메뉴 건너뛰기




Volumn 203, Issue 5, 2008, Pages 25-47

Inductive and Coinductive Components of Corecursive Functions in Coq

Author keywords

Accessibility Predicates; Coinduction; Coq; Guardedness; Induction; Productiveness

Indexed keywords

ALGORITHMS; FUNCTION EVALUATION; FUNCTIONS; NUMBER THEORY; SYNTACTICS;

EID: 44649150140     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2008.05.018     Document Type: Article
Times cited : (20)

References (44)
  • 1
    • 44649144827 scopus 로고    scopus 로고
    • A. Abel. Type-Based Termination. A Polymorphic Lambda-Calculus with Sized Higher-Order Types. PhD thesis, Fakültat für Mathematik, Informatik und Statistik der Ludwig-Maximilians-Universität München, 2006
    • A. Abel. Type-Based Termination. A Polymorphic Lambda-Calculus with Sized Higher-Order Types. PhD thesis, Fakültat für Mathematik, Informatik und Statistik der Ludwig-Maximilians-Universität München, 2006
  • 2
    • 77956968984 scopus 로고
    • An introduction to inductive definitions
    • North-Holland Publishing Company
    • Aczel P. An introduction to inductive definitions. Handbook of Mathematical Logic (1977), North-Holland Publishing Company 739-782
    • (1977) Handbook of Mathematical Logic , pp. 739-782
    • Aczel, P.1
  • 4
    • 84949183434 scopus 로고    scopus 로고
    • Fixpoint equations for well-founded recursion in type theory
    • Theorem Proving in Higher-Order Logics: 13th International Conference. Harrison J., and Aagaard M. (Eds). TPHOLs 2000, Springer-Verlag
    • Balaa A., and Bertot Y. Fixpoint equations for well-founded recursion in type theory. In: Harrison J., and Aagaard M. (Eds). Theorem Proving in Higher-Order Logics: 13th International Conference. TPHOLs 2000. LNCS volume 1869 (2000), Springer-Verlag 1-16
    • (2000) LNCS , vol.1869 , pp. 1-16
    • Balaa, A.1    Bertot, Y.2
  • 6
    • 0001439401 scopus 로고
    • Lambda calculi with types
    • Abramsky S., Gabbay D., and Maibaum T. (Eds), Oxford University Press
    • Barendregt H. Lambda calculi with types. In: Abramsky S., Gabbay D., and Maibaum T. (Eds). Handbook of Logic in Computer Science, volume II (1992), Oxford University Press 117-309
    • (1992) Handbook of Logic in Computer Science, volume II , pp. 117-309
    • Barendregt, H.1
  • 7
    • 0013129691 scopus 로고    scopus 로고
    • Proof-checking using dependent type systems
    • Robinson A., and Voronkov A. (Eds), Elsevier Science chapter 18
    • Barendregt H., and Geuvers H. Proof-checking using dependent type systems. In: Robinson A., and Voronkov A. (Eds). Handbook of Automated Reasoning, volume II (2001), Elsevier Science 1149-1240 chapter 18
    • (2001) Handbook of Automated Reasoning, volume II , pp. 1149-1240
    • Barendregt, H.1    Geuvers, H.2
  • 8
    • 84878530374 scopus 로고    scopus 로고
    • The relevance of proof irrelevance
    • Authomata, Languages and Programming. (ICALP'98), Springer Verlag
    • Barthe G. The relevance of proof irrelevance. Authomata, Languages and Programming. (ICALP'98). LNCS volume 1443 (1998), Springer Verlag 755-768
    • (1998) LNCS , vol.1443 , pp. 755-768
    • Barthe, G.1
  • 10
    • 24944450386 scopus 로고    scopus 로고
    • Filters and co-inductive streams, an application to eratosthenes' sieve
    • TLCA, Springer Verlag
    • Bertot Y. Filters and co-inductive streams, an application to eratosthenes' sieve. TLCA. LNCS volume 3461 (2005), Springer Verlag 102-115
    • (2005) LNCS , vol.3461 , pp. 102-115
    • Bertot, Y.1
  • 11
    • 33847693226 scopus 로고    scopus 로고
    • Affine functions and series with co-inductive real numbers
    • Bertot Y. Affine functions and series with co-inductive real numbers. Mathematical Structures in Computer Science 17 1 (2007) 37-63
    • (2007) Mathematical Structures in Computer Science , vol.17 , Issue.1 , pp. 37-63
    • Bertot, Y.1
  • 14
    • 24944542927 scopus 로고    scopus 로고
    • Simple general recursion in type theory
