## The Calculus of Constructions as a Framework for Proof Search with Set Variable Instantiation (2000)

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Citations: | 3 - 0 self |

### BibTeX

@MISC{Felty00thecalculus,

author = {Amy Felty},

title = {The Calculus of Constructions as a Framework for Proof Search with Set Variable Instantiation},

year = {2000}

}

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### Abstract

### Citations

884 |
A Formulation of the Simple Theory of Types
- Church
- 1940
(Show Context)
Citation Context ...tification. An important difference is that while in CC the type P can be an arbitrary CC type, in To appear in Theoretical Computer Science. higher-order logic (e:g:, Church's simple theory of types =-=[5]-=-) P must be a simple type. Although CC types include the types of the simply-typed -calculus, they also include much more. Formally establishing such correspondences provides a framework in which to s... |

720 | A framework for defining logics - Harper, Honsell, et al. - 1993 |

501 |
The calculus of constructions
- Coquand, Huet
- 1988
(Show Context)
Citation Context ...variety of interactive tactic-style theorem provers. For example, both HOL [14] and Isabelle [20] implement higher-order logic, while Coq [8] implements the Calculus of Constructions (CC) type theory =-=[7]-=- and Nuprl [6] implements Martin-Lof type theory [18]. Much work has been carried out in both kinds of systems on building tactics and automating proof search. However, little work has been done on pr... |

468 | The formulas-as-types notion of construction - Howard - 1980 |

437 | The Foundation of a Generic Theorem Prover - Paulson - 1989 |

387 | uniform proofs as a foundation for logic programming - Miller, Nadathur, et al. - 1991 |

358 | Intuitionistic Type Theory - Martin-Löf - 1984 |

103 | Higher-order unification via explicit substitutions - Dowek, Hardin, et al. - 2000 |

82 |
Constable et al., Implementing Mathematics with the NuPRL
- L
- 1986
(Show Context)
Citation Context ...eractive tactic-style theorem provers. For example, both HOL [14] and Isabelle [20] implement higher-order logic, while Coq [8] implements the Calculus of Constructions (CC) type theory [7] and Nuprl =-=[6]-=- implements Martin-Lof type theory [18]. Much work has been carried out in both kinds of systems on building tactics and automating proof search. However, little work has been done on providing the me... |

68 | Implementing tactics and tacticals in a higher-order logic programming language
- Felty
- 1993
(Show Context)
Citation Context ...corresponds fairly directly to a one-pass version of Bledsoe's procedure. We use a goal-directed tactic style framework where each of the search primitives of the procedure is implemented as a tactic =-=[12]-=-. The SetVar procedure as described here does not resolve all non-determinism in search. However, the set of tactics we have implemented can be combined fairly easily to obtain a procedure that can pr... |

66 |
Introduction to generalized type systems
- Barendregt
- 1992
(Show Context)
Citation Context ...tutions for set variables can be incorporated into a reformulation of the search procedure for CC given by Dowek [9, 10]. (Dowek's procedure actually operates on all type systems in Barendregt's cube =-=[2]-=-. We use only the restriction to CC.) In our formulation, we both adapt these techniques to the type theoretic setting as well as extend them to handle the extra expressivity of dependent types. To in... |

45 | The implementation of ALF - a proof editor based on Martin-Löf’s monomorhic type theory with explicit substitution - Magnusson - 1994 |

18 |
A Maximal Method for Set Variables in Automatic Theorem Proving
- Bledsoe
- 1979
(Show Context)
Citation Context ...a framework in which to study how theorem proving techniques designed for one kind of system can be applied to proof search in the other. In this paper we show how the techniques described in Bledsoe =-=[3]-=- for the automatic discovery of substitutions for set variables can be incorporated into a reformulation of the search procedure for CC given by Dowek [9, 10]. (Dowek's procedure actually operates on ... |

17 |
A complete proof synthesis method for the cube of type systems
- Dowek
- 1993
(Show Context)
Citation Context ... show how the techniques described in Bledsoe [3] for the automatic discovery of substitutions for set variables can be incorporated into a reformulation of the search procedure for CC given by Dowek =-=[9, 10]-=-. (Dowek's procedure actually operates on all type systems in Barendregt's cube [2]. We use only the restriction to CC.) In our formulation, we both adapt these techniques to the type theoretic settin... |

17 | Introduction to HOL:A Theorem Proving Environment for Higher-Order Logic - Gordon, Melham - 1993 |

17 | A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory - Muñoz - 1997 |

16 |
Demonstration Automatique dans le Calcul des Constructions
- Dowek
- 1991
(Show Context)
Citation Context ... show how the techniques described in Bledsoe [3] for the automatic discovery of substitutions for set variables can be incorporated into a reformulation of the search procedure for CC given by Dowek =-=[9, 10]-=-. (Dowek's procedure actually operates on all type systems in Barendregt's cube [2]. We use only the restriction to CC.) In our formulation, we both adapt these techniques to the type theoretic settin... |

10 | A uniform approach to type theory - Huet - 1990 |

9 |
Z-match: An Inference Rule for Incrementally Elaborating Set Instantiations
- Bailin, Barker-Plummer
- 1993
(Show Context)
Citation Context ..., however, relies heavily on resolution techniques which may be difficult to adapt to our setting. Another procedure for automating the instantiation of set variables is the Z-match inference rule in =-=[1]-=-, which should be possible to adapt to our setting fairly directly. In addition, many other theorem proving techniques in a variety of domains have been developed for both higher-order logic and highe... |

9 |
The Coq proof assistant reference manual
- Cornes, Courant, et al.
- 1996
(Show Context)
Citation Context ...gher-order type theories serve as the logical foundation of a variety of interactive tactic-style theorem provers. For example, both HOL [14] and Isabelle [20] implement higher-order logic, while Coq =-=[8]-=- implements the Calculus of Constructions (CC) type theory [7] and Nuprl [6] implements Martin-Lof type theory [18]. Much work has been carried out in both kinds of systems on building tactics and aut... |

4 | Encoding the calculus of constructions in a higher-order logic - Felty - 1993 |

2 | Proof search with set variable instantiation in the calculus of constructions
- Felty
- 1996
(Show Context)
Citation Context ...is simply a subset of this complete set of operations. In this way, we obtain a more practical procedure with fine-tuned control for better handling of our class of theorems. This paper extends Felty =-=[13]-=- in several ways. First, we separate the procedures SetVar and SetVar+. SetVar is more useful in practice because it eliminates the non-determinism that corresponds to enumerating types, while still h... |