Related papers: On Up-to Context Techniques in the $\pi$-calculus
We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad $T$, we construct a free--forgetful relative pseudoadjunction that exhibits the bicategory of $T$-pseudoalgebras as terminal among…
Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of…
We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…
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…
Up-to techniques' represent enhancements of the coinduction proof method and are widely used on coinductive behavioural relations such as bisimilarity. Abstract formulations of these coinductive techniques exist, using fixed-points or…
The pi-calculus is a widely used process calculus, which models communications between processes and allows the passing of communication links. Various operational semantics of the pi-calculus have been proposed, which can be classified…
Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator…
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
Large language models are able to learn new tasks in context, where they are provided with instructions and a few annotated examples. However, the effectiveness of in-context learning is dependent on the provided context, and the…
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…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
The overall problem addressed in this paper is the long-standing problem of program correctness, and in particular programs that describe systems of parallel executing processes. We propose a new method for proving correctness of parallel…
Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing…
In the field of ubiquitous computing, a class of applications called context-aware services attracted great interest especially since the emergence of wireless technologies and mobile devices. Context-aware application can dynamically…
We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that…
The success of transformers is often linked to their ability to perform in-context learning. Recent work shows that transformers are universal in context, capable of approximating any real-valued continuous function of a context (a…
Reactive Turing machines extend classical Turing machines with a facility to model observable interactive behaviour. We call a behaviour (finitely) executable if, and only if, it is equivalent to the behaviour of a (finite) reactive Turing…
We study a family of distributors-induced bicategorical models of lambda-calculus, proving that they can be syntactically presented via intersection type systems. We first introduce a class of 2-monads whose algebras are monoidal categories…