Systematic synthesis of functions

In this paper we introduce a new technique to synthesize functions matching a given set of input-output pairs. Using techniques similar to defunctionalisation the abstract syntax tree of the candidate functions is specified at a high level of abstraction. We use a recursive data type to represent the syntax tree of the candidate functions. The test system G∀ST is used for the systematic synthesis of candidate functions and the selection of functions matching the given condition. The representation of candidate functions as data structures gives us full control over them and the transformation of the syntax tree to the actual function is straight forward. Instances of the syntax tree are generated by a generic algorithm that can be tailored easily to specific needs. This yields a very flexible system to synthesize clear (recursive) function definitions efficiently.