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References

Published online by Cambridge University Press:  05 August 2013

Henk Barendregt
Affiliation:
Radboud Universiteit Nijmegen
Wil Dekkers
Affiliation:
Radboud Universiteit Nijmegen
Richard Statman
Affiliation:
Carnegie Mellon University, Pittsburgh, Pennsylvania
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References

Abadi, M., and Cardelli, L. 1996. A Theory of Objects. Springer.
Abadi, M., and Fiore, M. P. 1996. Syntactic considerations on recursive types. Pages 242–252 of: Logic in Computer Science. IEEE Computer Society Press.
Abadi, M., and Plotkin, G. D. 1990. A PER model of polymorphism and recursive types. Pages 355–365 of: Logic in Computer Science. IEEE Computer Society Press.
Abelson, H., Dybvig, R.K., Haynes, C.T., Rozas, G.J. IV, N.I., Adams, Friedman, D. P., Kohlbecker, E. Jr., G.L., Steele, Bartley, D. H., Halstead, R., Oxley, D., Sussman, G. J., Brooks, G., Hanson, C., Pitman, K. M., Wand, M., Clinger, W., and Rees, J. 1991. Revised report on the algorithmic language Scheme. ACM SIGPLAN Lisp Pointers, IV(3), 1–55.Google Scholar
Abramsky, S. 1990. The lazy lambda calculus. Pages 65–116 of: Research Topics in Functional Programming, Turner, D. A. (ed). Addison-Wesley.
Abramsky, S. 1991. Domain theory in logical form. Annals of Pure and Applied Logic, 51(1–2), 1–77.Google Scholar
Abramsky, S., and Jung, A. 1994. Domain theory. Pages 1–168 of: Handbook for Logic in Computer Science, vol. 3, Abramsky, S., Gabbay, D. M., and Maibaum, T. S. E. (eds). Clarendon Press.
Abramsky, S., and Ong, C.-H. L. 1993. Full abstraction in the lazy lambda calculus. Information and Computation, 105(2), 159–267.Google Scholar
Ackermann, W. 1928. Zum Hilbertschen Aufbau der reellen Zahlen. Mathematische Annalen, 99, 118–133.Google Scholar
Aczel, P. 1988. Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford.
Aho, A. V., Sethi, R., and Ullman, J. D. 1986. Compilers. Addison-Wesley.
Alessi, F. 1991. Strutture di Tipi, Teoria dei Domini e Modelli del Lambda Calcolo. Ph.D. thesis, Torino University.
Alessi, F. 1993. The p model. Internal Report, Udine University.
Alessi, F., and Barbanera, F. 1991. Strong conjunction and intersection types. Pages 64–73 of: Mathematical Foundations of Computer Science. Lecture Notes in Computer Science. Springer.
Alessi, F., Dezani-Ciancaglini, M., and Honsell, F. 2001. Filter models and easy terms. Pages 17–37 of: Italian Conference on Theoretical Computer Science. Lecture Notes in Computer Science, vol. 2202. Springer.
Alessi, F., Barbanera, F., and Dezani-Ciancaglini, M. 2003. Intersection types and computational rules. Pages 1–15 of: Workshop on Logic, Language, Information and Computation. Electronic Notes in Theoretical Computer Science, 84. Elsevier.
Alessi, F., Dezani-Ciancaglini, M., and Honsell, F. 2004a. Inverse limit models as filter models. Pages 3–25 of: International Workshop on Higher-Order Rewriting. RWTH Aachen.
Alessi, F., Barbanera, F., and Dezani-Ciancaglini, M. 2004b. Tailoring filter models. Pages 17–33 of: Types. Lecture Notes in Computer Science, vol. 3085. Springer.
Alessi, F., Barbanera, F., and Dezani-Ciancaglini, M. 2006. Intersection types and lambda models. Theoretical Computer Science, 355(2), 108–126.Google Scholar
Allouche, J.-P., and Shallit, J. 2003. Automatic Sequences. Cambridge University Press.
Amadio, R. M. 1991. Recursion over realizability structures. Information and Computation, 91(1), 55–85.Google Scholar
Amadio, R. M., and Cardelli, L. 1993. Subtyping recursive types. ACM Transactions on Programming Languages and Systems, 15(4), 575–631.Google Scholar
Amadio, R. M., and Curien, P.-L. 1998. Domains and Lambda-Calculi. Cambridge University Press.
Andrews, Peter B. 2002. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Applied Logic, vol. 27. Springer.
Appel, A. W. 1992. Compiling with Continuations. Cambridge University Press.
Appel, A. W., and McAllester, D. 2001. An indexed model of recursive types for foundational proof-carrying code. ACM Transactions on Programming Languages and Systems, 23(5), 657–683.Google Scholar
Ariola, Z. M., and Klop, J. W. 1994. Cyclic lambda graph rewriting. Pages 416–425 of: Logic in Computer Science. IEEE Computer Society Press.
Ariola, Z. M., and Klop, J. W. 1996. Equational term graph rewriting. Fundamenta Informaticae, 26(3–4), 207–240.Google Scholar
Aspinall, D., and Compagnoni, A. 1996. Subtyping dependent types. Pages 86–97 of: Logic in Computer Science. IEEE Computer Society Press.
Augustson, L. 1999. Cayenne – a language with dependent types. Pages 240–267 of: Advanced Functional Programming. Lecture Notes in Computer Science, vol. 1608. Springer.
Avigad, J., Donnelly, K., Gray, D., and Raff, Paul. 2007. A formally verified proof of the prime number theorem. ACM Transactions on Computational Logic, 9(1–2), 1–23.Google Scholar
Baader, F., and Nipkow, T. 1998. Term Rewriting and All That. Cambridge University Press.
Baader, F., and Snyder, W. 2001. Unification theory. Pages 447–533 of: Handbook of Automated Reasoning, vol. I, Robinson, J.A., and Voronkov, A. (eds). Elsevier.
Backus, J. W. 1978. Can programming be liberated from the von Neumann style?Communication of the ACM, 21, 613–641.Google Scholar
Baeten, J., and Boerboom, B. 1979. Ω can be anything it shouldn't be. Indagationes Mathematicae, 41, 111–120.Google Scholar
van Bakel, S. 1992. Complete restrictions of the intersection type discipline. Theoretical Computer Science, 102(1), 135–163.Google Scholar
van Bakel, S. 1993. Principal type schemes for the strict type assignment system. Journal of Logic and Computation, 3(6), 643–670.Google Scholar
van Bakel, S., Barbanera, F., Dezani-Ciancaglini, M., and de Vries, F.-J. 2002. Intersection types for lambda-trees. Theoretical Computer Science, 272(1–2), 3–40.Google Scholar
Baldridge, J. 2002. Lexically Specified Derivational Control in Combinatory Categorial Grammar. Ph.D. thesis, University of Edinburgh.
Barbanera, F., Dezani-Ciancaglini, M., and de'Liguoro, U. 1995. Intersection and union types: syntax and semantics. Information and Computation, 119(2), 202–230.Google Scholar
Barendregt, H. P. 1974. Pairing without conventional restraints. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 20, 289–306.Google Scholar
Barendregt, H. P. 1984. The Lambda Calculus: its Syntax and Semantics. Revised edition. North-Holland.
Barendregt, H. P. 1991. Self-interpretation in lambda calculus. Journal of Functional Programming, 1(2), 229–233.Google Scholar
Barendregt, H. P. 1992. Lambda calculi with types. Pages 117–309 of: Handbook for Logic in Computer Science, Abramsky, S., Gabbay, D. M., and Maibaum, T. S. E. (eds). Oxford University Press.
Barendregt, H. P. 1994. Discriminating coded lambda terms. Pages 141–151 of: From Universal Morphisms to Megabytes: A Baayen Space-Odyssey, Apt, K.R., Schrijver, A.A., and Temme, N.M. (eds). CWI.
Barendregt, H. P. 1995. Enumerators of lambda terms are reducing constructively. Annals of Pure and Applied Logic, 73, 3–9.Google Scholar
Barendregt, H. P. 1996. The quest for correctness. Pages 39–58 of: Images of SMC Research. CWI.
Barendregt, H. P., and Barendsen, E. 1997. Efficient computations in formal proofs. Journal of Automated Reasoning, 321–336.Google Scholar
Barendregt, H. P., and Ghilezan, S. 2000. Lambda terms for natural deduction, sequent calculus and cut-elimination. Journal of Functional Programming, 10, 121–134.Google Scholar
Barendregt, H. P., and Rezus, A. 1983. Semantics for classical Automath and related systems. Information and Control, 59, 127–147.Google Scholar
Barendregt, H., and Wiedijk, F. 2005. The challenge of computer mathematics. Transactions A of the Royal Society, 1835, 2351–2375.Google Scholar
Barendregt, H. P., Coppo, M., and Dezani-Ciancaglini, M. 1983. A filter lambda model and the completeness of type assignment. The Journal of Symbolic Logic, 48(4), 931–940.Google Scholar
Barendregt, H. P., Bunder, M., and Dekkers, W. 1993. Systems of illative combinatory logic complete for first order propositional and predicate calculus. The Journal of Symbolic Logic, 58(3), 89–108.Google Scholar
Barendregt, H., Manzonetto, G., and Plasmeijer, R. 2013. The imperative and functional programming paradigm. In Alan Turing – His Work and Impact, Cooper, B. and van Leeuwen, J. (eds). Elsevier.
