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Volumn 145, Issue 2, 1998, Pages 107-152

Structural Induction and Coinduction in a Fibrational Setting

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EID: 0001055350     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1998.2725     Document Type: Article
Times cited : (191)

References (58)
  • 1
    • 80051905264 scopus 로고
    • A final coalgebra theorem
    • "Category Theory and Computer Science" (D. H. Pitt, A. Poigné, and D. E. Rydeheard, Eds.), Springer Springer-Verlag, Berlin
    • Aczel, P., and Mendler, N. (1989), A final coalgebra theorem, in "Category Theory and Computer Science" (D. H. Pitt, A. Poigné, and D. E. Rydeheard, Eds.), Springer LNCS 389, pp. 357-365, Springer-Verlag, Berlin.
    • (1989) LNCS , vol.389 , pp. 357-365
    • Aczel, P.1    Mendler, N.2
  • 2
    • 0001847686 scopus 로고
    • Domain theory
    • (S. Abramsky, Dov M. Gabbai, and T. S. E. Maibaum, Eds.), Oxford Univ. Press, London
    • Abramsky, S., and Jung, A. (1994), Domain theory, in "Handbook of Logic in Computer Science 3" (S. Abramsky, Dov M. Gabbai, and T. S. E. Maibaum, Eds.), pp. 1-68, Oxford Univ. Press, London.
    • (1994) Handbook of Logic in Computer Science , vol.3 , pp. 1-68
    • Abramsky, S.1    Jung, A.2
  • 3
    • 0000339283 scopus 로고
    • Solving reflexive domain equations in a category of complete metric spaces
    • America, P., and Rutten, J. (1989), Solving reflexive domain equations in a category of complete metric spaces, J. Comp. Syst. Sci. 39, No. 3, 343-375.
    • (1989) J. Comp. Syst. Sci. , vol.39 , Issue.3 , pp. 343-375
    • America, P.1    Rutten, J.2
  • 5
    • 0020086620 scopus 로고
    • Parametrized data types do not need highly constrained parameters
    • Arbib, M. A., and Manes, E. G. (1982), Parametrized data types do not need highly constrained parameters, Inform. Contr. 52, 139-158.
    • (1982) Inform. Contr. , vol.52 , pp. 139-158
    • Arbib, M.A.1    Manes, E.G.2
  • 6
    • 85030061030 scopus 로고
    • manuscript, Univ. Eindhoven, Presented at IFIP Working Group 2.3
    • Backhouse, R., and Bijsterveld, M. (1994), The "Beautiful Theorem", manuscript, Univ. Eindhoven, Presented at IFIP Working Group 2.3.
    • (1994) The "Beautiful Theorem"
    • Backhouse, R.1    Bijsterveld, M.2
  • 8
    • 38249010909 scopus 로고
    • Algebraically compact functors
    • Barr, M. (1992), Algebraically compact functors, J. Pure Appl. Alg. 82, 211-231.
    • (1992) J. Pure Appl. Alg. , vol.82 , pp. 211-231
    • Barr, M.1
  • 9
    • 0345792009 scopus 로고
    • Introduction to distributive categories
    • Cockett, J. R. B. (1991), Introduction to distributive categories, Math. Struct. Comp. Science 1, 1-20.
    • (1991) Math. Struct. Comp. Science , vol.1 , pp. 1-20
    • Cockett, J.R.B.1
  • 10
    • 0001139083 scopus 로고
    • Strong categorical datatypes I
    • "Category Theory 1991" (R. A. G. Seely, Ed.)
    • Cockett, J. R. B., and Spencer, D. (1992), Strong categorical datatypes I, in "Category Theory 1991" (R. A. G. Seely, Ed.), CMS Conference Proceedings 13, pp. 141-169.
    • (1992) CMS Conference Proceedings , vol.13 , pp. 141-169
    • Cockett, J.R.B.1    Spencer, D.2
  • 11
    • 0029637548 scopus 로고
    • Strong categorical datatypes II: A term logic for categorical programming
    • Cockett, J. R. B., and Spencer, D. (1995), Strong categorical datatypes II: A term logic for categorical programming, Theor. Comp. Sci. 139, 69-113.
    • (1995) Theor. Comp. Sci. , vol.139 , pp. 69-113
    • Cockett, J.R.B.1    Spencer, D.2
  • 12
    • 0004020078 scopus 로고
    • Cambridge Univ. Press, Cambridge, UK
    • Crole, R. L. (1993), "Categories for Types," Cambridge Univ. Press, Cambridge, UK.
