An Abstract Machine for Strong Call by Value

We present an abstract machine that implements a full-reducing (a.k.a. strong) call-by-value strategy for pure $λ$-calculus. It is derived using Danvy et al.'s functional correspondence from Crégut's KN by: (1) deconstructing KN to a call-by-name normalization-by-evaluation function akin to Filinski and Rohde's, (2) modifying the resulting normalizer so that it implements the right-to-left call-by-value function application, and (3) constructing the functionally corresponding abstract machine. This new machine implements a reduction strategy that subsumes the fireball-calculus variant of call by value studied by Accattoli et al. We describe the strong strategy of the machine in terms of a reduction semantics and prove the correctness of the machine using a method based on Biernacka et al.'s generalized refocusing. As a byproduct, we present an example application of the machine to checking term convertibility by discriminating on the basis of their partially normalized forms.

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