Funktory

Question 1

Aka je motivacia za funktormi?

Answer 1

Mame nejake funkcie, ale chceme ich pouzit na hodnoty v kontexte, napr Maybe. Chceme to spravit bez zbytocneho opakovania

Question 2

Co robime s funkciou f :: a -> b?

Answer 2

Pozdvihneme (lift) na fm :: Maybe a -> Maybe b

Question 3

Co nam staci zadefinovat pre Funktory?

Answer 3

fmap :: (a -> b) -> f a -> f b

Question 4

Co robi <$ ?

Answer 4

a -> f b -> f a

Question 5

Ake identity musi splnat fmap?

Answer 5

fmap id=id
fmap (f . g) = fmap f . fmap g

Question 6

Co robi $>?

Answer 6

Functor f=>fb->a->fa

Question 7

Ako piseme aj fmap?

Answer 7

<$>

Question 8

Co robi void?

Answer 8

Functor f=>fa->f()
void x = () <$ x

Question 9

Aka je motivacia za aplikativnymi funktormi?

Answer 9

potrebujeme aplikovať binárnu
funkciu na dve hodnoty uložené v kontexte Maybe

Question 10

Aka je signatura <*>?

Answer 10

pre maybe konkretne
Maybe (a->b)->Maybe a->Maybe b
aplikuje funkciu v kontexte na hodnotu v kontexte

Question 11

Preco spadne (++) <$> Just “AB” <$> Just “BA”?

Answer 11

Lebo (++) <$> Just “AB” je typu Maybe (String -> String)

Question 12

Co musime implementovat pre aplikativne funktory?

Answer 12

pure, <*>

Question 13

Co robi pure?

Answer 13

pure:: a->f a
vloží „čistú“ hodnotu do kontextu

Question 14

Ake identity musi splnat pure a <*>?

Answer 14

pure id <> v = v
pure (.) <> u <> v <> w = u <> (v <> w)
pure f <> pure x = pure (f x)
u <> pure y = pure ($ y) <*> u

Question 15

Co vyhodi ako vysledok [(+), ()] <> [1, 2] <*> [10, 20]?

Answer 15

[11,21,12,22,10,20,20,40]

Question 16

Co su teda I,S,K podla aplikativnych funktorov?

Answer 16

S=(⟨∗⟩) K=pure, I=SKK