Abstract
This chapter presents a deductive approach to program synthesis. Program synthesis is the systematic derivation of a program from a given specification. The chapter presents a deductive approach to program synthesis for the construction of recursive programs. This approach regards program synthesis as a theorem-proving task and relies on a theorem-proving method that combines the features of transformation rules, unification, and mathematical induction within a single framework. The chapter also describes a framework for program synthesis that again relies on a theorem-proving approach. This approach combines techniques of unification, mathematical induction, and transformation rules within a single deductive system. The chapter highlights the logical structure of this system without considering the strategic aspects of how deductions are directed. Although no implementation exists, the approach is machine-oriented and ultimately intended for implementation in automatic synthesis systems. The chapter also presents a few examples of specifications accepted by the system.
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