Interactive Theorem Proving: An Empirical Study of User Activity

@article{Aitken1998InteractiveTP,
  title={Interactive Theorem Proving: An Empirical Study of User Activity},
  author={J. Stuart Aitken and Philip D. Gray and Thomas F. Melham and Muffy Calder},
  journal={J. Symb. Comput.},
  year={1998},
  volume={25},
  pages={263-284}
}
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… 

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References

SHOWING 1-10 OF 24 REFERENCES

Developing An Interface For HOL

  • Sara Kalvala
  • Computer Science
    1991., International Workshop on the HOL Theorem Proving System and Its Applications
  • 1991
TLDR
A set of tools designed at Cambridge for improving interaction with the HOL proof environment provide the same degree of transparency which allows close control of the proof environment-an aspect exploited by many users-while providing an easier interaction.

Proof by Pointing

TLDR
This principle provides a natural and effective use of the mouse in the user-interface of computer proof assistants and annotates the inference rules to specify an algorithm that associates the construction of a proof tree to a location within a goal sequent.

A Tree-based, Graphical Interface for Large Proof Development

TLDR
The centerpiece of xhol is a graphical display that depicts the entire active proof tree that presents not only a road map of what has and hasn't been proved, but also provides the user with clues about what techniques or tactics may be useful in proving the remaining unsolved subgoals.

A Parameterized Proof Manager

TLDR
A simple proof manager is described that derives a large measure of its power from being parameterized by structures that separately manage 1) proof-specific information and 2) the relationships between proofs.

Direct Manipulation Interfaces

TLDR
A cognitive account of both the advantages and disadvantages of direct manipulation interfaces is sought and two underlying phenomena that give rise to the feeling of directness of manipulation are identified.

Annotations in formal specifications and proofs

TLDR
This paper describes a system of annotations that can be used to incorporate informal semantic information concerning the domain being reasoned about into a formal proof environment, in such a way as to guide proof development and provide proof explanation.

A Virtual Protocol Model for Computer-Human Interaction

The ALF Proof Editor and Its Proof Engine

TLDR
Alf is an interactive proof editor based on the idea that to prove a mathematical theorem is to build a proof object for the theorem, and it is shown that the validity of the incomplete object is preserved by admissible insertions and deletions.

Real theorem provers deserve real user-interfaces

This paper explains how to add a modern user interface to existing theorem provers, using principles and tools designed for programming environments.

Introduction to HOL: a theorem proving environment for higher order logic

TLDR
A tutorial on goal-directed proof: tactics and tacticals and theorem-Proving With HOL, a simple proof tool for goal-oriented proof of the binomial theorem.