We abstract a denotational trace semantics
for an imperative language into
a compositional and focussed watchpoint semantics.
Every abstraction of its computational domain induces an
abstract, still compositional and focussed watchpoint semantics.
We describe its implementation and
instantiation with a domain of signs.
It shows that its space and time costs
are proportional to the number of watchpoints and that
abstract compilation reduces those costs significantly.