Substitution in non-wellfounded syntax with variable binding

Theoretical Computer Science

Volumn 327, Issue 1-2, 2004, Pages 155-174

  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; COMPUTATION THEORY; COMPUTER PROGRAMMING LANGUAGES; DATA STRUCTURES; MATHEMATICAL OPERATORS; RECURSIVE FUNCTIONS;

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

SYNTACTICS;

EID: 4944265294     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.07.025     Document Type: Conference Paper

References (43)

1. A. Abel, R. Matthes, (Co-)iteration for higher-order nested datatypes, in: H. Geuvers, F. Wiedijk (Eds.), Selected Papers from Second International Workshop on Types for Proofs and Programs, TYPES 2002, Berg en Dal, The Netherlands, 24-28 April 2002, Vol. 2646 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 1-20.
2. A. Abel, R. Matthes, T. Uustalu, Generalized iteration and coiteration for higher-order nested datatypes, in: A.D. Gordon (Ed.), Proceedings of the Sixth International Conference on Foundations of Software Science and Computation Structures FoSSaCS 2003, Warsaw, Poland, 7-9 April 2003, Vol. 2620 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 54-69.
3. P. Aczel, Frege structures and the notions of proposition, truth and set, in: J. Barwise, H.J. Keisler, K. Kunen (Eds.), The Kleene Symp.: Proceedings of Symposium, Madison, WI, USA, 18-24 June 1978, Vol. 101 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1980, pp. 31-59.
4. P. Aczel, Algebras and coalgebras, in: R. Backhouse, R. Crole, J. Gibbons (Eds.), Revised Lectures from International Summer School and Workshop on Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, Oxford, UK, 10-14 April 2000, Vol. 2297 of Lecture Notes in Computer Science, Springer, Berlin, 2002, pp. 79-88, (Chapter 3).
5. P. Aczel, J. Adámek, S. Milius, J. Velebil, Infinite trees and completely iterative theories: a coalgebraic view, Theoret. Comput. Sci. 300 (1-3) (2003) 1-45.
6. K. Aehlig, F. Joachimski, On continuous normalization, in: J.C. Bradfield (Ed.), Proceedings of 16th International Workshop on Computer Science Logic, CSL 2002, Edinburgh, UK, 22-25 Sept. 2002, Vol. 2471 of Lecture Notes in Computer Science, Springer, Berlin, 2002, pp. 59-73.
7. T. Altenkirch, B. Reus, Monadic presentations of lambda terms using generalized inductive types, in: J. Flum, M. Rodríguez-Artalejo (Eds.), Proceedings of 13th International Workshop on Computer Science Logic, CSL'99, Madrid, Spain, 20-25 September 1999, Vol. 1683 of Lecture Notes in Computer Science, Springer, Berlin, 1999, pp. 453-468.
8. M. Barr, Coequalizers and free triples, Math. Z. 116 (1970) 307-322.
9. F. Bellegarde, J. Hook, Substitution: a formal methods case study using monads and transformations, Sci. Comput. Programming 23 (2-3) (1994) 287-311.
10. R. Bird, L. Meertens, Nested datatypes, in: J. Jeuring (Ed.), Proceedings of Fourth International Conference on Mathematics of Program Construction MPC'98, Marstrand, Sweden, 15-17 June 1998, Vol. 1422 of Lecture Notes in Computer Science, Springer, Berlin, 1998, pp. 52-67.
11. R. Bird, R. Paterson, Generalised folds for nested datatypes, Formal Aspects Comput. 11 (2) (1999) 200-222.
12. R.S. Bird, R. Paterson, De Bruijn notation as a nested datatype, J. Functional Programming 9 (1) (1999) 77-91.
