Substitution in non-wellfounded syntax with variable binding

Electronic Notes in Theoretical Computer Science

Volumn 82, Issue 1, 2003, Pages 191-205

  Matthes, Ralph ^a   Uustalu, Tarmo ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

Author keywords

Final coalgebra; Functor category; Monad; Non wellfounded syntax; Primitive corecursion; Substitution; Variable binding

Indexed keywords

ALGEBRA; COMPUTER SCIENCE; DIFFERENTIATION (CALCULUS); ITERATIVE METHODS; MATHEMATICAL OPERATORS; SEMANTICS;

FINAL COALGEBRA; FUNCTOR CATEGORY; MONAD; NON-WELLFOUNDED SYNTAX; PRIMITIVE CORECURSION; SUBSTITUTION; VARIABLE BINDING;

COMPUTER PROGRAMMING LANGUAGES;

EID: 0942302122     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1571-0661(04)80639-X     Document Type: Conference Paper

References (35)

1. Abel A., Matthes R. (Co-)interation for higher-order nested datatypes. Geuvers H., Wiedijk F. Selected Papers from 2nd Int. Wksh. on Types for Proofs and Programs, TYPES'02 (Berg en Dal near Nijmegen, Apr. 2002). Lect. Notes in Comput. Sci. 2646 :2003;1-20 Springer-Verlag, Berlin
2. Abel A., Matthes R., Uustalu T. Generalized iteration and coiteration for higher-order nested datatypes. Gordon A.D. Proc. of 6th Int. Conf. on Foundations of Software Science and Computation Structures, FoSSaCS'03 (Warsaw, Apr. 2003). Lect. Notes in Comput. Sci. 2620 :2003;54-69 Springer-Verlag, Berlin
3. Aczel P., Frege structures and the notions of proposition, truth and set, in: J. Barwise, H. J. Keisler and K. Kunen, eds., Proc. of The Kleene Symp. (Madison, WI, June 1978), Studies in Logic and Found. of Math. 101, North Holland, Amsterdam, 1980 pp. 31-59.
4. Aczel P. Algebras and coalgebras. Backhouse R., Crole R., Gibbons J. Revised Lectures from Int. Summer School and Wksh. on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction (Oxford, April 2000). Lect. Notes in Comput. Sci. 2297 :2002;79-88 Springer-Verlag, Berlin
5. Aczel, P. J., Adàmek and J. Velebil, A coalgebraic view of infinite trees and iteration, in: A. Corradini, M. Lenisa and U. Montanari, eds., Proc. of 4th Wksh. on Coalgebraic Methods in Computer Science, CMCS'01 (Genova, Apr. 2001), Electr. Notes in Theoret. Comput. Sci. 44(1), Elsevier, Amsterdam, 2001. Journal version with S. Milius as an additional coauthor to appear in Theoret. Comput. Sci.
6. Aehlig K. and F. Joachimski, On continuous normalization, in: J. C. Bradfield, ed., Proc. of 16th Int. Wksh. on Computer Science Logic, CSL 2002 (Edinburgh, Sept. 2002), Lect. Notes in Comput. Sci. 2471, Springer-Verlag, Berlin, 2002 pp. 59-73.
7. Altenkirch T. and B. Reus, Monadic presentations of lambda terms using generalized inductive types, in: J. Flum and M. Rodríguez-Artalejo, eds., Proc. of 13th Int. Wksh. on Computer Science Logic, CSL'99 (Madrid, Sept. 1999), Lect. Notes in Comput. Sci. 1683, Springer-Verlag, Berlin, 1999 pp. 453-468.
8. Barr M. Coequalizers and free triples. Math. Z. 116:1970;307-322
9. Bellegarde F., Hook J. Substitution: A formal methods case study using monads and transformations. Sci. of Comput. Program. 23:1994;287-311
10. Bird R. and L. Meertens, Nested datatypes, in: J. Jeuring, ed., Proc. of 4th Int. Conf. on Mathematics of Program Construction, MPC'98 (Marstrand, June 1998), Lect. Notes in Comput. Sci. 1422, Springer-Verlag, Berlin, 1998 pp. 52-67.
11. Bird R., Paterson R. Generalised folds for nested datatypes. Formal Aspects of Computing. 11:1999;200-222
12. Bird R.S., Paterson R. De Bruijn notation as a nested datatype. J. of Functional Programming. 9:1999;77-91
13. de Bruijn N.G. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with applications to the Church-Rosser theorem. Indagationes Math. 34:1972;381-392
