Abstract
This paper describes principles behind a declarative programming language CL (Clausal Language) which comes with its own proof system for proving properties of defined functions and predicates. We use our own implementation of CL in three courses in the first and second years of undergraduate study. By unifying the domain of LISP’s S-expressions with the domain ℕ of natural numbers we have combined the LISP-like simplicity of coding with the simplicity of semantics. We deal just with functions over ℕ within the framework of formal Peano arithmetic. We believe that most of the time this is as much as is needed. CL is thus an extremely simple language which is completely based in mathematics.
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References
Buss, S.R.: The witness function method and provably recursive functions of Peano arithmetic. In: Prawitz, D., Skyrms, B., Westerstahl, D. (eds.) Logic, Methodology and Philosophy of Science IX (1991). North-Holland, Amsterdam (1994)
Cobham, A.: The intristic computational difficulty of functions. In: Bar- Hillel, Y. (ed.) Logic, Methodology and Philosophy of Science II, pp. 24–30. North-Holland, Amsterdam (1965)
Colson, L.: About primitive recursive algorithms. Theoretical Computer Science 83(1), 57–69 (1991)
Davis, M.: Computability and Unsolvability, 2nd edn. McGraw-Hill, New York (1985)
Hájek, P., Pudlák, P.: Metamathematics of First-Order Arithmetic. Springer, Heidelberg (1993)
Kalmár, L.: A simple example of an undecidable arithmetical problem (Hungarian with German abstract). Matematikai és Fizikai Lapok 50, 1–23 (1943)
Kreisel, G.: On the interpretation of non-finitist proofs II. Journal of Symbolic Logic 17, 43–58 (1952)
Komara, J., Voda, P.J.: Syntactic reduction of predicate tableaux to prepositional tableaux. In: Baumgartner, P., Posegga, J., Hähnle, R. (eds.) TABLEAUX 1995. LNCS (LNAI), vol. 918, pp. 231–246. Springer, Heidelberg (1995)
Mints, G.: Quantifier-free and one-quantifier systems. Journal of Soviet Mathematics 1, 71–84 (1973)
Parsons, C.: On a number-theoretic choice schema and its relation to induction. In: Intuitionism and Proof Theory: proceedings of the summer conference, Buffalo, N.Y.(1968), pp. 459–473. North-Holland, Amsterdam (1970)
Péter, R.: Über den Zusammenhang der verschiedenen Begriffe der rekursiven Funktion. Mathematische Annalen 110, 612–632 (1932)
Péter, R.: Recursive Functions. Academic Press, London (1967)
Rose, H.E.: Subrecursion: Functions and Hierarchies. Oxford Logic Guides, vol. 9. Clarendon Press, Oxford (1982)
Sieg, W.: Herbrand analyses. Archive for Mathematical Logic 30, 409–441 (1991)
Smullyan, R.: First Order Logic. Springer, Heidelberg (1968)
Voda, P.J.: Subrecursion as a basis for a feasible programming language. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 324–338. Springer, Heidelberg (1995)
Wainer, S.S.: Basic proof theory and applications to computation. In: Schwichtenberg, H. (ed.) Logic of Computation. Series F: Computer and Systems Sciences, vol. 157, NATO Advanced Study Institute, International Summer School held in Marktoberdorf, Germany, July 25–August 6 (1995), pp. 349–394. Springer, Heidelberg (1997)
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Komara, J., Voda, P.J. (1999). Theorems of Péter and Parsons in Computer Programming. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_15
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DOI: https://doi.org/10.1007/10703163_15
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