    • Bove A. Simple general recursion in type theory. Nordic Journal of Computing 8 1 (2001) 22-42
    • (2001) Nordic Journal of Computing , vol.8 , Issue.1 , pp. 22-42
    • Bove, A.1
  • 15
    • 44649130944 scopus 로고    scopus 로고
    • A. Bove. General Recursion in Type Theory. PhD thesis, Department of Computing Science, Chalmers University of Technology, 2002
    • A. Bove. General Recursion in Type Theory. PhD thesis, Department of Computing Science, Chalmers University of Technology, 2002
  • 16
    • 35248820187 scopus 로고    scopus 로고
    • A. Bove. General recursion in type theory. In TYPES, pages 39-58, 2002
    • A. Bove. General recursion in type theory. In TYPES, pages 39-58, 2002
  • 17
    • 84949501091 scopus 로고    scopus 로고
    • A. Bove and V. Capretta. Nested general recursion and partiality in type theory. In TPHOLs, pages 121-135, 2001
    • A. Bove and V. Capretta. Nested general recursion and partiality in type theory. In TPHOLs, pages 121-135, 2001
  • 19
    • 23944460284 scopus 로고    scopus 로고
    • A term calculus for (co-)recursive definitions on streamlike data structures
    • Buchholz W. A term calculus for (co-)recursive definitions on streamlike data structures. Ann. Pure Appl. Logic 136 1-2 (2005) 75-90
    • (2005) Ann. Pure Appl. Logic , vol.136 , Issue.1-2 , pp. 75-90
    • Buchholz, W.1
  • 21
    • 44649171229 scopus 로고    scopus 로고
    • T. Coquand. Pattern-matching in type theory. In Informal Proceedings of the 1992 workshop on Types for Proofs and Programs, pages 71-84. B. Nordström and K. Petersson and G. Plotkin, 1992
    • T. Coquand. Pattern-matching in type theory. In Informal Proceedings of the 1992 workshop on Types for Proofs and Programs, pages 71-84. B. Nordström and K. Petersson and G. Plotkin, 1992
  • 22
    • 84947980041 scopus 로고
    • Infinite objects in type theory
    • Types for Proofs and Programs. Int. Workshop TYPES'93, Springer-Verlag
    • Coquand T. Infinite objects in type theory. Types for Proofs and Programs. Int. Workshop TYPES'93. LNCS volume 806 (1994), Springer-Verlag 62-78
    • (1994) LNCS , vol.806 , pp. 62-78
    • Coquand, T.1
  • 24
    • 44649143454 scopus 로고    scopus 로고
    • E. Dijkstra. On the productivity of recursive definitions, 1980. EWD749
    • E. Dijkstra. On the productivity of recursive definitions, 1980. EWD749
  • 25
    • 18944383627 scopus 로고    scopus 로고
    • A new representation for exact real numbers
    • MFPS XIII Elsevier
    • Edalat A., and Potts J. A new representation for exact real numbers. MFPS XIII. ENTCS 6 (1997) Elsevier
    • (1997) ENTCS , vol.6
    • Edalat, A.1    Potts, J.2
  • 26
    • 38149000695 scopus 로고    scopus 로고
    • J. Endrullis, C. Grabmayer, D. Hendriks, A. Isihara, and J.W. Klop. Productivity of stream definitions. In FCT, pages 274-287, 2007
    • J. Endrullis, C. Grabmayer, D. Hendriks, A. Isihara, and J.W. Klop. Productivity of stream definitions. In FCT, pages 274-287, 2007
  • 27
    • 44649091530 scopus 로고    scopus 로고
    • H. Geuvers. Logics and Type Systems. PhD thesis, University of Nijmegen, 1993
    • H. Geuvers. Logics and Type Systems. PhD thesis, University of Nijmegen, 1993
  • 28
    • 44649134158 scopus 로고    scopus 로고
    • P.D. Gianantonio. A Functional Approach to Computability on Real Numbers. PhD thesis, Universita di Pisa-Genova-Udine, 1993
    • P.D. Gianantonio. A Functional Approach to Computability on Real Numbers. PhD thesis, Universita di Pisa-Genova-Udine, 1993
  • 29
    • 24944517159 scopus 로고    scopus 로고
    • P.D. Gianantonio and M. Miculan. A unifying approach to recursive and co-recursive definitions. In TYPES, pages 148-161, 2002
    • P.D. Gianantonio and M. Miculan. A unifying approach to recursive and co-recursive definitions. In TYPES, pages 148-161, 2002
  • 30
    • 24944483301 scopus 로고    scopus 로고
    • P.D. Gianantonio and M. Miculan. Unifying recursive and co-recursive definitions in sheaf categories. In FoSSaCS, pages 136-150, 2004
