Technical reports
Verifying the unification algorithm in LCF
March 1984, 28 pages
DOI: 10.48456/tr-50
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.
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BibTeX record
@TechReport{UCAM-CL-TR-50,
author = {Paulson, Lawrence},
title = {{Verifying the unification algorithm in LCF}},
year = 1984,
month = mar,
url = {https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-50.pdf},
institution = {University of Cambridge, Computer Laboratory},
doi = {10.48456/tr-50},
number = {UCAM-CL-TR-50}
}