The Virtues of Eta-Expansion

Abstract

Abstract Interpreting η-conversion as an expansion rule in the simply-typed λ-calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where β-contraction, as the local counit, and η-expansion, as the local unit, are linked by local triangle laws. The latter form reduction loops, but strong normalization (to the long βη-normal forms) can be recovered by ‘cutting’ the loops.