Barendsen, E., and Smetsers, J. E. W. 1993. Conventional and uniqueness typing in graph rewrite systems (extended abstract). Pages 41–51 of: Foundations of Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science, vol. 761. Springer.
Barendsen, E., and Smetsers, J. E. W. 1996. Uniqueness typing for functional languages with graph rewriting semantics. Mathematical Structures in Computer Science, 6(6), 579–612.Google Scholar
Bekič, H. 1984. Programming languages and their definition. Selected Papers, C. B., Jones (ed). Lecture Notes in Computer Science, vol. 177. Springer.
van Benthem, J. F. A. K. 1995. Language in Action: Categories, Lambdas, and Dynamic Logic. The MIT Press.
van Benthem, J. F. A. K., and ter Meulen, A. (eds). 1997. Handbook of Logic and Language. Elsevier and MIT Press.
van Benthem Jutting, L. S. 1977. Checking Landau's “Grundlagen” in the Automath System. Ph.D. thesis, Eindhoven University of Technology.
Berarducci, A., and Böhm, C. 1993. A self-interpreter of lambda calculus having a normal form. Pages 85–99 of: Computer Science Logic. Lecture Notes in Computer Science, vol. 702. Springer.
Berline, C. 2000. From computation to foundations via functions and applications: the lambda-calculus and its webbed models. Theoretical Computer Science, 249, 81–161.Google Scholar
Bernardi, R. 2002. Reasoning with Polarity in Categorial Type Logic. Ph.D. thesis, Utrecht Institute of Linguistics OTS.
Bertot, Y., and Castéran, P. 2004. Interactive Theorem Proving and Program Development. Texts in Theoretical Computer Science. Springer.
Bezem, M. A. 1985. Strong normalization of bar recursive terms without using infinite terms. Archiv für Mathematische Logik und Grundlagenforschung, 25, 175–181.Google Scholar
Birkedal, L., and Harper, R. 1999. Constructing interpretations of recursive types in an operational setting. Information and Computation, 155, 3–63.Google Scholar
Böhm, C. 1966. The CUCH as a formal and description language. Pages 179–197 of: Formal Languages Description Languages for Computer Programming. North-Holland.
Böhm, C. (ed). 1975. λ-calculus and Computer Science Theory. Lecture Notes in Computer Science, vol. 37. Springer.
Böhm, C., and Berarducci, A. 1985. Automatic synthesis of typed λ-programs on term algebras. Theoretical Computer Science, 39, 135–154.Google Scholar
Böhm, C., and Dezani-Ciancaglini, M. 1975. λ-terms as total or partial functions on normal forms. Pages 96–121 of: λ-Calculus and Computer Science Theory. Lecture Notes in Computer Science, vol. 37. Springer.
Böhm, C., and Gross, W. 1966. Introduction to the CUCH. Pages 35–65 of: Automata Theory, Caianiello, E.R. (ed). Academic Press.
Böhm, C., Piperno, A., and Guerrini, S. 1994. Lambda-definition of function(al)s by normal forms. Pages 135–154 of: European Symposium on Programming, vol. 788. Springer.
Bono, V., Venneri, B., and Bettini, L. 2008. A typed lambda calculus with intersection types. Theoretical Computer Science, 398(1–3), 95–113.Google Scholar
Bove, A., Dybjer, P., and Norell, U. 2009. A brief overview of Agda –a functional language with dependent types. Pages 73–78 of: Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science, vol. 5674. Springer.
Brandt, M., and Henglein, F. 1998. Coinductive axiomatization of recursive type equality and subtyping. Fundamenta Informaticæ, 33, 309–338.Google Scholar
Breazu-Tannen, V., and Meyer, A. R. 1985. Lambda calculus with constrained types. Pages 23–40 of: Logics of Programs. Lecture Notes in Computer Science, vol. 193. Springer.
Bruce, K. B., Meyer, A. R., and Mitchell, J. C. 1990. The semantics of second-order lambda calculus. Pages 213–272 of: Logical Foundations of Functional Programming. University of Texas at Austin Year of Programming Series. Addison Wesley.
de Bruijn, N. G. 1968. AUTOMATH, a language for mathematics. Tech. rept. 68-WSK-05. T.H.-Reports.
de Bruijn, N. G. 1970. The mathematical language AUTOMATH, its usage and some of its extensions. Pages 29–61 of: Symposium on Automatic Demonstration. Lecture Notes in Mathematics, no. 125. Springer.
de Bruijn, N. G. 1972. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagationes Mathematicae, 34, 381–392.Google Scholar
de Bruijn, N. G. 1994a. A survey of the project Automath. Pages 141–161 of: Selected Papers on Automath, Nederpelt, R. P., Geuvers, J. H., and de Vrijer, R. C. (eds). Studies in Logic and the Foundations of Mathematics, 133. North-Holland.
de Bruijn, N. G. 1994b. Reflections on Automath. Pages 201–228 of: Selected Papers on Automath, Nederpelt, R. P., Geuvers, J. H., and de Vrijer, R. C. (eds). Studies in Logic and the Foundations of Mathematics, 133. North-Holland.
Burstall, R. M. 1969. Proving properties of programs by structural induction. Computer Journal, 12(1), 41–48.Google Scholar
Buszkowski, W., and Penn, G. 1990. Categorial grammars determined from linguistic data by unification. Studia Logica, 49(4), 431–454.Google Scholar
Buszkowski, W., Marciszewski, W., and Benthem, J. F. A. K. van (eds). 1988. Categorial Grammar. Linguistic & Literary Studies in Eastern Europe 25. John Benjamins.
Capitani, B., Loreti, M., and Venneri, B. 2001. Hyperformulae, parallel deductions and intersection types. Electronic Notes in Theoretical Computer Science, 50(2), 1–18.Google Scholar
Capretta, V., and Valentini, S. 1998. A general method for proving the normalization theorem for first and second order typed λ-calculi. Mathematical Structures in Computer Science, 9(6), 719–739.Google Scholar
Caprotti, O., and Oostdijk, M. 2001. Formal and efficient primality proofs by use of computer algebra oracles. Journal of Symbolic Computation, 32, 55–70.Google Scholar
Cardelli, L. 1988. A semantics of multiple inheritance. Information and Computation, 76(2–3).Google Scholar
Cardone, F. 1989. Relational semantics for recursive types and bounded quantification. Pages 164–178 of: Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 372. Springer.
Cardone, F. 1991. Recursive types for fun. Theoretical Computer Science, 83, 29–56.Google Scholar
Cardone, F. 2002. A coinductive completeness proof for the equivalence of recursive types. Theoretical Computer Science, 275, 575–587.Google Scholar
Cardone, F., and Coppo, M. 1990. Two extensions of Curry's type inference system. Pages 19–76 of: Logic and Computer Science, Odifreddi, P. (ed). APIC Studies in Data Processing, vol. 31. Academic Press.
Cardone, F., and Coppo, M. 1991. Type inference with recursive types. Syntax and Semantics. Information and Computation, 92(1), 48–80.Google Scholar
Cardone, F., and Coppo, M. 2003. Decidability properties of recursive types. Pages 242–255 of: Italian Conference on Theoretical Computer Science. Lecture Notes in Computer Science, vol. 2841. Springer.
Cardone, F., and Hindley, J. R. 2009. Lambda-calculus and combinators in the 20th century. Pages 723–817 of: Handbook of the History of Logic, vol. 5: Logic from Russell to Church, Gabbay, D. M., and Woods, J. (eds). Elsevier.
Cardone, F., Dezani-Ciancaglini, M., and de'Liguoro, U. 1994. Combining type disciplines. Annals of Pure and Applied Logic, 66(3), 197–230.Google Scholar
Church, A. 1932. A set of postulates for the foundation of logic (1). Annals of Mathematics, 33, 346–366.Google Scholar
Church, A. 1933. A set of postulates for the foundation of logic (2). Annals of Mathematics, 34, 839–864.Google Scholar
Church, A. 1936. An unsolvable problem of elementary number theory. American Journal of Mathematics, 58, 354–363.Google Scholar
Church, A. 1940. A formulation of the simple theory of types. The Journal of Symbolic Logic, 5, 56–68.Google Scholar
Church, A. 1941. The calculi of lambda-conversion. Princeton University Press. Annals of Mathematics Studies, no. 6.
Church, A., and Rosser, J. B. 1936. Some properties of conversion. Transactions of the American Mathematical Society, 39, 472–482.Google Scholar
Clinger, W., and (editors), Jonathan, Rees. 1991. Revised4 Report on the Algorithmic Language Scheme. LISP Pointers, IV(3), 1–55.
