Program synthesis is the transformation of a specification of a user's problem into a computer program. A problem reduction approach to program synthesis is presented. During synthesis the user's problem is decom posed in a top-down manner into a hierarchy of subprob lems. with directly solveable subproblems at the bottom. Solving these subproblems results in the bottom-up com position of a program whose structure reflects the subproblem hierarchy. The program is guaranteed to satisfy the

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... ication and to terminate on all legal inputs. We illustrate this approach by presenting the knowledge needed to synthesize a class of divide and conquer algo rithms and by deriving a Merge sort algorithm.