[TYPES] Full abstraction of applicative contexts in call-by-value

Francesco Gavazzo <[email protected]> Mon, 3 Apr 2023 14:56:21 +0200
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Dear all,

It is well-known that applicative bisimilarity is fully abstract on the
untyped call-by-value λ-calculus. A direct consequence of that is that
contextual equivalence can be restricted to applicative contexts (namely
contexts defined by the grammar E ::= [-] | Ev) leaving its discriminated
power unchanged. Such a result is, in principle, independent of applicative
bisimilarity and I was wondering if any of you is aware of any direct (i.e.
not going through applicative bisimilarity) proof that applicative contexts
suffice to characterise contextual equivalence.
Thanks a lot in advance!
Best,
Francesco Gavazzo and Ugo Dal Lago