Comon, H., and Jurski, Y. 1998. Higher-order matching and tree automata. Pages 157–176 of: Computer Science Logic. Lecture Notes in Computer Science, vol. 1414. Springer.
Coppo, M. 1985. A completeness theorem for recursively defined types. Pages 120–129 of: Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 194. Springer.
Coppo, M., and Dezani-Ciancaglini, M. 1980. An extension of the basic functionality theory for the λ-calculus. Notre Dame Journal of Formal Logic, 21(4), 685–693.Google Scholar
Coppo, M., Dezani-Ciancaglini, M., and Sallé, P. 1979. Functional characterization of some semantic equalities inside lambda-calculus. Pages 133–146 of: Automata, Languages and Programming.
Coppo, M., Dezani-Ciancaglini, M., and Venneri, B. 1981. Functional characters of solvable terms. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 27(1), 45–58.Google Scholar
Coppo, M., Dezani-Ciancaglini, M., and Longo, G. 1983. Applicative information systems. Pages 35–64 of: Colloquium on Trees in Algebra and Programming. Lecture Notes in Computer Science, vol. 159. Springer.
Coppo, M., Dezani-Ciancaglini, M., Honsell, F., and Longo, G. 1984. Extended type structures and filter lambda models. Pages 241–262 of: Logic Colloquium. North-Holland.
Coppo, M., Dezani-Ciancaglini, M., and Zacchi, M. 1987. Type theories, normal forms, and D∞-lambda-models. Information and Computation, 72(2), 85–116.Google Scholar
Cosmadakis, S. 1989. Computing with recursive types (Extended Abstract). Pages 24–38 of: Logic in Computer Science. IEEE Computer Society Press.
Courcelle, B. 1983. Fundamental properties of infinite trees. Theoretical Computer Science, 25, 95–169.Google Scholar
Courcelle, B., Kahn, G., and Vuillemin, J. 1974. Algorithmes d'équivalence et de réduction à des expressions minimales, dans une classe d'équations récursives simples. Pages 200–213 of: Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 14. Springer.
Cousineau, G., Curien, P.-L., and Mauny, M. 1987. The categorical abstract machine. Science of Computer Programming, 8(2), 173–202.Google Scholar
Crossley, J. N. 1975. Reminiscences of logicians. Pages 1–62 of: Algebra and Logic, Crossley, J. N. (ed). Lecture Notes in Mathematics, vol. 450. Springer.
Curien, P.-L. 1993. Categorical Combinators, Sequential Algorithms, and Functional Programming. 2nd edition. Progress in Theoretical Computer Science. Birkhäuser.
Curry, H. B. 1934. Functionality in combinatory logic. Proceedings of the National Academy of Science of the USA, 20, 584–590.Google Scholar
Curry, H. B. 1969. Modified basic functionality in combinatory logic. Dialectica, 23, 83–92.Google Scholar
Curry, H. B., and Feys, R. 1958. Combinatory Logic. Vol. I. North-Holland.
David, R., and Nour, K. 2007. An arithmetical proof of the strong normalization for the lambda-calculus with recursive equations on types. Pages 84–101 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 4583. Springer.
Davis, M. 1973. Hilbert's tenth problem is unsolvable. American Mathematical OPmonthly, 80, 233–269.Google Scholar
Davis, M., Robinson, J., and Putnam, H. 1961. The decision problem for exponential Diophantine equations. Annals of Mathematics, second series, 74(3), 425–436.Google Scholar
Dedekind, R. 1901. Essays on the Theory of Numbers. Open Court Publishing Company. Translation by W.W. Beman of Stetigkeit und irrationale Zahlen (1872) and Was sind und was sollen die Zahlen? (1888), reprinted 1963 by Dover Press.
Dekkers, W. 1988. Reducibility of types in typed lambda calculus. Comment on: “On the existence of closed terms in the typed λ-calculus, I” (Statman (1980a)). Information and Computation, 77(2), 131–137.Google Scholar
Dekkers, W., Bunder, M., and Barendregt, H. P. 1998. Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic. The Journal of Symbolic Logic, 63(3), 869–890.Google Scholar
Dezani-Ciancaglini, M., and Margaria, I. 1986. A characterization of F-complete type assignments. Theoretical Computer Science, 45(2), 121–157.Google Scholar
Dezani-Ciancaglini, M., Ghilezan, S., and Venneri, B. 1997. The “relevance” of intersection and union types. Notre Dame Journal of Formal Logic, 38(2), 246–269.Google Scholar
Dezani-Ciancaglini, M., Honsell, F., and Motohama, Y. 2001. Approximation theorems for intersection type systems. Journal of Logic and Computation, 11(3), 395–417.Google Scholar
Dezani-Ciancaglini, M., Honsell, F., and Alessi, F. 2003. A complete characterization of complete intersection-type preorders. ACM Transactions on Computational Logic, 4(1), 120–147.Google Scholar
Dezani-Ciancaglini, M., Ghilezan, S., and Likavec, S. 2004. Behavioural inverse limit lambda-models. Theoretical Computer Science, 316(1–3), 49–74.Google Scholar
Dezani-Ciancaglini, M., Honsell, F., and Motohama, Y. 2005. Compositional characterization of λ-terms using Intersection Types. Theoretical Computer Science, 340(3), 459–495.Google Scholar
Di Gianantonio, P., and Honsell, F. 1993. An abstract notion of application. Pages 124–138 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 664. Springer.
Došen, K. 1992. A brief survey of frames for the Lambek calculus. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 38, 179–187.Google Scholar
Dowek, G. 1994. Third order matching is decidable. Annals of Pure and Applied Logic, 69(2–3), 135–155.Google Scholar
van Draanen, J.-P. 1995. Models for Simply Typed Lambda-Calculi with Fixed Point Combinators and Enumerators. Ph.D. thesis, Catholic University of Nijmegen.
Dyckhoff, R., and Pinto, L. 1999. Permutability of proofs in intuitionistic sequent calculi. Theoretical Computer Science, 212, 141–155.Google Scholar
van Eekelen, M. C. J. D., and Plasmeijer, M. J. 1993. Functional Programming and Parallel Graph Rewriting. Addison-Wesley.
Elbers, H. 1996. Personal communication.
Endrullis, J., Grabmayer, C., Klop, J. W., and van Oostrom, V. 2011. On equal μterms. Theoretical Computer Science, 412, 3175–3202. Festschrift in Honour of Jan Bergstra.Google Scholar
Engeler, E. 1981. Algebras and combinators. Algebra Universalis, 13(3), 389–392.Google Scholar
ten Eikelder, H. M. M. 1991. Some algorithms to decide the equivalence of recursive types. URL: <alexandria.tue.nl/extra1/wskrap/publichtml/9211264.pdf>.
Euclid of Alexandria. –300. The Elements. English translation in Heath (1956).
Fiore, M. 1996. A coinduction principle for recursive data types based on bisimulation. Information and Computation, 127(2), 186–198.Google Scholar
Fiore, M. 2004. Isomorphisms of generic recursive polynomial types. SIGPLAN Notices, 39(1), 77–88.Google Scholar
Flajolet, P., and Sedgewick, R. 1993. The average case analysis of algorithms: counting and generating functions. Tech. rept. 1888. INRIA.
Fortune, S., Leivant, D., and O'Donnel, M. 1983. The expressiveness of simple and second-order type structures. Journal of the ACM, 30(1), 151–185.Google Scholar
Fox, A. 2003. Formal specification and verification of ARM6. In: Basin, D. A., and Wolff, B. (eds), Theorem Proving in Higher Order Logics 2003. Lecture Notes in Computer Science, vol. 2758. Springer.
Freyd, P. J. 1990. Recursive types reduced to inductive types. Pages 498–507 of: Logic in Computer Science. IEEE Computer Society Press.
Freyd, P. J. 1991. Algebraically complete categories. Pages 131–156 of: Como Category Theory Conference. Lecture Notes in Mathematics, vol. 1488. Springer.
Freyd, P. J. 1992. Remarks on algebraically compact categories. Pages 95–106 of: Applications of Categories in Computer Science. London Mathematical Society Lecture Notes Series, vol. 177. Cambridge University Press.
Friedman, H. M. 1975. Equality between functionals. In: Logic Colloqium. Lecture Notes in Mathematics, vol. 453. Springer.
Gandy, R. O. 1980. An early proof of normalization by A. M. Turing. Pages 453–457 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Gapeyev, V., Levin, M. Y., and Pierce, B. C. 2002. Recursive subtyping revealed. Journal of Functional Programming, 12(6), 511–548.Google Scholar
Gentzen, G. 1936a. Die Widerspruchfreiheit der reinen Zahlentheorie. Mathematische Annalen, 112, 493–565. Translated as ‘The consistency of arithmetic’, in Szabo (1969).Google Scholar
Gentzen, G. 1936b. Untersuchungen über das logischen Schliessen. Mathematische Zeitschrift, 39, 405–431. Translation In: Collected Papers of Gerhard Gentzen, ed. M. E. Szabo, North-Holland [1969], 68–131.Google Scholar
Gentzen, G. 1943. Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie. Mathematische Annalen, 120, 140–161.Google Scholar
Gentzen, G. 1969. Investigations into logical deduction. Pages 68–131 of: The Collected Papers of Gerhard Gentzen, Szabo, M. E. (ed). North-Holland.
