Connection-Driven Inductive Theorem Proving

Christoph Kreitz, Brigitte Pientka.

Studia Logica 69(2):293-326, 2001.


We present a method for integrating rippling-based rewriting into matrix-based theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverse-rippling heuristic. Conditional substitutions are generated whenever a uniform substitution is impossible. We illustrate the integrated method by discussing several inductive proofs for the integer square root problem as well as the algorithms extracted from these proofs.

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Bibtex Entry

@Article{ar:KreitzPientka01a, author = "Christoph Kreitz and Brigitte Pientka", title = "Connection-Driven Inductive Theorem Proving", journal = "Studia Logica", year = "2001", volume = 69, number = 2, pages = "293--326" }