  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.
