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Volumn 68, Issue 1-2, 2005, Pages 131-174

The open calculus of constructions (part I): An equational type theory with dependent types for programming, specification, and interactive theorem proving

Author keywords

Equational Specification; Rewriting Logic; Type Theory

Indexed keywords

FORMAL LOGIC; LOGIC PROGRAMMING; SEMANTICS; SYSTEMS ENGINEERING; THEOREM PROVING;

EID: 33645292352     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (11)

References (68)
  • 3
    • 0024132809 scopus 로고
    • Towards a computation system based on set theory
    • M. J. Beeson. Towards a computation system based on set theory. Theoretical Computer Science, 60:297-340, 1988.
    • (1988) Theoretical Computer Science , vol.60 , pp. 297-340
    • Beeson, M.J.1
  • 4
    • 0003398278 scopus 로고
    • Towards a mathematical analysis of the Coquand-Huet calculus of constructions and other systems in Barendregt's cube
    • Carnegie Mellon University and Universita di Torino
    • S. Berardi. Towards a mathematical analysis of the Coquand-Huet calculus of constructions and other systems in Barendregt's cube. Technical report, Carnegie Mellon University and Universita di Torino, 1988.
    • (1988) Technical Report
    • Berardi, S.1
  • 5
    • 35248869192 scopus 로고    scopus 로고
    • Inductive types in the calculus of algebraic constructions
    • M. Hofmann, editor, Valencia, Spain, June 10-12, 2003, Proceedings, Lecture Notes in Computer Science, page Inductive types in the Calculus of Algebraic Constructions. Springer-Verlag
    • F. Blanqui. Inductive types in the calculus of algebraic constructions. In M. Hofmann, editor, Typed Lambda Calculi and Applications, 6th International Conference, TLCA 2003, Valencia, Spain, June 10-12, 2003, Proceedings, number 2701 in Lecture Notes in Computer Science, page Inductive types in the Calculus of Algebraic Constructions. Springer-Verlag, 2003.
    • (2003) Typed Lambda Calculi and Applications, 6th International Conference, TLCA 2003 , Issue.2701
    • Blanqui, F.1
  • 6
    • 84957655853 scopus 로고    scopus 로고
    • The calculus of algebraic constructions
    • P. Narendran and M. Rusinowitch, editors, Rewriting Techniques and Applications, 10th International Conference, RTA-99, Trento, Italy, July 2-4, 1999, Springer-Verlag
    • F. Blanqui, J.-P. Jouannaud, and M. Okada. The calculus of algebraic constructions. In P. Narendran and M. Rusinowitch, editors, Rewriting Techniques and Applications, 10th International Conference, RTA-99, Trento, Italy, July 2-4, 1999, volume 1631 of Lecture Notes in Computer Science. Springer-Verlag, 1999.
    • (1999) Lecture Notes in Computer Science , vol.1631
    • Blanqui, F.1    Jouannaud, J.-P.2    Okada, M.3
  • 8
    • 0022103846 scopus 로고
    • Automatic synthesis of typed λ-programs on term algebras
    • C. Böhm and A. Berarducci. Automatic synthesis of typed λ-programs on term algebras. Theoretical Computer Science, 39, 1985.
    • (1985) Theoretical Computer Science , vol.39
    • Böhm, C.1    Berarducci, A.2
  • 10
    • 0003427467 scopus 로고
    • A polymorphic lambda-calculus with Type:Type
    • Digital Equipment Corporation
    • L. Cardelli. A polymorphic lambda-calculus with Type:Type. Technical report, Digital Equipment Corporation, 1986.
    • (1986) Technical Report
    • Cardelli, L.1
  • 12
    • 18944399781 scopus 로고    scopus 로고
    • Towards maude 2.0
    • K. Futatsugi, editor, The 3rd International Workshop on Rewriting Logic and its Applications, Kanazawa City Cultural Hall, Kanzawa, Japan, September 18-20, 2000, Proceedings, Elsevier
    • M. Clavel, F. Durán, S. Eker, P. Lincoln, N. Martí-Oliet, J. Meseguer, and J. Quesada. Towards Maude 2.0. In K. Futatsugi, editor, The 3rd International Workshop on Rewriting Logic and its Applications, Kanazawa City Cultural Hall, Kanzawa, Japan, September 18-20, 2000, Proceedings, volume 36 of Electronic Notes in Theoretical Computer Science, pages 297 - 318. Elsevier, 2000.
