# Instances of List and Maybe

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This pages compares the Typeclassopedia classes of List and Maybe, with examples of use. You can run the examples in GHCi.

Semigroup
List Maybe
```> import Data.Semigroup
> [1,2] <> [3,4]
[1,2,3,4]
```
```> import Data.Semigroup
> (Just [1,2]) <> (Just [3,4])
Just [1,2,3,4]
```

Monoid
List Maybe
```> mempty :: [Int]
[]
> [1,2] <> mempty
[1,2]
```
```> mempty :: Maybe [Int]
Nothing
> (Just [1,2]) <> mempty
Just [1,2]
```

Functor
List Maybe
```> fmap (+1) [2, 3]
[3, 4]
> fmap (+1) []
[]
```
```> fmap (+1) (Just 2)
Just 3
> fmap (+1) Nothing
Nothing
```

Applicative
List Maybe
```> [(+1),(+2)] <*> [3,4]
[4,5,5,6]
> [] <*> [3,4]
[]
```
```> (Just (+1)) <*> (Just 2)
Just 3
> Nothing <*> (Just 2)
Nothing
```

Alternative
List Maybe
```> import Control.Applicative
> [1] <|> empty <|> [2]
[1,2]
> empty <|> [2]
[2]
```
```> import Control.Applicative
> (Just 1) <|> empty <|> (Just 2)
Just 1
> Nothing <|> (Just 2)
Just 2
```

List Maybe
```> mul xs ys = do x<-xs; y<-ys; return (x*y)
> mul [1,2] [3,4,5]
[3,4,5,6,8,10]
```
```> mul x' y' = do x<-x'; y<-y' return (x*y)
> mul (Just 2) (Just 5)
Just 10
```

List Maybe
```> import Control.Monad
> squares5 x' = do x<-x'; guard (x*x<5); return (x*x)
> squares5 [1,2,3]
[1,4]
> squares5 []
[]
```
```> import Control.Monad
> squares5 x' = do x<-x'; guard (x*x<5); return (x*x)
> squares5 (Just 2)
Just 4
> squares5 (Just 3)
Nothing
> squares5 Nothing
Nothing
```

Foldable
List Maybe
```> foldr (+) 0 [1,2]
3
```
```> foldr (+) 1 (Just 2)
3
```

Traversable
List Maybe
```> traverse (\x -> [0..x]) [0..2]
[[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2]]
> sequenceA [[1,2],[3,4]]
[[1,3],[1,4],[2,3],[2,4]]
```
```> traverse (\x -> [x, x*x]) (Just 3)
[Just 3,Just 9]
> sequenceA [Just 3, Just 4]
Just [3,4]
> sequenceA [Just 3, Nothing]
Nothing
> sequenceA (Just [3,4])
[Just 3,Just 4]
```