Reseña: Automatic data refinement

PorJosé A. Alonso

Se ha publicado un artículo de automatización del razonamiento en Isabelle/HOL titulado Automatic data refinement.

Su autor es Peter Lammich (de la Universidad Técnica de Munich).

El trabajo se presentará en julio en la ITP 2013 (4th Conference on
Interactive Theorem Proving).

Su resumen es

We present the Autoref tool for Isabelle/HOL, which automatically refines algorithms specified over abstract concepts like maps and sets to algorithms over concrete implementations like red-black-trees, and produces a refinement theorem. It is based on ideas borrowed from relational parametricity due to Reynolds and Wadler.

The tool allows for rapid prototyping of verified, executable algorithms. Moreover, it can be configured to fine-tune the result to the user’s needs. Our tool is able to automatically instantiate generic algorithms, which greatly simplifies the implementation of executable data structures.

Thanks to its integration with the Isabelle Refinement Framework and the Isabelle Collection Framework, Autoref can be used as a backend to a stepwise refinement based development approach, having access to a rich library of verified data structures. We have evaluated the tool by synthesizing efficiently executable refinements for some complex algorithms, as well as by implementing a library of generic algorithms for maps and sets.

La implementación de Autoref, junto con algunos casos de estudio, se encuentra aquí.

Reseña: Type classes and filters for mathematical analysis in Isabelle/HOL

PorJosé A. Alonso

Se ha publicado un artículo de razonamiento formalizado en Isabelle/HOL sobre análisis matemático titulado Type classes and filters for mathematical analysis in Isabelle/HOL.

Sus autores son Johannes Hölzl, Fabian Immler y Brian Huffman.

El trabajo se presentará en julio en la ITP 2013 (4th Conference on
Interactive Theorem Proving).

Su resumen es

The theory of analysis in Isabelle/HOL derives from earlier formalizations that were limited to specific concrete types: ℝ, C and ℝⁿ. Isabelle’s new analysis theory unifies and generalizes these earlier efforts. The improvements are centered on two primary contributions: a generic theory of limits based on filters, and a new hierarchy of type classes that includes various topological, metric, vector, and algebraic spaces. These let us apply many results in multivariate analysis to types which are not Euclidean spaces, such as the extended real numbers, bounded continuous functions, or finite maps.

RA2012: Verificación en Isabelle de propiedades de funciones sobre listas (1)

PorJosé A. Alonso

En la clase de hoy del curso de Razonamiento automático se han comentado las soluciones de los ejercicios de verificación en Isabelle de propiedades de funciones sobre listas de las siguientes relaciones: