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We present a name free λ-calculus with explicit substitutions, based on a generalised notion of director strings. Terms are annotated with information -directors -that indicate how substitutions should be propagated. We first present a calculus where we can simulate arbitrary β-reduction steps, and then simplify the rules to model the evaluation of functional programs (reduction to weak head normal form). We also show that we can define the closed reduction strategy. This is a weak strategydoi:10.1007/s00200-005-0169-9 fatcat:lrqsh6g6bbf6zfeeqbvy7kpbi4