One of the goals of this paper is to demonstrate that denotational semantics is useful
for operational issues like implementation of functional languages by abstract machines.
This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name
λ-calculus with Felleisen's control operator [Cscr ].
We derive the transition rules for an
abstract machine from a continuation semantics which appears as a generalization of the
¬¬-translation known from logic. The resulting abstract machine
appears as an extension of Krivine's machine implementing head reduction. Though
the result, namely Krivine's machine,
is well known our method of deriving it from continuation semantics is new and applicable to
other languages (as e.g. call-by-value variants). Further new results
are that Scott's D∞-models
are all instances of continuation models. Moreover, we extend our continuation semantics to
Parigot's λμ-calculus from which we derive an extension of Krivine's
machine for λμ-calculus. The relation between continuation semantics
and the abstract machines is made precise by
proving computational adequacy results employing an elegant method introduced by Pitts.