Summary: Multivariate Amortized Resource Analysis
Jan Hoffmann Klaus Aehlig Martin Hofmann
We study the problem of automatically analyzing the worst-case
resource usage of procedures with several arguments. Existing au-
tomatic analyses based on amortization, or sized types bound the
resource usage or result size of such a procedure by a sum of unary
functions of the sizes of the arguments.
In this paper we generalize this to arbitrary multivariate polyno-
mial functions thus allowing bounds of the form mn which had to
be grossly overestimated by m2
before. Our framework even
encompasses bounds like
i,jn mimj where the mi are the sizes
of the entries of a list of length n.
This allows us for the first time to derive useful resource bounds