    • (1993) Categories for Types
    • Crole, R.L.1
  • 13
    • 38249011731 scopus 로고
    • New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic
    • Crole, R. L., and Pitts, A. M. (1992), New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic, Inform. Comput. 98, No. 2, 171-210.
    • (1992) Inform. Comput. , vol.98 , Issue.2 , pp. 171-210
    • Crole, R.L.1    Pitts, A.M.2
  • 14
    • 0024130793 scopus 로고
    • A categorical semantics of constructions
    • IEEE Comp. Sci. Press, Los Alamitos, CA
    • Ehrhard, Th. (1988), A categorical semantics of constructions, in "Logic in Comp. Sci. 3," pp. 264-273, IEEE Comp. Sci. Press, Los Alamitos, CA.
    • (1988) Logic in Comp. Sci. , vol.3 , pp. 264-273
    • Ehrhard, Th.1
  • 15
    • 0347683960 scopus 로고
    • Colimits in the category Cpo
    • Kansas State University
    • Fiech, A. (1992), Colimits in the category Cpo, Technical Report, Kansas State University.
    • (1992) Technical Report
    • Fiech, A.1
  • 16
    • 0006407653 scopus 로고    scopus 로고
    • A coinduction principle for recursive data types based on bisimulation
    • Fiore, M. (1996), A coinduction principle for recursive data types based on bisimulation, Inform. Comput. 127, No. 2, 186-198.
    • (1996) Inform. Comput. , vol.127 , Issue.2 , pp. 186-198
    • Fiore, M.1
  • 18
    • 0025683783 scopus 로고
    • Recursive types reduced to inductive types
    • IEEE Comp. Sci. Press, Los Alamitos, CA
    • Freyd, P. J. (1990), Recursive types reduced to inductive types, in "Logic in Comp. Sci. 5" pp. 498-507, IEEE Comp. Sci. Press, Los Alamitos, CA.
    • (1990) Logic in Comp. Sci. , vol.5 , pp. 498-507
    • Freyd, P.J.1
  • 19
    • 0001817274 scopus 로고
    • Remarks on algebraically compact categories
    • (M. P. Fourman, P. T. Johnstone, and A. M. Pitts, Eds.), Cambridge Univ. Press, Cambridge, UK
    • Freyd, P. J. (1992), Remarks on algebraically compact categories, in "Applications of Categories in Computer Science" (M. P. Fourman, P. T. Johnstone, and A. M. Pitts, Eds.), pp. 95-106, Cambridge Univ. Press, Cambridge, UK.
    • (1992) Applications of Categories in Computer Science , pp. 95-106
    • Freyd, P.J.1
  • 20
    • 0004470101 scopus 로고
    • Categories, Allegories
    • North-Holland, Amsterdam
    • Freyd, P. J., and Scedrov, A. (1990), "Categories, Allegories," Math. Library 39, North-Holland, Amsterdam.
    • (1990) Math. Library , vol.39
    • Freyd, P.J.1    Scedrov, A.2
  • 21
    • 0002424767 scopus 로고
    • An initial algebra approach to the specification, correctness and implementatiton of abstract data types
    • (R. Yeh, Ed.), Prentice Hall, New York
    • Goguen, J. A., Thatcher, J., and Wagner, E. (1978), An initial algebra approach to the specification, correctness and implementatiton of abstract data types, "Current Trends in Programming Methodology," (R. Yeh, Ed.), pp. 80-149, Prentice Hall, New York.
    • (1978) Current Trends in Programming Methodology , pp. 80-149
    • Goguen, J.A.1    Thatcher, J.2    Wagner, E.3
  • 22
    • 85034647614 scopus 로고
    • A typed lambda calculus with categorical type constructors
    • "Category and Computer Science" (D. H. Pitt, A. Poigné, and D. E. Rydeheard, Eds.), Springer Springer-Verlag, Berlin
    • Hagino, T. (1987), A typed lambda calculus with categorical type constructors, in "Category and Computer Science" (D. H. Pitt, A. Poigné, and D. E. Rydeheard, Eds.), Springer LNCS 283, pp. 140-157, Springer-Verlag, Berlin.
    • (1987) LNCS , vol.283 , pp. 140-157
    • Hagino, T.1
  • 23
    • 84949196162 scopus 로고    scopus 로고
    • Proof principles for datatypes with iterated recursion
    • ́Category Theory and Computer Sciencé (E. Moggi and G. Rosolini, Eds.), Springer Springer-Verlag, Berlin
    • Hensel, U., and Jacobs, B. (1997), Proof principles for datatypes with iterated recursion, in ́Category Theory and Computer Sciencé (E. Moggi and G. Rosolini, Eds.), Springer LNCS 1290, pp. 220-241, Springer-Verlag, Berlin.
