## Interactive Theorem Proving: An Empirical Study of User Activity (1995)

Venue: | Journal of Symbolic Computation |

Citations: | 13 - 3 self |

### BibTeX

@ARTICLE{Aitken95interactivetheorem,

author = {J. S. Aitken and P. Gray and T. Melham and M. Thomas},

title = {Interactive Theorem Proving: An Empirical Study of User Activity},

journal = {Journal of Symbolic Computation},

year = {1995},

volume = {25},

pages = {263--284}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper the interaction between users and the interactive theorem prover HOL is investigated from a human-computer interaction perspective. First, we outline three possible views of interaction, and give a brief survey of some current interfaces and how they may be described in terms of these views. Second, we describe and present the results of an empirical study of intermediate and expert HOL users. The results are analysed for evidence in support of the proposed view of proof activity in HOL. We believe that this approach provides a principled basis for the assessment and design of interfaces to theorem provers.

### Citations

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378 |
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(Show Context)
Citation Context ...ate 1970s by Robin Milner, means that theorems are represented by the values of an abstract data type in a strongly-typed functional programming language. In the case of HOL, this is the language ML (=-=Paulson, 1991-=-). Theorem proving in HOL takes place by executing ML functions that operate on theorems. These functions may be primitive inference rules or more complex, user-defined ML functions. In all cases, how... |

350 |
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(Show Context)
Citation Context ...ts of selection---choosing an operation to perform on the current goal. 3.3 Proof as structure editing Some logical formalisms include an object-language notion of proof. For example, in type theory (=-=Martin-Lof, 1984-=-) one has the `propositions-as-types' reading, in which one views a type A as a proposition and a well-typed term a :: A as a proof of A. Here, the logical term a is a formal proof object---a syntacti... |

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(Show Context)
Citation Context ...local context is defined by the current goal and the current assumptions and is a component of the abstract interaction level as illustrated in Figure 2. It is certainly the case that task structure (=-=Norman, 1988-=-), or logical, considerations also play a very important role in decision making. However, there is no means 3 In fact, the questionnaire also asked other questions, but these are of no relevance here... |

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(Show Context)
Citation Context ... tree is a natural representation of the decomposition of a goal into subgoals. In backwards proof, a proof tree shows what has been proven and what subgoals remain to be proven. It has been claimed (=-=Schubert and Biggs, 1994-=-) that such a display provides clues about the techniques and tactics that may be useful in completing the proof attempt. 10 Schubert and Biggs are concerned with the needs of large proof development ... |

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(Show Context)
Citation Context ...erence rules and may be able to solve any simple subgoals that arise. In tactic-based provers, proof by pointing is intended to free the user from having to edit commands during goal-directed proofs (=-=Bertot, 1994-=-). The user may then concentrate directly on the goals and theorems of the proof. The proof by pointing tool in the Coq theorem prover deals with the logical connectives ; ; oe; :; 8 and 9. If a subex... |

1 |
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(Show Context)
Citation Context ... proof construction and exploration consist in editing proof objects using a structure editor. One theorem-proving system that exemplifies the proof as structure editing view is the ALF proof editor (=-=Nordstrom, 1993-=-). In ALF, the process of proving a conjecture A consists in building a proof object for A. The proof state has two components: the goal A, together with an incomplete proof object that represents the... |

1 |
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(Show Context)
Citation Context ... levels of abstraction are necessary to characterise an interaction? This will depend upon the purpose and nature of the explanation or design rationals which the characterisation is used to support (=-=Pylyshn, 1986-=-). We have found that for a design-oriented description of user interfaces to theorem-provers it is sufficient to use three levels: A logical level. This is a description solely in terms of logical co... |

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