A Domain-Theoretic Approach to Statistical Programming Languages
نویسندگان
چکیده
We give a domain-theoretic semantics to statistical programming language, using the plain old category of dcpos, in contrast some more sophisticated recent proposals. Remarkably, our monad minimal valuations is commutative, which allows for program transformations that permute order independent random draws, as one would expect. A similar property not known Jones and Plotkin’ s continuous valuations. Instead working with true real numbers, we work exact arithmetic, providing bridge towards possible implementations. (Implementations by themselves are addressed here.) Rather remarkably, show restricting ourselves does restrict us much: all measures on line can be modeled domain \(\mathbf {I}\mathbb {R}_\bot \) arithmetic. three operational they adequate respect denotational semantics. also explore quite few examples demonstrate computes exactly expect, debunk myth based maps expressive enough encode non-compact support only compact support, or via non-continuous density functions, instance. Our include useful, non-trivial cases distributions higher-order objects.
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2023
ISSN: ['0004-5411', '1557-735X']
DOI: https://doi.org/10.1145/3611660