## Generalization and Reuse of Tactic Proofs (0)

Venue: | In Proc. Int. Conf. Logic Programming and Automated Reasoning (LPAR |

Citations: | 12 - 0 self |

### BibTeX

@INPROCEEDINGS{Felty_generalizationand,

author = {Amy Felty and Douglas Howe},

title = {Generalization and Reuse of Tactic Proofs},

booktitle = {In Proc. Int. Conf. Logic Programming and Automated Reasoning (LPAR},

year = {},

pages = {1--15},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

A tactic proof is a tree-structured sequent proof where steps may be justified by tactic programs. We describe a prototype of a generic interactive theorem-proving system that supports the construction and manipulation of tactic proofs containing metavariables. The emphasis is on proof reuse. Examples of proof reuse are proof by analogy and reconstruction of partial proofs as part of recovering from errors in definitions or in proof strategies. Our reuse operations involve solving higherorder unification problems, and their effectiveness relies on a proof-generalization step that is done after a tactic is applied. The prototype is implemented in Prolog.

### Citations

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- Harper, Honsel, et al.
- 1987
(Show Context)
Citation Context ...ort for metavariables, variable-binding and backtracking. The design of our system is generic, in the sense that it can easily accommodate most logics that can be specified in the general style of LF =-=[5]-=-. The exact style of encoding of logics in our system is very similar to [3], except that we have made a commitment to sequent-calculus presentations. The next section describes the structure of proof... |

384 | Uniform proofs as a foundation for logic programming
- Miller, Nadathur, et al.
- 1991
(Show Context)
Citation Context ...tem includes a command interface for building and viewing tactic proofs. We have also implemented a reuse command that attempts to reuse a proof when the statement of the root goal is changed. Prolog =-=[9]-=- is both the implementation language and the tactic programming language in our system. Using ML as an implementation language would give us a greater degree of control over unification and metavariab... |

187 |
Isabelle: The next 700 theorem provers
- Paulson
- 1990
(Show Context)
Citation Context ...erforming proof generalization, making use of metavariables in proofs. Inference rules of the logic are implemented as schemas with metavariables in a manner very similar to what is found in Isabelle =-=[10]. A r-=-ule schema justifies any inference which can be obtained by instantiating metavariables in the schema. When a tactic produces a proof using these rule schemas, we can generalize to find a "minima... |

106 |
et al. Implementing Mathematics with the NUPRL Development System
- Constable
- 1986
(Show Context)
Citation Context ... may be justified by tactics tactic proofs. If we also require that g be identical to the conclusion g 0 of the inference justified by a tactic, then this proof structure is the same as that of Nuprl =-=[1]-=-. We do not make this restriction because it is incompatible with the use of metavariables in proofs. The focus of this paper is the reuse of tactic proofs. One obvious example of proof reuse is proof... |

67 | Implementing tactics and tacticals in a higher-order logic programming language
- Felty
- 1993
(Show Context)
Citation Context ...system is generic, in the sense that it can easily accommodate most logics that can be specified in the general style of LF [5]. The exact style of encoding of logics in our system is very similar to =-=[3]-=-, except that we have made a commitment to sequent-calculus presentations. The next section describes the structure of proofs in our system and gives a somewhat abstract account of proof generalizatio... |

36 |
G.: The COQ Proof Assistant Userâ€™s Guide
- Dowek, Felty, et al.
- 1993
(Show Context)
Citation Context ...ation can be added to this collection. To do so, additional data must be stored in tactic justifications and reuse must be modified to update this data as it builds a new proof. Isabelle [10] and Coq =-=[2]-=- have metavariables and support tactic-style theoremproving, but refinement trees are implicit, and operations on these trees are limited. This also applies to KIV [6], even though it explicitly suppo... |

31 |
Tactical theorem proving in program verification
- Heisel, Reif, et al.
- 1990
(Show Context)
Citation Context ...new proof. Isabelle [10] and Coq [2] have metavariables and support tactic-style theoremproving, but refinement trees are implicit, and operations on these trees are limited. This also applies to KIV =-=[6]-=-, even though it explicitly supports a form of refinement trees. In contrast to ALF [8] and Coq, our system only supports simple types for metavariables. If the object logic has a richer type system, ... |

7 | and D.Howe. Tactic theorem proving with refinement-tree proofs and metavariables
- Felty
- 1994
(Show Context)
Citation Context ... 2 T such that e produces an output on input g, there is a justificationsj e;g . Let p be the proof returned by e on input g. One possibility for s(j e;g ) is to take the conclusion and premises of p =-=[4]-=-. Since proofs are closed under instantiation, any instance of this step is sound. However, this is restrictive. If there is a proof p 0 of which p is an instance, then the step derived from p 0 is al... |

5 | The NurPRL Proof Development System - Horn - 1988 |

2 |
Refinement and local undo in the interactive proof editor ALF
- Magnussan
- 1993
(Show Context)
Citation Context ...mproving, but refinement trees are implicit, and operations on these trees are limited. This also applies to KIV [6], even though it explicitly supports a form of refinement trees. In contrast to ALF =-=[8]-=- and Coq, our system only supports simple types for metavariables. If the object logic has a richer type system, then types must be represented explicitly, for example as predicates in the object logi... |