Multi-Stage Programming: Axiomatization and Type Safety

Multi staged programming provides a new paradigm for constructing e cient 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 se mantics 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 nat ural 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