PROGOL

The idea in the PROGOL system is to reduce the combinatorial explosion by generating the most specific acceptable $h$.
User specifies $H$ by stating predicates, functions, and forms of arguments allowed for each.
PROGOL uses sequential covering algorithm. For each $\langle x_i, f(x_i) \rangle$ it finds the most specific hypothesis $h_i$ s.t. $B \wedge h_i \wedge x_{i} \entails f(x_{i})$. (actually, it considers only $k$-step entailment).
It then conducts a general-to-specific search bounded by specific hypothesis $h_i$, choosing hypotheses with minimum description length.