# Automatic Derivation and Application of Induction Schemes for Mutually Recursive Functions

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## Abstract

This paper advocates and explores the use of *multi-predicate* induction schemes for proofs about mutually recursive functions. The *interactive* application of multi-predicate schemes stemming from datatype definitions is already well-established practice; this paper describes an *automated* proof procedure based on multi-predicate schemes. Multi-predicate schemes may be formally derived from (mutually recursive) function definitions; such schemes are often helpful in proving properties of mutually recursive functions where the recursion pattern does not follow that of the underlying datatypes. These ideas have been implemented using the HOL theorem prover and the *Clam* proof planner.

## Keywords

Theorem Prove Recursive Function Induction Scheme High Order Logic Proof Procedure
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© Springer-Verlag Berlin Heidelberg 2000