# Strict Functionals for Termination Proofs

```@inproceedings{Pol1995StrictFF,
title={Strict Functionals for Termination Proofs},
author={Jaco van de Pol and Helmut Schwichtenberg},
booktitle={International Conference on Typed Lambda Calculus and Applications},
year={1995}
}```
• Published in
International Conference on…
10 April 1995
• Computer Science
A semantical method to prove termination of higher order rewrite systems (HRS) is presented. Its main tool is the notion of a strict functional, which is a variant of Gandy's notion of a hereditarily monotonic functional [1]. The main advantage of the method is that it makes it possible to transfer ones intuitions about why an HRS should be terminating into a proof: one has to nd a \strict" interpretation of the constants involved in such a way that the left hand side of any rewrite rule gets a…
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## References

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This paper deals with termination proofs for Higher-Order Rewrite Systems (HRSs), introduced in [12], which combines the computational aspects of term rewriting and simply typed lambda calculus and produces a proof technique similar to the proof technique for the termination of a well-founded monotone algebra.

### Orthogonal Higher-Order Rewrite Systems are Confluent

The results about higher-order critical pairs and the confluence of OHRSs provide a firm foundation for the further study of higher-order rewrite systems. It should now be interesting to lift more

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Introduction: Elementary Proof Theory. The Fall of Hilbert's Program. Hilbert's Program. Recursive Functions. The First Incompleteness Theorem. The Second Incompleteness Theorem. Exercises. Annex:

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• Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism
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