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Volumn 26, Issue 1, 2001, Pages 1-49

Induction proofs with partial functions

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS;

EID: 0034831855     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006408829523     Document Type: Article
Times cited : (7)

References (79)
  • 2
    • 0024126961 scopus 로고
    • Proof by consistency in equational theories
    • Edinburgh, Scotland, IEEE Press
    • Bachmair, L.: Proof by consistency in equational theories, in Proc. 3rd IEEE Symp. Logic in Computer Science, Edinburgh, Scotland, IEEE Press, 1988.
    • (1988) Proc. 3rd IEEE Symp. Logic in Computer Science
    • Bachmair, L.1
  • 3
    • 84959697692 scopus 로고
    • On the structure of abstract algebras
    • Birkhoff, G.: On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1934), 433-454.
    • (1934) Proc. Cambridge Philos. Soc. , vol.31 , pp. 433-454
    • Birkhoff, G.1
  • 4
    • 0000491397 scopus 로고
    • Implicit induction in conditional theories
    • Bouhoula, A. and Rusinowitch, M.: Implicit induction in conditional theories, J. Automated Reasoning 14 (1995), 189-235.
    • (1995) J. Automated Reasoning , vol.14 , pp. 189-235
    • Bouhoula, A.1    Rusinowitch, M.2
  • 9
    • 0343150515 scopus 로고
    • A mechanical proof of the Turing completeness of pure LISP
    • W. W. Bledsoe and D. W. Loveland (eds), Amer. Math. Soc., RI
    • Boyer, R. S. and Moore, J S.: A mechanical proof of the Turing completeness of pure LISP, in W. W. Bledsoe and D. W. Loveland (eds), Automated Theorem Proving: After 25 Years, Amer. Math. Soc., RI, 1984.
    • (1984) Automated Theorem Proving: After 25 Years
    • Boyer, R.S.1    Moore, J.S.2
  • 10
    • 0008443776 scopus 로고
    • The addition of bounded quantification and partial functions to a computational logic and its theorem prover
    • Boyer, R. S. and Moore, J S.: The addition of bounded quantification and partial functions to a computational logic and its theorem prover, J. Automated Reasoning 4 (1988), 117-172.
    • (1988) J. Automated Reasoning , vol.4 , pp. 117-172
    • Boyer, R.S.1    Moore, J.S.2
  • 11
    • 0008497268 scopus 로고    scopus 로고
    • Termination analysis for partial functions
    • Aachen, Germany, Lecture Notes in Computer Sei. 1145, Springer, Extended version appeared as Technical Report IBN 96/33, TU Darmstadt. Available from http://www.inferenzsysteme.informatik.tu-darmstadt.de/~reports/notes/ ibn-96-33.ps
    • Brauburger, J. and Giesl, J.: Termination analysis for partial functions, in Proc. 3rd Int. Static Analysis Symp., Aachen, Germany, Lecture Notes in Computer Sei. 1145, Springer, 1996. Extended version appeared as Technical Report IBN 96/33, TU Darmstadt. Available from http://www.inferenzsysteme.informatik.tu-darmstadt.de/~reports/notes/ ibn-96-33.ps
    • (1996) Proc. 3rd Int. Static Analysis Symp.
    • Brauburger, J.1    Giesl, J.2
  • 12
    • 79951857108 scopus 로고    scopus 로고
    • Termination analysis by inductive evaluation
    • Lindau, Germany, Lecture Notes in Artif. Intell. 1421, Springer
    • Brauburger, J. and Giesl, J.: Termination analysis by inductive evaluation, in Proc. 15th Int. Conf. Automated Deduction, Lindau, Germany, Lecture Notes in Artif. Intell. 1421, Springer, 1998.
    • (1998) Proc. 15th Int. Conf. Automated Deduction
    • Brauburger, J.1    Giesl, J.2
  • 13
    • 0033224819 scopus 로고    scopus 로고
    • Approximating the domains of functional and imperative programs
    • Brauburger, J. and Giesl, J.: Approximating the domains of functional and imperative programs, Sci. Comput. Programming 35 (1999), 113-136.
    • (1999) Sci. Comput. Programming , vol.35 , pp. 113-136
    • Brauburger, J.1    Giesl, J.2
  • 15
    • 0041648863 scopus 로고
    • A rational reconstruction and extension of recursion analysis
    • Detroit, MI, Morgan Kaufmann
    • Bundy, A.: A rational reconstruction and extension of recursion analysis, in Proc. 11th Int. Joint Conf. AI, Detroit, MI, Morgan Kaufmann, 1989.
