Observationally-induced Algebras in Domain Theory

We investigate the observationally-induced free algebra approach for constructing computational monads in the categories of classical domain theory. Our investigation yields that the free algebra construction exists for all finitary algebraic signatures and computational prototypes. We furthermore investigate the classical powerdomain constructions in the observationally-induced approach. For the Hoare, Smyth and probabilistic powerdomain constructions we build on established results, showing that they can be recovered observationally-induced. However, the Plotkin powerdomain turns out to be more problematic. Here we show that with the obvious prototype algebra, Heckmanns algebra A, one does not get the classical Plotkin powerdomain.