zipList

applicative/CustomList.hs

@@ -0,0 +1,13 @@
+newtype CustomList a = CustomList [a] deriving Show
+
+instance Functor CustomList where
+    fmap f (CustomList lst) = CustomList $ fmap f lst
+
+instance Applicative CustomList where
+    pure x = CustomList $ repeat x 
+    {-
+    -- default implementation
+    pure x = CustomList [x]
+    (CustomList fs) <*> (CustomList xs) = CustomList $ [f x | f <- fs, x <- xs] 
+    -}
+    (CustomList fs) <*> (CustomList xs) = CustomList $ zipWith ($) fs xs

applicative/list.md

@@ -16,7 +16,7 @@ u <*> (v <*> w) == pure (.) <*> u <*> v <*> w
 
 ## Доказательство
 
-### Identity
+### 1.Identity
 
 ```
 pure id <*> CustomList lst == 
@@ -45,10 +45,6 @@ pure ($ y) <*> u ==
 CustomList $ repeat ($ y) <*> CustomList fs ==
 CustomList $ zipWith ($) (repeat ($ y)) fs [2]
 
-Type of ($ y): (a -> b) -> b
-Type of ($): (a -> b) -> a -> b
-Type of ($) ($ y): (a -> b) -> b
-
 ($) f x == ($) ($ x) f
 
 => [1] == [2]
@@ -62,10 +58,10 @@ CustomList fs2 <*> (CustomList fs1 <*> CustomList xs) ==
 CustomList fs2 <*> CustomList $ zipWith ($) fs1 xs ==
 CustomList fs2 <*> CustomList xs1 ==
 ... ==
-CustomList xs12 (Длина xs12 - наименьшая из длин fs1, fs2 и xs)
+CustomList xs12 (Длина xs12 - наименьшая из длин fs1, fs2 и xs, сначала применены ф-ии из fs1, потом - из fs2)
 
 pure (.) <*> u <*> v <*> w ==
 pure (.) CustomList fs2 <*> CustomList fs1 <*> CustomList xs ==
 CustomList fs12 <*> Custom xs == (fs12 - список из композиций соответствующих функций, длина fs12 - наименьшая из длин fs1 и fs2)
-CustomList xs12 (длина xs12 - наименьшая из длин fs12 и xs)
+CustomList xs12 (длина xs12 - наименьшая из длин fs12 и xs, сначала применены ф-ии из fs1, потом - из fs2))
 ```