An ordinal measure based procedure for termination of functions

Monin, François; Simonot, Marianne

doi:10.1016/s0304-3975(99)00118-8

Cited by 4 publications

(12 citation statements)

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“…However, in the standard approach, finding suitable orderings is essential for the automation of the termination. In [8] a method was developed to automatically synthesise suitable measures based on polynomial orderings and in [22] a termination procedure was proposed to generate orderings with the use of ordinal measures.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown in [22,10] that it is possible to extract well-founded orderings, namely ordinal measures, from the above formal proofs devised in the fully automated system ProPre [21,20], such that the arguments in each recursive call of the given function are smaller than the initially given input (i.e., the calls decrease wrt the well-founded ordering). The extraction of a special class of measures, called ramified measures, appears as a useful way to find out new orderings as these measures are in particular not limited to lexicographic orderings.…”

Section: Introductionmentioning

confidence: 99%

“…Like the above approaches, we make use of some kind of trees as in [22] with some refinements, in particular to deal specifications of incompletely defined functions. However, the novelty of our termination method relies on the hierarchical property developed in this paper and on the introduction of new measures.…”

Section: Introductionmentioning

confidence: 99%

“…But usually the measures are a lexicographic combination of a fixed ordering or are given by the user. The present method aims at providing suitable measures in an automated way and therefore could be used by other theorem provers by providing the measures obtained from the formal proofs in ProPre [22,12].…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of the formal proof trees obtained in the system made it possible to relate measures [22,10,11] that have the decreasing property in the recursive calls of the specifications of the functions. These measures can be defined from distributing trees, devised in [20], which are partial trees; and their decreasing property relies on the notion of a right terminal state property that must satisfy the distributing trees in ProPre in order to be extended into a complete formal proof trees.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Extension of an Automated Termination Method of Recursive Functions

Kamareddine¹,

Monin

2002

Int. J. Found. Comput. Sci.

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Inductive proofs are commonly used in automated deduction systems or functional programming, such as for instance the ProPre system, for establishing the termination of recursively defined functions. Such proofs deal with the structural orderings of the term algebras that define the domain of the functions. However there exists other interesting functions whose termination requires different underlying orderings. To treat a class of such functions that are not taken into account by systems such as ProPre, we develop termination properties that can be shown automatically. In contrast with the ProPre system that builds formal trees based on inductive proofs, we generate measures that satisfy an extended termination property and well-founded orderings which ensure the termination of the functions.

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Section: Introductionmentioning

confidence: 99%