    • P.D. Gianantonio and M. Miculan. Unifying recursive and co-recursive definitions in sheaf categories. In FoSSaCS, pages 136-150, 2004
  • 31
    • 44649175984 scopus 로고    scopus 로고
    • E. Gimenez. Un Calcul de Constructions Infinies et son Application a la Verification des Systemes Communcants. PhD thesis, Laboratoire de l'Informatique du Parallelism, Ecole Normale Superiere de Lyon, 1996
    • E. Gimenez. Un Calcul de Constructions Infinies et son Application a la Verification des Systemes Communcants. PhD thesis, Laboratoire de l'Informatique du Parallelism, Ecole Normale Superiere de Lyon, 1996
  • 33
    • 44649136327 scopus 로고
    • Induction principles formalised in calculus of constructions
    • Seldin J., and Hindley J. (Eds), Academic Press
    • Huet G. Induction principles formalised in calculus of constructions. In: Seldin J., and Hindley J. (Eds). To H.B. Curry: Essays on Combinatory Logic, Lmabda Calculus, and formalism (1988), Academic Press 479-490
    • (1988) To H.B. Curry: Essays on Combinatory Logic, Lmabda Calculus, and formalism , pp. 479-490
    • Huet, G.1
  • 34
    • 0043210203 scopus 로고    scopus 로고
    • Exercises in coalgebraic specification
    • Algebraic and Coalgebraic Methods in the Mathematics of Program Construction. Backhouse R., Crole R., and Gibbons J. (Eds), Springer
    • Jacobs B. Exercises in coalgebraic specification. In: Backhouse R., Crole R., and Gibbons J. (Eds). Algebraic and Coalgebraic Methods in the Mathematics of Program Construction. LNCS number 2297 (2002), Springer 237-280
    • (2002) LNCS , vol.number 2297 , pp. 237-280
    • Jacobs, B.1
  • 35
    • 0000892681 scopus 로고    scopus 로고
    • A tutorial on (co)algebras and (co)induction
    • Jacobs B., and Rutten J. A tutorial on (co)algebras and (co)induction. EATCS Bulletin 62 (1997) 222-259
    • (1997) EATCS Bulletin , vol.62 , pp. 222-259
    • Jacobs, B.1    Rutten, J.2
  • 36
    • 84957798227 scopus 로고    scopus 로고
    • J. Matthews. Recursive function definition over coinductive types. In TPHOLs, pages 73-90, 1999
    • J. Matthews. Recursive function definition over coinductive types. In TPHOLs, pages 73-90, 1999
  • 37
    • 44649141539 scopus 로고    scopus 로고
    • M. Niqui. Formalising Exact Arithmetic: Representations, Algorithms and Proofs. PhD thesis, Radbout Universiteit Nijmegen, 2004
    • M. Niqui. Formalising Exact Arithmetic: Representations, Algorithms and Proofs. PhD thesis, Radbout Universiteit Nijmegen, 2004
  • 38
    • 33749569490 scopus 로고    scopus 로고
    • Coinductive field of exact real numbers and general corecursion
    • Proc. of CMCS'06 ELSEVIER
    • Niqui M. Coinductive field of exact real numbers and general corecursion. Proc. of CMCS'06. ENTCS 164 (2006) 121-139 ELSEVIER
    • (2006) ENTCS , vol.164 , pp. 121-139
    • Niqui, M.1
  • 39
    • 0011521179 scopus 로고
    • Terminating general recursion
    • Nordstöm B. Terminating general recursion. BIT 28 3 (1988) 605-619
    • (1988) BIT , vol.28 , Issue.3 , pp. 605-619
    • Nordstöm, B.1
  • 40
    • 84947743461 scopus 로고    scopus 로고
    • C. Paulin-Mohring. Inductive definitions in the system coq - rules and properties. In TLCA, pages 328-345, 1993
    • C. Paulin-Mohring. Inductive definitions in the system coq - rules and properties. In TLCA, pages 328-345, 1993
  • 41
    • 0346801207 scopus 로고    scopus 로고
    • Mechanizing coinduction and corecursion in higher-order logic
    • Paulson L. Mechanizing coinduction and corecursion in higher-order logic. Logic and Computation 2 7 (1997) 175-204
    • (1997) Logic and Computation , vol.2 , Issue.7 , pp. 175-204
    • Paulson, L.1
  • 42
    • 49149133038 scopus 로고
    • The temporal semantics of concurrent programs
    • Pnueli A. The temporal semantics of concurrent programs. Theoretical Computer Science 31 (1981) 45-60
    • (1981) Theoretical Computer Science , Issue.31 , pp. 45-60
    • Pnueli, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.