# Automated Mathematical Induction

@article{Bouhoula1995AutomatedMI, title={Automated Mathematical Induction}, author={Adel Bouhoula and Emmanuel Kounalis and Micha{\"e}l Rusinowitch}, journal={J. Log. Comput.}, year={1995}, volume={5}, pages={631-668} }

Proofs by induction are important in many computer science and artifical intelligence applications, in particular, in program verification and specification systems. We present a new method to prove (and disprove) automatically inductives properties. Given a set of axioms, a well-suited induction scheme is constructed automatically. We call such and induction scheme a test set. Then, for proving a property, we just instantiate it with terms from the test set and apply pure algebraicâ€¦Â

## 35 Citations

### Customised induction rules for proving correctness of imperative programs

- MathematicsThird IEEE International Conference on Software Engineering and Formal Methods (SEFM'05)
- 2005

This paper develops a method for automatic construction of customised induction rules for use in a semi-interactive theorem prover and creates an induction rule, in destructor style, that is customised to make the proving of the loop simpler.

### Using Induction and Rewriting to Verify and Complete Parameterized Specifications

- Computer ScienceTheor. Comput. Sci.
- 1996

### Austrian-Japanese Workshop on Symbolic Computation in Software Science

- Computer Science
- 2008

A refined system of rewriting induction is presented with an increased capability of non-orientable theorems and a capability of disproving incorrect conjectures.

### General Framework for Mechanizing Induction using Test Set

- Computer Science, MathematicsPRICAI
- 1996

A test set induction procedure which is refutationally complete for conditional specifications (not restricted to Boolean specifications), in that it refutes any conjecture which is not an inductive theorem.

### Induction as Deduction Modulo

- Computer Science
- 2004

This paper extends slightly the original version of the deduction modulo framework and provides modularity properties for it and shows how this applies to a uniform understanding of the so called induction by rewriting method and how this relates directly to the general use of an induction principle.

### Sufficient Completeness and Parameterized Proofs by Induction

- Computer Science, MathematicsALP
- 1994

This new method when limited to non-parameterized conditional specifications, can refute general clauses; refutational completeness is also preserved for boolean ground convergent rewrite systems even if the functions are not sufficiently complete and the constructors are not free.

### Inductive Theorem Proving in Non-terminating Rewriting Systems and Its Application to Program Transformation

- Computer SciencePPDP
- 2019

A framework for proving inductive theorems of first-order equational theories, using techniques of implicit induction developed in the field of term rewriting, is presented, which makes use of automated confluence provers as well as a novel condition of sufficient completeness, called localsufficient completeness.

### RAPPORT Implicit induction techniques for the verification of PIMa transformational toolkit for compilers

- Computer Science
- 1996

This paper proposes new implicit induction techniques adequate for solving the indicated proof problem for Pim, a transformational toolkit for compilers that consists of the untyped lambda calculus extended with an algebraic rewriting system.

### Mechanizable Inductive Proofs for a Class of Forall Exists Formulas

- MathematicsCADE
- 1994

We show how to prove formulas of the form âˆ€ xâˆƒ yÎ¦(x, y) in the initial model of an equational variety by using purely algebraic simplifications. This allows to tackle theorems whose proofs requiresâ€¦

### Automatic inductive theorem proving and program construction methods using program transformation

- Computer Science, Mathematics
- 2007

The use of distillation in the framework of Poitin has eased the automation of the proof and program construction techniques in a reduced search space to make it fully automatic and efficient.

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