Related papers: Stability Property for the Call-by-Value $\lambda$…
We show that an intuitionistic version of counting propositional logic corresponds, in the sense of Curry and Howard, to an expressive type system for the probabilistic event lambda-calculus, a vehicle calculus in which both call-by-name…
Effect and coeffect tracking integrate many types of compile-time analysis, such as cost, liveness, or dataflow, directly into a language's type system. In this paper, we investigate the addition of effect and coeffect tracking to the type…
This paper studies useful sharing, which is a sophisticated optimization for lambda-calculi, in the context of call-by-need evaluation in presence of open terms. Useful sharing turns out to be harder in call-by-need than in call-by-name or…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
Many calculi exist for modelling various features of object-oriented languages. Many of them are based on $\lambda$-calculus and focus either on statically typed class-based languages or dynamic prototype-based languages. We formalize…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
We give an arithmetical proof of the strong normalization of the $\lambda$-calculus (and also of the $\lambda\mu$-calculus) where the type system is the one of simple types with recursive equations on types. The proof using candidates of…
This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on…
We consider the probabilistic applicative bisimilarity (PAB), a coinductive relation comparing the applicative behaviour of probabilistic untyped lambda terms according to a specific operational semantics. This notion has been studied with…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it…
In this paper, we develop a theoretical framework for bounding the CVaR of a random variable $X$ using another related random variable $Y$, under assumptions on their cumulative and density functions. Our results yield practical tools for…
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…
We introduce the $L_!^S$-calculus, a linear lambda-calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ILL). These algebraic operations enable the direct expression…
In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus…
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…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
The intuitionistic fragment of the call-by-name version of Curien and Herbelin's \lambda\_mu\_{\~mu}-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a…
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF…