[1]
Abramsky, S., Gabbay, D. M., and Maibaum, T. S. E. (editors), Handbook of logic in computer science, Volume 2: Background: Computational structures, Oxford University Press, 1992.
[2]
Ackermann, W., Zum Hilbertschen Aufbau der reellen Zahlen, Mathematische Annalen, vol. 99 (1928), pp. 118–133.
[3]
Appel, A. W., Compiling with continuations, Cambridge University Press, 1992.
[4]
Aspinall, D. and Compagnoni, A., Subtyping dependent types, Proceedings of the 11th annual symposium on logic in computer science (New Brunswick, New Jersey) (Clarke, E., editor), IEEE Computer Society Press, 07
1996, pp. 86–97.
[5]
Backus, J. W., Can programming be liberatedfrom the von Neuman style?, Comm. ACM, vol. 21 (1978), pp. 613–641.
[6]
Barendregt, H. P., The lambda calculus: its syntax and semantics, revised ed., North-Holland, Amsterdam, 1984.
[7]
Barendregt, H. P., Theoretical pearls: Self-interpretation in lambda calculus, Journal of Functional Programming, vol. 1 (1991), no. 2, pp. 229–233.
[8]
Barendregt, H. P., Lambda calculi with types, 1992, in [1], pp. 117–309.
[9]
Barendregt, H. P., Discriminating coded lambda terms, From universal morphisms to megabytes: A Baayen space-odyssey (Apt, K. R., Schrijver, A. A., and Temme, N. M., editors), CWI, Kruislaan 413, 1098 SJ Amsterdam, 1994, pp. 141–151.
[10]
Barendregt, H. P., Enumerators of lambda terms are reducing constructively, Annals of Pure and Applied Logic, vol. 73 (1995), pp. 3–9.
[11]
Barendregt, H. P., The quest for correctness, Images of SMC research, Stichting Mathematisch Centrum, P.O. Box 94079, 1090 GB Amsterdam, 1996, pp. 39–58.
[12]
Barendregt, H. P. and Barendsen, E., Efficient computations in formal proofs, to appear, 1997.
[13]
Barendregt, H. P., Bunder, M., and Dekkers, W., Systems of illative combinatory logic complete for first order propositional and predicate calculus, Journal of Symbolic Logic, vol. 58 (1993), no. 3, pp. 89–108.
[14]
Barendsen, E. and Smetsers, J. E. W., Conventional and uniqueness typing in graph rewrite systems (extended abstract), 1993, in [105], pp. 41–51.
[15]
Barendsen, E. and Smetsers, J. E. W., Uniqueness typing for functional languages with graph rewriting semantics, to appear in Mathematical Structures in Computer Science, 1997.
[16]
Beeson, M. J., Foundations of constructive mathematics, Springer-Verlag, Berlin, 1980.
[17]
van Benthem, J. F. A. K., Language in action: Categories, lambdas and dynamic logic, Studies in Logic and the Foundations of Mathematics, vol. 130, North-Holland, Amsterdam, 1991.
[18]
Jutting, L. S. van Benthem, Checking Landau's “Grundlagen” in the AUTOMATH system,
Ph.D. thesis
, Eindhoven University of Technology, 1977.
[19]
Berarducci, A. and Böhm, C., A self-interpreter of lambda calculus having a normal form, Lecture Notes in Computer Science, vol. 702 (1993), pp. 85–99.
[20]
Bezem, M. and Groote, J. F. (editors), Typed lambda calculi and applications, TLCA'93, Lecture Notes in Computer Science, vol. 664, Berlin and New York, Springer-Verlag, 1993.
[21]
Böhm, C., The CUCH as a formal and description language, Annual review in automatic programming (Goodman, Richard, editor), vol. 3, Pergamon Press, Oxford, 1963, pp. 179–197.
[22]
Böhm, C. and Berarducci, A., Automatic synthesis of typed λ-programs on term algebras, Theoretical Computer Science, vol. 39 (1985), pp. 135–154.
[23]
Böhm, C. and Gross, W., Introduction to the CUCH, Automata theory (Caianiello, E. R., editor), Academic Press, New York, 1966, pp. 35–65.
