LOGICAL AND SEMIOTIC ANALYSIS OF THE CONTENT OF STUDYING THE MONOMORPHIC TYPE SYSTEM
The author offers the direction of development of content of training in theoretical programming, which is the science of mathematical models of the concept of “program” and includes the following topics: lambda calculus, type theory, combinators theory, theory of categories. The author carried out a logical and semiotic analysis of the one of the sections of studying theoretical programming “The monomorphic type system λ→” (showing dependence of terms on terms). The main emphasis is placed on the methods of solution of the main types of tasks of system with use of the GHC interpreter, containing tools on establishment of existence of an output of the typified λ-term and type inference of a λ-term. The competences acquired by trainees following the results of study of monomorphic type system are as a result formulated.
Keywords: theoretical programming, λ-cube, monomorphic type system, logical and semiotic analysis of the content, Curry-Howard isomorphism, minimum propositional logic (Prop)
References:
1. Pierce B. C. Types and programming languages. The MIT Press, Cambridge, Massachusetts, London, England, 2002. 645 p. (Russ. ed.: Pirs B. Tipy v yazykakh programmirovaniya: per. s angl. Moscow, Lyambda press: Dobrosvet Publ., 2012. 656 p.).
2. Barendregt H. Lambda calculi with types. Handbook of logic in computer science. Oxford University Press, vol. 2, 1993.
3. Dowek G., Levy J.-J. Introduction to the Theory of Programming Languages. Springer-Verlag London Limited, 2011. 108 p. (Russ. ed.: Dovek Zh., Levi Zh.-Zh. Vvedeniye v teoriyu yazykov programmirovaniya: per. s angl. Moscow, DMK Press, 2013. 134 p.).
4. Mitchell John C. Foundations for Programming Languages. The MIT Press, Cambridge, Massachusetts, London, England, 1996, 854 p. (Russ. ed.: Mitchell Dzh. Osnovaniya yazykov programmirovaniya. Moscow, Izhevsk, NIC “Regulyarnaya i khaoticheskaya dinamika” Publ., 2010. 720 p.).
5. Vekovtseva T. A. Sistema sodeystviya professoinal’nomu samorazvitiyu prepodavatelya vuza [The scheme of assistance in professional selfdevelopment of university teachers]. Nauchno-pedagogicheskoye obozreniye – Pedagogical Review, 2014, vol. 2 (4), pp. 68–72 (in Russian).
6. Artemenko N. A., Belogurov S. V. Ob osobennostyakh organizatsii protsessa formirovaniya informatsionnoy kompetentnosti budushchego spetsialista [Some features of the organization process of formation of information competence of the future expert]. Nauchno-pedagogicheskoye obozreniye – Pedagogical Review, 2014, vol. 1 (3), pp. 13–18 (in Russian).
7. Laptev V. V., Ryzhova N. I., Shvetskiy M. V. Metodicheskaya teoriya obucheniya informatike. Aspekty fundamental’noy podgotovki [Methodical theory of learning to computer science. Aspects of fundamental preparation]. St. Petersburg, S.-Peterb. un-t Publ., 2003. 352 p. (in Russian).
8. Fraenkel A. A., Bar-Hillel Y. Foundations of set theoty. North-holland publishing company, Amsterdam, 1958. 412 p. (Russ. ed.: Frenkel’ A., Bar-Hillel I. Osnovaniya teorii mnozhestv: per. s angl. Moscow, Mir Publ., 1966. 555 p.)
9. Barendregt H. The lambda calculus, its syntax and semantics (studies in logic and the foundations of mathematics). North-Holland, 1984. 654 p. (Russ. ed.: Barendregt H. Lambda-ischisleniye. Ego sintaksis i semantika: per. s angl. Moscow, Mir Publ., 1985. 606 p.).
10. Hindley J. R. Combinators and lambda-calculus, a short outline. Combinators and functional programming languages, Thirteenth spring school of the LITP Val d’Ajol, France, May 6–10, 1985 Proceedings, 1986. Pp. 104–122. DOI: 10.1007/3-540-17184-3_42. (Rus. ed.: Khindli Dzh.R. Kombinatory i lyambda-ischisleniye. Kratkiy obzor. Matematicheskaya logika v programmirovanii: sb. statey 1980–1988 gg.: per. s angl. Moscow, Mir Publ., 1991. Pp. 119–140).
11. Gentzen G. Untersuchungen uber das logische Schliessen. Mathematische Zeitschriff. 1935. (Rus. ed.: Gentsen G. Issledovaniya logicheskikh vyvodov. Matematicheskaya teoriya logicheskogo vyvoda: per. s nem. Moscow, Nauka Publ., 1967. Pp. 9–76).
12. Kompetentnostnyy podkhod v pedagogicheskom obrazovanii [Competence-based approach in pedagogical education: Collective monograph]. Under the editorship of V. A. Kozyrev, N. F. Radionova, A. P. Tryapichyna. St. Petersburg, Herzen State Pedagogical University Publ., 2005. 392 p. (in Russian).
Issue: 12, 2016
Series of issue: Issue 12
Rubric: DIDACTICS OF HIGHER EDUCATION
Pages: 143 — 150
Downloads: 679