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We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
We propose a type system for reasoning on protocol conformance and deadlock freedom in networks of processes that communicate through unordered mailboxes. We model these networks in the mailbox calculus, a mild extension of the asynchronous…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Dynamic languages are praised for their flexibility and expressiveness, but static analysis often yields many false positives and verification is cumbersome for lack of structure. Hence, unit testing is the prevalent incomplete method for…
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…
The Dependent Object Type (DOT) calculus was designed to put Scala on a sound basis, but while DOT relies on structural subtyping, Scala is a fundamentally class-based language. This impedance mismatch means that a proof of DOT soundness by…
We present a timed process calculus for modelling wireless networks in which individual stations broadcast and receive messages; moreover the broadcasts are subject to collisions. Based on a reduction semantics for the calculus we define a…
The purpose of this paper is to present a method for automatic classification of dialogue utterances and the results of applying that method to a corpus. Superficial features of a set of training utterances (which we will call cues) are…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
We present a calculus that models a form of process interaction based on copyless message passing, in the style of Singularity OS. The calculus is equipped with a type system ensuring that well-typed processes are free from memory faults,…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
This paper is focused on the language modelling for task-oriented domains and presents an accurate analysis of the utterances acquired by the Dialogos spoken dialogue system. Dialogos allows access to the Italian Railways timetable by using…
We apply the principles of the intersection type discipline to the study of class-based object oriented programs and; our work follows from a similar approach (in the context of Abadi and Cardelli's Varsigma-object calculus) taken by van…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…