The π-calculus is a process algebra that supports mobility by focusing on the communication of channels. Milner's presentation of the π-calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. We extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed λ-calculi. The greater precision of our type discipline yields stronger versions of standard theorems on the π-calculus. These can be used, for example, to obtain the validity of β-reduction for the more efficient of Milner's encodings of the call-by-value λ-calculus, which fails in the ordinary π-calculus. We define the syntax, typing, subtyping, and operational semantics of our calculus, prove that the typing rules are sound, apply the system to Milner's λ-calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.

We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions, we show how to construct a colimit for any functor F from a small category Ω into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate under what conditions the colimit object is algebraic.

We study a natural generalization of System Fω with intersection types, establishing basic structural properties and constructing a semantic model based on partial equivalence relations to prove the soundness of typing. As an application of this calculus, we define a simple typed model of object-oriented programming with multiple inheritance.