Verifying the Unification Algorithm in LCF
Abstract
Manna and Waldinger's theory of substitutions and unification has been verified using the Cambridge LCF theorem prover. A proof of the monotonicity of substitution is presented in detail, as an example of interaction with LCF. Translating the theory into LCF's domain-theoretic logic is largely straightforward. Well-founded induction on a complex ordering is translated into nested structural inductions. Correctness of unification is expressed using predicates for such properties as idempotence and most-generality. The verification is presented as a series of lemmas. The LCF proofs are compared with the original ones, and with other approaches. It appears difficult to find a logic that is both simple and flexible, especially for proving termination.
Keywords
Cite
@article{arxiv.cs/9301101,
title = {Verifying the Unification Algorithm in LCF},
author = {Lawrence C. Paulson},
journal= {arXiv preprint arXiv:cs/9301101},
year = {2008}
}