## The Ergo 5 Generic Proof Engine (1997)

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Utting97theergo,

author = {Mark Utting},

title = {The Ergo 5 Generic Proof Engine},

institution = {},

year = {1997}

}

### OpenURL

### Abstract

This paper describes the design principles and the architecture of the latest version of the Ergo proof engine, Ergo 5. Ergo 5 is a generic interactive theorem prover, similar to Isabelle, but based on sequent calculus rather than natural deduction and with a quite different approach to handling variable scoping. An efficient implementation of Ergo 5, based on Qu-Prolog, is also described, together with some benchmark results.

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Citation Context ...s by giving schemas a semantic model in a ZFC theory based on classical predicate calculus, whereas the program refinement tool project [CHN + 96b] uses a modal logic to model the refinement calculus =-=[Mor94]-=-. Ergo 5 is the latest in a series of proof tools designed to fulfill these reasoning requirements. Our design goals included the following. 1. Provide a generic interactive proof tool that supports a... |

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Citation Context ... ask, why build yet another interactive proof tool? Why not use an existing tool? There are several excellent interactive theorem provers freely available, including Isabelle [Law94], HOL [GM93], PVS =-=[ORSvH95]-=-, Mural [JJLM91] and ACL2 [KM94]. The one that comes closest to meeting the above requirements is Isabelle. However, at the time that we started designing Ergo 5 (early 1995), Isabelle did not produce... |

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Citation Context ...propriate to ask, why build yet another interactive proof tool? Why not use an existing tool? There are several excellent interactive theorem provers freely available, including Isabelle [Law94], HOL =-=[GM93]-=-, PVS [ORSvH95], Mural [JJLM91] and ACL2 [KM94]. The one that comes closest to meeting the above requirements is Isabelle. However, at the time that we started designing Ergo 5 (early 1995), Isabelle ... |

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Citation Context ...ily handle different kinds of context, rather than just a single kind. For example, earlier versions of Ergo [UW94] support only implication assumptions and the HOL implementation of window inference =-=[Gru91]-=- supports only derivability assumptions. That is, the window (Context ; Focus ; Reln; Goal) represents Context ) (Focus Reln Goal) in Ergo 4, but Context ` (Focus Reln Goal) in the HOL implementation ... |

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Citation Context ...eory database, support for theory interpretation and instantiation [HNTU96, UNT96], details of the textual and graphical user interfaces and the tactic language for proof construction (based on ANGEL =-=[MGW96]-=-), are beyond the scope of this paper. 2 Ergo 5 Proof Engine Architecture The Ergo 5 architecture can be regarded as a development of the Isabelle theorem prover [Pau86]. Isabelle is a generic success... |

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Citation Context ...ffl We wanted sophisticated theory construction facilities, such as theory interpretation, separate name spaces and support for delayed proof of postulates. These facilities already existed in Ergo 4 =-=[HNTU96]-=-, so we wanted to reuse them. In fact, we were able to build Ergo 5 by simply slotting in a new proof engine, leaving most of the theory facilities of Ergo 4 unchanged. ffl We had experimented with bu... |

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1 |
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Citation Context ...tive proof tool? Why not use an existing tool? There are several excellent interactive theorem provers freely available, including Isabelle [Law94], HOL [GM93], PVS [ORSvH95], Mural [JJLM91] and ACL2 =-=[KM94]-=-. The one that comes closest to meeting the above requirements is Isabelle. However, at the time that we started designing Ergo 5 (early 1995), Isabelle did not produce explicit proof records, which w... |

1 |
with contributions by Tobias Nipkow. Isabelle: A Generic Theorem
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Citation Context ...o 5, it is appropriate to ask, why build yet another interactive proof tool? Why not use an existing tool? There are several excellent interactive theorem provers freely available, including Isabelle =-=[Law94]-=-, HOL [GM93], PVS [ORSvH95], Mural [JJLM91] and ACL2 [KM94]. The one that comes closest to meeting the above requirements is Isabelle. However, at the time that we started designing Ergo 5 (early 1995... |

1 |
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Citation Context ..., where correctly means that capture of variables free in T by bindings in B is avoided by suitable changes of bound variables. 21 ffl It provides a set of global variables called implicit parameters =-=[RNS98]-=-, with an assignment operation that is automatically undone on backtracking. These implicit parameters turn out to be ideal for representing the explicit proof trees of our architecture, as described ... |

1 |
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Citation Context ...au87]. Experience with Isabelle has demonstrated that it is sufficiently generic to model many different styles of reasoning, including natural deduction, sequent calculi [Law94] and window inference =-=[Sta95]-=-. One of the main advances made by Isabelle was its representation of inference rules as data, rather than as ML functions like the LCF provers. This gives more flexibility in the way that inference r... |

1 |
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Citation Context ...milton, New Zealand. Email: marku@cs.waikato.ac.nz 1 other kinds of proofs, such as allowing proofs to be displayed in various formats, transformed into tactics, edited and reused within other proofs =-=[Tra94]-=-. 3. Support for schematic proofs, with constraints on the schematic variables. For example, we want to be able to prove theorems like: (8 x (A ) B)) , (A ) (8 x B)) provided x not free in A 4. Suppor... |