One Binary Horn Clause is Enough (1994)
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BibTeX
@MISC{Devienne94onebinary,
author = {Philippe Devienne and Patrick Lebègue and Jean-Christophe Routier and Jörg Würtz},
title = {One Binary Horn Clause is Enough},
year = {1994}
}
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Abstract
. This paper proposes an equivalent form of the famous BohmJacopini theorem for declarative languages. C. Bohm and G. Jacopini [1] proved that all programming can be done with at most one single whiledo. That result is cited as a mathematical justification for structured programming. A similar result can be shown for declarative programming. Indeed the simplest class of recursive programs in Horn clause languages can be defined by the following scheme : ( A1 / : A2 / A3 : that is 8x1 \Delta \Delta \Delta 8xm [A1 (A2 :A3) :A4 ] / A4 : where A i are positive first--order literals. This class is shown here to be as expressive as Turing machines and all simpler classes would be trivial. The proof is based on a remarkable and not enough known codification of any computable function by unpredictable iterations proposed by [5]. Then, we prove effectively by logical transformations that all conjunctive formulas of Horn clauses can be translated into an equivalent conjuctive ...
