1,682 research outputs found
Formulas as Programs
We provide here a computational interpretation of first-order logic based on
a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary
interpretation. In this approach the formulas themselves are programs. This
contrasts with the so-called formulas as types approach in which the proofs of
the formulas are typed terms that can be taken as programs. This view of
computing is inspired by logic programming and constraint logic programming but
differs from them in a number of crucial aspects.
Formulas as programs is argued to yield a realistic approach to programming
that has been realized in the implemented programming language ALMA-0 (Apt et
al.) that combines the advantages of imperative and logic programming. The work
here reported can also be used to reason about the correctness of non-recursive
ALMA-0 programs that do not include destructive assignment.Comment: 34 pages, appears in: The Logic Programming Paradigm: a 25 Years
Perspective, K.R. Apt, V. Marek, M. Truszczynski and D.S. Warren (eds),
Springer-Verlag, Artificial Intelligence Serie
Inference of termination conditions for numerical loops
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 to
overcome these difficulties. Our approach is 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. Such an integration not only
contributes to the understanding of termination behaviour of numerical
computations, but also allows to perform a correct analysis of such
computations automatically, thus, extending previous work on a
constraints-based approach to termination. In the last section of the paper we
discuss possible extensions of the technique, including incorporating general
term orderings.Comment: Presented at WST200
Experiments with a Convex Polyhedral Analysis Tool for Logic Programs
Convex polyhedral abstractions of logic programs have been found very useful
in deriving numeric relationships between program arguments in order to prove
program properties and in other areas such as termination and complexity
analysis. We present a tool for constructing polyhedral analyses of
(constraint) logic programs. The aim of the tool is to make available, with a
convenient interface, state-of-the-art techniques for polyhedral analysis such
as delayed widening, narrowing, "widening up-to", and enhanced automatic
selection of widening points. The tool is accessible on the web, permits user
programs to be uploaded and analysed, and is integrated with related program
transformations such as size abstractions and query-answer transformation. We
then report some experiments using the tool, showing how it can be conveniently
used to analyse transition systems arising from models of embedded systems, and
an emulator for a PIC microcontroller which is used for example in wearable
computing systems. We discuss issues including scalability, tradeoffs of
precision and computation time, and other program transformations that can
enhance the results of analysis.Comment: Paper presented at the 17th Workshop on Logic-based Methods in
Programming Environments (WLPE2007
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