A parametric logical relation between the phrases of an Algol-like language
is presented. Its definition involves the structural operational semantics
of the language, but was inspired by recent denotationally-based work of
O'Hearn and Reynolds on translating Algol into a predicatively polymorphic
linear lambda calculus. The logical relation yields an applicative
characterisation of contextual equivalence for the language and provides a
useful (and complete) method for proving equivalences. Its utility is
illustrated by giving simple and direct proofs of some contextual
equivalences, including an interesting equivalence due to O'Hearn which
hinges upon the undefinability of `snapback' operations (and which goes
beyond the standard suite of `Meyer-Sieber' examples). Whilst some of the
mathematical intricacies of denotational semantics are avoided, the hard
work in this operational approach lies in establishing the `fundamental
property' for the logical relation---the proof of which makes use of a
compactness property of fixpoint recursion with respect to evaluation of
phrases. But once this property has been established, the logical relation
provides a verification method with an attractively low mathematical
overhead.