    • (2000) Electronic Notes in Theoretical Computer Science , vol.36 , pp. 297-318
    • Clavel, M.1    Durán, F.2    Eker, S.3    Lincoln, P.4    Martí-Oliet, N.5    Meseguer, J.6    Quesada, J.7
  • 16
    • 0001922492 scopus 로고
    • Metamathematical investigations of a calculus of constructions
    • P. Odifreddi, editor, APIC Studies in Data Processing. Academic Press
    • T. Coquand. Metamathematical investigations of a calculus of constructions. In P. Odifreddi, editor, Logic and Computer Science, number 31 in APIC Studies in Data Processing. Academic Press, 1990.
    • (1990) Logic and Computer Science , Issue.31
    • Coquand, T.1
  • 17
    • 85025498813 scopus 로고
    • Constructions: A higher order proof system for mechanizing mathematics
    • B. Buchberger, editor, EUROCAL'85, European Conference on Computer Algebra, Linz, Austria, April 1-3, 1985, Proceedings Volume 1: Invited Lectures, SpringerVerlag
    • T. Coquand and G. Huet. Constructions: A higher order proof system for mechanizing mathematics. In B. Buchberger, editor, EUROCAL'85, European Conference on Computer Algebra, Linz, Austria, April 1-3, 1985, Proceedings Volume 1: Invited Lectures, volume 203 of Lecture Notes in Computer Science. SpringerVerlag, 1985.
    • (1985) Lecture Notes in Computer Science , vol.203
    • Coquand, T.1    Huet, G.2
  • 18
    • 0023965424 scopus 로고
    • The calculus of constructions
    • T. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76(2/3):95-120, 1988.
    • (1988) Information and Computation , vol.76 , Issue.2-3 , pp. 95-120
    • Coquand, T.1    Huet, G.2
  • 19
    • 84944233413 scopus 로고
    • Inductively defined types
    • COLOG-88, International Conference on Computer Logic, Tallinn, USSR, December 1988, Proceedings, Springer-Verlag
    • T. Coquand and C. Paulin-Mohring. Inductively defined types. In COLOG-88, International Conference on Computer Logic, Tallinn, USSR, December 1988, Proceedings, volume 417 of Lecture Notes in Computer Science. Springer-Verlag, 1990.
    • (1990) Lecture Notes in Computer Science , vol.417
    • Coquand, T.1    Paulin-Mohring, C.2
  • 20
    • 0003266602 scopus 로고
    • Inductive sets and families in Martin-Löf's type theory and their set-theoretic semantics
    • Cambridge University Press
    • P. Dybjer. Inductive sets and families in Martin-Löf's type theory and their set-theoretic semantics. In Logical Frameworks, pages 280-306. Cambridge University Press, 1991.
    • (1991) Logical Frameworks , pp. 280-306
    • Dybjer, P.1
  • 21
    • 84949206194 scopus 로고    scopus 로고
    • A finite axiomatization of inductive-recursive definitions
    • J.-Y. Girard, editor, Typed Lambda Calculi and Applications. Proceedings of TLCA'99, L'Aquila, Italy, Springer-Verlag
    • P. Dybjer and A. Setzer. A finite axiomatization of inductive-recursive definitions. In J.-Y. Girard, editor, Typed Lambda Calculi and Applications. Proceedings of TLCA'99, L'Aquila, Italy, volume 1581 of Lecture Notes in Computer Science, pages 129 - 146. Springer-Verlag, 1999.
    • (1999) Lecture Notes in Computer Science , vol.1581 , pp. 129-146
    • Dybjer, P.1    Setzer, A.2
  • 23
    • 0002293333 scopus 로고
    • A language and axioms for explicit mathematics
    • J. N. Crossley, editor, Algebra and Logic, Springer-Verlag
    • S. Feferman. A language and axioms for explicit mathematics. In J. N. Crossley, editor, Algebra and Logic, volume 450 of Lecture Notes in Mathematics, pages 87-139. Springer-Verlag, 1975.
    • (1975) Lecture Notes in Mathematics , vol.450 , pp. 87-139
    • Feferman, S.1
  • 25
    • 0000268375 scopus 로고
    • Order-sorted algebra solves the constructor-selector, multiple-representation, and coercion problems
    • J. A. Goguen and J. Meseguer. Order-sorted algebra solves the constructor-selector, multiple-representation, and coercion problems. Information and Computation, 103:114-158, 1993.
    • (1993) Information and Computation , vol.103 , pp. 114-158
    • Goguen, J.A.1    Meseguer, J.2
  • 29
    • 0009925498 scopus 로고    scopus 로고
    • Membership equational logic, calculus of inductive constructions, and rewrite logic. in International Workshop on Rewriting Logic and its Applications, Abbaye des Prémontrés at Pont-à-Mousson, France, September 1998, Proceedings
    • Elsevier
    • J.-P. Jouannaud. Membership equational logic, calculus of inductive constructions, and rewrite logic. In International Workshop on Rewriting Logic and its Applications, Abbaye des Prémontrés at Pont-à-Mousson, France, September 1998, Proceedings, volume 15 of Electronic Notes in Theoretical Computer Science. Elsevier, 1998.
