Meaningfulness and Genericity in a Subsuming Framework

Abstract: This paper studies the notion of meaningfulness for a unifying framework called dBang-calculus, which subsumes both call-by-name (dCbN) and call-by-value (dCbV). We first characterize meaningfulness in dBang by means of typability and inhabitation in an associated non-idempotent intersection type system previously proposed in the literature. We validate the proposed notion of meaningfulness by showing two properties (1) consistency of the theory $\mathcal{H}$ equating meaningless terms and (2) genericity, stating that meaningless subterms have no bearing on the significance of meaningful terms. The theory $\mathcal{H}$ is also shown to have a unique consistent and maximal extension. Last but not least, we show that the notions of meaningfulness and genericity in the literature for dCbN and dCbV are subsumed by the respectively ones proposed here for the dBang-calculus.