We introduce a general theory of quantitative and metric rewriting systems, namely systems
with a rewriting relation enriched over quantales modelling abstract quantities. We develop …

We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value λ-
calculi with algebraic effects. We first of all endow a computational λ-calculus with a monadic …

This paper studies quantitative refinements of Abramsky's applicative similarity and
bisimilarity in the context of a generalisation of Fuzz, a call-by-value λ-calculus with a linear …

Constructive type theory combines logic and programming in one language. This is useful
both for reasoning about programs written in type theory, as well as for reasoning about …

It is well-known that constructing models of higher-order probabilistic programming
languages is challenging. We show how to construct step-indexed logical relations for a …

Normal form bisimulation, also known as open bisimulation, is a coinductive technique for
higher-order program equivalence in which programs are compared by looking at their …

We present a complete reasoning principle for contextual equivalence in an untyped
probabilistic language. The language includes continuous (real-valued) random variables …

In the last two decades, there has been much progress on model checking of both
probabilistic systems and higher-order programs. In spite of the emergence of higher-order …

In any setting in which observable properties have a quantitative flavor, it is natural to
compare computational objects by way of metrics rather than equivalences or partial orders …

We present Ellora, a sound and relatively complete assertion-based program logic, and
demonstrate its expressivity by verifying several classical examples of randomized …