The importance of being Extrinsic: Coherence and adequacy for a call-by-value language

In this paper we mechanize in Coq a typed, call-by-value language by specifying its operational semantics and giving intrinsic and extrinsic denotational semantics, both using domain theory. We also prove that the denotational semantics are equivalent; this is interesting because it leads to a direct proof of coherence for the intrinsic semantics. Finally, we prove the adequacy of the operational semantics with respect to the denotational semantics. As far as we know, this is the first mechanization of Reynolds' bracketing theorem and also the use of biorthogonality with extrinsic semantics instead of intrinsic semantics.