Reasoning About Call-by-need by Means of Types

We first develop a (semantical) characterization of call-by-need normalization by means of typability, i.e. we show that a term is normalizing in call-by-need if and only if it is typable in a suitable system with non-idempotent intersection types. This first result is used to derive a new completeness proof of call-by-need w.r.t. call-by-name. Concretely, we show that call-by-need and call-by-name are observationally equivalent, so that in particular, the former turns out to be a correct implementation of the latter.

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