On Formalised Proofs of Termination of Recursive Functions

Kamareddine, Fairouz; Monin, François

doi:10.1007/10704567_2

Cited by 3 publications

(4 citation statements)

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“…In [22,10] it was shown that ordinal functions can also be associated to distributing trees. These functions were proven to have the decreasing property in the recursive calls of the specifications if the trees satisfy the terminal state property too.…”

Section: The Theorem Of Generalisationmentioning

confidence: 99%

“…-u * (1 + lg(x)) + 1 and Sl A (s(x), s(y)) = u * (1 4-lg(x)) + (1 4-lg(y)). Another class of measures could also be defined from new formal proofs using an extended version of ProPre (see [10]) in which new inductive rules were introduced.…”

Section: Sj=smentioning

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%

“…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%

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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: The Theorem Of Generalisationmentioning

confidence: 99%

Section: Sj=smentioning

confidence: 99%