69,293 research outputs found
Non-Termination Inference of Logic Programs
We present a static analysis technique for non-termination inference of logic
programs. Our framework relies on an extension of the subsumption test, where
some specific argument positions can be instantiated while others are
generalized. We give syntactic criteria to statically identify such argument
positions from the text of a program. Atomic left looping queries are generated
bottom-up from selected subsets of the binary unfoldings of the program of
interest. We propose a set of correct algorithms for automating the approach.
Then, non-termination inference is tailored to attempt proofs of optimality of
left termination conditions computed by a termination inference tool. An
experimental evaluation is reported. When termination and non-termination
analysis produce complementary results for a logic procedure, then with respect
to the leftmost selection rule and the language used to describe sets of atomic
queries, each analysis is optimal and together, they induce a characterization
of the operational behavior of the logic procedure.Comment: Long version (algorithms and proofs included) of a paper submitted to
TOPLA
Classes of Terminating Logic Programs
Termination of logic programs depends critically on the selection rule, i.e.
the rule that determines which atom is selected in each resolution step. In
this article, we classify programs (and queries) according to the selection
rules for which they terminate. This is a survey and unified view on different
approaches in the literature. For each class, we present a sufficient, for most
classes even necessary, criterion for determining that a program is in that
class. We study six classes: a program strongly terminates if it terminates for
all selection rules; a program input terminates if it terminates for selection
rules which only select atoms that are sufficiently instantiated in their input
positions, so that these arguments do not get instantiated any further by the
unification; a program local delay terminates if it terminates for local
selection rules which only select atoms that are bounded w.r.t. an appropriate
level mapping; a program left-terminates if it terminates for the usual
left-to-right selection rule; a program exists-terminates if there exists a
selection rule for which it terminates; finally, a program has bounded
nondeterminism if it only has finitely many refutations. We propose a
semantics-preserving transformation from programs with bounded nondeterminism
into strongly terminating programs. Moreover, by unifying different formalisms
and making appropriate assumptions, we are able to establish a formal hierarchy
between the different classes.Comment: 50 pages. The following mistake was corrected: In figure 5, the first
clause for insert was insert([],X,[X]
A Polyvariant Binding-Time Analysis for Off-line Partial Deduction
We study the notion of binding-time analysis for logic programs. We formalise
the unfolding aspect of an on-line partial deduction system as a Prolog
program. Using abstract interpretation, we collect information about the
run-time behaviour of the program. We use this information to make the control
decisions about the unfolding at analysis time and to turn the on-line system
into an off-line system. We report on some initial experiments.Comment: 19 pages (including appendix) Paper (without appendix) appeared in
Programming Languages and Systems, Proceedings of the European Symposium on
Programming (ESOP'98), Part of ETAPS'98 (Chris Hankin, eds.), LNCS, vol.
1381, 1998, pp. 27-4
Verifying termination and error-freedom of logic programs with block declarations
We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to eliminate the well-known problem of speculative output bindings. The second approach is based on identifying the predicates for which the textual position of an atom using this predicate is irrelevant with respect to termination.
Three features are distinctive of this work: it allows for predicates to be used in several modes; it shows that block declarations, which are a very simple delay construct, are sufficient to ensure the desired properties; it takes the selection rule into account, assuming it to be as in most Prolog implementations. The methods can be used to verify existing programs and assist in writing new programs
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Size-Change Termination, Monotonicity Constraints and Ranking Functions
Size-Change Termination (SCT) is a method of proving program termination
based on the impossibility of infinite descent. To this end we may use a
program abstraction in which transitions are described by monotonicity
constraints over (abstract) variables. When only constraints of the form x>y'
and x>=y' are allowed, we have size-change graphs. Both theory and practice are
now more evolved in this restricted framework then in the general framework of
monotonicity constraints. This paper shows that it is possible to extend and
adapt some theory from the domain of size-change graphs to the general case,
thus complementing previous work on monotonicity constraints. In particular, we
present precise decision procedures for termination; and we provide a procedure
to construct explicit global ranking functions from monotonicity constraints in
singly-exponential time, which is better than what has been published so far
even for size-change graphs.Comment: revised version of September 2
Automatic Termination Analysis of Programs Containing Arithmetic Predicates
For logic programs with arithmetic predicates, showing termination is not
easy, since the usual order for the integers is not well-founded. A new method,
easily incorporated in the TermiLog system for automatic termination analysis,
is presented for showing termination in this case.
The method consists of the following steps: First, a finite abstract domain
for representing the range of integers is deduced automatically. Based on this
abstraction, abstract interpretation is applied to the program. The result is a
finite number of atoms abstracting answers to queries which are used to extend
the technique of query-mapping pairs. For each query-mapping pair that is
potentially non-terminating, a bounded (integer-valued) termination function is
guessed. If traversing the pair decreases the value of the termination
function, then termination is established. Simple functions often suffice for
each query-mapping pair, and that gives our approach an edge over the classical
approach of using a single termination function for all loops, which must
inevitably be more complicated and harder to guess automatically. It is worth
noting that the termination of McCarthy's 91 function can be shown
automatically using our method.
In summary, the proposed approach is 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. Consequently, the
whole process of proving termination can be done automatically in the framework
of TermiLog and similar systems.Comment: Appeared also in Electronic Notes in Computer Science vol. 3
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