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A higher-order unification algorithm for inductive types and dependent types

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Abstract

This paper presents a method to define a set of mutually recursive inductive types, and develops a higher-order unification algorithm for λΠΣ extended with inductive types. The algorithm is an extension of Elliott's algorithm for λΠΣ. The notation of normal forms plays a vital role in higher-order unification. The weak head normal forms in the extended type theory is defined to reveal the ultimate “top level structures” of the fully normalized terms and types. Unification transformation rules are designed to deal with inductive types, a recursive operator and its reduction rule. The algorithm can construct recursive functions automatically.

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References

  1. Elliott C. Extensions and applications of higher-order unification. Ph.D. Thesis, Carnegie Mellon University, 1990.

  2. Tan Qingping. Program design environments based on type theory. Ph.D. Thesis, Changsha Institute of Technology, 1992.

  3. Huet G. A unification algorithm for typed λ-calculus.Theor. Comput. Sci., 1975, 1.

  4. Harper R, Honsell F, Plotkin G. A framework for defining logics. InProc. of LICS'87, 1987.

  5. Jensen D, Pietrzykowski T. Mechanizing ω-order type theory through unification.Theor. Comput. Sci., 1976, 3.

  6. Synder W, Gallier J H. Higher-order unification revisited: Complete set of transformations.Bulletin of EATCS, 1990, (40).

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Authors and Affiliations

  1. Department of Computer Science, Changsha Institute of Technology, 410073, Changsha

    Tan Qingping

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  1. Tan Qingping
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Tan Qingping received his Ph.D. degree in computer science from Changsha Institute of Technology in 1992. Now he is an Associate Professor of Computer Science at Changsha Institute of Technology. His research centers around the formal development of software, type theory, higher order logic and software engineering. Dr. Tan is a member of the IEEE Computer Society.

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Tan, Q. A higher-order unification algorithm for inductive types and dependent types. J. of Comput. Sci. & Technol. 12, 231–243 (1997). https://doi.org/10.1007/BF02948973

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  • DOI: https://doi.org/10.1007/BF02948973

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