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--- pp:functors [2021/04/19 11:11]
lfa [6. Functors, Foldables]
+++ pp:functors [2021/04/21 15:51] (current)
alexandru.rait Changed 6 to 7 in title
@@ Line 1: / Line 1: @@
-====== 6. Functors, Foldables ======
+====== 7. Functors, Foldables ======
 Functors are data types over which we can ''map'' a function (that is, apply a function on each element while keeping the overall structure). You've already encountered a Functor, namely haskell lists. For historical reasons, ''map'' only works on lists (''map :: (a -%%>%% b) -%%>%% [a] -%%>%% [b]''), but there exists a more general function ''fmap'' (''fmap :: (Functor f) =%%>%% (a -%%>%% b) -%%>%% f a -%%>%% f b'').
@@ Line 7: / Line 7: @@
 <code haskell>
 class Functor f where
-    fmap :: (a -%%>%% b) -%%>%% f a -%%>%% f b
+    fmap :: (a -> b) -> f a -> f b
 </code>
@@ Line 86: / Line 86: @@
 </code>
-Now our functions work and can handle the empty list without throwing an exception. However, it should be obvious that we now need to change any ''Int -> a'' function we want to apply on our result to a ''Maybe Int -> Maybe a'' function, which seems like a lot of work. Plus the change will be as dull in all cases:
+Now our functions work and can handle the empty list without throwing an exception. However, it should be obvious that we now need to change any ''Int -%%>%% a'' function we want to apply on our result to a ''Maybe Int -%%>%% Maybe a'' function, which seems like a lot of work. Plus the change will be as dull in all cases:
   - if we get a ''Nothing'', we return a ''Nothing''
   - if we get a ''Just'', we unpack it, do with it what the function did originally, then repack it in a ''Just''.
-It would be great if we could just have a function which does this transformation for us. And we do. Remember currying and how multiple-argument functions actually take on argument and return another function and so on. Thus we can reinterpret ''fmap'''s signature as: ''(a -> b) -> (f a) -> (f b)''. That is: it takes a function from ''a'' to ''b'' and returns a function from a functor ''a'' to a functor ''b''. Set the functor ''f'' to ''Maybe'' and that's  it!
+It would be great if we could just have a function which does this transformation for us. And we do. Remember currying and how multiple-argument functions actually take on argument and return another function and so on. Thus we can reinterpret ''fmap'''s signature as: ''(a -%%>%% b) -%%>%% (f a -%%>%% f b)''. That is: it takes a function from ''a'' to ''b'' and returns a function from a functor ''a'' to a functor ''b''. Set the functor ''f'' to ''Maybe'' and that's  it!
 <code haskell>