The algebraic approach to the semantics of (nonterminating) processes based on the metric completion of process algebras is extended in two directions. Instead of adopting the predefined metric, it is proposed to define the metric internally, using a suitable family of projections as part of the specification and deal with projection spaces rather than metric spaces. It is also proposed to define the data type along with the processes, to allow nonconstant actions and internally defined communication functions. Combined data type and process specifications find a suitable basis for their algebraic semantics in projection algebras.