## Mathematics and Proof Presentation in Pcoq (2001)

Venue: | IN: PROCEEDINGS OF PROOF TRANSFORMATION AND PRESENTATION AND PROOF COMPLEXITIES (PTP’01 |

Citations: | 9 - 1 self |

### BibTeX

@INPROCEEDINGS{Amerkad01mathematicsand,

author = {Ahmed Amerkad and Yves Bertot and Loïc Pottier and Laurence Rideau},

title = {Mathematics and Proof Presentation in Pcoq},

booktitle = {IN: PROCEEDINGS OF PROOF TRANSFORMATION AND PRESENTATION AND PROOF COMPLEXITIES (PTP’01},

year = {2001},

publisher = {}

}

### OpenURL

### Abstract

PCOQ is the latest product in a decade-long effort to produce graphical user-interfaces for proof systems. It inherits many characteristics from the previous CTCOQ system...

### Citations

141 | Centaur: the system
- Borras, Clement, et al.
(Show Context)
Citation Context ...acteristics from the previous CtCoq system, that provided such a graphical user-interface based on the programming tools available in the generic interactive programming environment generator Centaur =-=[6]-=-. The new graphical interface is programmed in a dioeerent language, Java, and most of the design decisions that had been made for CtCoq have been re-considered. The CtCoq system advocated a few basic... |

97 |
The Coq proof assistant reference manual : Version 6.1
- Barras, Boutin, et al.
- 1997
(Show Context)
Citation Context ...d been made for CtCoq have been re-considered. The CtCoq system advocated a few basic principles, mainly described in [15, 4, 2]: the user-interface is a separate process from the logical engine, Coq =-=[1]-=-, the logical data in the user-interface is manipulated as structured, tree-like data, and the user-interface manipulates the sequence of commands sent to the logical engine as a complete document, th... |

96 |
The ALF proof editor and its proof engine
- Magnusson, Nordström
- 1994
(Show Context)
Citation Context ...ral deduction tree, as in Jape [5], or a tactic tree as in older experiments by T. GriOEn [8]. Other systems based on type theory also simply display the type-theoretic -term that describes the proof =-=[12]-=-. Type-theory can even be used to lead command parsing and displaying for the subset of natural language used in proofs, as in [9]. In our case, the data-structure used as a basis to produce the proof... |

56 | Real theorem provers deserve real user interfaces
- Thèry, Bertot, et al.
- 1992
(Show Context)
Citation Context ...programmed in a dioeerent language, Java, and most of the design decisions that had been made for CtCoq have been re-considered. The CtCoq system advocated a few basic principles, mainly described in =-=[15, 4, 2]-=-: the user-interface is a separate process from the logical engine, Coq [1], the logical data in the user-interface is manipulated as structured, tree-like data, and the user-interface manipulates the... |

43 | Proof by pointing
- Bertot, Kahn, et al.
- 1994
(Show Context)
Citation Context ... data, we have been able to instrument the proof development environment with capabilities that increase the bandwidth between the user and the logical engine. An example is that of Proof-by-pointing =-=[3]-=-, where complex commands can be constructed in one click by the user, through an analysis of the mouse position in the formula. Another capability that is instrumental in enhancing the bandwidth betwe... |

39 | Extracting text from proofs
- Coscoy, Kahn, et al.
- 1995
(Show Context)
Citation Context ...roofs, as in [9]. In our case, the data-structure used as a basis to produce the proof presentation is closer to a tactic tree. Still, we also benet from insights coming from earlier work in our team =-=[7]-=- where the primitive data-structure was directly the -term. This work also showed that it was relevant to use information from the tactic tree to get more concise proof presentations. In our case, the... |

32 | A generic approach to building user interfaces for theorem provers
- Bertot, Théry
- 1998
(Show Context)
Citation Context ...programmed in a dioeerent language, Java, and most of the design decisions that had been made for CtCoq have been re-considered. The CtCoq system advocated a few basic principles, mainly described in =-=[15, 4, 2]-=-: the user-interface is a separate process from the logical engine, Coq [1], the logical data in the user-interface is manipulated as structured, tree-like data, and the user-interface manipulates the... |

23 | An extensible proof text editor
- Hallgren, Ranta
- 2000
(Show Context)
Citation Context ...lso simply display the type-theoretic -term that describes the proof [12]. Type-theory can even be used to lead command parsing and displaying for the subset of natural language used in proofs, as in =-=[9]-=-. In our case, the data-structure used as a basis to produce the proof presentation is closer to a tactic tree. Still, we also benet from insights coming from earlier work in our team [7] where the pr... |

8 | The CtCoq system: Design and architecture
- Bertot
- 1999
(Show Context)
Citation Context ...programmed in a dioeerent language, Java, and most of the design decisions that had been made for CtCoq have been re-considered. The CtCoq system advocated a few basic principles, mainly described in =-=[15, 4, 2]-=-: the user-interface is a separate process from the logical engine, Coq [1], the logical data in the user-interface is manipulated as structured, tree-like data, and the user-interface manipulates the... |

4 |
Jape: a literal, lightweight, interactive proof assistant
- Bornat, Sufrin
- 1994
(Show Context)
Citation Context ...of display. 4 Conclusion The idea of organizing the interface for a theorem prover around the structure that describes the proof is not new. This structure may be a natural deduction tree, as in Jape =-=[5]-=-, or a tactic tree as in older experiments by T. GriOEn [8]. Other systems based on type theory also simply display the type-theoretic -term that describes the proof [12]. Type-theory can even be used... |

4 |
A certied version of Buchberger's algorithm
- Thry
- 1998
(Show Context)
Citation Context ...e problem very dioeerent than passive mathematical layout as in T E X[10]. The CtCoq proof development environment has been used intensively for a variety of ambitious, large-scale proof developments =-=[14, 11]-=-. The Pcoq environment is planned to replace it from the next version of Coq on. It is available on internet at address http://www-sop.inria.fr/lemme/pcoq and it has already been tested for teaching c... |

1 |
Notational denition and top-down renement for interactive proof development systems
- GriOEn
- 1988
(Show Context)
Citation Context ...ce for a theorem prover around the structure that describes the proof is not new. This structure may be a natural deduction tree, as in Jape [5], or a tactic tree as in older experiments by T. GriOEn =-=[8]-=-. Other systems based on type theory also simply display the type-theoretic -term that describes the proof [12]. Type-theory can even be used to lead command parsing and displaying for the subset of n... |

1 |
Formalizing St#lmarck's algorithm in Coq
- Letouzey, Thry
- 2000
(Show Context)
Citation Context ...e problem very dioeerent than passive mathematical layout as in T E X[10]. The CtCoq proof development environment has been used intensively for a variety of ambitious, large-scale proof developments =-=[14, 11]-=-. The Pcoq environment is planned to replace it from the next version of Coq on. It is available on internet at address http://www-sop.inria.fr/lemme/pcoq and it has already been tested for teaching c... |

1 |
AOEchage interactif, bidimensionnel et incr#mental de formules math#matiques
- Naciri, Rideau
(Show Context)
Citation Context ...cing the bandwidth between the user and the logical engine is the possibility to layout the mathematical formulas in a manner that is very close to the typesetting practice of mathematical literature =-=[13]-=-. Just increasing the readability of mathematical formulas speeds up the proving process in a signicant manner, especially for the kind of logical engine that we use, where interactive proof is prefer... |