Grammatical inference learns a grammar from a set of examples, where here it seems the paper is learning a program (a derivation in the grammar) from examples.

Grammatical inference learns a grammar from a set of examples, where here it seems the paper is learning a program (a derivation in the grammar) from examples. Which Dawn Song paper are you talking about here? I think among all the recent approaches proposed recently on neural program induction, this is the first one that is end-to-end trained and learns only from input-output examples without any hacks!