Mirroring Call-by-Need, or Values Acting Silly
Abstract
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 a call-by-silly abstract machine implementing the strategy. Moreover, we measure the number of steps taken by the strategy via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.
Keywords
Cite
@article{arxiv.2402.12078,
title = {Mirroring Call-by-Need, or Values Acting Silly},
author = {Beniamino Accattoli and Adrienne Lancelot},
journal= {arXiv preprint arXiv:2402.12078},
year = {2026}
}