[24]
Böhm, C., Piperno, A., and Guerrini, S., Lambda-definition of function(al)s by normal forms, Esop'94 (Berlin) (Sanella, D., editor), vol. 788, Springer-Verlag, 1994, pp. 135–154.
[25]
Braithwaite, R. B. (editor), F. P. Ramsay: The foundations of mathematics and other logical essays, Routledge & Kegan Paul, London, 1960.
[26]
de Bruijn, N. G., The mathematical language AUTOMATH, its usage and some of its extensions, Symposium on automatic demonstration (Berlin and New York) (Laudet, M., Lacombe, D., and Schuetzenberger, M., editors), Lecture Notes in Mathematics, vol. 125, Springer-Verlag, 1970, pp. 29–61, also in [88], pp. 73–100.
[27]
de Bruijn, N. G., Reflections on Automath, Eindhoven University of Technology, 1990, also in [88], pp. 201–228.
[28]
Church, A., An unsolvable problem of elementary number theory, American Journal of Mathematics, vol. 58 (1936), pp. 354–363.
[29]
Church, A., A formulation of the simple theory of types, Journal of Symbolic Logic, vol. 5 (1940), pp. 56–68.
[30]
Church, A., The calculi of lambda conversion, Princeton University Press, 1941.
[31]
Church, A. and Rosser, J. B., Some properties of conversion, Transactions of the American Mathematical Society, vol. 39 (1936), pp. 472–482.
[32]
Clinger, W. and Rees, J. (editors), Revised report on the algorithmic language Scheme, vol. IV, LISP Pointers, no. 3, 1991.
[33]
Coquand, T. and Huet, G., The calculus of constructions, Information and Computation, vol. 76 (1988), no. 2/3, pp. 95–120.
[34]
Cousineau, G., Curien, P.-L., and Mauny, M., The categorical abstract machine, Science of Computer Programming, vol. 8 (1987), no. 2, pp. 173–202.
[35]
Curien, P.-L., Categorical combinators, sequential algorithms, and functional programming, Research Notes in Theoretical Computer Science, Pitman, London, 1986.
[36]
Curry, H. B., Grundlagen der kombinatorischen Logik, American Journal of Mathematics, vol. 52 (1930), pp. 509–536, 789–834, in German.
[37]
Curry, H. B., Functionality in combinatory logic, Proceedings of the National Academy of Science of the USA, vol. 20 (1934), pp. 584–590.
[38]
Curry, H. B., Modified basic functionality in combinatory logic, Dialectica, vol. 23 (1969), pp. 83–92.
[39]
Dekkers, W., Bunder, M., and Barendregt, H. P., Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic, Journal of Symbolic Logic (1997), to appear.
[40]
van Eekelen, M. C. J. D. and Plasmeijer, M. J., Functional programming and parallel graph rewriting, Addison-Wesley, Reading, Massachusetts, 1993.
[41]
Elbers, H., Personal communication, 1996.
[42]
Euclid, , The elements, 325 B.C. English translation in [55], 1956.
[43]
Feferman, S., A language and axioms for explicit mathematics, Proof theory symposium (Berlin) (Diller, J. H. and Müller, G. H., editors), Lecture Notes in Mathematics, vol. 500, Springer-Verlag, 1975, pp. 87–139.
[44]
Feferman, S., Definedness, Erkentniss, vol. 43 (1995), pp. 295–320.
[45]
Gamut, L. T. F., Logic, language and meaning, Chicago University Press, Chicago, 1992.
[46]
Gandy, R. O., Church's Thesis and principles for mechanisms, The Kleene symposium, North-Holland Publishing Company, Amsterdam, 1980, pp. 123–148.
[47]
Gentzen, G., Investigations into logical deduction, in [111], 1969.
[48]
Gentzen, G., Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 39 (1935), pp. 176–210, 405–431, also available in [111], pp 68–131.
[49]
Girard, J.-Y., Interprétation fonctionelle et élimination des coupures de l'arithmétique d'ordre supérieur,
Ph.D. thesis
, Universite Paris VII, 1972.
