Olivier Danvy's "Rational Reconstruction of the SECD Machine" [0] explores the idea of this transformation as well, but frames it as a relationship between operational and denotational semantics:
> This deconstruction–reconstruction is actually interesting in itself because it provides a bridge between small-step operational semantics (in the form of an abstract machine) and denotational semantics (in the form of a compositional evaluation function)
His work on (de/re)functionalization is super interesting.