Binary lambda calculus and combinatory logic

Randomness and Complexity: From Leibniz to Chaitin

Volumn , Issue , 2007, Pages 237-262

  Tromp, John ^a  

^a CWI   (Netherlands)

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EID: 84967662808     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812770837_0014     Document Type: Chapter

References (24)

1. R. Penrose, The Emperor’s New Mind, Oxford University press, 1989.
2. G. Chaitin, An Invitation to Algorithmic Information Theory, DMTCS’96 Proceedings, Springer Verlag, Singapore, 1997, pp. 1-23 (http://www.cs.auckland.ac.nz/CDMTCS/chaitin/inv.html).
3. G. Chaitin, Exploring Randomness, Springer Verlag, 2001. (http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ait3.html)
4. R. Muller, M-LISP: A representation-independent dialect of LISP with reduction semantics, ACM Transactions on Programming Languages and Systems 14(4), 589-616, 1992.
5. L. Levin, On a Concrete Method of Assigning Complexity Measures, Doklady Akademii nauk SSSR, vol. 18(3), pp. 727-731, 1977.
6. M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications, Graduate Texts in Computer Science, second edition, Springer-Verlag, New York, 1997.
7. S.C. Kleene, Lambda-Definability and Recursiveness, Duke Mathematical Journal, 2, 340-353, 1936.
8. Frank Pfenning and Conal Elliot, Higher-Order Abstract Syntax, ACM SIGPLAN’ 88 Conference on Programming Language Design and Implementation, 199-208, 1988.
9. D. Friedman and M. Wand, Reification: Reflection without Metaphysics, Proc. ACM Symposium on LISP and Functional Programming, 348-355, 1984.
10. Gudmund S. Frandsen and Carl Sturtivant, What is an Efficient Implementation of the calculus?, Proc. ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, 289-312, 1991.
11. J. Steensgaard-Madsen, Typed representation of objects by functions, TOPLAS 11-1, 67-89, 1989.
12. N.G. de Bruijn, Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, Indagationes Mathematicae 34, 381-392, 1972.
13. H.P. Barendregt, Discriminating coded lambda terms, in (A. Anderson and M. Zeleny eds.) Logic, Meaning and Computation, Kluwer, 275-285, 2001.
14. Fran, cois-Nicola Demers and Jacques Malenfant, Reflection in logic, functional and object-oriented programming: a Short Comparative Study, Proc. IJCAI Workshop on Reflection and Metalevel Architectures and their Applications in AI, 29-38, 1995.
15. Daniel P. Friedman, Mitchell Wand, and Christopher T. Haynes, Essentials of Programming Languages-2nd ed, MIT Press, 2001.
16. Oleg Mazonka and Daniel B. Cristofani, A Very Short Self-Interpreter, http://arxiv.org/html/cs.PL/0311032, 2003.
17. D. Hofstadter, Godel, Escher, Bach: an Eternal Golden Braid, Basic Books, Inc., 1979.
18. H.P. Barendregt, The Lambda Calculus, its Syntax and Semantics, revised edition, North-Holland, Amsterdam, 1984.
19. Simon Peyton Jones, Tackling the awkward squad: monadic input/output, concurrency, exceptions, and foreign-language calls in Haskell, in "Engineeringtheories of software construction", ed. Tony Hoare, Manfred Broy, RalfSteinbruggen, IOS Press, 47-96, 2001.
20. The Haskell Home Page, http://haskell.org/.
21. Brainfuck homepage, http://www.muppetlabs.com/~breadbox/bf/.
22. Torben Æ. Mogensen, Linear-Time Self-Interpretation of the Pure Lambda Calculus, Higher-Order and Symbolic Computation 13(3), 217-237, 2000.
23. D. A. Turner, Another algorithm for bracket abstraction, J. Symbol. Logic 44(2), 267-270, 1979.
24. J. T. Tromp, http://www.cwi.nl/~tromp/cl/Lambda.lhs, 2004.