17,613 research outputs found
Automated Termination Proofs for Logic Programs by Term Rewriting
There are two kinds of approaches for termination analysis of logic programs:
"transformational" and "direct" ones. Direct approaches prove termination
directly on the basis of the logic program. Transformational approaches
transform a logic program into a term rewrite system (TRS) and then analyze
termination of the resulting TRS instead. Thus, transformational approaches
make all methods previously developed for TRSs available for logic programs as
well. However, the applicability of most existing transformations is quite
restricted, as they can only be used for certain subclasses of logic programs.
(Most of them are restricted to well-moded programs.) In this paper we improve
these transformations such that they become applicable for any definite logic
program. To simulate the behavior of logic programs by TRSs, we slightly modify
the notion of rewriting by permitting infinite terms. We show that our
transformation results in TRSs which are indeed suitable for automated
termination analysis. In contrast to most other methods for termination of
logic programs, our technique is also sound for logic programming without occur
check, which is typically used in practice. We implemented our approach in the
termination prover AProVE and successfully evaluated it on a large collection
of examples.Comment: 49 page
Polytool: polynomial interpretations as a basis for termination analysis of Logic programs
Our goal is to study the feasibility of porting termination analysis
techniques developed for one programming paradigm to another paradigm. In this
paper, we show how to adapt termination analysis techniques based on polynomial
interpretations - very well known in the context of term rewrite systems (TRSs)
- to obtain new (non-transformational) ter- mination analysis techniques for
definite logic programs (LPs). This leads to an approach that can be seen as a
direct generalization of the traditional techniques in termination analysis of
LPs, where linear norms and level mappings are used. Our extension general-
izes these to arbitrary polynomials. We extend a number of standard concepts
and results on termination analysis to the context of polynomial
interpretations. We also propose a constraint-based approach for automatically
generating polynomial interpretations that satisfy the termination conditions.
Based on this approach, we implemented a new tool, called Polytool, for
automatic termination analysis of LPs
Towards Parameterized Regular Type Inference Using Set Constraints
We propose a method for inferring \emph{parameterized regular types} for
logic programs as solutions for systems of constraints over sets of finite
ground Herbrand terms (set constraint systems). Such parameterized regular
types generalize \emph{parametric} regular types by extending the scope of the
parameters in the type definitions so that such parameters can relate the types
of different predicates. We propose a number of enhancements to the procedure
for solving the constraint systems that improve the precision of the type
descriptions inferred. The resulting algorithm, together with a procedure to
establish a set constraint system from a logic program, yields a program
analysis that infers tighter safe approximations of the success types of the
program than previous comparable work, offering a new and useful efficiency vs.
precision trade-off. This is supported by experimental results, which show the
feasibility of our analysis
Smart matching
One of the most annoying aspects in the formalization of mathematics is the
need of transforming notions to match a given, existing result. This kind of
transformations, often based on a conspicuous background knowledge in the given
scientific domain (mostly expressed in the form of equalities or isomorphisms),
are usually implicit in the mathematical discourse, and it would be highly
desirable to obtain a similar behavior in interactive provers. The paper
describes the superposition-based implementation of this feature inside the
Matita interactive theorem prover, focusing in particular on the so called
smart application tactic, supporting smart matching between a goal and a given
result.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
Superposition as a logical glue
The typical mathematical language systematically exploits notational and
logical abuses whose resolution requires not just the knowledge of domain
specific notation and conventions, but not trivial skills in the given
mathematical discipline. A large part of this background knowledge is expressed
in form of equalities and isomorphisms, allowing mathematicians to freely move
between different incarnations of the same entity without even mentioning the
transformation. Providing ITP-systems with similar capabilities seems to be a
major way to improve their intelligence, and to ease the communication between
the user and the machine. The present paper discusses our experience of
integration of a superposition calculus within the Matita interactive prover,
providing in particular a very flexible, "smart" application tactic, and a
simple, innovative approach to automation.Comment: In Proceedings TYPES 2009, arXiv:1103.311
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