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@takanuva
Created February 20, 2023 09:59
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Functional Programming - Class 6
foo = Just (not True)
bar = Just not
-- not :: Bool -> Bool
-- Just :: a -> Maybe a
-- Just not :: Maybe (Bool -> Bool)
--
baz = Just . not
-- Remember that the dot operator joins two functions
-- and creates a new one!
-- (.) :: (b -> c) -> (a -> b) -> a -> c
--
{-
Whenever I see "a b c", it means:
- [x] (a b) c
- [ ] a (b c)
-}
funcs :: [Integer -> Integer]
funcs = [\x -> x + 1, \y -> 0, \x -> x * 2]
map' :: (a -> b) -> [a] -> [b]
map' f [] = -- (1)
[]
map' f (x:xs) = -- (2)
f x : map' f xs
res = map' (\f -> f 10) funcs
{-
res =
map' (\f -> f 10) funcs =
map' (\f -> f 10) [\x -> x + 1, \y -> 0, \x -> x * 2] =
(\f -> f 10) (\x -> x + 1) : map' ... ... =
^^^^^^^^^^^^^^^^^^^^^^^^^^
(\x -> x + 1) 10 : map' ... ... =
^^^^^^^^^^^^^^^^
10 + 1 : map' ... ... =
11 : map' ... ... =
11 : 0 : 20
map' (\f -> f 10) [\x -> x + 1, \y -> 0, \x -> x * 2] =
I am just adding the function (\f -> f 10) before every item!
[(\f -> f 10) (\x -> x + 1),
(\f -> f 10) (\y -> 0),
(\f -> f 10) (\x -> x * 2)] =
And the function says we call each item with 10 as input!
[(\x -> x + 1) 10,
(\y -> 0) 10,
(\x -> x * 2) 10] =
-}
{-
Recall the Either datatype, which allows us to have two different
types together!
- Left :: a -> Either a b
- Right :: b -> Either a b
-}
example = [Left 42, Right 'h', Right 'i', Left 100]
-- Left 42 :: Either Integer b
-- Right 'h' :: Either a Char
-- So, example :: [Either Integer Char]
{-
What's the type of map Left?
map :: (a -> b) -> [a] -> [b]
Left :: c -> Either c d
I'm giving Left as input to map, so Haskell will try to match the types!
(a -> b) = c -> Either c d
We're allowed to replace variables, so we take a = c, and b = Either c d!
Since we have this replacement working, we'll apply that to the result!
We want [a] -> [b] with a = c and b = Either c d, so:
So map Left :: [c] -> [Either c d]
= [a] -> [Either a b]
-}
-- data Maybe a = Just a | Nothing
safeHead :: [a] -> Either String a
safeHead [] =
Left "the list was empty!"
safeHead (x:xs) =
Right x
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