A cost recurrence describes an upper bound for the running time of a
program in terms of the size of its input. Finding cost recurrences is a
frequent intermediate step in complexity analysis, and this step requires
an abstraction from data to data size. In this article, we use information
contained in dependent types to achieve such an abstraction: Dependent ML
(DML), a conservative extension of ML, provides dependent types that can
be used to associate data with size information, thus describing a
possible abstraction. We automatically extract cost recurrences from
first-order DML programs, guiding the abstraction from data to data size
with information contained in DML type derivations.
