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<title>The Haskell 1.3 Library Report: Monad Utilities</title>
<body bgcolor="#ffffff"> <i>The Haskell 1.4 Library Report</i><br> <a href="index.html">top</a> | <a href="char.html">back</a> | <a href="io.html">next</a> | <a href="libindex.html">contents</a> <br><hr>
<a name="Monad"></a><a name="sect10"></a>
<h2>10<tt> </tt>Monad Utilities</h2>
<p>
<table border=2 cellpadding=3>
<tr><td>
<tt><br>
module Monad (<br>
join, mapAndUnzipM, zipWithM, foldM, when, unless, ap,<br>
liftM, liftM2, liftM3, liftM4, liftM5<br>
) where<br>
<br>
join :: (Monad m) => m (m a) -> m a<br>
mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])<br>
zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]<br>
foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a<br>
zeroOrMore :: (MonadPlus m) => m a -> m [a]<br>
oneOrMore :: (MonadPlus m) => m a -> m [a]<br>
when :: (Monad m) => Bool -> m () -> m ()<br>
unless :: (Monad m) => Bool -> m () -> m ()<br>
ap :: (Monad a) => (m (a -> b)) -> (m a) -> m b<br>
liftM :: (Monad m) => (a -> b) -> (m a -> m b)<br>
liftM2 :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)<br>
liftM3 :: (Monad m) => (a -> b -> c -> d) -><br>
(m a -> m b -> m c -> m d)<br>
liftM4 :: (Monad m) => (a -> b -> c -> d -> e) -><br>
(m a -> m b -> m c -> m d -> m e)<br>
liftM5 :: (Monad m) => (a -> b -> c -> d -> e -> f) -><br>
(m a -> m b -> m c -> m d -> m e -> m f)<br>
<br>
</tt></td></tr></table>
<p>
These utilities provide some useful operations on monads.<p>
The <tt>join</tt> function is the conventional monad join operator. It is
used to remove one level of monadic structure, projecting its bound
argument into the outer level.<p>
The <tt>mapAndUnzipM</tt> function maps its first argument over a list,
returning the result as a pair of lists. This function is mainly used
with complicated data structures or a state-transforming monad.<p>
The <tt>zipWithM</tt> function generalises <tt>zipWith</tt> to arbitrary monads.
For instance the following function displays a file, prefixing
each line with its line number,
<tt><br>
<br>
listFile :: String -> IO ()<br>
listFile nm =<br>
do cts <- openFile nm<br>
zipWithM_ (\i line -> do putStr (show i); putStr ": "; putStrLn line)<br>
[1..]<br>
(lines cts)<br>
<br>
<p>
</tt>The <tt>foldM</tt> function is analogous to <tt>foldl</tt>, except that its result
is encapsulated in a monad. Note that <tt>foldM</tt> works from
left-to-right over the list arguments. This could be an issue where
<tt>(>>)</tt> and the "folded function" are not commutative.
<tt><br>
<br>
foldM f a1 [x1, x2, ..., xm ]<br>
== <br>
do<br>
a2 <- f a1 x1<br>
a3 <- f a2 x2<br>
...<br>
f am xm<br>
<br>
</tt>If right-to-left
evaluation is required, the input list should be reversed.<p>
The <tt>when</tt> and <tt>unless</tt> functions provide conditional execution of
monadic expressions. For example,
<tt><br>
<br>
when debug (putStr "Debugging\n")<br>
<br>
</tt>will output the string <tt>"Debugging\n"</tt> if the Boolean value <tt>debug</tt> is
<tt>True</tt>, and otherwise do nothing.<p>
The monadic lifting operators promote a function to a monad. The
function arguments are scanned left to right. For example,
<tt><br>
<br>
liftM2 (+) [0,1] [0,2] = [0,2,1,3]<br>
liftM2 (+) (Just 1) Nothing = Nothing<br>
<br>
<p>
</tt>In many situations, the liftM operations can be replaced by uses
of <tt>ap</tt>, which promotes function application.
<tt><br>
<br>
return f `ap` x1 `ap` ... `ap` xn<br>
<br>
</tt>is equivalent to
<tt><br>
<br>
liftMn f x1 x2 ... xn<br>
<br>
<p>
</tt><a name="sect10.1"></a>
<h3>10.1<tt> </tt>Library <tt>Monad</tt></h3>
<tt><br>
module Monad (<br>
join, mapAndUnzipM, zipWithM, zipWithM_, foldM, when, unless, ap,<br>
liftM, liftM2, liftM3, liftM4, liftM5<br>
) where<br>
<br>
join :: (Monad m) => m (m a) -> m a<br>
join x = x >>= id<br>
<br>
mapAndUnzipM :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])<br>
mapAndUnzipM f xs = accumulate (map f xs) >>= return . unzip<br>
<br>
zipWithM :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]<br>
zipWithM f xs ys = accumulate (zipWith f xs ys)<br>
<br>
zipWithM_ :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()<br>
zipWithM_ f xs ys = sequence (zipWith f xs ys)<br>
<br>
foldM :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a<br>
foldM f a [] = return a<br>
foldM f a (x:xs) = f a x >>= \ y -> foldM f y xs<br>
<br>
when :: (Monad m) => Bool -> m () -> m ()<br>
when p s = if p then s else return ()<br>
<br>
unless :: (Monad m) => Bool -> m () -> m ()<br>
unless p s = when (not p) s<br>
<br>
ap :: (Monad m) => m (a -> b) -> m a -> m b<br>
ap = liftM2 ($)<br>
<br>
liftM :: (Monad m) => (a -> b) -> (m a -> m b)<br>
liftM f = \a -> [f a' | a' <- a]<br>
<br>
liftM2 :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)<br>
liftM2 f = \a b -> [f a' b' | a' <- a, b' <- b] <br>
<br>
liftM3 :: (Monad m) => (a -> b -> c -> d) -><br>
(m a -> m b -> m c -> m d)<br>
liftM3 f = \a b c -> [f a' b' c' | a' <- a, b' <- b, c' <- c] <br>
<br>
liftM4 :: (Monad m) => (a -> b -> c -> d -> e) -><br>
(m a -> m b -> m c -> m d -> m e)<br>
liftM4 f = \a b c d -> [f a' b' c' d' |<br>
a' <- a, b' <- b, c' <- c, d' <- d] <br>
<br>
liftM5 :: (Monad m) => (a -> b -> c -> d -> e -> f) -><br>
(m a -> m b -> m c -> m d -> m e -> m f)<br>
liftM5 f = \a b c d e -> [f a' b' c' d' e' |<br>
a' <- a, b' <- b,<br>
c' <- c, d' <- d, e <- e']<br>
<p>
<hr><i>The Haskell 1.4 Library Report</i><br><a href="index.html">top</a> | <a href="char.html">back</a> | <a href="io.html">next</a> | <a href="libindex.html">contents</a> <br><font size=2>April 4, 1997</font>
<p>
</tt>
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