  In this paper, we present an Agda formalization of a normalizer for
simply-typed lambda terms. The normalizer consists of two coinductively defined
functions in the delay monad: One is a standard evaluator of lambda terms to
closures, the other a type-directed reifier from values to eta-long beta-normal
forms. Their composition, normalization-by-evaluation, is shown to be a total
function a posteriori, using a standard logical-relations argument.
  The successful formalization serves as a proof-of-concept for coinductive
programming and reasoning using sized types and copatterns, a new and presently
experimental feature of Agda.
