User interaction widgets for interactive theorem proving

Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using a script for storing textual commands for the system. In the tradition of LCF, the proof language of Matita is procedural and relies on tactic and tacticals to proceed toward proof completion. The interaction paradigm offered to the user is based on the script management technique at the basis of the popularity of the Proof General generic interface for interactive theorem provers: while editing a script the user can move forth the execution point to deliver commands to the system, or back to retract (or “undo”) past commands. Matita has been developed from scratch in the past 8 years by several members of the Helm research group, this thesis author is one of such members. Matita is now a full-fledged proof assistant with a library of about 1.000 concepts. Several innovative solutions spun-off from this development effort. This thesis is about the design and implementation of some of those solutions, in particular those relevant for the topic of user interaction with theorem provers, and of which this thesis author was a major contributor. Joint work with other members of the research group is pointed out where needed. The main topics discussed in this thesis are briefly summarized below. Disambiguation. Most activities connected with interactive proving require the user to input mathematical formulae. Being mathematical notation ambiguous, parsing formulae typeset as mathematicians like to write down on paper is a challenging task; a challenge neglected by several theorem provers which usually prefer to fix an unambiguous input syntax. Exploiting features of the underlying calculus, Matita offers an efficient disambiguation engine which permit to type formulae in the familiar mathematical notation. Step-by-step tacticals. Tacticals are higher-order constructs used in proof scripts to combine tactics together. With tacticals scripts can be made shorter, readable, and more resilient to changes. Unfortunately they are de facto incompatible with state-of-the-art user interfaces based on script management. Such interfaces indeed do not permit to position the execution point inside complex tacticals, thus introducing a trade-off between the usefulness of structuring scripts and a tedious big step execution behavior during script replaying. In Matita we break this trade-off with tinycals: an alternative to a subset of LCF tacticals which can be evaluated in a more fine-grained manner. Extensible yet meaningful notation. Proof assistant users often face the need of creating new mathematical notation in order to ease the use of new concepts. The framework used in Matita for dealing with extensible notation both accounts for high quality bidimensional rendering of formulae (with the expressivity of MathMLPresentation) and provides meaningful notation, where presentational fragments are kept synchronized with semantic representation of terms. Using our approach interoperability with other systems can be achieved at the content level, and direct manipulation of formulae acting on their rendered forms is possible too. Publish/subscribe hints. Automation plays an important role in interactive proving as users like to delegate tedious proving sub-tasks to decision procedures or external reasoners. Exploiting the Web-friendliness of Matita we experimented with a broker and a network of web services (called tutors) which can try independently to complete open sub-goals of a proof, currently being authored in Matita. The user receives hints from the tutors on how to complete sub-goals and can interactively or automatically apply them to the current proof. Another innovative aspect of Matita, only marginally touched by this thesis, is the embedded content-based search engine Whelp which is exploited to various ends, from automatic theorem proving to avoiding duplicate work for the user. We also discuss the (potential) reusability in other systems of the widgets presented in this thesis and how we envisage the evolution of user interfaces for interactive theorem provers in the Web 2.0 era.

Enabling computationally intensive bioinformatics applications on the Grid platform

Bioinformatics is a recent and emerging discipline which aims at studying biological problems through computational approaches. Most branches of bioinformatics such as Genomics, Proteomics and Molecular Dynamics are particularly computationally intensive, requiring huge amount of computational resources for running algorithms of everincreasing complexity over data of everincreasing size. In the search for computational power, the EGEE Grid platform, world's largest community of interconnected clusters load balanced as a whole, seems particularly promising and is considered the new hope for satisfying the everincreasing computational requirements of bioinformatics, as well as physics and other computational sciences. The EGEE platform, however, is rather new and not yet free of problems. In addition, specific requirements of bioinformatics need to be addressed in order to use this new platform effectively for bioinformatics tasks. In my three years' Ph.D. work I addressed numerous aspects of this Grid platform, with particular attention to those needed by the bioinformatics domain. I hence created three major frameworks, Vnas, GridDBManager and SETest, plus an additional smaller standalone solution, to enhance the support for bioinformatics applications in the Grid environment and to reduce the effort needed to create new applications, additionally addressing numerous existing Grid issues and performing a series of optimizations. The Vnas framework is an advanced system for the submission and monitoring of Grid jobs that provides an abstraction with reliability over the Grid platform. In addition, Vnas greatly simplifies the development of new Grid applications by providing a callback system to simplify the creation of arbitrarily complex multistage computational pipelines and provides an abstracted virtual sandbox which bypasses Grid limitations. Vnas also reduces the usage of Grid bandwidth and storage resources by transparently detecting equality of virtual sandbox files based on content, across different submissions, even when performed by different users. BGBlast, evolution of the earlier project GridBlast, now provides a Grid Database Manager (GridDBManager) component for managing and automatically updating biological flatfile databases in the Grid environment. GridDBManager sports very novel features such as an adaptive replication algorithm that constantly optimizes the number of replicas of the managed databases in the Grid environment, balancing between response times (performances) and storage costs according to a programmed cost formula. GridDBManager also provides a very optimized automated management for older versions of the databases based on reverse delta files, which reduces the storage costs required to keep such older versions available in the Grid environment by two orders of magnitude. The SETest framework provides a way to the user to test and regressiontest Python applications completely scattered with side effects (this is a common case with Grid computational pipelines), which could not easily be tested using the more standard methods of unit testing or test cases. The technique is based on a new concept of datasets containing invocations and results of filtered calls. The framework hence significantly accelerates the development of new applications and computational pipelines for the Grid environment, and the efforts required for maintenance. An analysis of the impact of these solutions will be provided in this thesis. This Ph.D. work originated various publications in journals and conference proceedings as reported in the Appendix. Also, I orally presented my work at numerous international conferences related to Grid and bioinformatics.