Related papers: Recovering Purity with Comonads and Capabilities
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
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…
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…
We present an imperative object calculus where types are annotated with qualifiers for aliasing and mutation control. There are two key novelties with respect to similar proposals. First, the type system is very expressive. Notably, it…
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…
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
We demonstrate a compactness result holding broadly across supervised learning with a general class of loss functions: Any hypothesis class $H$ is learnable with transductive sample complexity $m$ precisely when all of its finite…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
Lambda calculi with algebraic data types lie at the core of functional programming languages and proof assistants, but conceal at least two fundamental theoretical problems already in the presence of the simplest non-trivial data type, the…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
Recent work on combinatory logic demonstrates a compositional translation from lambda calculus that gives meaning to open terms. As the meaning of open terms is a key difficulty in the study of metaprogramming, we investigate whether this…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $\lambda$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a…
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for…