Proceedings of the APPSEM-II Workshop on the Krivine and ZINC Abstract Machines (KAZAM)

We materialize the common belief that calculi with explicit substitutions provide an intermediate step between an abstract specification of substitution in the λ-calculus and its actual implementations. To this end, we show a systematic derivation leading from a slight extension of Curien’s calculus of closures, capable of expressing one-step reduction strategies, to the environment-based Krivine’s abstract machine for call-by-name evaluation in the λ-calculus. The derivation consists of two phases: the first one employs Danvy and Nielsen’s refocusing method to construct an abstract machine for the calculus of closures; the second performs an unfolding of closures to make the environment part explicit in the resulting abstract machine.