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Semantic Domains

Those sets that are used as value spaces in denotational semantics.

• Primitive domains

  N, Z, B, ...

• Compound domains
  • Product domains A ×B
  • Sum domains A + B
  • Function domains A => B
  • Lifted domains A_{_|_} = A union {_|_}
    • _|_ = "bottom"
    • Non-termination, no value at all
    • Strict functions f:A_{_|_}==> B_{_|_}, f=lambda x.alpha

      f(_|_) = _|_
      f(a) = [a/x]alpha, for a in A