    • (1997) LNCS , vol.1290 , pp. 220-241
    • Hensel, U.1    Jacobs, B.2
  • 24
    • 0013115153 scopus 로고
    • Fibrations, logical predicates and indeterminates
    • Ph.D. thesis, Univ. of Edinburgh
    • Hermida, C. (1993), Fibrations, logical predicates and indeterminates, Ph.D. thesis, Univ. of Edinburgh, Techn. rep. LFCS-93-277. [Also available as Aarhus Univ. DAIMI Techn. rep. PB-462.]
    • (1993) Techn. Rep. LFCS-93-277.
    • Hermida, C.1
  • 25
    • 85030076896 scopus 로고    scopus 로고
    • Hermida, C. (1993), Fibrations, logical predicates and indeterminates, Ph.D. thesis, Univ. of Edinburgh, Techn. rep. LFCS-93-277. [Also available as Aarhus Univ. DAIMI Techn. rep. PB-462.]
    • Aarhus Univ. DAIMI Techn. Rep. PB-462
  • 26
    • 85030067271 scopus 로고    scopus 로고
    • Some properties of Fib as a fibred 2-category
    • to appear
    • Hermida, C., Some properties of Fib as a fibred 2-category, J. Pure Appl. Algebra, to appear.
    • J. Pure Appl. Algebra
    • Hermida, C.1
  • 27
    • 0009438015 scopus 로고
    • An algebraic view of structural induction
    • "Computer Science Logic 1994" (L. Pacholski and J. Tiuryn, Eds.), Springer Springer-Verlag, Berlin
    • Hermida, C., and Jacobs, B. (1995), An algebraic view of structural induction, in "Computer Science Logic 1994" (L. Pacholski and J. Tiuryn, Eds.), Springer LNCS 933, pp. 412-426, Springer-Verlag, Berlin.
    • (1995) LNCS , vol.933 , pp. 412-426
    • Hermida, C.1    Jacobs, B.2
  • 28
    • 84973958873 scopus 로고
    • Fibrations with indeterminates: Contextual and functional completeness for polymorphic lambda calculi
    • Hermida, C., and Jacobs, B. (1995), Fibrations with indeterminates: Contextual and functional completeness for polymorphic lambda calculi, Math. Struct. Comp. Sci. 5, 501-531.
    • (1995) Math. Struct. Comp. Sci. , vol.5 , pp. 501-531
    • Hermida, C.1    Jacobs, B.2
  • 30
    • 38249006283 scopus 로고
    • Comprehension categories and the semantics of type dependency
    • Jacobs, B. (1993), Comprehension categories and the semantics of type dependency, Theor. Comp. Sci. 107, 169-207.
    • (1993) Theor. Comp. Sci. , vol.107 , pp. 169-207
    • Jacobs, B.1
  • 31
    • 0001818904 scopus 로고
    • Semantics of weakening and contraction
    • Jacobs, B. (1994), Semantics of weakening and contraction, Ann. Pure Appl. Logic 69, No. 1, 73-106.
    • (1994) Ann. Pure Appl. Logic , vol.69 , Issue.1 , pp. 73-106
    • Jacobs, B.1
  • 33
    • 0029407450 scopus 로고
    • Parameters and parametrization in specification using distributive categories
    • Jacobs, B. (1995), Parameters and parametrization in specification using distributive categories, Fund. Informaticae 24, No. 3, 209-250.
    • (1995) Fund. Informaticae , vol.24 , Issue.3 , pp. 209-250
    • Jacobs, B.1
  • 34
    • 84947930619 scopus 로고    scopus 로고
    • Invariants, bisimulations and the correctness of coalgebraic refinements
    • "Algebraic Methodology and Software Technology" (M. Johnson, Ed.), Springer Springer-Verlag, Berlin
    • Jacobs, B. (1997), Invariants, bisimulations and the correctness of coalgebraic refinements, in "Algebraic Methodology and Software Technology" (M. Johnson, Ed.), Springer LNCS 1349, pp. 276-291, Springer-Verlag, Berlin.
    • (1997) LNCS , vol.1349 , pp. 276-291
    • Jacobs, B.1
  • 36
    • 84973960125 scopus 로고
    • Elementary observations on 2-categorical limits
    • Kelly, G. M. (1989), Elementary observations on 2-categorical limits, Bull. Austr. Math. Soc. 39, 301-317.
