The computer modelling of mathematical reasoning
The computer modelling of mathematical reasoning
The use of machines to assist in rigorous proof
Proc. of a discussion meeting of the Royal Society of London on Mathematical logic and programming languages
Writing programs that construct proofs
Journal of Automated Reasoning
Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Formalized Metareasoning in Type Theory
Formalized Metareasoning in Type Theory
A paradigm for reasoning by analogy
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
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A method is presented to express and use syntactic analogies between proofs in interactive theorem proving and proof checking. Up to now, very few papers have addressed instances of this problem. The paradigm of "proposition as types" is adopted and proofs are represented as terms. The proposed method is to transform a known proof of a theorem into what might become a proof of an "analogous" --according to the user-- proposition, namely the one to be proved. This transformation is expressed by means of second order pattern matching (this may be seen as a generalisation of rewriting rules), thus allowing the use of variable function symbols. For the moment, it is up to the user to discover the transformation rule, and the paper deals only with the problem of managing it. We explain the proposed analogy treatment with a fully developed running example.