functor

We know that any generic type F[_] with map method, which complies to some laws , is a functor . For instance, List[_] , Option[_] , and F[A] = Env => A are functors. I am just wondering if this functor abstraction is meaningful. How can I use the fact that they are functors ? Could you show an example of non-trivial computation, which would use the map and be actually useful ? One of the biggest benefits of concepts like functions is that there are generic constructions that allow you to build more complex types out of simpler functors, and guarantee that these complex types have certain

When you want to pull an element out of a data structure, you have to give its index. But the meaning of index depends on the data structure itself. class Indexed f where type Ix f (!) :: f a -> Ix f -> Maybe a -- indices can be out of bounds For example... Elements in a list have numeric positions. data Nat = Z | S Nat instance Indexed [] where type Ix [] = Nat [] ! _ = Nothing (x:_) ! Z = Just x (_:xs) ! (S n) = xs ! n Elements in a binary tree are identified by a sequence of directions. data Tree a = Leaf | Node (Tree a) a (Tree a) data TreeIx = Stop | GoL TreeIx | GoR TreeIx --

I need some idea how to write a C++ cross platform implementation of a few parallelizable problems in a way so I can take advantage of SIMD (SSE, SPU, etc) if available. As well as I want to be able at run time to switch between SIMD and not SIMD. How would you suggest me to approach this problem? (Of course I don't want to implement the problem multiple times for all possible options) I can see how this might not be very easy task with C++ but I believe that I'm missing something. So far my idea looks like this... A class cStream will be array of a single field. Using multiple cStreams I can

Brent Yorgey's Typeclassopedia gives the following exercise: Give an example of a type of kind * -> * which cannot be made an instance of Functor (without using undefined ). Please tell me what " cannot be made an instance of Functor " means. Also, I'd appreciate an example, but perhaps as a spoiler so that you can, please, guide me to the answer. J. Abrahamson Let's talk about variances. Here's the basic notion. Consider the type A -> B . What I want you to imagine is that such a type is similar to "having a B " and also "owing an A ". In fact, if you pay back your A you immediately receive

In my free time I'm learning Haskell, so this is a beginner question. In my readings I came across an example illustrating how Either a is made an instance of Functor : instance Functor (Either a) where fmap f (Right x) = Right (f x) fmap f (Left x) = Left x Now, I'm trying to understand why the implementation maps in the case of a Right value constructor, but doesn't in the case of a Left ? Here is my understanding: First let me rewrite the above instance as instance Functor (Either a) where fmap g (Right x) = Right (g x) fmap g (Left x) = Left x Now: I know that fmap :: (c -> d) -> f c -> f

For as far as I understand, a functor is a mapping between two categories, for example from objects in to objects in where and are categories. In Haskell there is Hask in which the objects are Haskell types and the morphisms are Haskell functions. However, the Functor type class has a function fmap which maps between these types (which are thus objects and not categories themselves): fmap :: (a -> b) -> f a -> f b f a and f b are both objects in Hask . Does this mean every instance of Functor in Haskell is an endofunctor, and if not does Functor really represent a functor? What am I missing

I have two vectors. One that actually holds the data (let's say floats) and one that holds the indices. I want to pass at nth_element the indices vector, but I want the comparison to be done by the vector that actually holds the data. I was thinking about a functor, but this provides only the () operator I guess. I achieved that by making the data vector a global one, but of course that's not desired. std::vector<float> v; // data vector (global) bool myfunction (int i,int j) { return (v[i]<v[j]); } int find_median(std::vector<int> &v_i) { size_t n = v_i.size() / 2; nth_element(v_i.begin(), v

I am using TRI DDS - here is the prototype for the function I am trying to call: template<typename T , typename Functor > dds::sub::cond::ReadCondition::ReadCondition ( const dds::sub::DataReader< T > & reader, const dds::sub::status::DataState & status, const Functor & handler ) So I have a class that looks a bit like this (with load of irrelevant stuff omitted): MyClass test{ public: test(){... mp_reader = ...}; // not complete start_reader() { dds::sub::cond::ReadCondition rc(*mp_reader, dds::sub::status::DataState::any(), do_stuff()); // This does not work } void do_stuff() {...} private: