Top-down synthesis of divide-and-conquer algorithms
Artificial Intelligence
Special relations in automated deduction
Journal of the ACM (JACM) - The MIT Press scientific computation series
Studies in Automatic Programming Logic
Studies in Automatic Programming Logic
On program synthesis knowledge
Artificial Intelligence
Fundamentals of Deductive Program Synthesis
IEEE Transactions on Software Engineering
An approach to automatic deductive synthesis of functional programs
Annals of Mathematics and Artificial Intelligence
Automatic deductive synthesis of lisp programs in the system ALISA
JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
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Using the deductive synthesis framework developed by Manna and Waldinger we have derived a wide variety of recursive sorting programs. These derivations represent the first application of the deductive framework to the derivation of nontrivial algorithms. While the programs given were derived manually, we ultimately hope that a computer implementation of the system (of which none currently exists) will find similar programs automatically. Our derivations are intended to suggest this possibility; the proofs are short in relation to program complexity (on the order of 40 steps per program) and individual derivation steps are uncontrived. We also present a new rule for the generation of auxiliary procedures, a common ''eureka'' step in program construction.