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・ domain calculus
・ domain engineering
・ domain maturity
・ domain model
・ domain name
・ domain name server
・ domain name system
・ domain selection
・ domain software engineering environment
・ domain squatter
domain theory
・ domain-specific language
・ domainist
・ domf
・ don't do that then!
・ donald knuth
・ dongle
・ dongle cracker
・ dongle-disk
・ donuts


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domain theory : FOLDOC
domain theory
A branch of mathematics introduced by Dana Scott in 1970 as a mathematical theory of programming languages, and for nearly a quarter of a century developed almost exclusively in connection with denotational semantics in computer science.
In denotational semantics of programming languages, the meaning of a program is taken to be an element of a domain. A domain is a mathematical structure consisting of a set of values (or "points") and an ordering relation, <= on those values. Domain theory is the study of such structures.
("<=" is written in LaTeX as subseteq)
Different domains correspond to the different types of object with which a program deals. In a language containing functions, we might have a domain X -> Y which is the set of functions from domain X to domain Y with the ordering f <= g iff for all x in X, f x <= g x. In the
pure lambda-calculus all objects are functions or applications of functions to other functions. To represent the
applications of functions to other functions. To represent the


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