Abstract
The deductive approach is a formal program-construction method in which the derivation of a program from a given specification is regarded as a theoremproving ask. To construct a program whose output satisfies the conditions of the specification, we prove a theorem stating the existence of such an output. The proof is restricted to be sufficiently constructive so that a program computing the desired output can be extracted directly from the proof. The program we obtain is applicative and may consist of several mutually recursive procedures. The proof constitutes a demonstration of the correctness of this program.
To exhibit the full power of the deductive approach, we apply it to a nontrivial example — the synthesis of a unification algorithm. Unification is the process of finding a common instance of two expressions. Algorithms to perform unification have been central to many theorem-proving systems and some programming-language processors. The task of deriving a unification algorithm automatically is beyond the power of existing program-synthesis systems. In this paper, we use the deductive approach to derive an algorithm from a simple, high-level specification of the unification task. We will identify some of the capabilities required of a theorem proving system to perform this derivation automatically.
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© 1983 D. Reidel Publishing Company
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Manna, Z., Waldinger, R. (1983). Deductive Synthesis of the Unification Algorithm. In: Biermann, A.W., Guiho, G. (eds) Computer Program Synthesis Methodologies. NATO Advanced Study Institutes Series, vol 95. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7019-9_8
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DOI: https://doi.org/10.1007/978-94-009-7019-9_8
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