Denotational Semantics for Probabilistic Recurrences

Barnaby, Celeste

doi:10.14418/wes01.1.1468

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…That would seem to correspond to interpreting the usually extracted recurrence in a model in which inductive types are interpreted by probability distributions or random variables. Barnaby (2018) has made preliminary progress in this direction, which indicates that it is probably necessary to have at least limited forms of dependent typing in the recurrence language.…”

Section: Related Workmentioning

confidence: 99%

Denotational semantics as a foundation for cost recurrence extraction for functional languages

Danner¹,

Licata²

2022

J. Funct. Prog.

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A standard informal method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input and then to compute a closed-form upper bound on that recurrence. We give a formal account of that method for functional programs in a higher order language with $\mathtt{let}$ -polymorphism. The method consists of two phases. In the first phase, a monadic translation is performed to extract a cost-annotated version of the original program. In the second phase, the extracted program is interpreted in a model. The key feature of this second phase is that different models describe different notions of size. This plays out in several ways. For example, when analyzing functions that take arguments of inductive types, different notions of size may be appropriate depending on the analysis. When analyzing polymorphic functions, our approach shows that one can formally describe the notion of size of an argument in terms of the data that is common to the notions of size for each type instance of the domain type. We give several examples of different models that formally justify various informal cost analyses to show the applicability of our approach.

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Section: Related Workmentioning

confidence: 99%

Denotational semantics as a foundation for cost recurrence extraction for functional languages

Danner¹,

Licata²

2022

J. Funct. Prog.

View full text Add to dashboard Cite

show abstract

“…That would seem to be a model in which inductive types are interpreted by random variables. Barnaby [2018] has made preliminary progress in this direction, which indicates that it is probably necessary to have at least limited forms of dependent typing in the recurrence language.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Denotational semantics as a foundation for cost recurrence extraction for functional languages

Danner,

Licata

2020

Preprint

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A standard method for analyzing the asymptotic complexity of a program is to extract a recurrence that describes its cost in terms of the size of its input, and then to compute a closed-form upper bound on that recurrence. In practice there is rarely a formal argument that the recurrence is in fact an upper bound; indeed, there is usually no formal connection between the program and the recurrence at all. Here we develop a method for extracting recurrences from functional programs in a higher-order language with let-polymorphism that provably bound their operational cost. The method consists of two phases. In the first phase, a monadic translation is performed to extract a costannotated version of the original program. In the second phase, the extracted program is interpreted in a model. The key feature of this second phase is that different models describe different notions of size. This plays out specifically for values of inductive type, where different notions of size may be appropriate depending on the analysis, and for polymorphic functions, where we show that the notion of size for a polymorphic function can be described formally as the data that is common to the notions of size of its instances. We give several examples of different models that formally justify various informal extracta-recurrence-and-solve cost analyses to show the applicability of our approach.

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Denotational Semantics for Probabilistic Recurrences

Cited by 2 publications

References 3 publications

Denotational semantics as a foundation for cost recurrence extraction for functional languages

Denotational semantics as a foundation for cost recurrence extraction for functional languages

Denotational semantics as a foundation for cost recurrence extraction for functional languages

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