Recovering purity with comonads and capabilities
نویسندگان
چکیده
منابع مشابه
Signals and Comonads
We propose a novel discipline for programming stream functions and for the semantic description of stream manipulation languages based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads. This seems to be a promising application for the old, but very little exploited idea that if monads abstract notions of computation of a value,...
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The notion of a coring was introduced by M. E. Sweedler in [20] with the objective of formulating and proving a predual to the Jacobson-Bourbaki theorem for extensions of division rings. A fundamental argument in [20] is the following: given division rings E ⊆ A, each coideal J of the A–coring A ⊗E A gives rise to a factor coring C = A ⊗E A/J . If g ∈ C denotes the group-like element 1 ⊗E 1 + J...
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The definition of Azumaya algebras over commutative rings R requires the tensor product of modules over R and the twist map for the tensor product of any two R-modules. Similar constructions are available in braided monoidal categories, and Azumaya algebras were defined in these settings. Here, we introduce Azumaya monads on any category A by considering a monad (F,m, e) on A endowed with a dis...
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The category-theoretic concept of a monad occurs widely as a design pattern for functional programming with effects. The utility and ubiquity of monads is such that some languages provide syntactic sugar for this pattern, further encouraging its use. We argue that comonads, the dual of monads, similarly provide a useful design pattern, capturing notions of context dependence. However, comonads ...
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ژورنال
عنوان ژورنال: Proceedings of the ACM on Programming Languages
سال: 2020
ISSN: 2475-1421
DOI: 10.1145/3408993