13. R.L. Crole, Basic category theory for models of syntax, in: R.C. Backhouse, J. Gibbons (Eds.), Revised Lectures from Summer School and Workshop on Generic Programming, SSGP 2002, Oxford, UK, 26-30 August 2002, Vol. 2793 of Lecture Notes in Computer Science, Springer, Berlin, 2003, pp. 133-177.
14. N.G. de Bruijn, Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with applications to the Church-Rosser theorem, Indagationes Math. (Koninglijke Nederlandse Akademie van Wetenschappen) 34 (1972) 381-392.
15. M. Fiore, Semantic analysis of normalisation by evaluation for typed lambda calculus, in: Proceedings of 4th International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, PPDP'02, Pittsburgh, PA, USA, 6-8 October 2002, ACM Press, New York, 2002, pp. 26-37.
16. M. Fiore, G.D. Plotkin, D. Turi, Abstract syntax and variable binding (extended abstract), in: Proceedings of 14th Annual IEEE Symposium on Logic in Computer Science, LICS'99, Trento, Italy, 2-5 July 1999, IEEE CS Press, Los Alamitos, CA, 1999, pp. 193-202.
17. N. Ghani, C. Lüth, F. de Marchi, Coalgebraic monads, in: L.S. Moss (Ed.), Proceedings of Fifth Workshop on Coalgebraic Methods in Computer Science, CMCS'02, Grenoble, France, 6-7 Apr. 2002, Vol. 65(1) of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2002.
18. N. Ghani, C. Lüth, F. de Marchi, J. Power, Dualising initial algebras, Math. Structures Comput. Sci. 13 (2) (2003) 349-370.
19. N. Ghani, T. Uustalu, Explicit substitutions and higher-order syntax, in: F. Honsell, M. Miculan, A. Momigliano (Eds.), Proceedings of Second ACM SIGPLAN Workshop on Mechanized Reasoning about Languages with Variable Binding, MERLIN 2003, Uppsala, Sweden, 26 August 2003, ACM Press, New York, 2003.
20. J.-Y. Girard, Locus solum: from the rules of logic to the logic of rules, Math. Structures Comput. Sci. 11 (3) (2001) 301-506.
21. R. Harper, F. Honsell, G. Plotkin, A framework for denning logics, J. ACM 40 (1) (1993) 143-184.
22. R. Hinze, Polytypic functions over nested datatypes, Discrete Math. Theoret. Comput. Sci. 3 (4) (1999) 193-214.
23. M. Hofmann, Semantical analysis of higher-order abstract syntax, in: Proceedings of 14th Annual IEEE Symposium on Logic in Computer Science, LICS'99, Trento, Italy, 2-5 July 1999, IEEE CS Press, Los Alamitos, CA, 1999, pp. 204-213.
24. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.-J. de Vries, Infinitary lambda calculus, Theoret. Comput. Sci. 175 (1) (1997) 93-125.
25. R. Matthes, Monotone inductive and coinductive constructors of rank 2, in: L. Fribourg (Ed.), Proceedings of 15th International Workshop on Computer Science Logic, CSL'01, Paris, France, 10-13 September 2001, Vol. 2142 of Lecture Notes in Computer Science, Springer, Berlin, 2001, pp. 600-614.
26. R. Matthes, T. Uustalu, Substitution in Non-wellfounded Syntax with Variable Binding, in: H.P. Gumm (Ed.), Proceedings of Sixth International Workshop on Coalgebraic Methods in Computer Science, CMCS'03, Warsaw, Poland, 5-6 April 2003, Vol. 82 (1) of Electronic Notes in Theoretical Computer Science, Elsevier, Amsterdam, 2003.
27. M. Miculan, I. Scagnetto, A framework for typed HOAS and semantics, in: Proceedings of Fifth International ACM SIGPLAN Conference on Principles and Practice of Declarative Programming, PPDP'03, Uppsala, Sweden, 27-29 August 2003, ACM Press, New York, 2003, pp. 184-194.
28. G. Mints, Finite investigations of infinite derivations, Zap. Nauchn. Semin. Leningr. Otd. Matem. Inst. 49 (1975); translation in: J. Soviet Math. 10 (1978) 548-596. Reprinted in: G. Mints, Selected papers in Proof Theory, Vol. 3 of Studies in Proof Theory, Monographs, Bibliopolis, Napoli, 1992, pp. 17-72.