Ghilezan, S. 1996. Strong normalization and typability with intersection types. Notre Dame Journal of Formal Logic, 37(1), 44–52.Google Scholar
Ghilezan, S. 2007. Terms for natural deduction, sequent calculus and cut elimination in classical logic. URL: <http://www.cs.ru.nl/barendregt60/essays/>. Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday.
Gierz, G. K., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. W., and Scott, D. S. 1980. A Compendium of Continuous Lattices. Springer.
Girard, J.-Y. 1971. Une extension de l'interprétation de Gödel à l'analyse, et son application à l'élimination des coupures dans l'analyse et la théorie des types. Pages 63–92 of: Scandinavian Logic Symposium. Studies in Logic and the Foundations of Mathematics, vol. 63. North-Holland.
Girard, J.-Y. 1995. Linear logic: its syntax and semantics. In: Advances in Linear Logic, Girard, J.-Y., Lafont, Y., and Regnier, L. (eds). London Mathematical Society Lecture Note Series. Cambridge University Press.
Girard, J.-Y., Lafont, Y. G. A., and Taylor, P. 1989. Proofs and Types. Cambridge Tracts in Theoretical Computer Science, vol. 7. Cambridge University Press.
Gödel, K. 1931. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173–198. German; English translation in Heijenoort (1967), pages 592-618.Google Scholar
Gödel, K. 1958. Ueber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica, 12, 280–287.Google Scholar
Goguen, J., Thatcher, J. W., Wagner, E. G., and Wright, J. B. 1977. Initial algebra semantics and continuous algebras. Journal of the ACM, 24, 68–95.Google Scholar
Goldfarb, W. D. 1981. The undecidability of the second-order unification problem. Theoretical Computer Science, 13(2), 225–230.Google Scholar
Gonthier, G. 2008. Formal proof –the four-color theorem. Notices of the American Mathematical Society, 55(11), 1382–1393.Google Scholar
Gordon, A. D. 1994. Functional Programming and Input/Output. Distinguished Dissertations in Computer Science. Cambridge University Press.
Gordon, M., Milner, R., and Wadsworth, C. P. 1979. Edinburgh LCF. A Mechanical Logic of Computation. Lecture Notes in Computer Science, vol. 78. Springer.
Gordon, M.J.C., and Melham, T.F. (eds). 1993. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press.
Grabmayer, C. 2005. Relating Proof Systems for Recursive Types. Ph.D. thesis, Vrije Universiteit Amsterdam.
Grabmayer, C. 2007. A duality between proof systems for cyclic term graphs. Mathematical Structures in Computer Science, 17, 439–484.Google Scholar
Grégoire, B., Théry, L., and Werner, B. 2006. A computational approach to Pocklington certificates in type theory. Pages 97–113 of: Functional and Logic Programming. Lecture Notes in Computer Science, vol. 3945. Springer.
de Groote, P. 1995. The Curry–Howard Isomorphism. Cahiers du Centre de Logique, vol. 8. Academia-Bruylant.
de Groote, P., and Pogodalla, S. 2004. On the expressive power of abstract categorial grammars: Representing context-free formalisms. Journal of Logic, Language and Information, 13(4), 421–438.Google Scholar
Grzegorczyk, A. 1964. Recursive objects in all finite types. Fundamenta Mathematicae, 54, 73–93.Google Scholar
Gunter, C. A. 1992. Semantics of Programming Languages: Structures and Techniques. MIT Press.
Gunter, C. A., and Scott, D. S. 1990. Semantic domains. Pages 633–674 of: Handbook of Theoretical Computer Science, vol. B, Leeuwen, J. Van, (ed). North-Holland, MIT-Press.
Hales, T. C. 2005. A proof of the Kepler conjecture. Annals of Mathematics, 162(3), 1065–1185.Google Scholar
Harrington, L. A., Morley, M. D., Ščedrov, A., and Simpson, S. G. (eds). 1985. Harvey Friedman's Research on the Foundations of Mathematics. Studies in Logic and the Foundations of Mathematics, vol. 117. North-Holland.
Harrison, J. 2009a. Formalizing an analytic proof of the prime number theorem. Journal of Automated Reasoning, 43(3), 243–261.Google Scholar
Harrison, J. 2009b. HOL Light: an overview. Pages 60–66 of: Theorem Proving in Higher Order Logics. Springer.
Harrop, R. 1958. On the existence of finite models and decision procedures for propositional calculi. Proceedings of the Cambridge Philosophical Society, 54, 1–13.Google Scholar
Heath, T. L. 1956. The Thirteen Books of Euclid's Elements. Dover Publications.
Heijenoort, J. van (ed). 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University Press.
Henderson, P. 1980. Functional Programming: Application and Implementation. Prentice-Hall.
Henkin, L. 1950. Completeness in the theory of types. The Journal of Symbolic Logic, 15, 81–91.Google Scholar
Herbelin, H. 1995. A lambda calculus structure isomorphic to Gentzen-style sequent calculus structure. Pages 61–75 of: Computer Science Logic. Lecture Notes in Computer Science, vol. 933. Springer.
Hilbert, D., and Ackermann, W. 1928. Grundzüge der Theoretischen Logik. Die Grundlehren der Mathematischen Wissenschaften in Einzeldars tellungen, Band XXVII. Springer.
Hindley, J. R. 1969. The principal type-scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146, 29–60.Google Scholar
Hindley, J. R. 1983. The completeness theorem for typing λ-terms. Theoretical Computer Science, 22, 127–133.Google Scholar
Hindley, J. R. 1992. Types with intersection: an introduction. Formal Aspects of Computing, 4(5), 470–486.Google Scholar
Hindley, J. R. 1997. Basic Simple Type Theory. Cambridge University Press.
Hindley, J. R., and Seldin, J. P. (eds). 1980. To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press.
Hinze, Ralf, Jeuring, J., and Löh, A. 2007. Comparing approaches to generic programming. In: Backhouse, R., Gibbons, J., Hinze, R., and Jeuring, J. (eds), Datatype-Generic Programming 2006. Lecture Notes in Computer Science, vol. 4719. Springer.
Hodges, A. 1983. The Enigma of Intelligence. Unwin paperbacks.
Hofmann, M. 1995. A simple model for quotient types. Pages 216–234 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 902. Springer.
Honsell, F., and Lenisa, M. 1993. Some results on the full abstraction problem for restricted lambda calculi. Pages 84–104 of: Mathematical Foundations of Computer Science. Springer.
Honsell, F., and Lenisa, M. 1999. Semantical analysis of perpetual strategies in λ-calculus. Theoretical Computer Science, 212(1–2), 183–209.Google Scholar
Honsell, F., and Ronchi Della Rocca, S. 1992. An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus. Journal of Computer and System Sciences, 45(1), 49–75.Google Scholar
Howard, W. A. 1970. Assignment of ordinals to terms for primitive recursive functionals of finite type. Pages 443–458 of: Intuitionism and Proof Theory, Kino, A., Myhill, J., and Vesley, R. E. (eds). Studies in Logic and the Foundations of Mathematics. North-Holland.
Howard, W. A. 1980. The formulas-as-types notion of construction. Pages 479–490 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Hudak, P., Peyton Jones, S., Wadler, P., Boutel, B., Fairbairn, J., Fasel, J., Guzman, M. M., Hammond, K., Hughes, J., Johnsson, T., Kieburtz, D., Nikhil, R., Partain, W., and Peterson, J. 1992. Report on the programming language Haskell: a non-strict, purely functional language (Version 1.2). ACM SIG-PLAN Notices, 27(5), 1–164.Google Scholar
Hudak, P., Peterson, J., and Fasel, J. H. 1999. A gentle introduction to Haskell 98. Technical Report. Dept. of Computer Science, Yale University, USA.
Huet, G. P. 1975. A unification algorithm for typed lambda-calculus. Theoretical Computer Science, 1, 27–57.Google Scholar
Hughes, R. J. M. 1984. The Design and Implementation of Programming Languages. Ph.D. thesis, University of Oxford.
Hughes, R. J. M. 1989. Why functional programming matters. The Computer Journal, 32(2), 98–107.Google Scholar
Hutton, G. 2007. Programming in Haskell. Cambridge University Press.
Hyland, M. 1975/1976. A syntactic characterization of the equality in some models for the lambda calculus. Proceedings of the London Mathematical Society (2), 12(3), 361–370.Google Scholar
Iverson, K. E. 1962. A Programming Language. Wiley.
