Abstract
Automating proofs of properties of functions defined on inductively constructed data structures is important in many computer science and artificial intelligence applications, in particular in program verification and specification systems. A new induction principle based on a constructor model of a data structure is developed. This principle along with a given function definition as a set of equations is used to construct automatically an induction scheme suitable for proving inductive properties of the function. The proposed induction principle thus gives different induction schema for different function definitions, just as Boyer and Moore's prover does. A novel feature of this approach is that it can also be used for proving properties by induction for data structures such as integers, finite sets, whose values cannot be freely constructed, i.e., constructors for such data structures are related to each other. This method has been implemented in RRL, a rewrite-rule based theorem prover. More than a hundred theorems in number theory including the unique prime factorization theorem, have been proved using the method.
Partially supported by the National Science Foundation Grant no. CCR-8408461.
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Zhang, H., Kapur, D., Krishnamoorthy, M.S. (1988). A mechanizable induction principle for equational specifications. In: Lusk, E., Overbeek, R. (eds) 9th International Conference on Automated Deduction. CADE 1988. Lecture Notes in Computer Science, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012831
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DOI: https://doi.org/10.1007/BFb0012831
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