The Virtues of Eta-Expansion

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