Related papers: From Semantics to Types: the Case of the Imperativ…
The Functional Machine Calculus (FMC, Heijltjes 2022) extends the lambda-calculus with the computational effects of global mutable store, input/output, and probabilistic choice while maintaining confluent reduction and simply-typed strong…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
Working in a variant of the intersection type assignment system of Coppo, Dezani-Ciancaglini and Venneri [1981], we prove several facts about sets of terms having a given intersection type. Our main result is that every strongly normalizing…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
System I is a simply-typed lambda calculus with pairs, extended with an equational theory obtained from considering the type isomorphisms as equalities. In this work we propose an extension of System I to polymorphic types, adding the…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
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…
The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to…
We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) has been originally designed for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and…
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…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
We present a new type system combining refinement types and the expressiveness of intersection type discipline. The use of such features makes it possible to derive more precise types than in the original refinement system. We have been…