    • (1989) Bull. Austr. Math. Soc. , vol.39 , pp. 301-317
    • Kelly, G.M.1
  • 37
    • 0003248906 scopus 로고
    • Introduction to Higher-Order Categorical Logic
    • Cambridge Univ. Press, Cambridge, UK
    • Lambek, J., and Scott, P. J. (1986), "Introduction to Higher-Order Categorical Logic," Studies in Adv. Math. 7, Cambridge Univ. Press, Cambridge, UK.
    • (1986) Studies in Adv. Math. , vol.7
    • Lambek, J.1    Scott, P.J.2
  • 38
    • 0000994313 scopus 로고
    • Equality in hyperdoctrines and comprehension scheme as an adjoint functor
    • (A. Heller, Ed.), AMS, Providence
    • Lawvere, F. W. (1970), Equality in hyperdoctrines and comprehension scheme as an adjoint functor, in "Applications of Categorical Algebra" (A. Heller, Ed.), pp. 1-14, AMS, Providence.
    • (1970) Applications of Categorical Algebra , pp. 1-14
    • Lawvere, F.W.1
  • 39
    • 0000803927 scopus 로고
    • Algebraic specification of datatypes: A synthetic approach
    • Lehmann, D., and Smyth, M. (1981), Algebraic specification of datatypes: A synthetic approach, Math. Systems Theory 14, 97-139.
    • (1981) Math. Systems Theory , vol.14 , pp. 97-139
    • Lehmann, D.1    Smyth, M.2
  • 40
    • 84972526310 scopus 로고
    • The fibrational formulation of intuitionistic predicate logic I: Completeness according to Gödel, Kripke, and Läuchli. Part 1
    • Makkai, M. (1993), The fibrational formulation of intuitionistic predicate logic I: Completeness according to Gödel, Kripke, and Läuchli. Part 1, Notre Dame J. Formal Logic 34, No. 3, 334-377.
    • (1993) Notre Dame J. Formal Logic , vol.34 , Issue.3 , pp. 334-377
    • Makkai, M.1
  • 41
    • 84972488126 scopus 로고
    • The fibrational formulation of intuitionistic predicate logic I: Completeness according to Gödel, Kripke, and Läuchli. Part 2
    • Makkai, M. (1993), The fibrational formulation of intuitionistic predicate logic I: Completeness according to Gödel, Kripke, and Läuchli. Part 2, Notre Dame J. Formal Logic 34, No. 4, 471-499.
    • (1993) Notre Dame J. Formal Logic , vol.34 , Issue.4 , pp. 471-499
    • Makkai, M.1
  • 43
    • 0347683945 scopus 로고
    • Categories of chain-complete posets
    • Markowsky, G. (1977), Categories of chain-complete posets, Theor. Comp. Sci. 4, 125-135.
    • (1977) Theor. Comp. Sci. , vol.4 , pp. 125-135
    • Markowsky, G.1
  • 45
    • 0038795232 scopus 로고
    • Maps I: Relative to a factorization system
    • 1995
    • Pavlović, D. (1995), Maps I: Relative to a factorization system, J. Pure Appl. Algebra 60, No. 2 (1995), 9-34.
    • (1995) J. Pure Appl. Algebra , vol.60 , Issue.2 , pp. 9-34
    • Pavlović, D.1
  • 46
    • 0346422976 scopus 로고    scopus 로고
    • Maps II: Chasing diagrams in categorical proof theory
    • Pavlović, D. (1996), Maps II: Chasing diagrams in categorical proof theory, J. IGPL 4, No. 2, 1-36. [Available from URL http://www.mpi-sb.mpg.de/igpl/Journal]
    • (1996) J. IGPL , vol.4 , Issue.2 , pp. 1-36
    • Pavlović, D.1
  • 47
    • 0028380721 scopus 로고
    • A co-induction principle for recursively defined domains
    • Pitts, A. M. (1994), A co-induction principle for recursively defined domains, Theor. Comp. Sci. 124, No. 2, 195-219.
    • (1994) Theor. Comp. Sci. , vol.124 , Issue.2 , pp. 195-219
    • Pitts, A.M.1
  • 48
    • 0002796916 scopus 로고    scopus 로고
    • Relational properties of domains
    • Pitts, A. M. (1996), Relational properties of domains, Inform. Comput. 127, No. 2, 66-90.