29. G. Mints, Finite investigations of infinite derivations, Zap. Nauchn. Semin. Leningr. Otd. Matem. Inst. 49 (1975); translation in: J. Soviet Math. 10 (1978) 548-596. Reprinted in: G. Mints, Selected papers in Proof Theory, Vol. 3 of Studies in Proof Theory, Monographs, Bibliopolis, Napoli, 1992, pp. 17-72.
30. G. Mints, Finite investigations of infinite derivations, Zap. Nauchn. Semin. Leningr. Otd. Matem. Inst. 49 (1975); translation in: J. Soviet Math. 10 (1978) 548-596. Reprinted in: G. Mints, Selected papers in Proof Theory, Vol. 3 of Studies in Proof Theory, Monographs, Bibliopolis, Napoli, 1992, pp. 17-72.
31. G. Mints, Reduction of finite and infinite derivations, Ann. Pure Appl. Logic 104 (1-3) (2000) 167-188.
32. L.S. Moss, Parametric corecursion, Theoret. Comput. Sci. 260 (1-2) (2001) 139-163.
33. C. Okasaki, From fast exponentiation to square matrices: an adventure in types, in: Proceedings of Fifth ACM SIGPLAN International Conference on Functional Programming, ICFP'99, Paris, France, 27-29 September 1999, Vol. 34 (9) of SIGPLAN Notices, ACM Press, New York, 1999, pp. 28-35.
34. F. Pfenning, C. Elliot, Higher-order abstract syntax, in: Proceedings of ACM SIGPLAN 1988 Conference on Programming Language Design and Implementation, PLDI'88, Atlanta, GA, 22-24 June 1988, Vol. 23 (7) of SIGPLAN Notices, ACM Press, New York, 1988, pp. 199-208.
35. G. Plotkin, An illative theory of relations, in: R. Cooper, K. Mukai, J. Perry (Eds.), Situation Theory and Its Applications 1, Vol. 22 of CSLI Lecture Notes, CSLI Publications, Stanford, CA, 1990, pp. 133-146.
36. J. Power, A unified category-theoretic approach to variable binding, in: F. Honsell, M. Miculan, A. Momigliano (Eds.), Proceedings of Second ACM SIGPLAN Workshop on Mechanized Reasoning about Languages with Variable Binding, MERLIN 2003, Uppsala, Sweden, 26 August 2003, ACM Press, New York, 2003.
37. P. Severi, F.-J. de Vries, An extensional Böhm model, in: S. Tison (Ed.), Proceedings of 13th International Conference on Rewriting Theory and Applications, RTA 2002, Copenhagen, Denmark, 22-24 July 2002, Vol. 2378 of Lecture Notes in Computer Science, Springer, Berlin, 2002, pp. 159-173.
38. Y. Sun, An algebraic generalization of Frege structures - binding signatures, Theoret. Comput. Sci. 211 (1-2) (1999) 189-232.
39. M. Tanaka, Abstract syntax and variable binding for linear binders, in: M. Nielsen, B. Rovan (Eds.), Proceedings of 25th International Symposium on Mathematics Foundation of Computer Science, MFCS 2000, Bratislava, Slovakia, 28 August-1 September 2000, Vol. 1893 of Lecture Notes in Computer Science, Springer, Berlin, 2000, pp. 670-679.
40. T. Uustalu, Generalizing substitution, Theoret. Inform. Appl. 37 (4) (2003) 315-336.
41. T. Uustalu, V. Vene, Primitive (co)recursion and course-of-value (co)iteration, categorically, Informatica 10 (1) (1999) 5-26.
42. T. Uustalu, V. Vene, The dual of substitution is redecoration, in: K. Hammond, S. Curties (Eds.), Trends in Functional Programming 3, Intellect, Bristol, Portland, OR, 2001, pp. 99-110.
43. T. Uustalu, V. Vene, An alternative characterization for complete iterativeness (extended abstract), in: Z. Esik, I. Waukiewicz (Eds.), Proceedings of the 5th International Workshop on Fixed Points in Computer Science, FICS 2003, Warsaw, Poland, 12-13 April 2003, University of Warsaw, 2003, pp. 81-83.