[50]
Girard, J.-Y., Linear logic: its syntax and semantics, Advances in linear logic ( Girard, J.-Y., Lafont, Y., and Regnier, L., editors), London Mathematical Society Lecture Note Series, Cambridge University Press, 1995, available by anonymous ftp from lmd.univ-mrs.fr as /pub/girard/Synsem.ps.Z.
[51]
Girard, J-Y., Lafont, Y. G. A., and Taylor, P., Proofs and types, Cambridge Tracts in Theoretical Computer Science, vol. 7, Cambridge University Press, 1989.
[52]
Gordon, A. D., Functional programming and Input/Output, Distinguished Dissertations in Computer Science, Cambridge University Press, 1994.
[53]
Grue, K., Map theory, Theoretical Computer Science (1992), pp. 1–133.
[54]
Gunter, C. A. and Scott, D. S., Semantic domains, Handbook of theoretical computer science, vol. B, in [78], 1990, pp. 633–674.
[55]
Heath, T. L., The thirteen books of Euclid's elements, Dover Publications, Inc., New York, 1956.
[56]
van Heijenoort, J. (editor), From Frege to Gödel: A source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge, Massachusetts, 1967.
[57]
Henderson, P., Functional programming: Application and implementation, Prentice-Hall, Englewood Cliffs, New Jersey, 1980.
[58]
Hilbert, D. and Ackermann, W., Grundzüge der theoretischen logik, first ed., Die Grundlehren der Mathematischen Wissenschaften in Einzeldars tellungen, Band XXVII, Springer-Verlag, Berlin and New York, 1928.
[59]
Hindley, R., The principal type-scheme of an object in combinatory logic, Transactions of the American Mathematical Society, vol. 146 (1969), pp. 29–60.
[60]
Hodges, A., The enigma of intelligence, Unwin paperbacks, London, 1983.
[61]
Hofmann, M., A simple model for quotient types, Typed lambda calculi and applications (Berlin and New York), Lecture Notes in Computer Science, Springer-Verlag, 1977, pp. 216–234.
[62]
Hudak, P.
et al., Report on the programming language Haskell: A non-strict, purely functional language (Version 1.2), ACM SIGPLAN Notices, vol. 27 (1992), no. 5, pp. Ri–Rx, R1–R163.
[63]
Hughes, R. J. M., The design and implementation of programming languages,
Ph.D. thesis
, University of Oxford, 1984.
[64]
Hughes, R. J. M., Why functional programming matters, The Computer Journal, vol. 32 (1989), no. 2, pp. 98–107.
[65]
Iverson, K. E., A programming language, Wiley, New York, 1962.
[66]
Johnsson, T., Efficient compilation of lazy evaluation, SIGPLAN Notices, vol. 19 (1984), no. 6, pp. 58–69.
[67]
Kleene, S. C., Lambda-definability and recursiveness, Duke Mathematical Journal, vol. 2 (1936), pp. 340–353.
[68]
Kleene, S. C., Introduction to metamathematics, The University Series in Higher Mathematics, D. Van Nostrand Comp., New York, Toronto, 1952.
[69]
Kleene, S. C., Reminiscences of logicians, Algebra and logic (Fourteenth summer res. inst., Austral. Math. Soc., Monash Univ., Clayton, 1974) (Crossley, J. N., editor), Lecture Notes in Mathematics, vol. 450, Springer-Verlag, Berlin and New York, 1975, pp. 1–62.
[70]
Kleene, S. C., Origins of recursive function theory, Annals of the History of Computing, vol. 3 (1981), no. 1, pp. 52–67.
[71]
Kleene, S. C. and Rosser, J. B., The inconsistency of certain formal logics, Annals of Mathematics, vol. 36 (1935), pp. 630–636.
[72]
Koymans, C. P. J., Models of the lambda calculus, Information and Control, vol. 52 (1982), no. 3, pp. 306–323.
[73]
Kreisel, G., Church's thesis: A kind of reducibility axiom for constructive mathematics, in [86], pp. 121–150.
