Related papers: Eager Functions as Processes (long version)
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
We introduce a novel approach to studying properties of processes in the {\pi}-calculus based on a processes-as-formulas interpretation, by establishing a correspondence between specific sequent calculus derivations and computation trees in…
We present a C-language implementation of the lambda-pi calculus by extending the (call-by-need) stack machine of Ariola, Chang and Felleisen to hold types, using a typeless- tagless- final interpreter strategy. It has the advantage of…
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…
We investigate the phenomenon that "every monad is a linear state monad". We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value…
In each variant of the lambda-calculus, factorization and normalization are two key-properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants…
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…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations 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…
Psi-calculi is a parametric framework for process calculi similar to popular pi-calculus extensions such as the explicit fusion calculus, the applied pi-calculus and the spi calculus. Mechanised proofs of standard algebraic and congruence…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
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 a type system to guarantee termination of pi-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. We show that our…
The higher-order pi-calculus is an extension of the pi-calculus to allow communication of abstractions of processes rather than names alone. It has been studied intensively by Sangiorgi in his thesis where a characterisation of a contextual…
We present a formalisation in Agda of the theory of concurrent transitions, residuation, and causal equivalence of traces for the pi-calculus. Our formalisation employs de Bruijn indices and dependently-typed syntax, and aligns the "proved…
We derive properties of $\pi(x)$ reminiscent of those of the logarithm and absolute value functions. Two of these properties are similar to the relations defining the linearity of a function. Several applications of these properties of…
We study whether, in the pi-calculus, the match prefix-a conditional operator testing two names for (syntactic) equality-is expressible via the other operators. Previously, Carbone and Maffeis proved that matching is not expressible this…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…