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A Note on Logical Relations Between Semantics and Syntax
, 1997
"... This note gives a new proof of the `operational extensionality' property of Abramsky's lazy lambda calculusnamely the coincidence of contextual equivalence with a coinductively defined notion of `applicative bisimilarity'. This purely syntactic result is here proved using a logica ..."
Abstract

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This note gives a new proof of the `operational extensionality' property of Abramsky's lazy lambda calculusnamely the coincidence of contextual equivalence with a coinductively defined notion of `applicative bisimilarity'. This purely syntactic result is here proved using a logical relation (due to Plotkin) between the syntax and its denotational semantics. The proof exploits a mixed inductive/coinductive characterisation of the logical relation recently discovered by the author.