    • (1989) Proc. 11th Int. Joint Conf. AI
    • Bundy, A.1
  • 19
    • 0028429645 scopus 로고
    • Termination of logic programs: The never-ending story
    • De Schreye, D. and Decorte, S.: Termination of logic programs: the never-ending story, J. Logic Programming 19, 20 (1994), 199-260.
    • (1994) J. Logic Programming , vol.19-20 , pp. 199-260
    • De Schreye, D.1    Decorte, S.2
  • 20
    • 84910829499 scopus 로고
    • Termination of rewriting
    • Dershowitz, N.: Termination of rewriting, J. Symbolic Comput. 3 (1987), 69-115.
    • (1987) J. Symbolic Comput. , vol.3 , pp. 69-115
    • Dershowitz, N.1
  • 21
    • 0042274944 scopus 로고
    • A partial function's version of Church's simple theory of types
    • Farmer, W. M.: A partial function's version of Church's simple theory of types, J. Symbolic Logic 55 (1990), 1269-1291.
    • (1990) J. Symbolic Logic , vol.55 , pp. 1269-1291
    • Farmer, W.M.1
  • 24
    • 84949993676 scopus 로고
    • Automated termination proofs with measure functions
    • Bielefeld, Germany, Lecture Notes in Artif. Intell. 981, Springer
    • Giesl, J.: Automated termination proofs with measure functions, in Proc. 19th Ann. German Conf. AI, Bielefeld, Germany, Lecture Notes in Artif. Intell. 981, Springer, 1995.
    • (1995) Proc. 19th Ann. German Conf. AI
    • Giesl, J.1
  • 25
    • 84955598929 scopus 로고
    • Termination analysis for functional programs using term orderings
    • Glasgow, Scotland, Lecture Notes in Comput. Sci. 983, Springer
    • Giesl, J.: Termination analysis for functional programs using term orderings, in Proc. 2nd Int. Static Analysis Symp., Glasgow, Scotland, Lecture Notes in Comput. Sci. 983, Springer, 1995.
    • (1995) Proc. 2nd Int. Static Analysis Symp.
    • Giesl, J.1
  • 26
    • 0031212315 scopus 로고    scopus 로고
    • Termination of nested and mutually recursive algorithms
    • Giesl, J.: Termination of nested and mutually recursive algorithms, J. Automated Reasoning 19 (1997), 1-29.
    • (1997) J. Automated Reasoning , vol.19 , pp. 1-29
    • Giesl, J.1
  • 27
    • 0342281005 scopus 로고    scopus 로고
    • Technical Report IBN 98/49, TU Darmstadt, 1998. Available from http://www. inferenzsysteme.informatik.tu-darmstadt. de/~reports/notes/ibn-98-49.ps
    • Giesl, J.: The critical pair lemma: A case study for induction proofs with partial functions, Technical Report IBN 98/49, TU Darmstadt, 1998. Available from http://www. inferenzsysteme.informatik.tu-darmstadt. de/~reports/notes/ibn-98-49.ps
    • The Critical Pair Lemma: A Case Study for Induction Proofs with Partial Functions
    • Giesl, J.1
  • 28
    • 0008457084 scopus 로고    scopus 로고
    • Termination analysis for functional programs
    • W. Bibel and P. Schmitt (eds), Applied Logic Series 10, Kluwer Acad. Publ.
    • Giesl, J., Walther, C., and Brauburger, J.: Termination analysis for functional programs, in W. Bibel and P. Schmitt (eds), Automated Deduction - A Basis for Applications, Vol. 3, Applied Logic Series 10, Kluwer Acad. Publ., 1998.
    • (1998) Automated Deduction - A Basis for Applications , vol.3
    • Giesl, J.1    Walther, C.2    Brauburger, J.3
  • 29
    • 84957628750 scopus 로고    scopus 로고
    • Transforming context-sensitive rewrite systems
    • Trento, Italy, Lecture Notes in Comput. Sci. 1631, Springer
    • Giesl, J. and Middeldorp, A.: Transforming context-sensitive rewrite systems, in Proc. 10th Int. Conf. Rewriting Techniques and Applications, Trento, Italy, Lecture Notes in Comput. Sci. 1631, Springer, 1999.
