Related papers: Les types de donn\'ees syntaxiques du syst\`eme F
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Network protocols are programs with inputs and outputs that follow predefined communication patterns to synchronize and exchange information. There are many protocols and each serves a different purpose, e.g., routing, transport, secure…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
We present a new, uniform semantics for Haskell-style overloading. We realize our approach in a new core language, System F$_\mathrm{D}$, whose metatheory we mechanize in the Lean4 interactive theorem prover. System F$_\mathrm{D}$ is…
The Stochastic Calculus of Looping Sequences is suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. We propose a type system for this calculus that models how the…
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
`Linguistic annotation' covers any descriptive or analytic notations applied to raw language data. The basic data may be in the form of time functions -- audio, video and/or physiological recordings -- or it may be textual. The added…
In this work we give a concise definition of information loss from a system-theoretic point of view. Based on this definition, we analyze the information loss in static input-output systems subject to a continuous-valued input. For a…
In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
The semantics of notation systems can naturally be meta-modelled as a network of transformations, starting with the syntactic elements of the notation and ending with the parameters of an execution. In this context, a digital encoding…
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…
Symbolic control is an abstraction-based controller synthesis approach that provides, algorithmically, certifiable-by-construction controllers for cyber-physical systems. Symbolic control approaches usually assume that full-state…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…