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Abstract:Package managers are legion. Every programming language and operating system has its own solution, each with subtly different semantics for dependency resolution. This fragmentation prevents multilingual projects from expressing precise dependencies across language ecosystems; it leaves external system and hardware dependencies implicit and unversioned; it obscures security vulnerabilities that lie in the full dependency graph. We present the \textit{Package Calculus}, a formalism for dependency resolution that unifies the core semantics of diverse package managers. Through a series of formal reductions, we show how this core is expressive enough to model the diversity that real-world package managers employ in their dependency expression languages. By using the Package Calculus as the intermediate representation of dependencies, we enable translation between distinct package managers and resolution across ecosystems.
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The N-closest or N-best dithering algorithm is a straightforward solution to the N-candidate problem. As the name suggests, the set of candidates is given by the closest palette colours to the input pixel. To determine their weights, we simply take the inverse of the distance to the input pixel. This is essentially the inverse distance weighting (IDW) method for multivariate interpolation, also known as Shepard’s method. The following pseudocode sketches out a possible implementation: