Higher-order probabilistic programming languages allow programmers to write
sophisticated models in machine learning and statistics in a succinct and structured way, but …

We study the semantic foundation of expressive probabilistic programming languages, that
support higher-order functions, continuous distributions, and soft constraints (such as …

We develop the operational semantics of an untyped probabilistic λ-calculus with continuous
distributions, and both hard and soft constraints, as a foundation for universal probabilistic …

We define a notion of stable and measurable map between cones endowed with
measurability tests and show that it forms a cpo-enriched cartesian closed category. This …

Probability theory and statistics are fundamental disciplines in a data-driven world. Synthetic
probability theory is a general, axiomatic formalism to describe their underlying structures …

We present a denotational semantics for higher-order probabilistic programs in terms of
linear operators between Banach spaces. Our semantics is rooted in the classical theory of …

We present a probabilistic version of PCF, a well-known simply typed universal functional
language. The type hierarchy is based on a single ground type of natural numbers. Even if …

Probabilistic applicative bisimulation is a recently introduced coinductive methodology for
program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is …

We introduce a Geometry of Interaction model for higher-order quantum computation, and
prove its adequacy for a fully fledged quantum programming language in which …

Randomized higher-order computation can be seen as being captured by a λ-calculus
endowed with a single algebraic operation, namely a construct for binary probabilistic …