A Multi-level Approach to Program Synthesis

. We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results achieved in the course of this development. 1 Introduction The development of programs from formal specifications is an activity which requires logical reasoning on various levels of abstraction. The design of the program 's overall structure involves reasoning about data and program structures. Inductive reasoning is necessary for determining a program's behavior on finite, but non-atomic data such as lists, arrays, queues, and sometimes even natural numbers. First-order reasoning is required to analyze the order of steps which are necessary to achieve a desired result. Propositional reasoning is used to make sure that all the formal details are correctly arranged. Program synthesis and t..