    • (1998) Electronic Notes in Theoretical Computer Science , vol.15
    • Jouannaud, J.-P.1
  • 32
    • 0025720808 scopus 로고
    • A higher-order calculus and theory abstraction
    • Z. Luo. A higher-order calculus and theory abstraction. Information and Computation, 90(1):107-137, 1991.
    • (1991) Information and Computation , vol.90 , Issue.1 , pp. 107-137
    • Luo, Z.1
  • 33
    • 84961322971 scopus 로고
    • A unifying theory of dependent types: The schematic approach. in Proceedings of Symposium on Logical Foundations of Computer Science (Logic at Tver 92)
    • Also as report ECS-LFCS-92-202, Department of Computer Science, Edinburgh University
    • Z. Luo. A unifying theory of dependent types: the schematic approach. In Proceedings of Symposium on Logical Foundations of Computer Science (Logic at Tver 92), volume 620 of Lecture Notes in Computer Science, 1992. Also as report ECS-LFCS-92-202, Department of Computer Science, Edinburgh University.
    • (1992) Lecture Notes in Computer Science , vol.620
    • Luo, Z.1
  • 35
    • 0003356530 scopus 로고
    • Categories for the working mathematician
    • Springer-Verlag
    • S. MacLane. Categories for the Working Mathematician, volume 5 of Graduate Texts in Mathematics. Springer-Verlag, 1971.
    • (1971) Graduate Texts in Mathematics , vol.5
    • MacLane, S.1
  • 36
    • 0001434253 scopus 로고
    • General logics and logical frameworks
    • D. Gabbay, editor, Oxford University Press
    • N. Martí-Oliet and J. Meseguer. General logics and logical frameworks. In D. Gabbay, editor, What is a Logical System?, pages 355-392. Oxford University Press, 1994.
    • (1994) What Is A Logical System? , pp. 355-392
    • Martí-Oliet, N.1    Meseguer, J.2
  • 37
    • 0003214794 scopus 로고    scopus 로고
    • Rewriting logic as a logical and semantic framework
    • RWLW'96, First International Workshop on Rewriting Logic and its Applications, Asilomar Conference Center, Pacific Grove, CA, USA, September 3-6, 1996, Proceedings, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996. To appear in D. M. Gabbay, F. Guenthner, (eds.), Kluwer Academic Publishers
    • N. Martí-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In RWLW'96, First International Workshop on Rewriting Logic and its Applications, Asilomar Conference Center, Pacific Grove, CA, USA, September 3-6, 1996, Proceedings, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996. To appear in D. M. Gabbay, F. Guenthner, (eds.), Handbook, of Philosophical Logic (2nd edition), Kluwer Academic Publishers.
    • Handbook, of Philosophical Logic (2nd Edition)
    • Martí-Oliet, N.1    Meseguer, J.2
  • 38
    • 0002531110 scopus 로고
    • An intuitionistic theory of types: Predicative part
    • H. Rose and J. Shepherdson, editors, North-Holland
    • P. Martin-Löf. An intuitionistic theory of types: Predicative part. In H. Rose and J. Shepherdson, editors, Logic Colloquium 73, pages 73-108. North-Holland, 1974.
    • (1974) Logic Colloquium , vol.73 , pp. 73-108
    • Martin-Löf, P.1
  • 41
    • 0027113376 scopus 로고
    • Conditional rewriting logic as a unified model of concurrency
    • J. Meseguer. Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science, 96:73-155, 1992.
    • (1992) Theoretical Computer Science , vol.96 , pp. 73-155
    • Meseguer, J.1
  • 42
    • 0002893365 scopus 로고
    • A logical theory of concurrent objects and its realization in the Maude language
    • G. Agha, P. Wegner, and A. Yonezawa, editors, MIT Press
    • J. Meseguer. A logical theory of concurrent objects and its realization in the Maude language. In G. Agha, P. Wegner, and A. Yonezawa, editors, Research Directions in Concurrent Object-Oriented Programming. MIT Press, 1993.
