Strong Call-by-Value is Reasonable, Implosively

Whether the number of β -steps in the λ-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy. Since the nineties, it is known that weak (that is, out of abstractio...

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Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 14
Main Authors: Accattoli, Beniamino, Condoluci, Andrea, Coen, Claudio Sacerdoti
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
Computer science
Turing machines
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Abstract Whether the number of β -steps in the λ-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy. Since the nineties, it is known that weak (that is, out of abstractions) call-by-value evaluation is a reasonable strategy while Lévy's optimal parallel strategy, which is strong (that is, it reduces everywhere), is not. The strong case turned out to be subtler than the weak one. In 2014 Accattoli and Dal Lago have shown that strong call-by-name is reasonable, by introducing a new form of useful sharing and, later, an abstract machine with an overhead quadratic in the number of β-steps.Here we show that also strong call-by-value evaluation is reasonable for time, via a new abstract machine realizing useful sharing and having a linear overhead. Moreover, our machine uses a new mix of sharing techniques, adding on top of useful sharing a form of implosive sharing, which on some terms brings an exponential speed-up. We give examples of families that the machine executes in time logarithmic in the number of β-steps.
AbstractList Whether the number of β -steps in the λ-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy. Since the nineties, it is known that weak (that is, out of abstractions) call-by-value evaluation is a reasonable strategy while Lévy's optimal parallel strategy, which is strong (that is, it reduces everywhere), is not. The strong case turned out to be subtler than the weak one. In 2014 Accattoli and Dal Lago have shown that strong call-by-name is reasonable, by introducing a new form of useful sharing and, later, an abstract machine with an overhead quadratic in the number of β-steps.Here we show that also strong call-by-value evaluation is reasonable for time, via a new abstract machine realizing useful sharing and having a linear overhead. Moreover, our machine uses a new mix of sharing techniques, adding on top of useful sharing a form of implosive sharing, which on some terms brings an exponential speed-up. We give examples of families that the machine executes in time logarithmic in the number of β-steps.
Author Coen, Claudio Sacerdoti
Accattoli, Beniamino
Condoluci, Andrea
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  givenname: Claudio Sacerdoti
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  fullname: Coen, Claudio Sacerdoti
  organization: University of Bologna
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Snippet Whether the number of β -steps in the λ-calculus can be taken as a reasonable time cost model (that is, polynomially related to the one of Turing machines) is...
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Turing machines
Title Strong Call-by-Value is Reasonable, Implosively
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