Theorems of Péter and Parsons in Computer Programming
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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- Bus94.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)Google Scholar
- Cob65.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)Google Scholar
- Dav85.Davis, M.: Computability and Unsolvability, 2nd edn. McGraw-Hill, New York (1985)Google Scholar
- KV95.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)Google Scholar
- Ros82.Rose, H.E.: Subrecursion: Functions and Hierarchies. Oxford Logic Guides, vol. 9. Clarendon Press, Oxford (1982)Google Scholar
- Wai97.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)Google Scholar