Jun 29, 2018 · 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:

Jan 9, 2010 · 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). –

May 7, 2012 · $\begingroup$ 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.

Sep 24, 2023 · 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;

Jun 4, 2016 · 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).

Aug 28, 2011 · A functor that is not applicative because the type signature of <*> cannot be implemented: data F a = Either (Int -> a) (String -> a). A functor that is not lawful applicative even though the type class methods can be implemented: data P a = P ((a -> Int) -> Maybe a) The type constructor P is a functor because it uses a only in covariant positions.

Jul 22, 2017 · 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.

Dec 3, 2009 · MyFunctor my_functor(/* setup parameters */); MyAlgorithmInC(input_data, MyFunctorInC, &my_functor); Otherwise the only normal way to do it (normal as in "without generating machine code at runtime" etc.) is to use some static (global) or thread local storage to pass the functor to an extern "C" function.

Jun 20, 2022 · 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.