The Design and Implementation of an Interactive Proof Editor

Brian Ritchie

Abstract: This thesis describes the design and implementation of the IPE, an interactive proof editor for first-order intuitionistic predicate calculus, developed at the University of Edinburgh during 1983-1986, by the author together with John Cartmell and Tatsuya Hagino. The IPE uses an attribute grammar to maintain the state of its proof tree as a context-sensitive structure. The interface allows free movement through the proof structure, and encourages a ``proof-by-experimentation'' approach, since no proof step is irrevocable.

We describe how the IPE's proof rules can be derived from natural deduction rules for first-order intuitionistic logic, how these proof rules are encoded as an attribute grammar, and how the interface is constructed on top of the grammar. Further facilities for the manipulation of the IPE's proof structures are presented, including a notion of IPE-tactic for their automatic construction.

We also describe an extension fo the IPE to enable the construction and use of simply-structured collections of axioms and results, the main provision here being an interactive ``theory browser'' which looks for facts which match a selected problem.

Ph.D thesis - price £7.00

LFCS report ECS-LFCS-88-68 (also published as CST-57-88)

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