Automatic differentiation plays a prominent role in scientific computing and in modern
machine learning, often in the context of powerful programming systems. The relation of the …

We present a novel abstraction for bounding the Clarke Jacobian of a Lipschitz continuous,
but not necessarily differentiable function over a local input region. To do so, we leverage a …

Logical relations are one among the most powerful techniques in the theory of programming
languages, and have been used extensively for proving properties of a variety of higher …

Deep learning is moving towards increasingly sophisticated optimization objectives that
employ higher-order functions, such as integration, continuous optimization, and root …

Abstract Stone Duality is a new paradigm for general topology in which computable
continuous functions are described directly, without using set theory, infinitary lattice theory …

We generalise the construction of the formal ball model for metric spaces due to A. Edalat
and R. Heckmann in order to obtain computational models for separated-categories. We …

In this paper we will discuss various aspects of computable/constructive analysis, namely
semantics, proofs and computations. We will present some of the problems and solutions of …

We introduce a typed lambda calculus in which real numbers, real functions, and in
particular continuously differentiable and more generally Lipschitz functions can be defined …

We develop a notion of derivative of a real-valued function on a Banach space, called the L-
derivative, which is constructed by introducing a generalization of Lipschitz constant of a …

We present a domain-theoretic version of Picard's theorem for solving classical initial value
problems in ℝn. For the case of vector fields that satisfy a Lipschitz condition, we construct …