    • (1999) Proc. 10th Int. Conf. Rewriting Techniques and Applications
    • Giesl, J.1    Middeldorp, A.2
  • 30
    • 0002424767 scopus 로고
    • An initial algebra approach to the specification, correctness, and implementation of abstract data types
    • R. T. Yeh (ed.), Prentice-Hall
    • Goguen, J. A., Thatcher, J. W., and Wagner, E. G.: An initial algebra approach to the specification, correctness, and implementation of abstract data types, in R. T. Yeh (ed.), Current Trends in Programming Methodology, Vol. 4, Prentice-Hall, 1978.
    • (1978) Current Trends in Programming Methodology , vol.4
    • Goguen, J.A.1    Thatcher, J.W.2    Wagner, E.G.3
  • 33
    • 0017504316 scopus 로고
    • Abstract data types and the development of data structures
    • Guttag, J. V.: Abstract data types and the development of data structures, Comm. ACM 20 (1977) 396-404.
    • (1977) Comm. ACM , vol.20 , pp. 396-404
    • Guttag, J.V.1
  • 34
    • 84976811006 scopus 로고
    • Confluent reductions: Abstract properties and applications to term rewriting systems
    • Huet, G.: Confluent reductions: Abstract properties and applications to term rewriting systems, J. ACM 27 (1980), 797-821.
    • (1980) J. ACM , vol.27 , pp. 797-821
    • Huet, G.1
  • 35
    • 0000673198 scopus 로고
    • Proofs by induction in equational theories with constructors
    • Huet, G. and Hullot, J.-M.: Proofs by induction in equational theories with constructors, J. Comput. and System Sci. 25 (1982) 239-266.
    • (1982) J. Comput. and System Sci. , vol.25 , pp. 239-266
    • Huet, G.1    Hullot, J.-M.2
  • 36
    • 84957679307 scopus 로고    scopus 로고
    • INKA: The next generation
    • New Brunswick, NJ, Lecture Notes in Artif. Intell. 1104, Springer
    • Hutter, D. and Sengler, C.: INKA: The next generation, in Proc. 13th Int. Conf. Automated Deduction, New Brunswick, NJ, Lecture Notes in Artif. Intell. 1104, Springer, 1996.
    • (1996) Proc. 13th Int. Conf. Automated Deduction
    • Hutter, D.1    Sengler, C.2
  • 37
    • 0024701540 scopus 로고
    • Automatic proofs by induction in theories without constructors
    • Jouannaud, J.-P. and Kounalis, E.: Automatic proofs by induction in theories without constructors, Inform, and Comput. 82 (1989) 1-33.
    • (1989) Inform, and Comput. , vol.82 , pp. 1-33
    • Jouannaud, J.-P.1    Kounalis, E.2
  • 38
    • 85028806405 scopus 로고
    • Proof by induction using test sets
    • Oxford, England, Lecture Notes in Comput. Sci. 230, Springer
    • Kapur, D., Narendran, P., and Zhang, H.: Proof by induction using test sets, in Proc. 8th Int. Conf. Automated Deduction, Oxford, England, Lecture Notes in Comput. Sci. 230, Springer, 1986.
    • (1986) Proc. 8th Int. Conf. Automated Deduction
    • Kapur, D.1    Narendran, P.2    Zhang, H.3
  • 40
    • 0023291769 scopus 로고
    • Proof by consistency
    • Kapur, D. and Musser, D. R.: Proof by consistency, Artif. Intell. 31 (1987), 125-157.
    • (1987) Artif. Intell. , vol.31 , pp. 125-157
    • Kapur, D.1    Musser, D.R.2
  • 41
    • 0003197380 scopus 로고
    • An overview of rewrite rule laboratory (RRL)
    • Kapur, D. and Zhang, H.: An overview of rewrite rule laboratory (RRL), J. Comput. and Math. Appl. 29 (1995) 91-114.
    • (1995) J. Comput. and Math. Appl. , vol.29 , pp. 91-114
    • Kapur, D.1    Zhang, H.2
  • 42
    • 0030101018 scopus 로고    scopus 로고
    • New uses of linear arithmetic in automated theorem proving by induction
    • Kapur, D. and Subramaniam, M.: New uses of linear arithmetic in automated theorem proving by induction, J. Automated Reasoning 16 (1996), 39-78.