Jacopini, G. 1975. A condition for identifying two elements of whatever model of combinatory logic. Pages 213–219 of: λ-Calculus and Computer Science theory. Lecture Notes in Computer Science, vol. 37. Springer.
Jay, B. 2009. Pattern Calculus. Springer.
Johnsson, T. 1984. Efficient compilation of lazy evaluation. SIGPLAN Notices, 19(6), 58–69.Google Scholar
Johnstone, P. T. 1986. Stone Spaces. Cambridge University Press.
Joly, T. 2001a. Constant time parallel computations in lambda-calculus. Theoretical Computer Science, 266(1), 975–985.Google Scholar
Joly, T. 2001b. The finitely generated types of the lambda-calculus. Pages 240–252 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 2044. Springer.
Joly, T. 2003. Encoding of the halting problem into the monster type & applications. Pages 153–166 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 2701. Springer.
Joly, T. 2005. On lambda-definability I: the fixed model problem and generalizations of the matching problem. Fundamenta Informaticae, 65(1–2), 135–151.Google Scholar
Jones, J. P. 1982. Universal Diophantine equation. The Journal of Symbolic Logic, 47(3), 549–571.Google Scholar
Jones, M. P. 1993. A system of constructor classes: overloading and implicit higher-order polymorphism. Pages 52–61 of: Functional Programming Languages and Computer Architecture. ACM Press.
Kamareddine, F., Laan, T., and Nederpelt, R. 2004. A Modern Perspective on Type Theory: From its Origins until Today. Applied Logic Series, vol. 29. Kluwer Academic Publishers.
Kanazawa, M. 1998. Learnable Classes of Categorial Grammars. Cambridge University Press.
Kaufmann, M., Manolios, P., and Moore, J. S. 2000. Computer-Aided Reasoning: An Approach. Kluwer.
Kfoury, A.J., and Wells, J. 1995. New notions of reduction and non-semantic proofs of strong β-normalization in typed λ-calculi. Pages 311–321 of: Logic in Computer Science. IEEE Computer Society Press.
Kleene, S. C. 1936. Lambda-definability and recursiveness. Duke Mathematical Journal, 2, 340–353.Google Scholar
Kleene, S. C. 1952. Introduction to Metamathematics. The University Series in Higher Mathematics. van Nostrand.
Kleene, S. C. 1959a. Countable functionals. Pages 81–100 of: Constructivity in Mathematics, Heyting, A. (ed). Studies in Logic and the Foundations of Mathematics. North-Holland.
Kleene, S. C. 1959b. Recursive functionals and quantifiers of finite types. I. Transactions of the American Mathematical Society, 91, 1–52.Google Scholar
Kleene, S. C. 1975. Reminiscences of logicians. Reported by J. N. Crossley. Pages 1–62 of: Algebra and Logic. Lecture Notes in Mathematics, vol. 450. Springer.
Klein, G., Elphinstone, K., Heiser, G., Andronick, J., Cock, D., Derrin, P., Elkaduwe, D., Engelhardt, K., Kolanski, R., Norrish, M., Sewell, T., Tuch, H., and Winwood, S. 2009. seL4: formal verification of an OS kernel. Pages 207–220 of: ACM Symposium on Principles of Operating Systems, Matthews, J.N., and Anderson, Th. (eds). Big Sky.
Klop, J. W. 1980. Combinatory Reduction Systems. Ph.D. thesis, Utrecht University.
Klop, J. W. 1992. Term Rewriting Systems. Pages 1–116 of: Handbook of Logic in Computer Science, Abramsky, S., Gabbay, D. M., and Maibaum, T. S. E. (eds). Oxford University Press.
Klop, J. W., and de Vrijer, R. C. 1989. Unique normal forms for lambda calculus with surjective pairing. Information and Computation, 80(2), 97–113.Google Scholar
Klop, J.-W., Oostrom, V. van, and Raamsdonk, F. van. 1993. Combinatory reduction systems: introduction and survey. Theoretical Computer Science, 121, 279–308.Google Scholar
Koopman, P., and Plasmeijer, M. J. 1999. Efficient combinator parsers. Pages 120–136 of: Implementation of Functional Languages, Hammond, K., Davie, A. J. T., and Clack, C. (eds). Lecture Notes in Computer Science, vol. 1595. Springer.
Koopman, P., and Plasmeijer, M. J. 2006. Fully automatic testing with functions as specifications. Pages 35–61 of: Selected Lectures of the 1st Central European Functional Programming School. Lecture Notes in Computer Science, vol. 4164. Springer.
Koster, C. H. A. 1969. On infinite modes. ALGOL Bulletin, 30, 86–89.Google Scholar
Koymans, C. P. J. 1982. Models of the lambda calculus. Information and Control, 52(3), 306–323.Google Scholar
Kozen, D. 1977. Complexity of finitely presented algebras. Pages 164–177 of: ACM Symposium on Theory of Computing. ACM Press.
Kozen, D. 1997. Automata and Computability. Springer.
Kozen, D., Palsberg, J., and Schwartzbach, M. I. 1995. Efficient recursive subtyping. Mathematical Structures in Computer Science, 5(1), 113–125.Google Scholar
Kreisel, G. 1959. Interpretation of analysis by means of constructive functionals of finite types. Pages 101–128 of: Constructivity in Mathematics, Heyting, A. (ed). North-Holland.
Kripke, S. A. 1965. Semantical analysis of intuitionistic logic I. Pages 92–130 of: Formal Systems and Recursive Functions, Crossley, J. N. and Dummett, M. (eds). North-Holland.
Krivine, J.-L. 1990. Lambda-Calcul Types et Modéles. Masson. English translation Krivine (1993).
Krivine, J.-L. 1993. Lambda-Calculus, Types and Models. Ellis Horwood. Translated from the 1990 French original by René Cori.
Kurata, T., and Takahashi, M. 1995. Decidable properties of intersection type systems. Pages 297–311 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 902. Springer.
Kurtonina, N. 1995. Frames and Labels. A Modal Analysis of Categorial Inference. Ph.D. thesis, OTS Utrecht, ILLC Amsterdam.
Kurtonina, N., and Moortgat, M. 1997. Structural control. Pages 75–113 of: Specifying Syntactic Structures, Blackburn, Patrick, and de Rijke, Maarten (eds). Center for the Study of Language and Information, Stanford.
Kuśmierek, D. 2007. The inhabitation problem for rank two intersection types. Pages 240–254 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 4583.
Lambek, J. 1958. The mathematics of sentence structure. American Mathematical Monthly, 65, 154–170. Also in Buszkowski et al. (1988).Google Scholar
Lambek, J. 1961. On the calculus of syntactic types. Pages 166–178 of: Structure of Language and its Mathematical Aspects, Jacobson, R. (ed). Proceedings of the Symposia in Applied Mathematics, vol. XII. American Mathematical Society.
Lambek, J. 1980. From λ-calculus to Cartesian closed categories. Pages 375–402 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism Hindley (Hindley and Seldin (1980)).
Lambek, J., and Scott, P. J. 1981. Intuitionist type theory and foundations. Journal of Philosophical Logic, 10, 101–115.Google Scholar
Landau, E. 1960. Grundlagen der Analysis. 3rd edition. Chelsea Publishing Company.
Landin, P. J. 1964. The mechanical evaluation of expressions. The Computer Journal, 6(4), 308–320.Google Scholar
Lax, P. D. 2002. Functional Analysis. Pure and Applied Mathematics. Wiley.
Lehmann, D. J., and Smyth, M. B. 1981. Algebraic specification of data types: a synthetic approach. Mathematical Systems Theory, 14, 97–139.Google Scholar
Leivant, D. 1983a. Polymorphic Type Inference. Pages 88–98 of: Symposium on Principles of Programming Languages. ACM Press.
Leivant, D. 1983b. Reasoning About functional programs and complexity classes associated with type disciplines. Pages 460–469 of: Symposium on Foundations of Computer Science. IEEE Computer Society Press.
Leivant, D. 1986. Typing and computational properties of lambda expressions. Theoretical Computer Science, 44(1), 51–68.Google Scholar
Leivant, D. 1990. Discrete polymorphism. Pages 288–297 of: ACM Conference on LISP and Functional Programming. ACM Press.
Leroy, X. 2009. A formally verified compiler back-end. Journal of Automated Reasoning, 43(4), 363–446.Google Scholar
Lévy, J.-J. 1978. Réductions Correctes et Optimales dans le Lambda-Calcul. Ph.D. thesis, Université Paris VII.
Liquori, L., and Ronchi Della Rocca, S. 2007. Intersection types à la Church. Information and Computation, 205(9), 1371–1386.Google Scholar
Loader, R. 1997. An algorithm for the minimal model. Unpublished manuscript, obtainable from <homepages.ihug.co.nz/~suckfish/papers/papers.html>.
Loader, R. 2001a. Finitary PCF is not decidable. Theoretical Computer Science, 266(1–2), 341–364.Google Scholar
Loader, R. 2001b. The undecidability of lambda definability. Pages 331–342 of: Church Memorial Volume: Logic, Language, and Computation (Zeleny and Anderson (2001)).
