This work demonstrates that theorem-proving methods can lead to program synthesis and algorithm implementation by using pairs of logic laws: a deductive law for proving the theorem and a constructive law for synthesizing the program or algorithm. A systematic examination of deductive laws and of constructive laws is presented. The set of all possible pairs of laws provides us with a tool for classifying the different approaches for materializing algorithms (such as hardware, microprogramming, algorithmic programming, declarative programming, deductive approach for recursive routines).

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Theorem in proving and P-functions.- Grammars, logics and declarative programming.- Grammars and Semantics.

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