Mathematical theory of domains
Mathematical theory of domains
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
Handbook of logic in computer science (vol. 3)
PCF extended with real numbers
Theoretical Computer Science - Special issue on real numbers and computers
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
A computational model for metric spaces
Theoretical Computer Science
A domain-theoretic approach to computability on the real line
Theoretical Computer Science - Special issue on real numbers and computers
Domains and lambda-calculi
Information and Computation - Special issue: LICS 1996—Part 1
Computable analysis: an introduction
Computable analysis: an introduction
Topological and geometric properties of interval solid models
Graphical Models
Foundation of a computable solid modelling
Theoretical Computer Science
A foundation for computation
Mathematical Structures in Computer Science
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
A Continuous Derivative for Real-Valued Functions
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Domain Theoretic Solutions of Initial Value Problems for Unbounded Vector Fields
Electronic Notes in Theoretical Computer Science (ENTCS)
A hybrid denotational semantics for hybrid systems
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
The formal ball model for -categories
Mathematical Structures in Computer Science
Denotational semantics of hybrid automata
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
A computational model for multi-variable differential calculus
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
A computational model for multi-variable differential calculus
Information and Computation
A language for differentiable functions
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
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We introduce a domain-theoretic framework for differential calculus. We define the set of primitive maps as well as the derivative of an interval-valued Scott continuous function on the domain of intervals, and show that they are dually related, providing an extension of the classical duality of differentiation and integration as in the fundamental theorem of calculus. It is shown that, for locally Lipschitz functions of a real variable, the domain-theoretic derivative coincides with the Clarke's derivative. We then construct a domain for differentiable real-valued functions of a real variable by pairing consistent information about the function and information about its derivative. The set of classical $C^1$ functions, equipped with its $C^1$ norm, is embedded into the set of maximal elements of this countably based, bounded complete continuous domain. This domain also provides a model for the differential properties of piecewise $C^1$ functions, locally Lipschitz functions and more generally of all continuous functions. We prove that consistency of function information and derivative information is decidable on rational step functions, which shows that our domain can be given an effective structure. We thus obtain a data type for differential calculus. As an immediate application, we present a domain-theoretic formulation of Picard's theorem, which provides a data type for solving differential equations.