    • (1993) Research Directions in Concurrent Object-Oriented Programming
    • Meseguer, J.1
  • 43
    • 84955586238 scopus 로고    scopus 로고
    • Rewriting logic as a semantic framework for concurrency. A progress report
    • U. Montanari and V. Sassone, editors, CONCUR '96: Concurrency Theory, 7th International Conference, Pisa, Italy, August 26-29, 1996, Springer-Verlag
    • J. Meseguer. Rewriting logic as a semantic framework for concurrency. A progress report. In U. Montanari and V. Sassone, editors, CONCUR '96: Concurrency Theory, 7th International Conference, Pisa, Italy, August 26-29, 1996, volume 1119 of Lecture Notes in Computer Science, pages 331-372. Springer-Verlag, 1996.
    • (1996) Lecture Notes in Computer Science , vol.1119 , pp. 331-372
    • Meseguer, J.1
  • 44
    • 84957873927 scopus 로고    scopus 로고
    • Membership algebra as a logical framework for equational specification
    • F. Parisi-Presicce, editor, Recent Trends in Algebraic Development Techniques, 12th International Workshop, WADT'97, Tarquinia, Italy, June 3-7, 1997, Selected Papers, Springer-Verlag
    • J. Meseguer. Membership algebra as a logical framework for equational specification. In F. Parisi-Presicce, editor, Recent Trends in Algebraic Development Techniques, 12th International Workshop, WADT'97, Tarquinia, Italy, June 3-7, 1997, Selected Papers, volume 1376 of Lecture Notes in Computer Science, pages 18 -61. Springer-Verlag, 1998.
    • (1998) Lecture Notes in Computer Science , vol.1376 , pp. 18-61
    • Meseguer, J.1
  • 45
    • 35248897660 scopus 로고
    • From abstract data types to logical frameworks
    • E. Astesiano, G. Reggio, and A. Tarlecki, editors, Recent Trends in Data Type Specification, 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop, S. Margherita, Italy, May 30 - June 3, 1994, Selected Papers, Springer-Verlag
    • J. Meseguer and N. Martí-Oliet. From abstract data types to logical frameworks. In E. Astesiano, G. Reggio, and A. Tarlecki, editors, Recent Trends in Data Type Specification, 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop, S. Margherita, Italy, May 30 - June 3, 1994, Selected Papers, volume 906 of Lecture Notes in Computer Science, pages 48-80. Springer-Verlag, 1995.
    • (1995) Lecture Notes in Computer Science , vol.906 , pp. 48-80
    • Meseguer, J.1    Martí-Oliet, N.2
  • 47
    • 84949493208 scopus 로고    scopus 로고
    • The HOL/NuPRL proof translator - A practical approach to formal interoperability
    • Theorem Proving in Higher Order Logics, 14th International Conference, TPHOLs'2001, Edinburgh, Scotland, UK, September 3-6, 2001, Proceedings, Springer-Verlag
    • P. Naumov, M.-O. Stehr, and J. Meseguer. The HOL/NuPRL proof translator - A practical approach to formal interoperability. In Theorem Proving in Higher Order Logics, 14th International Conference, TPHOLs'2001, Edinburgh, Scotland, UK, September 3-6, 2001, Proceedings, volume 2152 of Lecture Notes in Computer Science, pages 329 - 345. Springer-Verlag, 2001.
    • (2001) Lecture Notes in Computer Science , vol.2152 , pp. 329-345
    • Naumov, P.1    Stehr, M.-O.2    Meseguer, J.3
  • 48
    • 33750692203 scopus 로고    scopus 로고
    • Rewriting modulo in Deduction modulo
    • R. Nieuwenhuis, editor. Springer-Verlag
    • R. Nieuwenhuis, editor. Rewriting modulo in Deduction modulo, volume 2706 of Lecture Notes in Computer Science. Springer-Verlag, 2003.
    • (2003) Lecture Notes in Computer Science , vol.2706
  • 51
    • 85031934615 scopus 로고
    • Polymorphism is set-theoretic, constructively
    • Category Theory and Computer Science, Proceedings, Edinburgh, 1987, Springer-Varlag
    • A. Pitts. Polymorphism is set-theoretic, constructively. In Category Theory and Computer Science, Proceedings, Edinburgh, 1987, volume 283 of Lecture Notes in Computer Science, pages 12-39. Springer-Varlag, 1987.
    • (1987) Lecture Notes in Computer Science , vol.283 , pp. 12-39
    • Pitts, A.1
  • 56
    • 77956958316 scopus 로고
    • Axioms of set theory
    • J. Barwise, editor, North-Holland
    • J. R. Shoenfield. Axioms of set theory. In J. Barwise, editor, Handbook of Mathematical Logic, pages 321-344. North-Holland, 1977.
