We present ?CIL, a typed ?-calculus which serves as the foundation for a typed intermediate language for optimizing compilers for higher-order polymorphic programming languages. The key innovation of ?CIL is a novel formulation of intersection and union types and flow labels on both terms and types. These flow types can encode polyvariant control and data flow information within a polymorphically typed program representation. Flow types can guide a compiler in generating customized data representations in a strongly typed setting. Since ?CIL enjoys confluence, standardization, and subject reduction properties, it is a valuable tool for reasoning about programs and program transformations.