domain

domain
1. In general, a sphere of control, influence, or concern.

2. See function, relation, category. See also range.

3. of a network. Part of a larger network. A domain is usually defined in terms of some property, such as that part of the network that is under the jurisdiction of a single management body (a management domain), or where all the network addresses are assigned by a single controlling authority (a naming domain). See also domain name server.

4. In the relational model, a set of possible values from which the actual values in any column of a table (relation) must be drawn.

5. In denotational semantics, a structured set of mathematical entities in which meanings for programming constructs can be found. The idea first arose in the work of Dana Scott, who with Christopher Strachey pioneered this mathematical approach to programming language semantics. The approach focuses on fixed-point theorems. Scott required domains to be complete lattices, but this has been simplified through a great deal of mathematical research. There are now many kinds of domains, but a commonly used one is the Scott–Ershov domain, which is a consistently complete algebraic cpo (complete partial ordering). For such mathematical structures a fine theory of constructing new domains from old and solving fixed-point equations has been developed. The domain theory has many applications in finding semantics for programming and specification languages, and approximating data types. Mathematically the theory is closely linked to topology and algebra.

6. See protection domain.