## Knowledge Management of Formal Mathematics and Interactive Theorem Proving (2004)

Citations: | 3 - 1 self |

### BibTeX

@TECHREPORT{Coen04knowledgemanagement,

author = {Claudio Sacerdoti Coen},

title = {Knowledge Management of Formal Mathematics and Interactive Theorem Proving},

institution = {},

year = {2004}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

398 | Safe Kernel Extensions without Run-Time Checking
- Necula, Lee
- 2004
(Show Context)
Citation Context ...rms, making also the third characteristic of low-quality terms a critical issue. A totally different scenario in which term size and retyping time are critical is the one introduced by Necula and Lee =-=[93]-=- under the name Proof Carrying Code (PCC). PCC is a technique that can be used for safe execution of untrusted code. In a typical instance of PCC, a code receiver establishes a set of safety rules tha... |

154 |
de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the church-rosser theorem
- G
- 1972
(Show Context)
Citation Context ...q Implementation Details As for the most part of the systems based on the Curry-Howard isomorphism and developed after Automath [95], bound variables are internally represented as de Brujin's indexes =-=[91]-=-. In Coq de Brujin's indexes are also exploited for bound constants, such as mutual references between the entities mutually defined inside a single block. For instance, the internal representation of... |

72 | Grammatical Framework: A Type-Theoretical Grammar Formalism
- Ranta
- 2004
(Show Context)
Citation Context ...s heavily based on the refinement procedure, and represents a major improvement with respect to the traditional algorithm adopted for ambiguous parsing (e.g. the one used in the Grammatical Framework =-=[105]-=-). The idea underlying the algorithm, however, is quite simple: we can use refinement to prune not well-typed terms even before the parsing phase is completed. Thus the search space explored by the di... |

60 | Efficient representation and validation of proofs
- Necula, Lee
- 1998
(Show Context)
Citation Context ...terms that enter the environment are improved. While Coq adopts the approach of avoiding implicits118 Chapter 8. The Calculus of (Co)Inductive Constructions arguments in the kernel, Necula and Lee in =-=[94]-=- follow the alternative approach9. The results that they obtain are quite impressive: both the size of the proofs and their type-checking time are in O(n0.62) where n is the value obtained before intr... |

58 |
Une Théorie des Constructions Inductives
- Werner
- 1994
(Show Context)
Citation Context ...e exists no single paper were it is possible to find the syntax, reduction and typing rules of the whole calculus, as implemented in Coq. The three most relevant works are Werner's Ph.D. dissertation =-=[118]-=-, which proves the logical consistency of the original version of CIC, the paper of Gimenez [52] that introduces case analysis and (co)recursive definitions, and the habilitation dissertation [99] of ... |

55 | G.: Real Theorem Provers Deserve Real UserInterfaces
- Théry, Bertot, et al.
- 1992
(Show Context)
Citation Context ...st replay the script using Coq itself, or it must (dynamically) augment it with informations obtained by the execution in Coq to be able to use an external tool such as PCoq or CtCoq to understand it =-=[115, 21, 20]-=-. All the systems based on scripts were born as application centric systems. Recently, though, there has been a number of proposals [117, 121, 16, 59] to adopt a verbose set of tactics, similar to the... |

25 | Some points in formal topology
- Sambin
(Show Context)
Citation Context ... definition, leading to a much richer theory. An example is given by (constructive) formal topology: whereas in classical topology closed sets can be defined in terms of open sets, in formal topology =-=[112]-=- they must be defined independently (even if duality plays an important role). Another difference induced from the choice of a constructive logic is the difference between decidable and undecidable pr... |

22 | Formal Proof Sketches
- Wiedijk
- 2004
(Show Context)
Citation Context ...n external tool such as PCoq or CtCoq to understand it [115, 21, 20]. All the systems based on scripts were born as application centric systems. Recently, though, there has been a number of proposals =-=[117, 121, 16, 59]-=- to adopt a verbose set of tactics, similar to the commands of the Mizar tool, that completely describe the steps that the system will take. The system limits itself to checking the correctness of the... |

