Claudio Sacerdoti Coen

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The paper describes the general philosophy and the main architectural and technological solutions adopted in the HELM Project for the management of large repositories of mathematical knowledge. The leitmotiv is the extensive use of XML technology, and the exploitation of information in the “Web way”, that is without a central authority, with few basic(More)
Matita is a new, document-centric, tactic-based interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, characterized mostly by the organization of the library as a searchable knowledge base, the emphasis on a high-quality notational rendering, and the complex interplay between syntax,(More)
Most of the state-of-the-art proof assistants are based on procedural proof languages, scripts, and rely on LCF tacticals as the primary tool for tactics composition. In this paper we discuss how these ingredients do not interact well with user interfaces based on the same interaction paradigm of Proof General (the de facto standard in this field),(More)
The prototype of a content based search engine for mathematical knowledge supporting a small set of queries requiring matching and/or typing operations is described. The prototype — called Whelp — exploits a metadata approach for indexing the information that looks far more flexible than traditional indexing techniques for structured expressions like(More)
Proof assistants are complex applications whose development has never been properly systematized or documented. This work is a contribution in this direction, based on our experience with the development of Matita: a new interactive theorem prover based—as Coq—on the Calculus of Inductive Constructions (CIC). In particular, we analyze its architecture(More)
The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms(More)
In the past few years, a number of constraint languages for XML documents has been proposed. They are cumulatively called <i>schema languages</i> or validation languages and they comprise, among others, DTD, XML Schema, RELAX NG, Schematron, DSD, xlinkit. One major point of discrimination among schema languages is the support of co-constraints, or(More)
The λ̄μμ̃-calculus, introduced by Curien and Herbelin, is a calculus isomorphic to (a variant of) the classical sequent calculus LK of Gentzen. As a proof format it has very remarkable properties that we plan to study in future works. In this paper we embed it with a rendering semantics that provides explanations in pseudo-natural language of its proof(More)