Domain theory - Wikipedia
Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory.
Domain theory is a comprehensive mathematical framework for defining the data values and primitive operations of a programming language. A critical feature of domain theory (and expressive programming languages like Scheme and ML) is …
Domain Theory - University of Wisconsin–Madison
Our motivation for studying domain theory is to allow us to define the meanings of constructs like loops, whose "natural" definitions are recursive. For example, the "natural" way to define the meaning of a while loop, i.e., to define the "command" valuation function for this case, is:
[1605.05858] Domain Theory: An Introduction - arXiv.org
May 19, 2016 — Abstract: This monograph is an ongoing revision of "Lectures On A Mathematical Theory of Computation" by Dana Scott. Scott's monograph uses a formulation of domains called neighborhood systems in which finite elements are selected subsets of …
•Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. •The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. •Logics of programs. The key to our synthesis is the mathematical theory of Stone duality, which
to a general theory of solutions of recursive domain equations. In conjunction with (1), this showed that domains form a suitable universe for the semantics of programming languages. In this way, Scott provided a mathematical foundation for the work of Christopher Strachey on denotational semantics [MS76, Sto77].
This text is based on the chapter Domain Theory in the Handbook for Logic in Computer Science , volume 3, edited by S. Abramsky, Dov M. Gabbay, and T. S. E. Maibaum, published by Clarendon Press, Oxford in 1994.
Domain theory is a comprehensive mathematical framework for de ning the data values and primitive operations of a programming language. A critical feature of domain theory (and expressive programming languages like Scheme, ML and Haskell) is the fact that program operations are also data values; in domain theory both operations and data values ...
[PDF] Domain Theory: An Introduction | Semantic Scholar
May 19, 2016 — This paper discusses many examples in an informal way that should serve as an introduction to the theory of domains and proves many things that were done previously axiomatically can now be proved in a straightfoward way as theorems.
Domain Theory - an overview | ScienceDirect Topics
Domain Theory was introduced by Dana Scott c. 1970 [Scott, 1970] as a mathematical foundation for the denotational semantics of programming languages which had been pioneered by Christopher Strachey. A domain is a partially ordered structure (D, ⊑). The best intuitive reading of elements of D is as information states.