Loader, R. 2003. Higher order β matching is undecidable. Logic Journal of the Interest Group in Pure and Applied Logics, 11(1), 51–68.Google Scholar
Longo, G. 1988. The lambda-calculus: connections to higher type recursion theory, proof theory, category theory. Annals of Pure and Applied Logic, 40, 93–133.Google Scholar
Lopez-Escobar, E. G. K. 1983. Proof functional connectives. Pages 208–221 of: Methods in Mathematical Logic. Lecture Notes in Mathematics, vol. 1130.
Luo, Z., and Pollack, R. 1992. The LEGO Proof Development System: A User's Manual. Tech. rept. ECS-LFCS-92-211. University of Edinburgh.
MacQueen, D., Plotkin, G. D., and Sethi, R. 1986. An ideal model for recursive polymorphic types. Information and Control, 71((1/2)), 95–130.Google Scholar
Mairson, H. G. 1992. A simple proof of a theorem of Statman. Theoretical Computer Science, 103(2), 387–394.Google Scholar
Makanin, G. S. 1977. The problem of solvability of equations in a free semigroup. Mathematics of the USSR-Sbornik, 32(2), 129–198.Google Scholar
Martin-Löf, P. 1984. Intuitionistic Type Theory. Studies in Proof Theory. Bibliopolis.
Marz, M. 1999. An algebraic view on recursive types. Applied Categorical Structures, 7(1–2), 147–157.Google Scholar
Matiyasevič, Y. V. 1972. Diophantine representation of recursively enumerable predicates. Mathematical Notes, 12(1), 501–504.Google Scholar
Matiyasevič, Y. V. 1993. Hilbert's Tenth Problem. Foundations of Computing Series. MIT Press.
Mayr, R., and Nipkow, T. 1998. Higher-order rewrite systems and their confluence. Theoretical Computer Science, 192(1), 3–29.Google Scholar
McCarthy, J. 1963. A basis for a mathematical theory of computation. Pages 33–70 of: Computer Programming and Formal Systems, Braffort, P., and Hirschberg, D. (eds). North-Holland.
McCarthy, J., Abrahams, P.W., Edwards, D. J., Hart, T. P., and Levin, M. I. 1962. LISP 1.5 Programmer's Manual. MIT Press.
McCracken, N. J. 1979. An investigation of a programming language with a polymorphic type structure. Ph.D. thesis, Syracuse University.
Melliés, P.-A. 1996. Description Abstraite des Systémes de Réécriture. Ph.D. thesis, Université de Paris.
Mendler, N. P. 1987. Inductive Definitions in Type Theory. Ph.D. thesis, Department of Computer Science, Cornell University.
Mendler, N. P. 1991. Inductive types and type constraints in the second-order lambda calculus. Annals of Pure and Applied Logic, 51, 159–172.Google Scholar
Meyer, A. R. 1982. What is a model of the lambda calculus?Information and Control, 52(1), 87–122.Google Scholar
Milner, R. 1978. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17, 348–375.Google Scholar
Milner, R., Tofte, M., Harper, R., and McQueen, D. 1997. The Definition of Standard ML. The MIT Press.
Mints, G. E. 1989. The completeness of provable realizability. Notre Dame Journal Formal Logic, 30, 420–441.Google Scholar
Mints, G. E. 1996. Normal forms for sequent derivations. Pages 469–492 of: Kreiseliana. About and Around Georg Kreisel, Odifreddi, P. (ed). A.K. Peters.
Mitchell, J. 1996. Foundation for Programmimg Languages. MIT Press.
Mitschke, G. 1976. λ-Kalkül, δ-Konversion und axiomatische Rekursionstheorie. Tech. rept. Preprint 274. Technische Hochschule, Darmstadt.
Mogensen, T. Æ. 1992. Efficient self-interpretation in lambda calculus. Journal of Functional Programming, 2(3), 345–364.Google Scholar
Moller, F., and Smolka, S. A. 1995. On the computational complexity of bisimulation. ACM Computing Surveys, 27(2), 287–289.Google Scholar
Montague, R. 1973. The proper treatment of quantification in ordinary English. In: Hintikka, J., Moravcsik, J. M. E., and Suppes, P. (eds), Approaches to Natural Language. Dordrecht.
Moot, R. 2002. Proof nets for linguistic analysis. Pages 65–72 of: Proceedings of TAG+9, The 9th International Workshop on Tree Adjoining Grammars and Related Formalisms, Tübingen, Gardent, Claire and Sarkar, A. (eds).
Moot, R. 2008. Lambek Grammars, Tree Adjoining Grammars and Hyperedge Replacement Grammars. Ph.D. thesis, Utrecht University.
Moot, R., and Retoré, C. 2012. The Logic of Categorial Grammars. Lecture Notes in Computer Science, vol. 6850. Springer.
Morrill, G. 1994. Type Logical Grammar. Kluwer.
Morris, J. H. 1968. Lambda-calculus Models of Programming Languages. Ph.D. thesis, Massachusetts Institute of Technology.
Muzalewski, M. 1993. An Outline of PC Mizar. Brussels: Fondation Philippe le Hodey.
Nadathur, G., and Miller, D. 1988. An overview of λProlog. Pages 810–827 of: Logic Programming Conference. MIT Press.
Nederpelt, R. P. 1973. Strong Normalisation in a Typed Lambda Calculus with Lambda Structured Types. Ph.D. thesis, Eindhoven University.
Nederpelt, R. P., Geuvers, J. H., and de Vrijer, R. C. (eds). 1994. Selected Papers on Automath. Studies in Logic and the Foundations of Mathematics, no. 133. North-Holland.
Nerode, A., Odifreddi, P., and Platek, R. In preparation. The Four Noble Truths of Logic. To appear.
Nikhil, R. S. 2008. Bluespec: a general-purpose approach to high-Level synthesis based on parallel atomic transactions. Pages 129–146 of: High-Level Synthesis, Coussy, Philippe and Morawiec, Adam (eds). Springer.
Nipkow, T., Paulson, L. C., and Wenzel, M. 2002. Isabelle/HOL. A Proof Assistant for Higher-Order Logic. Lecture Notes in Computer Science, vol. 2283. Springer.
Oostdijk, M. 1996. Proof by Calculation. M.Phil. thesis, Nijmegen University.
van Oostrom, V. 2007. α-free-μ. Unpublished manuscript, Vincent.vanOostrom@phil.uu.nl.
Padovani, V. 1996. Filtrage d'ordre Supérieur. Ph.D. thesis, Université de Paris VII.
Padovani, V. 2000. Decidability of fourth order matching. Mathematical Structures in Computer Science, 3(10), 361–372.Google Scholar
Pair, C. 1970. Concerning the syntax of ALGOL 68. ALGOL Bulletin, 31, 16–27.Google Scholar
Parigot, M. 1992. λμ-calculus: an algorithmic interpretation of classical natural deduction. Pages 190–201 of: Logic Programming and Automated Reasoning. Proceedings of the International Conference LPAR'92, St. Petersburg, Voronkov, A. (ed). Lecture Notes in Computer Science, vol. 624. Springer.
Parikh, R. 1973. On the length of proofs. Transactions of the American Mathematical Society, 177, 29–36.Google Scholar
Park, D. 1976. The Y combinator in Scott's lambda calculus models. Theory of Computation Report 13. University of Warwick, Department of Computer Science.
Pentus, M. 1993. Lambek grammars are context free. Pages 429–433 of: Logic in Computer Science. IEEE Computer Society Press.
Pentus, M. 2006. Lambek calculus is NP-complete. Theoretical Computer Science, 357(1–3), 186–201.Google Scholar
Péter, R. 1967. Recursive Functions. 3rd revised edition. Academic Press.
Peyton-Jones, S. 1987. The Implementation of Functional Programming Languages. Prentice Hall.
Peyton Jones, S. (ed). 2003. Haskell 98 Language and Libraries: the Revised Report. Cambridge University Press.
Peyton Jones, S. L., and Wadler, P. 1993. Imperative functional programming. Pages 71–84 of: Principles of Programming Languages. ACM Press.
Peyton Jones, S. and Hughes, J. [Editors]; Augustsson, L., Barton, D., Boutel, B., Burton, W., Fraser, S., Fasel, J., Hammond, K., Hinze, R., Hudak, P., Johnsson, T., Jones, M., Launchbury, J., Meijer, E., Peterson, J., Reid, A., Runciman, C., and Wadler, P. 1999. Haskell 98 — A Non-strict, Purely Functional Language. URL <www.haskell.org/definition/>.
Peyton Jones, S., Vytiniotis, D., Weirich, S., and Washburn, G. 2006. Simple unification-based type inference for GADTs. Pages 50–61 of: International Conference on Functional Programming, ACM Press..
Pierce, B. C. 2002. Types and Programming Languages. MIT Press.
