A Modal Analysis of Staged Computation

We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λ-calculi and functional languages. We directly demonstrate the sense in which our λ_e→^□-calculus captures staging, and also give a conservative embeddng of Nielson and Nielson's two-level functional language in our functional language Mini-ML ^□ , thus proving that binding-time correctness is equivalent to modal correctness on this fragment. In addition, Mini-ML^□; can also express immediate evaluation and sharing of code across multiple stages, thus supporting run-time code generation as well as partial evaluation.