Strong Call by Value is Reasonable for Time
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The invariance thesis of Slot and van Emde Boas states that all reasonable models of computation simulate each other with polynomially bounded overhead in time and constant-factor overhead in space. In this paper we show that a family of strong call-by-value strategies in the λ-calculus are reasonable for time. The proof is based on a construction of an appropriate abstract machine, systematically derived using Danvy et al.'s functional correspondence that connects higher-order interpreters with abstract-machine models by a well-established transformation technique. This is the first machine that implements a strong CbV strategy and simulates β-reduction with the overhead polynomial in the number of β-steps and in the size of the initial term. We prove this property using a form of amortized cost analysis à la Okasaki.
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