A static calculus of dependencies for the λ-cube

Dependency analysis aims at identifying how different parts of a program depend on each other. It is the kernel of many issues in program analysis such as dead-code, binding time, strictness, program slicing etc. We address the problem of dependency analysis in the context of typed λ-calculus. We consider all systems of the λ-cube and extend them conservatively by the addition of new typing rules in order to determine which parts of a λ-term may contribute to its evaluation. We show how typing information can be used to statically identify dependencies