From: jim
Date: Sun, 22 Mar 2015 16:19:51 +0000 (-0400)
Subject: tweak List.>>= explanation
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=57588efa1216a1f500e9ae42521604fd2f488924
tweak List.>>= explanation
---
diff --git a/topics/week7_introducing_monads.mdwn b/topics/week7_introducing_monads.mdwn
index 840521a0..39dcdaf0 100644
--- a/topics/week7_introducing_monads.mdwn
+++ b/topics/week7_introducing_monads.mdwn
@@ -383,7 +383,7 @@ That can be helpful, but it only enables us to have _zero or one_ elements in th
| [] -> []
| x' :: xs' -> List.append (k x') (catmap f xs')
-Now we can have as many elements in the result for a given `Î±` 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 `Î±` 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 `Î±`-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.