arXiv subjects

Herman Geuvers

Publications and source records attributed to Herman Geuvers.

23 records · Page 2Linked to original sources

arXiv2011

Proceedings Sixth International Workshop on Logical Frameworks and Meta-languages: Theory and Practice

This volume constitutes the proceedings of LFMTP 2011, the Sixth International Workshop on Logical Frameworks and Meta-languages: Theory and Practice. The LFMTP workshop series brings together designers, implementors, and practitioners to discuss varied aspects of the structure of logical frameworks and meta-languages that impinge on their use in representing, implementing, and reasoning about a wide variety of deductive systems of interest in logic and computer science. LFMTP 2011 was held on August 26, 2011 in Nijmegen, Netherlands, as a workshop associated with ITP 2011, the Second International Conference on Interactive Theorem Proving. Its program consisted of contributed and invited presentations and was integrated with that of MLPA 11, the Third Workshop on Modules and Libraries for Proof Assistants. This proceedings contains only the contributed papers that were accepted for presentation at the workshop. Each of these papers was accepted based on the reviews of three members of the program committee. Authors were subsequently given the opportunity to revise their submissions based on the comments provided by the reviewers and the feedback obtained during their presentations at the workshop.

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arXiv2010

Pure Type Systems without Explicit Contexts

We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free and bound variables even in pseudo-terms. Specifically we give the rules of the "Pure Type System" class of type theories in this style. We prove that the typing judgments of these systems correspond in a natural way with those of Pure Type Systems as traditionally formulated. I.e., our systems have exactly the same well-typed terms as traditional presentations of type theory. Our system can be seen as a type theory in which all type judgments share an identical, infinite, typing context that has infinitely many variables for each possible type. For this reason we call our system "Gamma_infinity". This name means to suggest that our type judgment "A : B" should be read as "Gamma_infinity |- A : B", with a fixed infinite type context called "Gamma_infinity".

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arXiv2010

A Wiki for Mizar: Motivation, Considerations, and Initial Prototype

Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe a preliminary system for such collaborative development based on the Git DVCS. We focus, initially, on the Mizar system and its library of formalized mathematics.

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arXiv2010

Proviola: A Tool for Proof Re-animation

To improve on existing models of interaction with a proof assistant (PA), in particular for storage and replay of proofs, we in- troduce three related concepts, those of: a proof movie, consisting of frames which record both user input and the corresponding PA response; a camera, which films a user's interactive session with a PA as a movie; and a proviola, which replays a movie frame-by-frame to a third party. In this paper we describe the movie data structure and we discuss a proto- type implementation of the camera and proviola based on the ProofWeb system. ProofWeb uncouples the interaction with a PA via a web- interface (the client) from the actual PA that resides on the server. Our camera films a movie by "listening" to the ProofWeb communication. The first reason for developing movies is to uncouple the reviewing of a formal proof from the PA used to develop it: the movie concept enables users to discuss small code fragments without the need to install the PA or to load a whole library into it. Other advantages include the possibility to develop a separate com- mentary track to discuss or explain the PA interaction. We assert that a combined camera+proviola provides a generic layer between a client (user) and a server (PA). Finally we claim that movies are the right type of data to be stored in an encyclopedia of formalized mathematics, based on our experience in filming the Coq standard library.

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arXiv2009

Degrees of Undecidability in Rewriting

Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of undecidability, starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy, where also quantification over function variables is allowed. In this paper we consider properties of first order term rewriting systems and classify them in this hierarchy. Weak and strong normalization for single terms turn out to be Sigma-0-1-complete, while their uniform versions as well as dependency pair problems with minimality flag are Pi-0-2-complete. We find that confluence is Pi-0-2-complete both for single terms and uniform. Unexpectedly weak confluence for ground terms turns out to be harder than weak confluence for open terms. The former property is Pi-0-2-complete while the latter is Sigma-0-1-complete (and thereby recursively enumerable). The most surprising result is on dependency pair problems without minimality flag: we prove this to be Pi-1-1-complete, which means that this property exceeds the arithmetical hierarchy and is essentially analytic.

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