Abstract
In the Prolog language, Horn clauses of first-order logic are regarded as programs, and the resolution procedure is used as an interpreter.
In this paper, we present the formalism of Horn oriented equational clauses (Horn clauses with a rewrite rule as the head part, and a list of equations as the body part). We show that such a formalism can be interpreted as a logic language with built-in equality, and that a procedure, based on clausal superposition, can be used as an interpreter.
We define, the operational, model-theoretic and fixpoint semantics of the language, and prove their equivalence.
Then we point out the advantages of such a programming language:
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embodying Prolog,
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mixing functional and relational features,
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handling the equality relation
Lastly, we present experiments performed with an implemented interpreter.
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References
Bellia,M.,Degano,P. & Levi,G.,A functional plus predicate logic programming language,Proc. Logic Programming Workshop (Jul. 1980),334–347.
Colmerauer,A., Van Caneghem,M. & Kanoui,H.,PROLOG II, manuels de reference, d'utilisation et d'exemples,GIA:Groupe d'Intelligence Artificelle, Marseille, 1982.
Colmerauer,A.,Prolog in 10 figures,Proc. IJCAI,Karslruhe,1983,487–499.
Dershowitz, N., Computing with rewrite systems, Report No ATR-83 (8478)-1, The Aerospace Corporation, El Segundo, California,1983.
van Emden M.H. & Kowalski R.A., The Semantics of Predicate Logic as a Programming Language,JACM 23,4 (Oct. 1976),733–742.
Fages,F.,Associative-Commutative Unification,Proc. CADE-7,Napa, 1984.
Fribourg,L.,A Superposition Oriented Theorem Prover,Technical Report 83/11,L.I.T.P (to appear in TCS,short version in Proc. IJCAI-83,923–925).
Fribourg,L.,Oriented equational clauses as a programming language, Technical Report 83/51,L.I.T.P,Paris,1983.
Hoffman, C.M. & O'Donnell, M.J.,Programming with equations, ACM trans on programming languages and systems 4,1 (Jan. 1982),83–112.
Hsiang,J. & Dershowitz,N.,Rewrite methods for clausal and non-clausal theorem proving,Proc. 10th ICALP,Barcelona, 1983.
Huet G. & Oppen D.C.,Equations and Rewrite Rules: A Survey, Formal language theory: perspectives and open problems,ed. Ronald V. Book,Academic Press, New-York,1980,349–405.
Kornfeld,W.,Equality for Prolog,Proc. IJCAI,Karlsruhe,1983,514–519.
Plotkin, G.,Building in equational theories, Machine Intelligence 7, B Meltzer and D. Michie,Eds,Halsted Press, New-York,1973,73–90.
Robinson, J.A.,A machine-oriented logic based on the resolution principle, J.ACM 12,1 (Jan. 1965),23–41.
Robinson, G.A. & Wos L.,Paramodulation and theorem proving in first order theories with equality, Machine Intelligence 4, Meltzer & Michie,Eds,American Elsevier, New-York,1969,135–150.
Slagle, J.R., Automated Theorem-Proving for Theories with Simplifiers, Commutativity and Associativity, J.ACM 21:4 (Oct 1974),622–642.
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© 1984 Springer-Verlag Berlin Heidelberg
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Fribourg, L. (1984). Oriented equational clauses as a programming language. In: Paredaens, J. (eds) Automata, Languages and Programming. ICALP 1984. Lecture Notes in Computer Science, vol 172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13345-3_15
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DOI: https://doi.org/10.1007/3-540-13345-3_15
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