[74]
Kreisel, G., The formalist-positivist doctrine of mathematical precision in the light of experience, L'age de la Science, vol. 3 (1970), pp. 17–46.
[75]
Kuper, J., An axiomatic theory for partial functions, Information and Computation (1993), pp. 104–150.
[76]
Landau, E., Grundlagen der analysis, third ed., Chelsea Publishing Company, 1960.
[77]
Landin, P. J., The mechanical evaluation of expressions, The Computer Journal, vol. 6 (1964), no. 4, pp. 308–320.
[78]
van Leeuwen, J. (editor), Handbook of theoretical computer science, vol. A, B, North-Holland, MIT-Press, 1990.
[79]
Leivant, D., Reasoning about functional programs and complexity classes associated with type disciplines, 24th annual symposium on foundations of computer science, IEEE, 1983, pp. 460–469.
[80]
Luo, Z. and Pollack, R., The LEGO proof development system: A user's manual, Technical Report ECS-LFCS-92-211, University of Edinburgh, 05
1992.
[81]
Martin-Löf, P., Intuitionistic type theory, Studies in Proof Theory, Bibliopolis, Napoli, 1984.
[82]
Matijasevič, Yu.V., On recursive unsolvability of hilbert's tenth problem, Fourth international congress for logic, methodology and philosophy of science, Studies in Logic and the Foundations of Mathematics, vol. 74, North-Holland, Amsterdam, 1971, pp. 89–110.
[83]
McCarthy, J.
et al., Lisp 1.5 programmer's manual, MIT Press, Cambridge, Massachusetts, 1962.
[84]
Milner, R., A theory of type polymorphism in programming, Journal of Computer and System Sciences, vol. 17 (1978), pp. 348–375.
[85]
Mogensen, T.Æ., Theoretical pearls: Efficient self-interpretation in lambda calculus, Journal of Functional Programming, vol. 2 (1992), no. 3, pp. 345–364.
[86]
Myhill, J., Vesley, R. E., and Kino, A. (editors), Intuitionism and proof theory, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1970.
[87]
Nadathur, G. and Miller, D., An overview of λProlog, Logic programming: Proceedings of the fifth international conference and symposium, Volume 1 (Cambridge, Massachusetts) (Kowalski, Robert A. and Bowen, Kenneth A., editors), MIT Press, 08
1988, pp. 810–827.
[88]
Nederpelt, R. P., Geuvers, J. H., and de Vrijer, R. C. (editors), Selected papers on automath, Studies in Logic and the Foundations of Mathematics, vol. 133, North-Holland, Amsterdam, 1994.
[89]
von Neumann, J., Eine axiomatisierung der mengenlehre, Journal für die Reine und Angewandte Mathematik, vol. 154 (1925), pp. 219–240.
[90]
Oostdijk, M., Proof by calculation,
Master's thesis, 385
, Universitaire School voor Informatica, Catholic University Nijmegen, 1996.
[91]
Paulin-Mohring, C., Inductive definitions in the system Coq; rules and properties, 1993, in [20], pp. 328–345.
[92]
Jones, S. L. Peyton and Wadler, P., Imperative functional programming, Conference record ofthe twentieth annual ACM SIGPLAN-SIGACT symposium on principles of programming languages, Charleston, South Carolina, January 10-13, 1992, ACM Press, 1993, pp. 71–84 (English).
[93]
Plotkin, G. D., Call-by-name, call-by-value and the λ-calculus, Theoretical Computer Science, vol. 1 (1975), pp. 125–159.
[94]
Poincaré, H., La science et l'hypothèse, Flammarion, Paris, 1902.
[95]
Ramsey, F. P., The foundations of mathematics, Proceedings of the London Mathematical Society, Series 2, vol. 25 (1925), pp. 338–384, translated in [25].
[96]
Reynolds, J. C., Definitional interpreters for higher-order programming languages, Proceedings of 25th ACM national conference (Boston, Massachusetts), 1972, pp. 717–740.
[97]
Reynolds, J. C., The discoveries of continuations, LISP and Symbolic Computation, vol. 6 (1993), no. 3/4, pp. 233–247.
