On Tuesday 27th October at 1:15pm (UK time), Mario Alvarez-Picallo, The Difference Lambda Calculus Abstract: Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of “infinitesimal” arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only “up to an infinitesimal […]

by Dan R. Ghica We propose a core calculus for programming languages with effects, interpreted using a hypergraph-rewriting abstract machine. The intrinsic calculus syntax and semantics only deals with the basic structural aspects of programming languages: variables, names, and thunks. Everything else, including function abstraction and application, must be provided as extrinsic operations with associated […]

by Mario Alvarez Picallo When you hear the word ‘derivative’, differential calculus immediately comes to mind. This is, however, far from the only place where one can find them! Many ad-hoc notions of derivative have popped up over the years, in fields as disparate as incremental computation and digital circuits. In this talk we introduce […]

by Dan R. Ghica The interaction between (pure) computation and the physical world happens in two ways. The computation may act upon the world, which is usually called an effect, which is managed using the well known mechanism of monads in the type system of the programming language. But the computation may also require a resource, which is by symmetry called a co-effect, […]