Simplicitly: foundations and applications of implicit function types
نویسندگان
چکیده
منابع مشابه
Foundations of Implicit Function Types
Implicit parameters are used pervasively in Scala and are also present in a number of other programming and theorem proving languages. is paper describes a generalization of implicit parameters as they are currently found in Scala to implicit function types. We motivate the construct by a series of examples and provide formal foundations that closely follow the semantics implemented by the Sca...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
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The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipschitz maps. Under a sign-preserving condition, we prove that an implicit function exists in the case of a set of inequ...
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The Implicit function theorem due to Lagrange is generalized to enable high order implicit rate calculations of general implicit functions about a nominal solution of interest. The sensitivities thus calculated are subsequently used in determining neighboring solutions about a nominal point, or in the case of a dynamical system, a trajectory. The generalization to dynamical systems, as a specia...
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Virtual types have been proposed as a notation for generic programming in object-oriented languages—an alternative to the more familiar mechanism of parametric classes. The tradeoffs between the two mechanisms are a matter of current debate: for many examples, both appear to offer convenient (indeed almost interchangeable) solutions; in other situations, one or the other seems to be more satisf...
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ژورنال
عنوان ژورنال: Proceedings of the ACM on Programming Languages
سال: 2018
ISSN: 2475-1421
DOI: 10.1145/3158130