Data-Driven Learning of Functions over Algebraic Datatypes from Input/Output-Examples

We describe a technique for inducing recursive functional programs over algebraic datatypes from few non-recursive and only positive ground example-equations. Induction is data-driven and based on structural regularities between example terms. In our approach, functional programs are represented as constructor term rewriting systems containing recursive rewrite rules. In addition to the examples for the target functions, background knowledge functions that may be called by the induced functions can be given in form of ground equations. Our algorithm induces several dependent recursive target functions over arbitrary user-defined algebraic datatypes in one step and automatically introduces auxiliary subfunctions if needed. We have implemented a prototype of the described method and applied it to a number of problems.