    • (1977) Handbook of Mathematical Logic , pp. 321-344
    • Shoenfield, J.R.1
  • 57
    • 18944375475 scopus 로고    scopus 로고
    • CINNI - A generic calculus of explicit substitutions and its application to λ-, σ- and π-calculi
    • K. Futatsugi, editor, The 3rd International Workshop on Rewriting Logic and its Applications, Kanazawa City Cultural Hall, Kanzawa, Japan, September 18-20, 2000, Proceedings, Elsevier
    • M.-O. Stehr. CINNI - A Generic Calculus of Explicit Substitutions and its Application to λ-, σ- and π-calculi. In K. Futatsugi, editor, The 3rd International Workshop on Rewriting Logic and its Applications, Kanazawa City Cultural Hall, Kanzawa, Japan, September 18-20, 2000, Proceedings, volume 36 of Electronic Notes in Theoretical Computer Science, pages 71-92. Elsevier, 2000.
    • (2000) Electronic Notes in Theoretical Computer Science , vol.36 , pp. 71-92
    • Stehr, M.-O.1
  • 59
    • 33645318804 scopus 로고    scopus 로고
    • Higher-order rewriting via conditional first-order rewriting in the open calculus of constructions
    • number AIB-2004-03 in Aachener Informatik Berichte. Department of Computer Science, June
    • M.-O. Stehr. Higher-order rewriting via conditional first-order rewriting in the open calculus of constructions. In Proceedings of HOR'04, 2nd International Workshop on Higher-Order Rewriting, Aachen, Germany, June 2, 2004, number AIB-2004-03 in Aachener Informatik Berichte. Department of Computer Science, June 2004. http://formal.cs.uiuc.edu/stehr/biblio_stehr_eng.html.
    • (2004) Proceedings of HOR'04, 2nd International Workshop on Higher-Order Rewriting, Aachen, Germany, June 2, 2004
    • Stehr, M.-O.1
  • 60
    • 9444283908 scopus 로고    scopus 로고
    • Pure type systems in rewriting logic: Specifying typed higher-order languages in a first-order logical framework
    • Essays in Memory of Ole-Johan Dahl, Springer-Verlag
    • M.-O. Stehr and J. Meseguer. Pure type systems in rewriting logic: Specifying typed higher-order languages in a first-order logical framework. In Essays in Memory of Ole-Johan Dahl, volume 2635 of LNCS, pages 334-375. Springer-Verlag, 2004.
    • (2004) LNCS , vol.2635 , pp. 334-375
    • Stehr, M.-O.1    Meseguer, J.2
  • 62
    • 19044377295 scopus 로고    scopus 로고
    • PLAN in Maude: Specifying an active network programming language
    • F. Gadducci and U. Montanari, editors, The 4th International Workshop on Rewriting Logic and its Applications, Pisa, Italy, September 19-21, 2002, Proceedings, Elsevier
    • M.-O. Stehr and C. L. Talcott. PLAN in Maude: Specifying an active network programming language. In F. Gadducci and U. Montanari, editors, The 4th International Workshop on Rewriting Logic and its Applications, Pisa, Italy, September 19-21, 2002, Proceedings, volume 71 of Electronic Notes in Theoretical Computer Science. Elsevier, 2002.
    • (2002) Electronic Notes in Theoretical Computer Science , vol.71
    • Stehr, M.-O.1    Talcott, C.L.2
  • 63
    • 0342836027 scopus 로고
    • Über Unerreichbare Kardinalzahlen
    • A. Tarski. Über Unerreichbare Kardinalzahlen. Fundamenta Mathematicae, 30:176-183, 1938.
    • (1938) Fundamenta Mathematicae , vol.30 , pp. 176-183
    • Tarski, A.1
  • 64
    • 0000735030 scopus 로고
    • On well-ordered subsets of any set
    • A. Tarski. On well-ordered subsets of any set. Fundamenta Mathematicae, 32:176-183, 1939.
    • (1939) Fundamenta Mathematicae , vol.32 , pp. 176-183
    • Tarski, A.1
  • 67
    • 84957659192 scopus 로고    scopus 로고
    • Sets in types, types in sets
    • M. Abadi and T. Ito, editors, Theoretical Aspects of Computer Software, Third International Symposium, TACS'97, Sendai, Japan, September 23-26, 1997, Proceedings, Springer-Verlag
    • B. Werner. Sets in types, types in sets. In M. Abadi and T. Ito, editors, Theoretical Aspects of Computer Software, Third International Symposium, TACS'97, Sendai, Japan, September 23-26, 1997, Proceedings, volume 1281 of Lecture Notes in Computer Science. Springer-Verlag, 1997.
    • (1997) Lecture Notes in Computer Science , vol.1281
    • Werner, B.1


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