  We unify various \'etale groupoid reconstruction theorems such as:
  1) Kumjian-Renault's reconstruction from a groupoid C*-algebra.
  2) Exel's reconstruction from an ample inverse semigroup.
  3) Steinberg's reconstruction from a groupoid ring.
  4) Choi-Gardella-Thiel's reconstruction from a groupoid L^p-algebra.
  We do this by working with certain bumpy semigroups S of functions defined on
an \'etale groupoid G. The semigroup structure of S together with the diagonal
subsemigroup D then yields a natural domination relation < on S. The groupoid
of <-ultrafilters is then isomorphic to the original groupoid G.
