Previously, we had several reimplementations of the same basic
caching mechanisms. In particular, `cleanAfterRun()`-based removal
of caches not used in a given run.

In this commit, we introduce common caching utilities. The provide
common implementations of the various idioms that we use. This
simplifies all the use sites, which can now focus on their core
logic, instead of mixing it with caching mechanisms.

The abstraction is not zero-cost everywhere. It may introduce some
constant overhead.