Inference of termination conditions for numerical loops in Prolog

@article{Serebrenik2004InferenceOT,
  title={Inference of termination conditions for numerical loops in Prolog},
  author={Alexander Serebrenik and Danny De Schreye},
  journal={Theory and Practice of Logic Programming},
  year={2004},
  volume={4},
  pages={719 - 751}
}
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these difficulties. Our approach is based on transforming a program in a way that allows integrating and extending techniques originally developed for analysis of numerical computations in the framework of query-mapping pairs with the well-known framework of… 
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References

SHOWING 1-10 OF 85 REFERENCES
Inference of termination conditions for numerical loops
TLDR
An approach based on transforming a program in way that allows integrating and extending techniques originally developed for analysis of numerical computations in the framework of query-mapping pairs with the well-known framework of acceptability to perform a correct analysis of such computations automatically, thus, extending previous work on a constraints-based approach to termination.
Detecting Optimal Termination Conditions of Logic Programs
TLDR
This framework relies on an extension of the Lifting Theorem, where some specific argument positions can be instantiated while others are generalized, and is tailored to attempt proofs of optimality of left termination conditions computed by a termination inference tool.
Applying Static Analysis Techniques for Inferring Termination Conditions of Logic Programs
TLDR
The implementation of cTI is presented, a system for universal left-termination inference of logic programs, where all provably terminating classes to all related predicates are inferred at once.
Unfolding the Mystery of Mergesort
This paper outlines a fully automatic transformation for proving termination of queries to a class of logic programs, for which existing methods do not work directly. The transformation consists of…
Constraint-based termination analysis of logic programs
TLDR
A new termination analysis is presented which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs and the need for multiple analyses is considerably reduced.
A declarative approach for first-order built-in's of Prolog
TLDR
A new, declarative semantics is proposed and it is shown that this semantics is fully abstract in an appropriate sense and proves completeness of the Prolog computation mechanism w.r.t. this semantics.
Reuse of Results in Termination Analysis of Typed Logic Programs
TLDR
It is shown that by considering polymorphic types the authors reduce, without sacrificing precision, the number of type-based norms which should be combined to provide the candidate norm and that when a generic polymorphic typed program component occurs in one or more specific type contexts, they need not reanalyze it.
Termination detection in logic programs using argument sizes (extended abstract)
TLDR
A method ofding a nonnegative linear combination of bound argument sizes that is guaranteed to decrease during top-down execution of recursive rules is described, which can handle nonlinear recursion, mutual recursions, and cases in which no speci c argument is certain to decrease.
Proving Termination of Logic Programs by Exploiting Term Properties
In this paper semi-linear norms, a class of functions to weight the terms occurring in a program, are defined and studied. All the functions in this class have the nice property of allowing a…
A General Framework for Automatic Termination Analysis of Logic Programs
TLDR
A new method is presented, based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case.
...
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