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Logic Journal of IGPL 1997 5(4):589-601; doi:10.1093/jigpal/5.4.589
© 1997 by Oxford University Press
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A note on logical relations between semantics and syntax

AM Pitts

Cambridge University Computer Laboratory, Cambridge CB2 3QG, UK. Email: Andrew.Pitts@cl.cam.ac.uk

This note gives a new proof of the 'operational extensionality' property of Abramsky's lazy lambda calculus-namely the coincidence of contextual equivalence with a co-inductively defined notion of 'applicative bisimilarity'. This purely syntactic results 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.

Keywords: denotational semantics, logical relation, lambda calculus, contextual equivalence


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