Inductive programming (IP), usually defined as a search in a space of candidate programs, is an inherent exponentially complex problem. To constrain the search space, program templates have ever been one of the first choices. In previous approaches to incorporate program schemes, either an (often very well) informed expert user has to provide a template in advance, or templates are used simply on suspicion, regardless whether they are target-aiming or not. Instead of rather fit the data to the template, we present an approach to fit a template to the data. We propose to utilise universal properties of higher-order functions to detect the appropriateness of a certain template in the input/output examples. We use this technique to introduce catamorphisms on lists in our IP system Igor2.

We present a new method and system, called IGOR2, for the induction of recursive functional programs from few nonrecursive, possibly non-ground example equations describing a subset of the input-output behaviour of a function to be implemented.

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.