| [] -> []
| x' :: xs' -> List.append (k x') (catmap f xs')
-Now we can have as many elements in the result for a given `α` as `k` cares to return. Another way to write `catmap k xs` is as `List.concat (map k xs)`. And this is just the definition of `mbind` or `>>=` for the List Monad. The definition of `mcomp` or `<=<`, that we gave above, differs only in that it's the way to compose two functions `j` and `k`, that you'd want to `catmap`, rather than the way to `catmap` one of those functions over a value that's already a list.
+Now we can have as many elements in the result for a given `α` as `k` cares to return. Another way to write `catmap k xs` is as (Haskell) `concat (map k cs)` or (OCaml) `List.flatten (List.map k xs)`. And this is just the definition of `mbind` or `>>=` for the List Monad. The definition of `mcomp` or `<=<`, that we gave above, differs only in that it's the way to compose two functions `j` and `k`, that you'd want to `catmap`, rather than the way to `catmap` one of those functions over a value that's already a list.
This example is a good intuitive basis for thinking about the notions of `mbind` and `mcomp` more generally. Thus `mbind` for the option/Maybe type takes an option value, applies `k` to its element (if there is one), and returns the resulting option value. `mbind` for a tree with `α`-labeled leaves would apply `k` to each of the leaves, and return a tree containing arbitrarily large subtrees in place of all its former leaves, depending on what `k` returned.
Some a >>=<sub>α option</sub> (\a -> Some 0) ==> Some 0
None >>=<sub>α option</sub> (\a -> Some 0) ==> None
- . _____
- / \ . / \
- . 3 >>=<sub>(α,unit) tree</sub> (\a -> / \ ) ==> _/_ .
- / \ a a / \ / \
-1 2 . . 3 3
+ .
+ / \
+ . / \
+ / \ . . \
+ . 3 >>=<sub>(α,unit) tree</sub> (\a -> / \ ) ==> / \ .
+ / \ a a / \ / \
+1 2 . . 3 3
/ \ / \
1 1 2 2
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