Proof-relevant resolution : the foundations of constructive proof automation

Dependent type theory is an expressive programming language. This language allows to write programs that carry proofs of their properties. This in turn gives high confidence in such programs, making the software trustworthy. Yet, the trustworthiness comes for a price: type inference involves an increasing number of proof obligations. Automation of this process becomes necessary for any system with dependent types that aims to be usable in practice. At the same time, implementation of automation in a verified manner is prohibitively complex. Sometimes, external solvers are used to aid the automation. These solvers may be based on classical logic and may not be themselves verified, thus compromising the guarantees provided by constructive nature of type theory. In this thesis, we explore the idea of proof relevant resolution that allows automation of type inference in type theory in a verifiable and constructive manner, hence to restore the confidence in programs and the trustworthiness of software. Technical content of this thesis is threefold. First, we propose a novel framework for proof-relevant resolution. We take two constructive logics, Horn-clause and hereditary Harrop formulae logics as a starting point. We formulate the standard big-step operational semantics of these logics. We expose their Curry-Howard nature by treating formulae of these logics as types and proofs as terms thus developing a theory of proof-relevant resolution. We develop small-step operational semantics of proof-relevant resolution and prove it sound with respect to the big-step operational semantics. Secondly, we demonstrate our approach on an example of type inference in Logical Framework (LF). We translate a type-inference problem in LF into resolution in proof-relevant Horn-clause logic. Such resolution provides, besides an answer substitution to logic variables, a proof term that captures the resolution tree. We interpret the proof term as a derivation of well-formedness judgement of the object in the original problem. This allows for a straightforward implementation of type checking of the resolved solution since type checking is reduced to verifying the derivation captured by the proof term. The theoretical development is substantiated by an implementation. Finally, we demonstrate that our approach allows to reason about semantic properties of code. Type class resolution has been well-known to be a proof-relevant fragment of Horn-clause logic, and recently its coinductive extensions were introduced. In this thesis, we show that all of these extensions amalgamate with the theoretical framework we introduce. Our novel result here is exposing that the coinductive extensions are actually based on hereditary Harrop logic, rather than Horn-clause logic. We establish a number of soundness and completeness results for them. We also discuss soundness of program transformation that are allowed by proof-relevant presentation of type class resolution

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Políticas de Copyright de Publicações Científicas em Repositórios Institucionais: O Caso do INESC TEC

A progressiva transformação das práticas científicas, impulsionada pelo desenvolvimento das novas Tecnologias de Informação e Comunicação (TIC), têm possibilitado aumentar o acesso à informação, caminhando gradualmente para uma abertura do ciclo de pesquisa. Isto permitirá resolver a longo prazo uma adversidade que se tem colocado aos investigadores, que passa pela existência de barreiras que limitam as condições de acesso, sejam estas geográficas ou financeiras. Apesar da produção científica ser dominada, maioritariamente, por grandes editoras comerciais, estando sujeita às regras por estas impostas, o Movimento do Acesso Aberto cuja primeira declaração pública, a Declaração de Budapeste (BOAI), é de 2002, vem propor alterações significativas que beneficiam os autores e os leitores. Este Movimento vem a ganhar importância em Portugal desde 2003, com a constituição do primeiro repositório institucional a nível nacional. Os repositórios institucionais surgiram como uma ferramenta de divulgação da produção científica de uma instituição, com o intuito de permitir abrir aos resultados da investigação, quer antes da publicação e do próprio processo de arbitragem (preprint), quer depois (postprint), e, consequentemente, aumentar a visibilidade do trabalho desenvolvido por um investigador e a respetiva instituição. O estudo apresentado, que passou por uma análise das políticas de copyright das publicações científicas mais relevantes do INESC TEC, permitiu não só perceber que as editoras adotam cada vez mais políticas que possibilitam o auto-arquivo das publicações em repositórios institucionais, como também que existe todo um trabalho de sensibilização a percorrer, não só para os investigadores, como para a instituição e toda a sociedade. A produção de um conjunto de recomendações, que passam pela implementação de uma política institucional que incentive o auto-arquivo das publicações desenvolvidas no âmbito institucional no repositório, serve como mote para uma maior valorização da produção científica do INESC TEC.The progressive transformation of scientific practices, driven by the development of new Information and Communication Technologies (ICT), which made it possible to increase access to information, gradually moving towards an opening of the research cycle. This opening makes it possible to resolve, in the long term, the adversity that has been placed on researchers, which involves the existence of barriers that limit access conditions, whether geographical or financial. Although large commercial publishers predominantly dominate scientific production and subject it to the rules imposed by them, the Open Access movement whose first public declaration, the Budapest Declaration (BOAI), was in 2002, proposes significant changes that benefit the authors and the readers. This Movement has gained importance in Portugal since 2003, with the constitution of the first institutional repository at the national level. Institutional repositories have emerged as a tool for disseminating the scientific production of an institution to open the results of the research, both before publication and the preprint process and postprint, increase the visibility of work done by an investigator and his or her institution. The present study, which underwent an analysis of the copyright policies of INESC TEC most relevant scientific publications, allowed not only to realize that publishers are increasingly adopting policies that make it possible to self-archive publications in institutional repositories, all the work of raising awareness, not only for researchers but also for the institution and the whole society. The production of a set of recommendations, which go through the implementation of an institutional policy that encourages the self-archiving of the publications developed in the institutional scope in the repository, serves as a motto for a greater appreciation of the scientific production of INESC TEC

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019