2018年6月29日 · A functor is a higher-order function that applies a function to the parametrized(ie templated) types. It is a generalization of the map higher-order function. For example, we could define a functor for std::vector like this:

2010年1月9日 · One could say 'a functor is a class that implements the Functor interface' (Of course, this interface might not be physically there, but you could lift the 'map' logic out to that interface, and have all of your mappable classes share it -- as long as your type system allows typing things this general, that is). –

2012年5月7日 · $\begingroup$ This is slightly more intuitive for a less mathematically knowledgeable crowd. A book that I states that functions take numbers and return numbers, while functionals take functions and return numbers - it seems here that you are saying functors can take both 1) functions and return functions, and 2) take numbers and return functions.

2023年9月24日 · according to the first one, a functor can be defined as a(n ordered) quadruplet in which the first two components are categories, called respectively domain and codomain of the functor, and the others are functions (possibly class functions) between the objects and the morphisms of the latter categories, satisfying appropriate conditions;

2016年6月4日 · For one, the functor can contain internal state; a state that is valid for this invocation of the function object only. You could add static variables to your function, but those would be used for any invocation of the function. Second, the compiler can inline calls to the functor; it cannot do the same for a function pointer.

The notion of a "$\delta$-functor," (or connected sequence of functors $\{T_i\}$) due to Grothendieck in his Tohoku paper, axiomatizes the notion of a derived functor (namely, there is required to be a functorial long exact sequence associated to each les).

2022年6月20日 · From this perspective, being representable is to “might as well” be a hom functor, or to be able to be replaced by a hom functor in any evil-free proof or construction. This is a long way of saying the importance and the definition of a representable functor is a bit subtle.

2009年6月2日 · But I just can't figure out the proper syntax to specify template parameters with a parameterless functor. Is there a proper way to do this? Obviously, this code would work since it bypasses the functor syntax: a.operator()<1>(); but that kinda defeats the purpose of it …

2012年10月24日 · A functor for iteration: For any kind of collection of things (e.g. lists), if you can iterate them, you can automatically fold them. You can also create different structures for different ways to fold across the same datatype (e.g. pre-order, in-order and post-order traversal of trees).

2017年8月5日 · A definition of a Functor in Haskell: "class Functor f where fmap :: (a -> b) -> f a -> f b". As you see it provides a way to map from f a -> f b. The notion that you can "map over it" is not the definition of a Functor but it's usage outside mathematical scope.