Computer Science Department
School of Computer Science, Carnegie Mellon University


Efficient Representation and Validation of Logical Proofs

George C. Necula, Peter Lee

October 1997

Keywords: Proof representation, proof checking, logical frameworks, type reconstruction, predicate logic, explicit substitutions, unification, occurs-check optimization, proof-carrying code

This report describes a framework for representing and validating formal proofs in various axiomatic systems. The framework is based on the Edinburgh Logical Framework (LF) but is optimized for minimizing the size of proofs and the complexity of proof validation, by removing redundant representation components. Several variants of representation algorithms are presented with the resulting representations being a factor of 15 smaller than similar LF representations. The validation algorithm is a reconstruction algorithm that runs about 7 times faster than LF typechecking. We present a full proof of correctness of the reconstruction algorithm and hints for the efficient implementation using explicit substitutions. We conclude with a quantitative analysis of the algorithms.

72 pages

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