    • (1996) J. Automated Reasoning , vol.16 , pp. 39-78
    • Kapur, D.1    Subramaniam, M.2
  • 46
    • 84956993662 scopus 로고
    • A mechanization of strong Kleene logic for partial functions
    • Nancy, France, Lecture Notes in Artif. Intell. 814, Springer
    • Kerber, M. and Kohlhase, M.: A mechanization of strong Kleene logic for partial functions, in Proc. 12th Int. Conf. Automated Deduction, Nancy, France, Lecture Notes in Artif. Intell. 814, Springer, 1994.
    • (1994) Proc. 12th Int. Conf. Automated Deduction
    • Kerber, M.1    Kohlhase, M.2
  • 50
    • 84904736392 scopus 로고
    • Partial algebras flow from algebraic specifications
    • Karlsruhe, Germany, Lecture Notes in Comput. Sci. 267, Springer
    • Kreowski, H.-J.: Partial algebras flow from algebraic specifications, in Proc. 14th Int. Coll. on Automata, Languages, and Programming, Karlsruhe, Germany, Lecture Notes in Comput. Sci. 267, Springer, 1987.
    • (1987) Proc. 14th Int. Coll. on Automata, Languages, and Programming
    • Kreowski, H.-J.1
  • 51
    • 84947770521 scopus 로고    scopus 로고
    • Conditional equational specifications of data types with partial operations for inductive theorem proving
    • Sitges, Spain, Lecture Notes in Comput. Sci. 1232, Springer
    • Kühler, U. and Wirth, C.-P.: Conditional equational specifications of data types with partial operations for inductive theorem proving, in Proc. 8th Int. Conf. Rewriting Techniques and Applications, Sitges, Spain, Lecture Notes in Comput. Sci. 1232, Springer, 1997.
    • (1997) Proc. 8th Int. Conf. Rewriting Techniques and Applications
    • Kühler, U.1    Wirth, C.-P.2
  • 53
    • 0003006419 scopus 로고    scopus 로고
    • Context-sensitive computations in functional and functional logic programs
    • Lucas, S.: Context-sensitive computations in functional and functional logic programs, J. Functional and Logic Programming 1 (1998), 1-61.
    • (1998) J. Functional and Logic Programming , vol.1 , pp. 1-61
    • Lucas, S.1
  • 55
    • 0011517639 scopus 로고
    • Deductive synthesis of the unification algorithm
    • Manna, Z. and Waldinger, R.: Deductive synthesis of the unification algorithm, Sci. Comput. Programming 1 (1981), 5-48.
    • (1981) Sci. Comput. Programming , vol.1 , pp. 5-48
    • Manna, Z.1    Waldinger, R.2
  • 56
    • 84936896337 scopus 로고
    • Recursive functions of symbolic expressions and their computation by machine
    • McCarthy, J.: Recursive functions of symbolic expressions and their computation by machine, Comm. ACM 3 (1960), 184-195.
    • (1960) Comm. ACM , vol.3 , pp. 184-195
    • McCarthy, J.1
  • 57
    • 0017482402 scopus 로고
    • Subgoal induction
    • Morris, J. H. and Wegbreit, B.: Subgoal induction, Comm. ACM 20 (1977) 209-222.
    • (1977) Comm. ACM , vol.20 , pp. 209-222
    • Morris, J.H.1    Wegbreit, B.2
  • 59
    • 84957702937 scopus 로고    scopus 로고
    • More Church-Rosser proofs (in ISABELLE/HOL)
    • New Brunswick, NJ, Lecture Notes in Artif. Intell. 1104, Springer
    • Nipkow, T.: More Church-Rosser proofs (in ISABELLE/HOL), in Proc. 13th Int. Conf. Automated Deduction, New Brunswick, NJ, Lecture Notes in Artif. Intell. 1104, Springer, 1996.
    • (1996) Proc. 13th Int. Conf. Automated Deduction
    • Nipkow, T.1
  • 61
    • 0022083772 scopus 로고
    • Verifying the unification algorithm in LCF
    • Paulson, L. C.: Verifying the unification algorithm in LCF, Sci. of Comput. Programming 5 (1985), 143-169.
    • (1985) Sci. of Comput. Programming , vol.5 , pp. 143-169
    • Paulson, L.C.1
  • 65
    • 85031788351 scopus 로고
    • Term rewriting induction
    • Kaiserslautern, Germany, Lecture Notes in Comput. Sci. 449, Springer
    • Reddy, U. S.: Term rewriting induction, in Proc. 10th Int. Conf. Automated Deduction, Kaiserslautern, Germany, Lecture Notes in Comput. Sci. 449, Springer, 1990.
