A Computational Model for Multi-variable Differential Calculus

Abstract. We introduce a domain-theoretic computational model for multivariable differential calculus, which for the first time gives rise to data types for differentiable functions. The model, a continuous Scott domain for differentiable functions of n variables, is built as a sub-domain of the product of n + 1 copies of the function space on the domain of intervals by tupling together consistent information about locally Lipschitz (piecewise differentiable) functions and their differential properties (partial derivatives). The main result of the paper is to show, in two stages, that consistency is decidable on basis elements, which implies that the domain can be given an effective structure. First, a domain-theoretic notion of line integral is used to extend Green’s theorem to interval-valued vector fields and show that integrability of the derivative information is decidable. Then, we use techniques from the theory of minimal surfaces to construct the least and the greatest piec...

• Type: Conference
• Year: 2005
• Where: FOSSACS
• Authors: Abbas Edalat, André Lieutier, Dirk Pattinson
• Keywords: Applied Computing, Basis Elements, Continuous Scott Domain, Domain-theoretic Computational Model, FOSSACS 2005