Constructing applicative functors

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible

A Library for Declarative Resolution-Independent 2D Graphics

The design of most 2D graphics frameworks has been guided by what the computer can draw efficiently, instead of by how graphics can best be expressed and composed. As a result, such frameworks restrict expressivity by providing a limited set of shape primitives, a limited set of textures and only affine transformations. For example, non-affine transformations can only be added by invasive modification or complex tricks rather than by simple composition. More general frameworks exist, but they make it harder to describe and analyze shapes. We present a new declarative approach to resolution-independent 2D graphics that generalizes and simplifies the functionality of traditional frameworks, while preserving their efficiency. As a real-world example, we show the implementation of a form of focus+context lenses that gives better image quality and better performance than the state-of-the-art solution at a fraction of the code. Our approach can serve as a versatile foundation for the creation of advanced graphics and higher level frameworks

A Library for Declarative Resolution-Independent 2D Graphics

htmlabstractThe design of most 2D graphics frameworks has been guided by what the computer can draw efficiently, instead of by how graphics can best be expressed and composed. As a result, such frameworks restrict expressivity by providing a limited set of shape primitives, a limited set of textures and only affine transformations. For example, non-affine transformations can only be added by invasive modification or complex tricks rather than by simple composition. More general frameworks exist, but they make it harder to describe and analyze shapes. We present a new declarative approach to resolution-independent 2D graphics that generalizes and simplifies the functionality of traditional frameworks, while preserving their efficiency. As a real-world example, we show the implementation of a form of focus+context lenses that gives better image quality and better performance than the state-of-the-art solution at a fraction of the code. Our approach can serve as a versatile foundation for the creation of advanced graphics and higher level frameworks