Abstract: Branching Types: squashing typing derivations in systems with intersection types.

Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of lambda^B, a typed lambda calculus with branching types and types with quantification over type selection parameters. The new system lambda^B is an explicitly typed system with the same expressiveness as a system with intersection types. Typing derivations in lambda^B use branching types to squash together what would be separate parallel derivations in earlier systems with intersection types.