We study a notion of local time for a continuous path, defined as a limit of
suitable discrete quantities along a general sequence of partitions of the time
interval. Our approach subsumes other existing definitions and agrees with the
usual (stochastic) local times a.s. for paths of a continuous semimartingale.
We establish pathwise version of the It\^o-Tanaka, change of variables and
change of time formulae. We provide equivalent conditions for existence of
pathwise local time. Finally, we study in detail how the limiting objects, the
quadratic variation and the local time, depend on the choice of partitions. In
particular, we show that an arbitrary given non-decreasing process can be
achieved a.s. by the pathwise quadratic variation of a standard Brownian motion
for a suitable sequence of (random) partitions; however, such degenerate
behavior is excluded when the partitions are constructed from stopping times.