Related papers: The Vectorial $\lambda$-Calculus
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…
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 present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear…
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…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in 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 extend the linear {\pi}-calculus with composite regular types in such a way that data containing linear values can be shared among several processes, if there is no overlapping access to such values. We describe a type reconstruction…
The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension…
Calculi with control operators have been studied as extensions of simple type theory. Real programming languages contain datatypes, so to really understand control operators, one should also include these in the calculus. As a first step in…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
In this paper, we define a 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. This result serves to give characterizations of the…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
Particle-style token machines are a way to interpret proofs and programs, when the latter are defined according to the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are…
Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the…
We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…
We propose an implementation of lambda+, a recently introduced simply typed lambda-calculus with pairs where isomorphic types are made equal. The rewrite system of lambda+ is a rewrite system modulo an equivalence relation, which makes its…