16 | A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory
- Muñoz
- 1997
(Show Context)
Citation Context ...Thus an incomplete, partially correct proof must be a well-typed lambda-term with holes therein. To extend the notion of well-typing to terms with holes, a hole (called metavariable in the literature =-=[90]-=-) cannot simply be a missing term, but must be associated to a sequent. So a metavariable has a given type and a typed context. The two main operations on metavariables are instantiation and restricti... |

14 |
Définitions Inductives en Théorie des Types d’Ordre Supérieur. Habilitation à diriger les recherches
- Paulin-Mohring
- 1996
(Show Context)
Citation Context ...on [118], which proves the logical consistency of the original version of CIC, the paper of Gimenez [52] that introduces case analysis and (co)recursive definitions, and the habilitation dissertation =-=[99]-=- of Christine Paulin-Mohring that reviews the rules related to mutual inductive and coinductive definitions. The recent Ph.D. dissertation of Alexandre Miquel [84] is also very interesting, since it i... |

12 | Sets in types, types in sets - Werner - 1997 |

11 |
Construction and Deduction in Type Theories
- Strecker
- 1998
(Show Context)
Citation Context ...hieve all the previous goals, the proof assistants and theorem provers developers have designed systems of open terms. For instance, there exists systems of open terms for dependently typed *-calculi =-=[66, 78, 82, 114]-=-. A recent work [51] of Geuvers and Jojgov describes a logic of open proofs and open terms out of a type-system of open terms. The translation between the two systems is also yet another application o... |

10 | The Not So Simple Proof-Irrelevant Model of CC
- Miquel, Werner
- 2002
(Show Context)
Citation Context ...n S. Variable A : Prop. Variable B : Prop. Theorem AB_A_B : (A -> B) -> A -> B. Proof. 10To have complete proof-irrelevance, any two terms inhabiting the same type of sort Prop should be convertible. =-=[85]-=- is a preliminary proposal to provide a proof-irrelevant version of CIC11The restriction is unrelated to the consistency of the system. Indeed it is still possible for the user to add some code outsid... |

5 | MathML Formatting
- Padovani
(Show Context)
Citation Context ... browses the HELM Web interface [63].sChapter 7. Requirements and Architecture 97 The gtkmathview library is an OCaml binding of the GtkMathView Gtk widget for rendering MathML Presentation documents =-=[98]-=-. The widget also allows semantic (multiple) selection, that is the possibility of constraining the user to select only subexpressions that correspond to wellformed CIC subterms. Finally, the library ... |

3 | Towards a Semantic Web for Formal Mathematics
- Schena
- 2002
(Show Context)
Citation Context ...apter. The aim is not to provide a detailed description (that can be found in the MoWGLI technical reports and in several papers, Ph.D. dissertations and Master dissertations of the HELM team members =-=[113, 88, 62]-=-). Our goal is just to give an idea of the state of the art of the technology available for the implementation of the proof assistant prototype that is the main topic of this dissertation. 3.1 Levels ... |

3 | A new implementation of Automath
- Wiedijk
(Show Context)
Citation Context ...nger available in any exploitable form for several years. Only in 2002 the formalization was retrieved and made live again by Wiedijk, that reimplemented from scratch a version of the Automath system =-=[120]-=-. 2. Encoding of the information in machine readable formats. Digital documents can be accessible at very different levels. The less interesting one is the presentation level, where only the notation ... |

2 |
Conception et r'ealisation d'outils d'aide au d'eveloppement de grosse th'eories dans les syst`emes de preuve interactifs. Th`ese de Doctorat, Conservatoire National des Arts et M'etiers
- Pons
- 1999
(Show Context)
Citation Context ...ctics and locally undo the generated parts of the proof that can be improved by hand. Moreover, we can also implement additional operations on the proof object, similar to those presented in [82] and =-=[102]-=-, to rearrange the proof by applying commuting conversions to some parts of the proof, or by "taking out" and making lemmas of interesting subproofs. All these operations can be implemented more or le... |

