7,693 research outputs found
Verification of Timed Automata Using Rewrite Rules and Strategies
ELAN is a powerful language and environment for specifying and prototyping
deduction systems in a language based on rewrite rules controlled by
strategies. Timed automata is a class of continuous real-time models of
reactive systems for which efficient model-checking algorithms have been
devised. In this paper, we show that these algorithms can very easily be
prototyped in the ELAN system. This paper argues through this example that
rewriting based systems relying on rules and strategies are a good framework to
prototype, study and test rather efficiently symbolic model-checking
algorithms, i.e. algorithms which involve combination of graph exploration
rules, deduction rules, constraint solving techniques and decision procedures
Strategic Computation and Deduction
We introduce the notion of abstract strategies for abstract reduction systems. Adequate properties of termination, confluence and normalization under strategy can then be defined. Thanks to this abstract concept, we draw a parallel between strategies for computation and strategies for deduction. We define deduction rules as rewrite rules, a deduction step as a rewriting step and a proof construction step as a narrowing step in an adequate abstract reduction system. Computation, deduction and proof search are thus captured in the uniform foundational concept of abstract reduction system in which abstract strategies have a clear formalisation
Maude: specification and programming in rewriting logic
Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude
Maude's Internal Strategies
AbstractMaude is a reflective language supporting both rewriting logic and membership equational logic. Reflection is systematically exploited in Maude, endowing the language with powerful metaprogramming capabilities, including declarative strategies to guide the deduction process
A Reflective Theorem Prover for the Connection Calculus
Rewriting logic can be used to prototype systems for automated
deduction. In this paper, we illustrate how this approach allows
experiments with deduction strategies in a flexible and conceptually
satisfying way.
This is achieved by exploiting the reflective property of rewriting
logic. By specifying a theorem prover in this way one quickly
obtains a readable, reliable and reasonably efficient system which
can be used both as a platform for tactic experiments and as a basis
for an optimized implementation. The approach is illustrated by
specifying a calculus for the connection method in rewriting logic
which clearly separates rules from tactics
Canonical Abstract Syntax Trees
This paper presents Gom, a language for describing abstract syntax trees and
generating a Java implementation for those trees. Gom includes features
allowing the user to specify and modify the interface of the data structure.
These features provide in particular the capability to maintain the internal
representation of data in canonical form with respect to a rewrite system. This
explicitly guarantees that the client program only manipulates normal forms for
this rewrite system, a feature which is only implicitly used in many
implementations
Extensional and Intensional Strategies
This paper is a contribution to the theoretical foundations of strategies. We
first present a general definition of abstract strategies which is extensional
in the sense that a strategy is defined explicitly as a set of derivations of
an abstract reduction system. We then move to a more intensional definition
supporting the abstract view but more operational in the sense that it
describes a means for determining such a set. We characterize the class of
extensional strategies that can be defined intensionally. We also give some
hints towards a logical characterization of intensional strategies and propose
a few challenging perspectives
Deduction modulo theory
This paper is a survey on Deduction modulo theor
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