From 26319cf2ffc188af7fc324143881d45fd7c322c8 Mon Sep 17 00:00:00 2001
From: Jim Pryor
Date: Wed, 1 Dec 2010 03:23:12 -0500
Subject: [PATCH] manip trees: tweaks
Signed-off-by: Jim Pryor
---
manipulating_trees_with_monads.mdwn | 31 ++++++++++++++++++++-----------
1 file changed, 20 insertions(+), 11 deletions(-)
diff --git a/manipulating_trees_with_monads.mdwn b/manipulating_trees_with_monads.mdwn
index 20039c28..de8fc5fa 100644
--- a/manipulating_trees_with_monads.mdwn
+++ b/manipulating_trees_with_monads.mdwn
@@ -28,9 +28,9 @@ internal nodes?]
We'll be using trees where the nodes are integers, e.g.,
- let t1 = Node ((Node ((Leaf 2), (Leaf 3))),
- (Node ((Leaf 5),(Node ((Leaf 7),
- (Leaf 11))))))
+ let t1 = Node (Node (Leaf 2, Leaf 3),
+ Node (Leaf 5, Node (Leaf 7,
+ Leaf 11)))
.
___|___
| |
@@ -47,8 +47,8 @@ Our first task will be to replace each leaf with its double:
let rec treemap (newleaf : 'a -> 'b) (t : 'a tree) : 'b tree =
match t with
| Leaf x -> Leaf (newleaf x)
- | Node (l, r) -> Node ((treemap newleaf l),
- (treemap newleaf r));;
+ | Node (l, r) -> Node (treemap newleaf l,
+ treemap newleaf r);;
`treemap` takes a function that transforms old leaves into new leaves,
and maps that function over all the leaves in the tree, leaving the
@@ -122,7 +122,7 @@ type `int -> int`.
It's easy to figure out how to turn an `int` into an `int reader`:
- let int2int_reader (x : 'a) : 'b reader = fun (op : 'a -> 'b) -> op x;;
+ let int2int_reader : 'a -> 'b reader = fun (a : 'a) -> fun (op : 'a -> 'b) -> op a;;
int2int_reader 2 (fun i -> i + i);;
- : int = 4
@@ -142,7 +142,7 @@ something of type `'a` into an `'b reader`, and I'll show you how to
turn an `'a tree` into an `'a tree reader`. In more fanciful terms,
the `treemonadizer` function builds plumbing that connects all of the
leaves of a tree into one connected monadic network; it threads the
-monad through the leaves.
+`'b reader` monad through the leaves.
# treemonadizer int2int_reader t1 (fun i -> i + i);;
- : int tree =
@@ -158,18 +158,18 @@ result:
- : int tree =
Node (Node (Leaf 4, Leaf 9), Node (Leaf 25, Node (Leaf 49, Leaf 121)))
-Now that we have a tree transformer that accepts a monad as a
+Now that we have a tree transformer that accepts a reader monad as a
parameter, we can see what it would take to swap in a different monad.
For instance, we can use a state monad to count the number of nodes in
the tree.
type 'a state = int -> 'a * int;;
- let state_unit x i = (x, i+.5);;
- let state_bind u f i = let (a, i') = u i in f a (i'+.5);;
+ let state_unit a = fun i -> (a, i);;
+ let state_bind u f = fun i -> let (a, i') = u i in f a (i' + 1);;
Gratifyingly, we can use the `treemonadizer` function without any
modification whatsoever, except for replacing the (parametric) type
-`reader` with `state`:
+`'b reader` with `'b state`, and substituting in the appropriate unit and bind:
let rec treemonadizer (f : 'a -> 'b state) (t : 'a tree) : 'b tree state =
match t with
@@ -198,6 +198,15 @@ Then we can count the number of nodes in the tree:
Notice that we've counted each internal node twice---it's a good
exercise to adjust the code to count each node once.
+
+
+
One more revealing example before getting down to business: replacing
`state` everywhere in `treemonadizer` with `list` gives us
--
2.11.0