Minds and Machines

, Volume 17, Issue 2, pp 203–216 | Cite as

Understanding Programming Languages

  • Raymond Turner
Original Paper


We document the influence on programming language semantics of the Platonism/formalism divide in the philosophy of mathematics.


Programming language semantics Operational Denotational 


  1. Barendregt, H. P. (1992). Lambda Calculus With Types. Handbook of Logic in Computer Science. In S. Abramsky, D. M. Gabbay, & T. S. E. Maibaum (Eds.), Oxford Science Publications (pp. 118–310).Google Scholar
  2. Benacerraf, P. (1996). What mathematical truth could not be -I.1973. Reprinted in Benacerraf and His Critics, Morton, Adam (Ed.), Blackwell.Google Scholar
  3. Burstall, R., & Honsell, F. (1988). A natural deduction treatment of operational semantics. In Proceedings of the 8th Conf. on Foundations of Software Technology and Theoretical Computer Science, volume LNCS, Vol. 338 (pp. 250–269). NewYork: Springer-Verlag.Google Scholar
  4. Church, A. (1941). The calculi of lambda conversion. Princeton: Princeton University Press.Google Scholar
  5. Dummett, M. (1975) What is a theory of meaning ? In mind and language. Oxford: Oxford University Press.Google Scholar
  6. Dummett, M. (1976). What is a theory of meaning II. In J. McDowell, & G. Evans (Eds.), Truth and meaning: Essays in semantics (pp. vii-xxiii). Oxford: Clarendon Press.Google Scholar
  7. Feferman et al (Eds.) (1986, 1990, 1995), Gödel. Collected works, Vols. I–III. Oxford: Oxford University Press.Google Scholar
  8. Feferman, S. (1979). Constructive theories of functions and classes. In: M. Boffa, & D. van Dalen, K. Mc Aloon (Eds.), Logic Colloquium ’78 (pp. 159–225). Amsterdam: North Holland.Google Scholar
  9. Field, H. (1982). Realism, mathematics, and modality. Oxford: Basil Blackwell.Google Scholar
  10. Gödel, K. (1931) Undecidable diophantine propositions. In Collected Works III:164–175.Google Scholar
  11. Gödel, K. (1951/1995). Some basic theorems on the foundations of mathematics and their implications. In Collected works III (pp. 304–323). Oxford: Oxford University Press.Google Scholar
  12. Gödel K. (1983) What is cantor’s continuum problem? reprinted in Benacerraf and Putnam’s collection philosophy of mathematics (2nd ed.). Cambridge University Press.Google Scholar
  13. Hersh, R. (1997). What is mathematics, really? London: Vintage.Google Scholar
  14. Hindley, J. R., & Seldin, J. P. (1986). Introduction to combinators and the λ-calculus. London: London Mathematical Society Texts.Google Scholar
  15. Hoare, C. A. R. (1969). An axiomatic basis for computer programming. Communications of the ACM, 12(10), 576585, October.CrossRefGoogle Scholar
  16. Landin, P. J. (1964). The mechanical evaluation of expressions. Computer Journal, 6, 308–320.MATHGoogle Scholar
  17. Landin, P. J. (1966). The next 700 programming languages Landin PJ. Communications of the ACM, 9(3), 157–403.MATHCrossRefGoogle Scholar
  18. Miller, A. (1998). Philosophy of language (London: University College London Press/Routledge, Fundamentals of Philosophy Series, xviii + 348 pp).Google Scholar
  19. Maddy, P. (1990). Realism in mathematics. Oxford: Oxford University Press.Google Scholar
  20. Maddy, P. (1997). Naturalism in mathematics. Oxford: Oxford University Press.Google Scholar
  21. McGettrick, A. D. (1980). The Definition of Programming Languages. New York: Cambridge University Press, NY, USA, ISBN:0521226317.MATHGoogle Scholar
  22. Milne, R., & Strachey, C. A. (1977). Theory of programming language semantics. New York, NY, USA: Halsted Press, ISBN:0470989068.Google Scholar