14. Crole, R. L., Basic category theory for models of syntax, Course notes for Summer School on Generic Programming, SSGP'02 (Oxford, Aug. 2002), to appear.
15. Fiore M., G. D. Plotkin and D. Turi, Abstract syntax and variable binding (extended abstract), in: Proc. of 14th Ann. IEEE Symp. on Logic in Computer Science, LICS'99 (Trento, July 1999), IEEE CS Press, Los Alamitos, CA, 1999, pp. 193-202.
16. Ghani N., C. Lüth and F. de Marchi, Coalgebraic monads, in: L. S. Moss, ed., Proc. of 5th Wksh. on Coalgebraic Methods in Computer Science, CMCS'02 (Grenoble, Apr. 2002), Electr. Notes in Theoret. Comput. Science 65.1, Elsevier, Amsterdam, 2002.
17. Ghani N., Lüth C., de Marchi F., Power J. Dualising initial algebras. Math. Struct. in Comput. Sci. 13:2003;349-370
18. Girard J.-Y. Locus solum: From the rules of logic to the logic of rules. Math. Struct. in Comput. Sci. 11:2001;301-506
19. Harper H., Honsell F., Plotkin G. A framework for defining logics. J. of ACM. 40:1993;143-184
20. Hinze R. Polytypic functions over nested datatypes. Discrete Math. and Theoret. Comput. Sci. 3:1999;193-214
21. Hofmann M., Semantical analysis of higher-order abstract syntax, in: Proc. of 14th Ann. IEEE Symp. on Logic in Computer Science, LICS'99 (Trento, July 1999), IEEE CS Press, Los Alamitos, CA, 1999 pp. 204-213.
22. Kennaway J.R., Klop J.W., Sleep M.R., de Vries F.J. Infinitary lambda calculus. Theoret. Comput. Sci. 175:1997;93-125
23. Matthes R., Monotone inductive and coinductive constructors of rank 2, in: L. Fribourg, ed., Proc. of 15th Int. Wksh. on Computer Science Logic, CSL'01 (Paris, Sept. 2001), Lect. Notes in Comput. Sci. 2142, Springer-Verlag, Berlin, 2001 pp. 600-614.
24. Mints, G., Finite investigations of infinite derivations, Zap. Nauchn. Semin. Leningr. Otd. Matem. Inst. 49 (1975).
25. Translation in: J. of Soviet Math. 10 (1978), pp. 548-596.
26. Reprinted in: Mints, G., "Selected Papers in Proof Theory", Studies in Proof Theory: Monographs 3, Bibliopolis, Napoli, 1992 pp. 17-72.
27. Mints G. Reduction of finite and infinite derivations. Ann. of Pure and Appl. Logic. 104:2000;167-188
28. Moss L.S. Parametric corecursion. Theoret. Comput. Sci. 260:2001;139-163
29. Okasaki C., From fast exponentiation to square matrices: An adventure in types, in: Proc. of 5th ACM SIGPLAN Int. Conf. on Functional Programming, ICFP'99 (Paris, Sept. 1999), ACM Press, New York, 1999 pp. 28-35.
30. Pfenning F. and C. Elliot, Higher-order abstract syntax, in: Proc. of ACM SIGPLAN 1988 Conf. on Programming Language Design and Implementation, PLDI'88 (Atlanta, GA, June 1988), ACM Press, New York, 1988 pp. 199-208.
31. Plotkin G. An illative theory of relations. Cooper R., Mukai K., Perry J. Situation Theory and Its Applications, Vol. 1. CSLI Lect. Notes 22 :1990;133-146 CSLI Publications, Stanford, CA
32. Severi P., and F.-J. de Vries, An extensional Böhm model, in: S. Tison, ed., Proc. of 13th Int. Conf. on Rewriting Theory and Applications, RTA 2002 (Copenhagen, July 2002), Lect. Notes in Comput. Sci. 2378, Springer-Verlag, Berlin, 2002 pp. 159-173.
33. Sun Y. An algebraic generalization of Frege structures - binding signatures. Theoret. Comput. Sci. 211:1999;189-232
34. Uustalu T. Generalizing substitution (extended abstract). Ésik Z., Ingólfsdóttir A. Prel. Proc. of 4th Int. Wksh. Fixed Points in Computer Science, FICS'02 (Copenhagen, July 2002). BRICS Notes Series NS-02-2, Dept. of Comput. Sci., Aarhus Univ. :2002;9-11. Full version accepted for publication in Theor. Inform. and Appl.
35. Uustalu T., Vene V. Primitive (co)recursion and course-of-value (co)iteration, categorically. Informatica. 10:1999;5-26