor expansion formula for various $\lambda$-calculi,…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
The resource calculus is an extension of the lambda-calculus allowing to model resource consumption. It is intrinsically non-deterministic and has two general notions of reduction - one parallel, preserving all the possible results as a…
The Geometry of Interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
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 present an algorithm turning any term of a linear quantum $\lambda$-calculus into a quantum circuit. The essential ingredient behind the proposed algorithm is Girard's geometry of interaction, which, differently from its well-known uses…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
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…
The relational semantics of linear logic is a powerful framework for defining resource-aware models of the $\lambda$-calculus. However, its quantitative aspects are not reflected in the preorders and equational theories induced by these…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally…
We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic:…