Examples of using Functor in English and their translations into Vietnamese
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A functor is any type construction T for which there exists a higher-order function, call it map, that transforms a function of type a-> b(given any two types a
Constant functor: The functor C→ D which maps every object of C to a fixed object X in D and every morphism in C to the identity morphism on X. Such a functor is called a constant or selection functor. .
For example, a type constructor called List is a functor if it comes equipped with a function of type(a-> b)-> List a-> List b which obeys the laws above.
D be(locally small) categories and let F: C→ D be a functor from C to D. The functor F induces a function.
you'll see that there's a Functor class constraint, which means that we can assume that both of<*>'s parameters are functors. .
we can map functions that take these functions as parameters over them, because whatever is inside a functor will be given to the function that we're mapping over it as a parameter.
Wrapper(A) and returns a new functor Wrapper(B) containing the result of applying said function onto the value
All this really means is that a functor is an entity that defines the behavior of(fmap) that, given a value and function(morphism), maps said function onto a value of certain type(category) and generates a new functor.
So we can't write instance Functor Either where, but we can write instance Functor(Either a) where
Forgetful functors: The functor U: Grp→ Set which maps a group to its underlying set and a group homomorphism to its underlying function of sets is a functor.[8] Functors like these, which"forget" some structure, are termed forgetful functors. Another example is the functor Rng→ Ab which maps a ring to its underlying additive abelian group.
You can think of fmap as either a function that takes a function and a functor and then maps that function over the functor, or you can think
When we looked at Maybe as a functor, we saw that if we want to fmap a function over it, it gets mapped over the insides if it's a Just value,
For instance, the programming language Haskell has a class Functor where fmap is a polytypic function used to map functions(morphisms on Hask, the category of Haskell types)[9] between existing types to functions between some new types.
We know that the first functor law states that if we map id over a functor, it should be the same as just calling id with the same functor, but as we have seen from this example, this is not true for our CMaybe functor.
be put in an order and then moved on to more interesting ones, like Functor and Applicative.
that aren't necessarily wrapped in functors and use that function to operate on several values that are in functor contexts.
a functor and applies the function inside the functor,<*> takes a functor that has a function in it and another functor and sort of extracts that function
Actually, you have been using functors all along without realizing it.
Functors sometimes appear in functional programming.
But with applicative functors, we can apply a function between several functors.