ﻻ يوجد ملخص باللغة العربية
This paper studies the quantitative refinements of Abramskys applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $lambda$-calculus with a linear type system that can express programs sensitivity, enriched with algebraic operations emph{`a la} Plotkin and Power. To do so a general, abstract framework for studying behavioural relations taking values over quantales is defined according to Lawveres analysis of generalised metric spaces. Barrs notion of relator (or lax extension) is then extended to quantale-valued relations adapting and extending results from the field of monoidal topology. Abstract notions of quantale-valued effectful applicative similarity and bisimilarity are then defined and proved to be a compatible generalised metric (in the sense of Lawvere) and pseudometric, respectively, under mild conditions.
Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or by the throw of dice. This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabili
Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky in 1990. Howe (1989) gave a direct proof that it is a congruence. We propose a categorical framework for s
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to c
Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes themselve