## Inductive Synthesis of Functional Programs: An Explanation Based Generalization Approach

** Emanuel Kitzelmann, Ute Schmid**; 7(Feb):429--454, 2006.

### Abstract

We describe an approach to the inductive synthesis of recursive equations from input/output-examples which is based on the classical two-step approach to induction of functional Lisp programs of Summers (1977). In a first step, I/O-examples are rewritten to traces which explain the outputs given the respective inputs based on a datatype theory. These traces can be integrated into one conditional expression which represents a non-recursive program. In a second step, this initial program term is generalized into recursive equations by searching for syntactical regularities in the term. Our approach extends the classical work in several aspects. The most important extensions are that we are able to induce a*set*of recursive equations in one synthesizing step, the equations may contain more than one recursive call, and additionally needed parameters are automatically introduced.

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