Standardization for the Coinductive

Abstract

In the calculus Λ co of possibly non-wellfounded λ-terms, standardization is proved for a parallel notion of reduction. For this system confluence has recently been established by means of a bounding argument for the number of reductions provoked by the joining function which witnesses the confluence statement. Similarly, bounds have to be introduced in order to turn the proof of standardization for the wellfounded λ-calculus into a sound coinductive argument, thus limiting the number of reduction steps arising in the process of standardization. This leads to elementary complexity bounds for the length of the resulting standard reduction sequence in terms of the length of the input sequence. A fortiori, these bounds also apply to the usual wellfounded λ-calculus, strengthening previous results by Xi