Pil, M. R. C. 1999. Dynamic types and type dependent functions. Pages 169–185 of: Implementation of Functional Languages, Hammond, K., Davie, A. J. T., and Clack, C. (eds). Lecture Notes in Computer Science, vol. 1595. Springer.
Pimentel, E., Ronchi Della Rocca, S., and Roversi, L. 2012. Intersection types from a proof-theoretic perspective. Fundamenta Informaticae, 121(1–4), 253–274.Google Scholar
Plasmeijer, M. J., and van Eekelen, M. 2002. Concurrent Clean language report (version 2.1). <www.cs.ru.nl/~clean>.
Plasmeijer, R., Achten, P., and Koopman, P. 2007. iTasks: Executable specifications of interactive work flow systems for the Web. Pages 141–152 of: International Conference on Functional Programming. ACM Press.
Platek, R. A. 1966. Foundations of Recursion Theory. Ph.D. thesis, Stanford University.
Plotkin, G. D. 1975. Call-by-name, call-by-value and the λ-calculus. Theoretical Computer Science, 1(2), 125–159.Google Scholar
Plotkin, G. D. 1977. LCF considered as a programming language. Theoretical Computer Science, 5, 225–255.Google Scholar
Plotkin, G. D. 1980. Lambda-definability in the full type hierarchy. Pages 363–373 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Plotkin, G. D. 1982. The category of complete partial orders: a tool for making meanings. Postgraduate lecture notes, Edinburgh University.
Plotkin, G. D. 1985. Lectures on Predomains and Partial Functions. Center for the Study of Language and Information, Stanford.
Plotkin, G. D. 1993. Set-theoretical and other elementary models of the λ-calculus. Theoretical Computer Science, 121(1–2), 351–409.Google Scholar
Poincaré, H. 1902. La Science et l'Hypothése. Flammarion.
Polonsky, A. 2011. Proofs, Types and Lambda Calculus. Ph.D. thesis, University of Bergen, Norway.
Post, E. 1947. Recursive unsolvability of a problem of Thue. The Journal of Symbolic Logic, 12(1), 1–11.Google Scholar
Pottinger, G. 1977. Normalization as a homomorphic image of cut-elimination. Annals of Mathematical Logic, 12, 323–357.Google Scholar
Pottinger, G. 1980. A type assignment for the strongly normalizable λ-terms. Pages 561–77 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Pottinger, G. 1981. The Church–Rosser theorem for the typed λ-calculus with surjective pairing. Notre Dame Journal of Formal Logic, 22(3), 264–268.Google Scholar
Prawitz, D. 1965. Natural Deduction. Almqvist & Wiksell.
Prawitz, D. 1971. Ideas and results in proof theory. Pages 235–307 of: Scandinavian Logic Symposium, Fenstad, J. E. (ed). North-Holland.
van Raamsdonk, F. 1996. Confluence and Normalisation for Higher-Order Rewriting. Ph.D. thesis, Vrije Universiteit.
van Raamsdonk, F., Severi, P., Sørensen, M.H., and Xi, H. 1999. Perpetual reductions in lambda calculus. Information and Computation, 149(2), 173–225.Google Scholar
Reynolds, J. C. 1972. Definitional interpreters for higher-order programming languages. Pages 717–740 of: ACM National Conference. ACM Press.
Reynolds, J. C. 1993. The discoveries of continuations. LISP and Symbolic Computation, 6(3/4), 233–247.Google Scholar
Robertson, N., Sanders, D., Seymour, P., and Thomas, R. 1997. The four-colour theorem. Journal of Combinatorial Theory. Series B, 70(1), 2–44.Google Scholar
Robinson, J. A. 1965. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12(1), 23–41.Google Scholar
Rogers, H. Jr. 1967. Theory of Recursive Functions and Effective Computability. McGraw-Hill.
Ronchi Della Rocca, S. 1988. Lecture Notes on Semantics and Types. Tech. rept. Torino University.
Ronchi Della Rocca, S. 2002. Intersection typed lambda-calculus. Pages 163–181 of: Intersection Types and Related Systems. Electronic Notes in Theoretical Computer Science, 70, no. 1. Elsevier.
Ronchi Della Rocca, S., and Paolini, L. 2004. The Parametric Lambda Calculus: A Metamodel for Computation. Texts in Theoretical Computer Science, vol. XIII. Springer.
Rosser, J. B. 1984. Highlights of the history of the lambda-calculus. Annals of the History of Computing, 6(4), 337–349.Google Scholar
Rutten, J. J. M. M. 2000. Universal coalgebra: a theory of systems. Theoretical Computer Science, 249(1), 3–80.Google Scholar
Rutten, J. J. M. M. 2005. A coinductive calculus of streams. Mathematical Structures in Computer Science, 15(1), 93–147.Google Scholar
Salvati, S. 2009. Recognizability in the simply typed lambda-calculus. Pages 48–60 of: Workshop on Logic, Language, Information and Computation. Lecture Notes in Computer Science, vol. 5514. Springer.
Salvati, S., Manzonetto, G., Gehrke, M., and Barendregt, H.P. 2012. Loader and Urzyczyn are logically related. Pages 364–376 of: Automata, Languages, and Programming –39th International Colloquium, ICALP 2012, Czumaj, A., Mehlhorn, K., Pitts, A.M., and Wattenhofer, R. (eds). LNCS, vol. 7392. Springer.
Schmidt-Schauß, M. 1999. Decidability of behavioural equivalence in unary PCF. Theoretical Computer Science, 216(1–2), 363–373.Google Scholar
Schrijvers, T., Jones, S. L. Peyton, Sulzmann, M., and Vytiniotis, D. 2009. Complete and decidable type inference for GADTs. Pages 341–352 of: Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming, ICFP 2009, Edinburgh, Scotland, UK, August 31 –September 2, 2009, Hutton, G., and Tolmach, A. P. (eds). ACM.
Schubert, A. 1998. Second-order unification and type inference for Church-style polymorphism. Pages 279–288 of: Symposium on Principles of Programming Languages.
Schwichtenberg, H. 1975. Elimination of higher type levels in definitions of primitive recursive functionals by means of transfinite recursion. Pages 279–303 of: Logic Colloquium. Studies in Logic and the Foundations of Mathematics, vol. 80. North-Holland.
Schwichtenberg, H. 1976. Definierbare Funktionen im λ-Kalkül mit Typen. Archief für Mathematische Logik, 25, 113–114.Google Scholar
Schwichtenberg, H. 1999. Termination of permutative conversion inintuitionistic Gentzen calculi. Theoretical Computer Science, 212(1–2), 247–260.Google Scholar
Schwichtenberg, H., and Berger, U. 1991. An inverse of the evaluation functional for typed λ-calculus. Pages 203–211 of: Logic in Computer Science. IEEE Computer Society Press.
Scott, D. S. 1970. Constructive validity. Pages 237–275 of: Symposium on Automated Demonstration. Lecture Notes in Mathematics, vol. 125. Springer.
Scott, D. S. 1972. Continuous lattices. Pages 97–136 of: Toposes, Algebraic Geometry and Logic. Lecture Notes in Mathematics, vol. 274. Springer.
Scott, D. S. 1975a. Open problem 4. Page 369 of: λ-calculus and Computer Science Theory (Böhm (1975)).
Scott, D. S. 1975b. Some philosophical issues concerning theories of combinators. Pages 346–366 of: λ-calculus and Computer Science Theory (Böhm (1975)).
Scott, D. S. 1976. Data types as lattices. SIAM Journal on Computing, 5, 522–587.Google Scholar
Scott, D. S. 1980. Relating theories of the λ-calculus. Pages 403–450 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Severi, P., and Poll, E. 1994. Pure type systems with definitions. Pages 316–328 of: Logical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 813. Springer.
Sheeran, M. 2005. Hardware design and functional programming: a perfect match. Journal of Universal Computer Systems, 11(7), 1135–1158.Google Scholar
Smyth, M. B., and Plotkin, G. D. 1982. The category-theoretic solution of recursive domain equations. SIAM Journal on Computing, 11(4), 761–783.Google Scholar
Sørensen, M. H. 1997. Strong normalization from weak normalization in typed λ-calculi. Information and Computation, 133, 35–71.Google Scholar
Sørensen, M. H., and Urzyczyn, P. 2006. Lectures on the Curry-Howard Isomorphism. Elsevier.
Spector, C. 1962. Provable recursive functionals of analysis. Pages 1–27 of: Recursive Function Theory, Dekker, J. C. E. (ed). American Mathematical Society.
Statman, R. 1979. The typed λ-calculus is not elementary recursive. Theoret. Comput. Sci., 9(1), 73–81.Google Scholar
Statman, R. 1979a. Intuitionistic propositional logic is polynomial-space complete. Theoret. Comput. Sci., 9(1), 67–72.Google Scholar
Statman, R. 1980a. On the existence of closed terms in the typed λ-calculus. I. Pages 511–534 of: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Hindley and Seldin (1980)).