2 |
Tactics in modern proof-assistants: The bad habit of overkilling
- Coen
- 2001
(Show Context)
Citation Context ...where we improved a tactic implementation to make it less overkilling without breaking backward compatibility. Even though these sections are logically stand-alone (it describes material presented in =-=[108]-=-), we prefer to put them before the description of the implemented tactics since they provides a good vocabulary and some insights to understand both the typical tactics implementation difficulties an... |

2 | Brokers and Web-services for automatic deduction: a case study
- Coen, Zacchiroli
(Show Context)
Citation Context ...quality of the generated terms. Chap. 12 briefly describes the interface of GTOPLEVEL, which is obtained by combining together several of the components developed in the first part of this thesis. In =-=[111]-=- an interesting extension of GTOPLEVEL is described: GTOPLEVEL is interfaced with H-BUGS, a network of distributed agents (called tutors) that try to automatically advance in the current proof, propos... |

1 |
MathML rendering/browsing engine
- Naciri, Padovani
- 2003
(Show Context)
Citation Context ...current goal" and "a subterm of the current sequent" means a physical pointer to a subterm of the current value. In our implementation, the physical pointer is generated by means of semantic selection=-=[92]-=-: the graphical user interface allows to highlight using the mouse only subexpressions that correspond to valid subterms; the selection associated to the highlighted expression is a physical pointer t... |

1 |
report: Building interactive digital libraries of formal algorithmic knowledge
- Progress
- 2002
(Show Context)
Citation Context ...nfirming the liveliness of the field. At the same time several projects related to MKM have also started in the USA, and cooperations with the European counterparts are envisioned (see, for instance, =-=[103]-=- and the proceedings of the forthcoming Second North American Workshop on Mathematical Knowledge Management1). The author of this dissertation has actively participated in both the MoWGLI and MKM-Net ... |

1 |
Progettazione e realizzazione con tecnologia XML di basi distribuite di conoscenza matematica formalizzata
- Coen
- 2000
(Show Context)
Citation Context ...tigated, among others, in the HELM project (Hypertextual Electronic Library of Mathematics, [62]) in Bologna, of which I have been a member almost since its birth. The topic of my Master Dissertation =-=[107]-=- has been the development of several prototypes of tools and libraries for MKM. After completion of my master dissertation, all the prototypes have been refined and turned into stable libraries and We... |

1 | A constructive proof of the soundness of the encoding of random access machines in a linda calculus with ordered semantics
- Coen
- 2003
(Show Context)
Citation Context ...hat holds about 40.000 theorems. The queries were not artificial: one of the authors used the query engine in order to retrieve some useful lemmas while developing a new medium-sized Coq contribution =-=[109]-=-. Even for queries involving only frequently used notions (e.g. algebraic operations), the accuracy of the filtering phase was always very high: the number of uninteresting false matches was very low ... |

1 |
Version 1.0. W3C Recommendation, 16 November 1999, http://www.w3.org/TR/xslt. References 301 [124] Stefano Zacchiroli. Web services per il supporto alla dimostrazione interattiva
- Transformations
- 2003
(Show Context)
Citation Context ...pted for a distributed library of mathematical knowledge. The library is constituted of both data (in XML format [43]), metadata (in RDF [106]) and programs that describe XML transformations (in XslT =-=[123]-=-). The preliminary requirements that motivated this choice will not be explained in this dissertation. The interested reader can find them in [10]. The adoption of a distribution model based on a dist... |

1 | The proof-assistant yarrow
- Zwanenburg
- 1998
(Show Context)
Citation Context ...ations of large programs). * We are not developing a proof assistant to experiment with more than one logic (as the Isabelle generic proof assistant or, to a lesser extent, the Yarrow proof assistant =-=[125]-=-). As a consequence the architectural choices have been similar to those of the "traditional" proof assistants based on the Curry-Howard isomorphism (e.g. Coq and NuPrL) instead of those of the generi... |