Mirroring Call-by-Need, or Values Acting Silly
<|reference_start|>Mirroring Call-by-Need, or Values Acting Silly: Call-by-need evaluation for the lambda-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name and call-by-value, namely silly duplications by-name and silly erasures by-value.   We validate the design of the call-by-silly calculus via rewriting properties and multi types. In particular, we mirror the main theorem about call-by-need -- that is, its operational equivalence with call-by-name -- showing that call-by-silly and call-by-value induce the same contextual equivalence. This fact shows the blindness with respect to efficiency of call-by-value contextual equivalence. We also define a call-by-silly strategy and measure its length via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.<|reference_end|>
@article{accattoli2024mirroring,
    title={Mirroring Call-by-Need, or Values Acting Silly},
    author={Beniamino Accattoli and Adrienne Lancelot},
    journal={arXiv preprint arXiv:2402.12078},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.12078},
    primaryClass={cs.LO}
}