    • (1996) Inform. Comput. , vol.127 , Issue.2 , pp. 66-90
    • Pitts, A.M.1
  • 49
    • 85028748723 scopus 로고
    • A logic for parametric polymorphism
    • ́Typed Lambda Calculi and Applicationś (M. Bezem and J. F. Groote, Eds.), Springer Springer-Verlag, Berlin
    • Plotkin, G., and Abadi, M. (1993), A logic for parametric polymorphism, in ́Typed Lambda Calculi and Applicationś (M. Bezem and J. F. Groote, Eds.), Springer LNCS 664, pp. 361-375, Springer-Verlag, Berlin.
    • (1993) LNCS , vol.664 , pp. 361-375
    • Plotkin, G.1    Abadi, M.2
  • 50
    • 84976111956 scopus 로고
    • An approach to object semantics based on terminal co-algebras
    • Reichel, H. (1995), An approach to object semantics based on terminal co-algebras, Math. Struct. Comp. Sci. 5, 129-152.
    • (1995) Math. Struct. Comp. Sci. , vol.5 , pp. 129-152
    • Reichel, H.1
  • 51
    • 84962687423 scopus 로고
    • On the foundations of final semantics: Non-standard sets, metric spaces and partial orders
    • ́Semantics: Foundations and Applicationś (J. W. de Bakker, W. P. de Roever, and G. Rozenberg, Eds.), Springer Springer-Verlag
    • Rutten, J., and Turi, D. (1993), On the foundations of final semantics: non-standard sets, metric spaces and partial orders, in ́Semantics: Foundations and Applicationś (J. W. de Bakker, W. P. de Roever, and G. Rozenberg, Eds.), Springer LNCS 666, pp. 477-530, Springer-Verlag.
    • (1993) LNCS , vol.666 , pp. 477-530
    • Rutten, J.1    Turi, D.2
  • 52
    • 84909932581 scopus 로고
    • Initial algebra and final coalgebra semantics for concurrency
    • "A Decade of Concurrency" (J. W. de Bakker, W. P. de Roever, and G. Rozenberg, Eds.), Springer Springer-Verlag, Berlin
    • Rutten, J., and Turi, D. (1994), Initial algebra and final coalgebra semantics for concurrency, in "A Decade of Concurrency" (J. W. de Bakker, W. P. de Roever, and G. Rozenberg, Eds.), Springer LNCS 803, pp. 530-582, Springer-Verlag, Berlin.
    • (1994) LNCS , vol.803 , pp. 530-582
    • Rutten, J.1    Turi, D.2
  • 54
    • 0000874096 scopus 로고
    • The category theoretic solution of recursive domain equations
    • Smyth, M. B., and Plotkin, G. D. (1982), The category theoretic solution of recursive domain equations, SIAM J. Comput. 11, 761-783.
    • (1982) SIAM J. Comput. , vol.11 , pp. 761-783
    • Smyth, M.B.1    Plotkin, G.D.2
  • 55
    • 0000447203 scopus 로고
    • The formal theory of monads
    • Street, R. (1972), The formal theory of monads, J. Pure Appl. Algebra 2, 149-168.
    • (1972) J. Pure Appl. Algebra , vol.2 , pp. 149-168
    • Street, R.1
  • 56
    • 0001105584 scopus 로고
    • Fibrations and Yoneda's Lemma in a 2-category
    • "Proc. Sydney Category Theory Seminar 1972/1973" (G. M. Kelly, Ed.), Springer Springer-Verlag, Berlin
    • Street, R. (1994), Fibrations and Yoneda's Lemma in a 2-category, "Proc. Sydney Category Theory Seminar 1972/1973" (G. M. Kelly, Ed.), Springer LNM 420, pp. 104-133, Springer-Verlag, Berlin.
    • (1994) LNM , vol.420 , pp. 104-133
    • Street, R.1
  • 57
    • 0001102730 scopus 로고
    • Yoneda structures on 2-Categories
    • Street, R., and Walters (1978), Yoneda structures on 2-Categories, J. Algebra 50, 350-379.
    • (1978) J. Algebra , vol.50 , pp. 350-379
    • Street, R.1    Walters2
  • 58
    • 0000382802 scopus 로고
    • Algebraic specification
    • (J. van Leeuwen, Ed.), Volume B, Elsevier/MIT Press, Amsterdam/Cambridge, MA
    • Wirsing, M. (1990), Algebraic specification, in "Handbook of Theoretical Computer Science" (J. van Leeuwen, Ed.), Volume B, pp. 673-788, Elsevier/MIT Press, Amsterdam/Cambridge, MA.
    • (1990) Handbook of Theoretical Computer Science , pp. 673-788
    • Wirsing, M.1


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