  23. Moore, G. H. (1982). Zermelo’s axiom of choice: Its origins, development, and influence. Berlin: Springer-Verlag.Google Scholar
  24. Pasquale, F. (1994). Wittgenstein’s philosophy of mathematics. London: Routledge.MATHGoogle Scholar
  25. Plotkin, G. D., (1981). A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, Aarhus, Denmark, September.Google Scholar
  26. Plotkin, G. D. (1975). Call-by-name, call-by-value, and the λ-calculus. Theoretical Computer Science, 1, 125–159.MATHCrossRefGoogle Scholar
  27. Potter, M. (2004). Set Theory and Its Philosophy: a Critical Introduction. Oxford: Oxford University Press. ISBN 0199270414.Google Scholar
  28. Reynolds, J. (1998). Definitional interpreters for higher-order programming languages. Higher-order and symbolic computation, 11(4):363–397, 1998. Reprinted from the proceedings of the 25th ACM National Conference (1972), with a foreword.Google Scholar
  29. Rydeheard, D. E., & Burstall, R. M. (1988). Computational category theory. Prentice Hall: New York.MATHGoogle Scholar
  30. Scott, D. S. (1970). Outline of a mathematical theory of computation. Technical Monograph PRG-2. Oxford: Oxford University Computing Laboratory, England, November.Google Scholar
  31. Scott, D. S. (1970). OWHY. Unpublished manuscript.Google Scholar
  32. Scott, D. S. (1972). Continuous lattices. In F. W. Lawvere, (Eds.), Toposes, algebraic geometry, and logic, number 274 in Lecture notes in mathematics (pp. 97–136), Springer-Verlag.Google Scholar
  33. Scott, D. S. (1974). Axiomatizing set-theory. In Jech, J. Thomas, (Ed.), Axiomatic Set Theory II, Proceedings of Symposia in Pure Mathematics 13. American Mathematical Society: 20714Google Scholar
  34. Shapiro, S. (1997). Philosophy of mathematics: Structure and ontology (p. xii + 279).Oxford: Oxford University Press.Google Scholar
  35. Stoy, J. E. (1977). Denotational semantics: The Scott-Strachey approach to programming language theory. Cambridge, MA: MIT Press.Google Scholar
  36. Strachey, C. (1967). Fundamental concepts in programming languages Strachey. Oxford: C. Oxford University Press, Oxford.Google Scholar
  37. Strachey, C. (1966). Towards a formal semantics. In Formal Language Description Languages for Computer Programming, North Holland, pp. 198–220.Google Scholar
  38. Scott, D. S., & Strachey, P. (1974). The varieties of programming languages. Oxford Computer LabGoogle Scholar
  39. Scott, D. S., & Strachey, C. (1971). Toward a mathematical semantics for computer languages. Programming Research Group Technical Monograph PRG-6, Oxford Univ. Computing Lab.Google Scholar
  40. White, G. (2004). The philosophy of computer languages. In L. Floridi (Ed.), The blackwell guide to the philosophy of computing & information. Oxford: Blackwell.Google Scholar
  41. Wang, H. (1974). From mathematics to philosophy. London: Routledge & Kegan PaulMATHGoogle Scholar
  42. Wittgenstein, L. (1939). Wittgenstein’s lectures on the foundations of mathematics, Cora Diamond (Ed.), CambridgeGoogle Scholar
  43. Wittgenstein, L. (1978). Remarks on the Foundation of Mathematics, (3rd ed.). In G. H. von Wright, R. Rhees, & G. E. M. Anscombe, trans. G. E. M. Anscombe. Basil Blackwell, Oxford.Google Scholar
  44. Wittgenstein, L. (1953). Philosophical Investigations. Oxford: Basil BlackwellGoogle Scholar
  45. Winskel, G. (1993). Formal semantics of programming languages. Cambridge: MIT pressMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of EssexColchesterUK

Personalised recommendations