[98]
Robinson, R. M., The theory of classes—a modification of von Neumann's system, Journal of Symbolic Logic, vol. 2 (1937), pp. 29–36.
[99]
Rosser, J. B., Highlights of the history of lambda-calculus, ACM symposium on Lisp and functional programming (Pennysylvania), ACM Press, 08
1982, pp. 216–225.
[100]
Russell, B. A. W. and Whitehead, A. N., Principia mathematica, vol. 1 and 2, Cambridge University Press, 1910–1913.
[101]
Schwichtenberg, H., Definierbare Funktionen im λ-Kalkül mit Typen, Archief für Mathematische Logik, vol. 25 (1976), pp. 113–114.
[102]
Scott, D. S., Constructive validity, Symposium on automated demonstration (Lacombe, D., Laudet, M. and Schuetzenberger, M., editors), Lecture Notes in Mathematics, vol. 125, Springer-Verlag, Berlin, 1970, pp. 237–275.
[103]
Scott, D. S., Continuous lattices, Toposes, algebraic geometry, and logic (Lawvere, F. W., editor), Lecture Notes in Mathematics, vol. 274, Springer-Verlag, Berlin and New York, 1972, pp. 97–136.
[104]
Severi, P. and Poll, E., Pure type systems with definitions, Proceedings of LFCS'94 (Berlin and New York) (Nerode, A. and Matijasevič, Yu.V., editors), Lecture Notes in Computer Science, vol. 813, LFCS'94, St. Petersburg, Springer-Verlag, 1994, pp. 316–328.
[105]
Shyamasundar, R. K. (editor), Proceedings of the 13th conference on foundations of software technology and theoretical computer science, Lecture Notes in Computer Science, vol. 761, Berlin and New York, Bombay, India, Springer-Verlag, 1993.
[106]
Skolem, T., Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Verënderlichen mit unendlichem Ausdehnungsbereich, Videnskapsselskapets skrifter, I. Matematisk-naturvidenskabelig klasse, vol. 6 (1923), English translation in [56], pp. 302–333.
[107]
Smyth, M. B. and Plotkin, G. D., The category-theoretic solution of recursive domain equations, SIAM Journal on Computing, vol. 11 (1982), no. 4, pp. 761–783.
[108]
Statman, R., The typed lambda calculus is not elementary recursive, Theoretical Computer Science, vol. 9 (1979), pp. 73–81.
[109]
Steele, Guy L. Jr., Rabbit: A compiler for Scheme, Technical Report AI-TR-474, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, 05
1978.
[110]
Steele, Guy L. Jr., Common Lisp: The language, Digital Press, 1984.
[111]
Szabo, M. E. (editor), The collected papers of Gerhard Gentzen, North-Holland, Amsterdam, 1969.
[112]
Troelstra, A. S. (editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, vol. 344, Springer-Verlag, Berlin and New York, 1973.
[113]
Turing, A. M., On computable numbers with an application to the Entscheidungsproblem, Proceeding of the London Mathematical Society. Second Series., vol. 42 (1936), pp. 230–265.
[114]
Turing, A. M., Computability and lambda definability, Journal of Symbolic Logic, vol. 2 (1937), pp. 153–163.
[115]
Turner, D. A., The SASL language manual, 1976.
[116]
Turner, D. A., A new implementation technique for applicative languages, Software—Practice andExperience, vol. 9 (1979), pp. 31–49.
[117]
Turner, D. A., The semantic elegance of functional languages, Proceedings of the ACM/MIT conference on functional languages and computer architecture, ACM Press, Pennsylvania, 1981, pp. 85–92.
[118]
Turner, D. A., Miranda—a non-strict functional language with polymorphic types, Functional programming languages and computer architectures (Berlin and New York) (Jouannaud, J. P., editor), Lecture Notes in Computer Science, vol. 201, Springer-Verlag, 1985, pp. 1–16.
[119]
Wadswortt, C., Semantics and pragmatics of the lambda-calculus,
D. Phil thesis
, University of Oxford, Programming Research Group, Oxford, U.K., 1971.
