A compiled implementation of strong reduction

Abstract

Motivated by applications to proof assistants based on dependent types, we develop and prove correct a strong reducer and ß-equivalence checker for the λ-calculus with products, sums, and guarded fixpoints. Our approach is based on compilation to the bytecode of an abstract machine performing weak reductions on non-closed terms, derived with minimal modifications from the ZAM machine used in the Objective Caml bytecode interpreter, and complemented by a recursive "read back" procedure. An implementation in the Coq proof assistant demonstrates important speed-ups compared with the original interpreter-based implementation of strong reduction in Coq.