    • (1990) Proc. 10th Int. Conf. Automated Deduction
    • Reddy, U.S.1
  • 67
    • 84918983692 scopus 로고
    • A machine oriented logic based on the resolution principle
    • Robinson, J. A.: A machine oriented logic based on the resolution principle, J. ACM 12 (1965), 23-41.
    • (1965) J. ACM , vol.12 , pp. 23-41
    • Robinson, J.A.1
  • 68
    • 0027910876 scopus 로고
    • A type-theoretic alternative to CUCH, ISWIM, PWHY, Notes, Oxford, 1969
    • Scott, D. S.: A type-theoretic alternative to CUCH, ISWIM, PWHY, Notes, Oxford, 1969. Annotated version in Theoret. Comput. Sci. 121 (1993), 411-440.
    • (1993) Theoret. Comput. Sci. , vol.121 , pp. 411-440
    • Scott, D.S.1
  • 69
    • 0024047773 scopus 로고
    • A mechanical proof of the Church-Rosser theorem
    • Shankar, N.: A mechanical proof of the Church-Rosser theorem, J. ACM 35 (1988), 475-522.
    • (1988) J. ACM , vol.35 , pp. 475-522
    • Shankar, N.1
  • 72
    • 84949677024 scopus 로고    scopus 로고
    • Derivation and use of induction schemes in higher-order logic
    • Murray Hill, NJ, Lecture Notes in Comput. Sci. 1275, Springer
    • Slind, K.: Derivation and use of induction schemes in higher-order logic, in Proc. 10th Int. Conf. on Theorem Proving in Higher Order Logics, Murray Hill, NJ, Lecture Notes in Comput. Sci. 1275, Springer, 1997.
    • (1997) Proc. 10th Int. Conf. on Theorem Proving in Higher Order Logics
    • Slind, K.1
  • 73
    • 0029369584 scopus 로고
    • Simplification orderings: History of results
    • Steinbach, J.: Simplification orderings: History of results, Fund. Inform. 24 (1995), 47-87.
    • (1995) Fund. Inform. , vol.24 , pp. 47-87
    • Steinbach, J.1
  • 74
    • 0023994541 scopus 로고
    • Efficient tests for top-down termination of logical rules
    • Ullman, J. D. and van Gelder, A.: Efficient tests for top-down termination of logical rules, J. ACM 35 (1988), 345-373.
    • (1988) J. ACM , vol.35 , pp. 345-373
    • Ullman, J.D.1    Van Gelder, A.2
  • 75
    • 0000001920 scopus 로고
    • Mathematical induction
    • D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Oxford Univ. Press
    • Walther, C.: Mathematical induction, in D. M. Gabbay, C. J. Hogger, and J. A. Robinson (eds), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 2, Oxford Univ. Press, 1994.
    • (1994) Handbook of Logic in Artificial Intelligence and Logic Programming , vol.2
    • Walther, C.1
  • 76
    • 0028538729 scopus 로고
    • On proving the termination of algorithms by machine
    • Walther, C.: On proving the termination of algorithms by machine, Artif. Intell. 71 (1994), 101-157.
    • (1994) Artif. Intell. , vol.71 , pp. 101-157
    • Walther, C.1
  • 77
    • 85026913360 scopus 로고
    • On notions of inductive validity for first-order equational clauses
    • Nancy, France, Lecture Notes in Artif. Intell. 814, Springer
    • Wirth, C.-P. and Gramlich, B.: On notions of inductive validity for first-order equational clauses, in Proc. 12th Int. Conf. Automated Deduction, Nancy, France, Lecture Notes in Artif. Intell. 814, Springer, 1994.
    • (1994) Proc. 12th Int. Conf. Automated Deduction
    • Wirth, C.-P.1    Gramlich, B.2
  • 79
    • 84958640069 scopus 로고
    • A mechanizable induction principle for equational specifications
    • Argonne, IL, Lecture Notes in Comput. Sci. 310, Springer
    • Zhang, H., Kapur, D., and Krishnamoorthy, M. S.: A mechanizable induction principle for equational specifications, in Proc. 9th Int. Conf. Automated Deduction, Argonne, IL, Lecture Notes in Comput. Sci. 310, Springer, 1988.
    • (1988) Proc. 9th Int. Conf. Automated Deduction
    • Zhang, H.1    Kapur, D.2    Krishnamoorthy, M.S.3


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