Light Genericity

Abstract

AbstractTo better understand Barendregt’s genericity for the untyped call-by-value $$\lambda $$ λ -calculus, we start by first revisiting it in call-by-name, adopting a lighter statement and establishing a connection with contextual equivalence. Then, we use it to give a new, lighter proof of maximality of head contextual equivalence, i.e. that $$\mathcal {H}^*$$ H ∗ is a maximal consistent equational theory. We move on to call-by-value, where we adapt these results and also introduce a new notion dual to light genericity, that we dub co-genericity. Lastly, we give alternative proofs of (co-)genericity based on applicative bisimilarity.