Abstract
A generalization procedure which reconstructs mathematical inductions that are expanded in a proof of an example is formulated under a typed λ-calculus that is designed for increasing the applicability of the procedure. The λ-calculus, an extension of Logical Framework, allows recursions and inductions on natural numbers, and inferences on linear arithmetical terms are built into its type system. The generalization procedure is iterated in a bottom-up fashion to construct nested inductions. Consequently, it can also find inductions whose induction formula is a limited form of bounded quantification.
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© 1993 Springer-Verlag Berlin Heidelberg
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Hagiya, M. (1993). A typed λ-calculus for proving-by-example and bottom-up generalization procedure. In: Jantke, K.P., Kobayashi, S., Tomita, E., Yokomori, T. (eds) Algorithmic Learning Theory. ALT 1993. Lecture Notes in Computer Science, vol 744. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57370-4_38
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DOI: https://doi.org/10.1007/3-540-57370-4_38
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