We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth ...

This paper is a contribution to the search for efficient and high-level mathematical tools specify reason about (abstract) programming languages or calculi. Generalising reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, big-step, simply-typed, ...

We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie derivatives with respect to arbitrary smooth ...