We study different behavioral metrics, such as those arising from both branching and linear-
time semantics, in a coalgebraic setting. Given a coalgebra α: X→ HX for a functor H: Set→ …

Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural
equivalences. We introduce up-to techniques for behavioural metrics between systems …

In quantitative reasoning one compares objects by distances, instead of equivalence
relations, so that one can measure how much they are similar, rather than just saying …

Differential privacy is rigorous framework for stating and enforcing privacy guarantees on
computations over sensitive data. Informally, differential privacy ensures that the presence or …

Semantics is traditionally concerned with program equivalence, in which all pairs of
programs which are not equivalent are treated the same, and simply dubbed as …

Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories,
have been widely applied in denotational semantics as a way to measure to which extent …

Differential privacy is a de facto standard for statistical computations over databases that
contain private data. Its main and rather surprising strength is to guarantee individual privacy …

We introduce a new form of logical relation which, in the spirit of metric relations, allows us to
assign each pair of programs a quantity measuring their distance, rather than a boolean …

Taking a quotient roughly means changing the notion of equality on a given object, set or
type. In a quantitative setting, equality naturally generalises to a distance, measuring how …

Behavioural distances provide a fine-grained measure of equivalence in systems involving
quantitative data, such as probabilistic, fuzzy, or metric systems. Like in the classical setting …