Multi-Stage Programming: Axiomatization and Type Safety

Multi-staged programming provides a new paradigm for constructing eecient solutions to complex problems. Techniques such as program generation, multi-level partial evaluation, and run-time code generation respond to the need for general purpose solutions which do not pay run-time interpretive overheads. This paper provides a foundation for the formal analysis of one such system. We introduce a multi-stage language and present its axiomatic, reduction, and natural semantics. Our axiomatic semantics is an extension of the call-by-value-calculus with staging constructs. We demonstrate the soundness of the axiomatic semantics with respect to the natural semantics. We show that staged-languages can \go Wrong" in new ways, and devise a type system that screens out such programs. Finally, we present a proof of the soundness of this type system with respect to the reduction semantics, and show how to extend this result to the natural semantics.