Abstract
Alf is an interactive proof editor. It is based on the idea that to prove a mathematical theorem is to build a proof object for the theorem. The proof object is directly manipulated on the screen, different manipulations correspond to different steps in the proof. The language we use is Martin-Löf's monomorphic type theory. This is a small functional programming language with dependent types. The language is open in the sense that it is easy to introduce new inductively defined sets. A proof is represented as a mathematical object and a proposition is identified with the set of its proof objects. The basic part of the proof editor can be seen as a proof engine with two basic commands, one which builds an object by replacing a placeholder in an object by a new object, and another one which deletes a part of an object by replacing a sub-object by a placeholder. We show that the validity of the incomplete object is preserved by admissible insertions and deletions.
This research has been done within the ESPRIT Basic Research Action “Types for Proofs and Programs”. It has been paid by NUTEK, Chalmers and the University of Göteborg.
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© 1994 Springer-Verlag Berlin Heidelberg
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Magnusson, L., Nordström, B. (1994). The Alf proof editor and its proof engine. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_78
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DOI: https://doi.org/10.1007/3-540-58085-9_78
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