Inductive Program Synthesis as Induction of Context - Free Tree Grammars

We present an application of grammar induction in the domain of inductive program synthesis. Synthesis of recursive programs from input/output examples involves the solution of two subproblems: transforming examples into straightforward programs and folding straightforward programs into (a set of) recursive equations. In this paper we focus on the second part of the synthesis problem, which corresponds to program synthesis from multiple traces or programming by demonstration. Instead of the original framework of synthesis of LISP functions and the currently prominent framework of inductive logic programming, we take a more general view covering both research areas: the synthesis of recursive program schemes. We show that this problem corresponds to the problem of inferring a context-free tree grammar from a single noise-free positive example and provide a synthesis method. While our method does (of course) not solve the synthesis problem for the unrestricted set of recursive program schemes, we can show that some limitations of known synthesis algorithms can be overcome. We argue that reformulating the program synthesis problem in the framework of grammatical inference provides for more transparency in what classes of problems really are covered by synthesis algorithms and can give rise to new algorithms with better performance. For the grammar induction community we hope to awaken interest in open problems in the inference of context-free tree grammars.