Abstract:
Abstract. In partial evaluation, a polyvariant function is specialized to dierent specialized versions, depending on the calling context. Usually, polyvariance is limited to named, top-level functions. We lift this restriction in a partial evaluator for a higher-order functional languages to obtain rst-class polyvariant functions. These functions are partially static and specialize to a memoization table. Arity raising splits a partially static parameter of a function into its dynamic components. Co-arity raising is the dual to arity raising. It splits a partially static result of a function into its dynamic components. A specializer that performs co-arity raising can transform a function returning one result into a function that returns any number of results, including zero. This technique enables polyvariant functions to return partially static results. We demonstrate the use of these techniques in combination by specializing a typed interpreter for a simply-typed applied lambda calculus so that no run-time tagging operations remain in the specialized program. The main technical contributions are the specication of a generalized binding-time analysis for polyvariant functions and co-arity raising, a structural operational semantics for the corresponding specializer, and a type soundness proof of the analysis with respect to the specializer. 1
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