Statman, R. 1980b. On the existence of closed terms in the typed λ-calculus. III. Dept. of Mathematics, CMU, Pittsburgh, USA.
Statman, R. 1981. On the existence of closed terms in the typed λ calculus. II. Transformations of unification problems. Theoret. Comput. Sci., 15(3), 329–338.Google Scholar
Statman, R. 1982. Completeness, invariance and λ-definability. The Journal of Symbolic Logic, 47(1), 17–26.Google Scholar
Statman, R. 1985. Equality between functionals revisited. Pages 331–338 of: Harvey Friedman's Research on the Foundations of Mathematics (Harrington et al. (1985)). Amsterdam: North-Holland.
Statman, R. 1994. Recursive types and the subject reduction theorem. Technical Report 94–164. Carnegie Mellon University.
Statman, R. 2000. Church's lambda delta calculus. Pages 293–307 of: Logic for Programming and Automated Reasoning (Reunion Island, 2000). Lecture Notes in Comput. Sci., vol. 1955. Springer.
Statman, R. 2007. On the complexity of α-conversion. The Journal of Symbolic Logic, 72(4), 1197–1203.Google Scholar
Steedman, M. 2000. The Syntactic Process. MIT Press.
Steele, G. L. Jr. 1978. RABBIT: A Compiler for SCHEME. Tech. rept. AI-TR-474. Artificial Intelligence Laboratory, MIT.
Steele, G. L. Jr. 1984. Common Lisp: The Language. Digital Press.
Stenlund, S. 1972. Combinators, λ-Terms and Proof Theory. Synthese Library. D. Reidel.
Stirling, C. 2009. Decidability of higher-order matching. Logical Methods in Computer Science, 5(3), 1–52.Google Scholar
Støvring, K. 2006. Extending the extensional lambda calculus with surjective pairing is conservative. Logical Methods in Computer Science, 2(2:1), 1–14.Google Scholar
Sudan, G. 1927. Sur le nombre transfini ωω. Bulletin mathématique de la Société Roumaine des Sciences, 30, 11–30.Google Scholar
Szabo, M. E. (ed). 1969. Collected Papers of Gerhard Gentzen. North-Holland.
Tait, W. W. 1965. Infinitely long terms of transfinite type I. Pages 176–185 of: Formal Systems and Recursive Functions, Crossley, J., and Dummett, M. (eds). North-Holland.
Tait, W. W. 1967. Intensional interpretations of functionals of finite type. I. The Journal of Symbolic Logic, 32, 198–212.Google Scholar
Tait, W. W. 1971. Normal form theorem for barrecursive functions of finite type. Pages 353–367 of: Scandinavian Logic Symposium. North-Holland.
Tatsuta, M., and Dezani-Ciancaglini, M. 2006. Normalisation is insensible to lambda-term identity or difference. Pages 327–336 of: Logic in Computer Science. IEEE Computer Society Press.
Tait, . 2003. Term Rewriting Systems. Cambridge University Press.
Terlouw, J. 1982. On definition trees of ordinal recursive functionals: reduction of the recursion orders by means of type level raising. The Journal of Symbolic Logic, 47(2), 395–402.Google Scholar
Thatcher, J. W. 1973. Tree automata: an informal survey. Chap. 4, pages 143–172 of: Currents in the Theory of Computing, Aho, A.V. (ed). Prentice-Hall.
Thompson, S. 1995. Miranda, The Craft of Functional Programming. Addison-Wesley.
Tiede, H. J. 2001. Lambek calculus proofs and tree automata. Pages 251–265 of: Logical Aspects of Computational Linguistics. Lecture Notes in Artificial Intelligence, vol. 2014. Springer.
Tiede, H. J. 2002. Proof tree automata. Pages 143–162 of: Words, Proofs, and Diagrams, Barker-Plummer, D., Beaver, D., van Benthem, J. F. A. K., and Scotto di Luzio, P. (eds). Center for the Study of Language and Information, Stanford.
Troelstra, A. S. 1973. Metamathematical Investigation of Intuitionistic Arithmetic and Analysis. Lecture Notes in Mathematics, no. 344. Springer.
Troelstra, A. S. 1999. Marginalia on sequent calculi. Studia Logica, 62(2), 291–303.Google Scholar
Troelstra, A. S., and Schwichtenberg, H. 1996. Basic Proof Theory. Cambridge University Press.
Turner, D. A. 1976. The SASL language manual. http://www.eis.mdx.ac.uk/staffpages/dat/saslman.pdf.
Turner, D. A. 1979. A new implementation technique for applicative languages. Software –Practice and Experience, 9, 31–49.Google Scholar
Turner, D. A. 1981. The semantic elegance of functional languages. Pages 85–92 of: Functional Programming Languages and Computer Architecture. ACM Press.
Turner, D. A. 1985. Miranda, a non-strict functional language with polymorphic types. Pages 1–16 of: Functional Programming Languages and Computer Architecture. Lecture Notes in Computer Science, vol. 201. Springer.
Urban, C., and Tasson, C. 2005. Nominal techniques in Isabelle/HOL. Pages 38–53 of: Automated deduction –CADE-20. Lecture Notes in Computer Science, vol. 3632. Springer.
Urban, C., Berghofer, S., and Norrish, M. 2007. Barendregt's variable convention in rule inductions. Pages 35–50 of: Proc. of the 21st International Conference on Automated Deduction (CADE). LNAI, vol. 4603.
Urzyczyn, P. 1999. The emptiness problem for intersection types. The Journal of Symbolic Logic, 64(3), 1195–1215.Google Scholar
Urzyczyn, P. 2009. Inhabitation of low-rank intersection types. Pages 356–370 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 5608. Springer.
Venneri, B. 1994. Intersection types as logical formulae. Journal of Logic and Computation, 4(2), 109–124.Google Scholar
Venneri, B. 1996. Private Communication. Florence University.
Vermaat, W. 2006. The Logic of Variation. A Cross-Linguistic Account of wh-Question Formation. Ph.D. thesis, Utrecht University.
Vogel, H. 1976. Ein starker Normalisationssatz für die barrekursiven Funktionale. Archiv für Mathematische Logik und Grundlagenforschung, 18, 81–84.Google Scholar
Voigtländer, J. 2009. Free theorems involving type constructor classes: functional pearl. Pages 173–184 of: ACM SIGPLAN International Conference on Functional Programming. ACM Press.
Vouillon, J., and Melliés, P.-A. 2004. Semantic types: a fresh look at the ideal model for types. Pages 24–38 of: Principles of Programming Languages. ACM Press.
de Vrijer, R. C. 1987a. Surjective Pairing and Strong Normalization: Two Themes in Lambda Calculus. Ph.D. thesis, University of Amsterdam.
de Vrijer, R.C. 1987b. Exactly estimating functionals and strong normalizationIndagationes Mathematicae, 49, 479–493.Google Scholar
de Vrijer, R. C. 1989. Extending the lambda calculus with surjective pairing is conservative. Pages 204–215 of: Logic in Computer Science. IEEE Computer Society Press.
Wadsworth, C. P. 1971. Semantics and Pragmatics of the Lambda-Calculus. Ph.D. thesis, University of Oxford.
Wadsworth, C. P. 1976. The relation between computational and denotational properties for Scott's D∞-models of the lambda-calculus. SIAM Journal of Computing, 5(3), 488–521.Google Scholar
Wand, M. 1987. A simple algorithm and proof for type inference. Fundamenta Informaticae, 10, 115–122.Google Scholar
Wansing, H. 2002. Sequent systems for modal logics. Pages 61–145 of: Handbook of Philosophical Logic, vol. 8, Gabbay, D., and Guenthner, F. (eds). Kluwer.
Wells, J. B. 1999. Typability and type checking in system F are equivalent and undecidable. Annals of Pure and Applied Logic, 98(1–3), 111–156.Google Scholar
Wells, J. B., Dimock, A., Muller, R., and Turbak, F. 1997. A typed intermediate language for flow-directed compilation. Pages 757–771 of: Theory and Practice of Software Development. Lecture Notes in Computer Science, no. 1214.
Whitehead, A.N., and Russell, B. 19101913. Principia Mathematica. Cambridge University Press.
Wiedijk, F. 2006. The Seventeen Provers of the World. Lecture Notes in Computer Science, vol. 3600. Springer.
van Wijngaarden, A. 1981. Revised report of the algorithmic language Algol 68. ALGOL Bulletin, 1–119.
Xi, H. 1997. Weak and strong beta normalisations in typed λ-calculi. Pages 390–404 of: Typed Lambda Calculi and Applications. Lecture Notes in Computer Science, vol. 1210. Springer.
Zeleny, M., and Anderson, C.A. (eds). 2001. Church Memorial Volume: Logic, Language, and Computation. Kluwer.
Zucker, J. 1974. Cut-elimination and normalization. Annals of Mathematical Logic, 7, 1–112.Google Scholar
Zylberajch, C. 1991. Syntaxe et Semantique de la Facilité en Lambda-Calcul. Ph.D. thesis, Université de Paris VII.