Semantic Domains
Those sets that are used as value spaces in denotational semantics are called semantic domains. To build a domain we make use of
- Primitive domains N, Z, B, ...
- Compound domains
- Product domains A x B
- Sum domains A+ B
- Function domains A ? B
- Lifted domains A ? = A U {?} (alternative to partial fcts)
- ? = ``bottom'' , Nontermination, no value at all
- Strict functions f : A ? ? B ? , f = ?x. ?
- f(?) = ?
- f(a) = [a/x] ? , for a ?A