# Termination Proofs for Higher-order Rewrite Systems

@inproceedings{Pol1993TerminationPF, title={Termination Proofs for Higher-order Rewrite Systems}, author={Jaco van de Pol}, booktitle={HOA}, year={1993} }

This paper deals with termination proofs for Higher-Order Rewrite Systems (HRSs), introduced in [12]. This formalism combines the computational aspects of term rewriting and simply typed lambda calculus. The result is a proof technique for the termination of a HRS, similar to the proof technique “Termination by interpretation in a well-founded monotone algebra”, described in [8, 19]. The resulting technique is as follows: Choose a higher-order algebra with operations for each function symbol in…

## 59 Citations

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### Strict Functionals for Termination Proofs

- Computer ScienceTLCA
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A semantical method to prove termination of higher order rewrite systems (HRS) is presented, which makes it possible to transfer intuitions about why an HRS should be terminating into a proof.

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It is shown how the computability closure can easily be turned into a reduction ordering which contains Jean-Pierre Jouannaud and Albert Rubio's higher-order recursive path ordering and, in the firstorder case, is equal to the usual first-order recursion path ordering.

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This paper studies termination of curryfied term rewriting systems (CTRSs), where functional values are introduced by “partial application” The limitations of syntactic simplification orderings for…

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New theorems of modular termination checking for second-order computation are presented, useful for proving termination of higher-order programs and foundational calculi and offering a decomposition technique for difficult termination problems.

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### Semantic Labelling for Proving Termination of Combinatory Reduction Systems

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A novel transformation method for proving termination of higher-order rewrite rules in Klop's format called Combinatory Reduction System (CRS), an extension of a method known in the theory of term rewriting.

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