Type Systems for Closure Conversions

We consider the problem of analyzing and proving correct simple closure conversion strategies for a higher-order functional language. We specify the conversions as deductive systems, making use of annotated types to provide constraints which guide the construction of the closures. We exploit the ability of deductive systems to specify concisely complex relationships between source terms and closure-converted terms. The resulting specifications and proofs are relatively clear and straightforward. The use of deductive systems is central to our work as we can subsequently encode these systems in the LF type theory and then code them in the Elf programming language. The correctness proofs can also be coded in this language, providing machine-checked versions of these proofs.