2,380 research outputs found
Lifting infinite normal form definitions from term rewriting to term graph rewriting
Infinite normal forms are a way of giving semantics to non-terminating rewrite systems. The notion is a generalization of the Boehm tree in the lambda calculus. It was first introduced in [AB97] to provide semantics for a lambda calculus on terms with letrec. In that paper infinite normal forms were defined directly on the graph rewrit e system. In [Blo01] the framework was improved by defining the infinite normal form of a term graph using the infinite normal form on terms. This approach of lifting the definition makes the non-confluence problems introduced into term graph rewriting by substitution rules much easier to deal with. In this paper, we give a simplified presentation of the latter approach
Transformation of Attributed Structures with Cloning (Long Version)
Copying, or cloning, is a basic operation used in the specification of many
applications in computer science. However, when dealing with complex
structures, like graphs, cloning is not a straightforward operation since a
copy of a single vertex may involve (implicitly)copying many edges. Therefore,
most graph transformation approaches forbid the possibility of cloning. We
tackle this problem by providing a framework for graph transformations with
cloning. We use attributed graphs and allow rules to change attributes. These
two features (cloning/changing attributes) together give rise to a powerful
formal specification approach. In order to handle different kinds of graphs and
attributes, we first define the notion of attributed structures in an abstract
way. Then we generalise the sesqui-pushout approach of graph transformation in
the proposed general framework and give appropriate conditions under which
attributed structures can be transformed. Finally, we instantiate our general
framework with different examples, showing that many structures can be handled
and that the proposed framework allows one to specify complex operations in a
natural way
Refinement Types as Higher Order Dependency Pairs
Refinement types are a well-studied manner of performing in-depth analysis on
functional programs. The dependency pair method is a very powerful method used
to prove termination of rewrite systems; however its extension to higher order
rewrite systems is still the object of active research. We observe that a
variant of refinement types allow us to express a form of higher-order
dependency pair criterion that only uses information at the type level, and we
prove the correctness of this criterion
Initial Algebra Semantics for Cyclic Sharing Tree Structures
Terms are a concise representation of tree structures. Since they can be
naturally defined by an inductive type, they offer data structures in
functional programming and mechanised reasoning with useful principles such as
structural induction and structural recursion. However, for graphs or
"tree-like" structures - trees involving cycles and sharing - it remains
unclear what kind of inductive structures exists and how we can faithfully
assign a term representation of them. In this paper we propose a simple term
syntax for cyclic sharing structures that admits structural induction and
recursion principles. We show that the obtained syntax is directly usable in
the functional language Haskell and the proof assistant Agda, as well as
ordinary data structures such as lists and trees. To achieve this goal, we use
a categorical approach to initial algebra semantics in a presheaf category.
That approach follows the line of Fiore, Plotkin and Turi's models of abstract
syntax with variable binding
Termination of Narrowing: Automated Proofs and Modularity Properties
En 1936 Alan Turing demostro que el halting problem, esto es, el problema de decidir
si un programa termina o no, es un problema indecidible para la inmensa mayoria de
los lenguajes de programacion. A pesar de ello, la terminacion es un problema tan
relevante que en las ultimas decadas un gran numero de tecnicas han sido desarrolladas
para demostrar la terminacion de forma automatica de la maxima cantidad posible de
programas. Los sistemas de reescritura de terminos proporcionan un marco teorico
abstracto perfecto para el estudio de la terminacion de programas. En este marco, la
evaluaci on de un t ermino consiste en la aplicacion no determinista de un conjunto de
reglas de reescritura.
El estrechamiento (narrowing) de terminos es una generalizacion de la reescritura
que proporciona un mecanismo de razonamiento automatico. Por ejemplo, dado un
conjunto de reglas que denan la suma y la multiplicacion, la reescritura permite calcular
expresiones aritmeticas, mientras que el estrechamiento permite resolver ecuaciones
con variables. Esta tesis constituye el primer estudio en profundidad de las
propiedades de terminacion del estrechamiento. Las contribuciones son las siguientes.
En primer lugar, se identican clases de sistemas en las que el estrechamiento tiene
un comportamiento bueno, en el sentido de que siempre termina. Muchos metodos
de razonamiento automatico, como el analisis de la semantica de lenguajes de programaci
on mediante operadores de punto jo, se benefician de esta caracterizacion.
En segundo lugar, se introduce un metodo automatico, basado en el marco teorico
de pares de dependencia, para demostrar la terminacion del estrechamiento en un
sistema particular. Nuestro metodo es, por primera vez, aplicable a cualquier clase
de sistemas.
En tercer lugar, se propone un nuevo metodo para estudiar la terminacion del
estrechamiento desde un termino particular, permitiendo el analisis de la terminacion
de lenguajes de programacion. El nuevo metodo generaliza losIborra López, J. (2010). Termination of Narrowing: Automated Proofs and Modularity Properties [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/19251Palanci
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