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>base-4.1.0.0: Basic libraries</TD
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><A HREF="index.html"
>Contents</A
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><FONT SIZE="6"
>Control.Monad.Instances</FONT
></TD
><TD ALIGN="right"
><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="infohead"
>Portability</TD
><TD CLASS="infoval"
>portable</TD
></TR
><TR
><TD CLASS="infohead"
>Stability</TD
><TD CLASS="infoval"
>provisional</TD
></TR
><TR
><TD CLASS="infohead"
>Maintainer</TD
><TD CLASS="infoval"
>libraries@haskell.org</TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> and <TT
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
></TT
> instances for <TT
>(-&gt;) r</TT
> and
 <TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> instances for <TT
>(,) a</TT
> and <TT
><TT
><A HREF="Data-Either.html#t%3AEither"
>Either</A
></TT
> a</TT
>.
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Synopsis</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
>  <A HREF="#t%3AFunctor"
>Functor</A
> f  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="#v%3Afmap"
>fmap</A
> ::  (a -&gt; b) -&gt; f a -&gt; f b</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
>  <A HREF="#t%3AMonad"
>Monad</A
> m  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3E%3E%3D"
>(&gt;&gt;=)</A
> :: <SPAN CLASS="keyword"
>forall</SPAN
> a b.  m a -&gt; (a -&gt; m b) -&gt; m b</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3E%3E"
>(&gt;&gt;)</A
> :: <SPAN CLASS="keyword"
>forall</SPAN
> a b.  m a -&gt; m b -&gt; m b</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Areturn"
>return</A
> ::  a -&gt; m a</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Afail"
>fail</A
> ::  <A HREF="Data-Char.html#t%3AString"
>String</A
> -&gt; m a</TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Documentation</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
>  <A NAME="t:Functor"
><A NAME="t%3AFunctor"
></A
></A
><B
>Functor</B
> f  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>The <TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> class is used for types that can be mapped over.
Instances of <TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> should satisfy the following laws:
</P
><PRE
> fmap id  ==  id
 fmap (f . g)  ==  fmap f . fmap g
</PRE
><P
>The instances of <TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> for lists, Data.Maybe.Maybe and System.IO.IO
defined in the <A HREF="Prelude.html"
>Prelude</A
> satisfy these laws.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
>Methods</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A NAME="v:fmap"
><A NAME="v%3Afmap"
></A
></A
><B
>fmap</B
> ::  (a -&gt; b) -&gt; f a -&gt; f b</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Functor')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Functor" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> []</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="System-IO.html#t%3AIO"
>IO</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> [::]</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="Text-ParserCombinators-ReadP.html#t%3AReadP"
>ReadP</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="Text-ParserCombinators-ReadPrec.html#t%3AReadPrec"
>ReadPrec</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="GHC-Conc.html#t%3ASTM"
>STM</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> <A HREF="Control-Applicative.html#t%3AZipList"
>ZipList</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> Id</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> ((-&gt;) r)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Data-Either.html#t%3AEither"
>Either</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="../ghc-prim/GHC-Tuple.html#t%3A%28%2C%29"
>(,)</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Monad-ST.html#t%3AST"
>ST</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="GHC-Arr.html#t%3AIx"
>Ix</A
> i =&gt; <A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="GHC-Arr.html#t%3AArray"
>Array</A
> i)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Monad-ST-Lazy.html#t%3AST"
>ST</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Applicative.html#t%3AWrappedMonad"
>WrappedMonad</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Applicative.html#t%3AConst"
>Const</A
> m)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (StateR s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (StateL s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrow"
>Arrow</A
> a =&gt; <A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
> (<A HREF="Control-Applicative.html#t%3AWrappedArrow"
>WrappedArrow</A
> a b)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
>  <A NAME="t:Monad"
><A NAME="t%3AMonad"
></A
></A
><B
>Monad</B
> m  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
><P
>The <TT
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
></TT
> class defines the basic operations over a <EM
>monad</EM
>,
a concept from a branch of mathematics known as <EM
>category theory</EM
>.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an <EM
>abstract datatype</EM
> of actions.
Haskell's <TT
>do</TT
> expressions provide a convenient syntax for writing
monadic expressions.
</P
><P
>Minimal complete definition: <TT
><A HREF="Control-Monad-Instances.html#v%3A%3E%3E%3D"
>&gt;&gt;=</A
></TT
> and <TT
><A HREF="Control-Monad-Instances.html#v%3Areturn"
>return</A
></TT
>.
</P
><P
>Instances of <TT
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
></TT
> should satisfy the following laws:
</P
><PRE
> return a &gt;&gt;= k  ==  k a
 m &gt;&gt;= return  ==  m
 m &gt;&gt;= (\x -&gt; k x &gt;&gt;= h)  ==  (m &gt;&gt;= k) &gt;&gt;= h
</PRE
><P
>Instances of both <TT
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
></TT
> and <TT
><A HREF="Control-Monad-Instances.html#t%3AFunctor"
>Functor</A
></TT
> should additionally satisfy the law:
</P
><PRE
> fmap f xs  ==  xs &gt;&gt;= return . f
</PRE
><P
>The instances of <TT
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
></TT
> for lists, Data.Maybe.Maybe and System.IO.IO
defined in the <A HREF="Prelude.html"
>Prelude</A
> satisfy these laws.
</P
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
>Methods</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A NAME="v:>>="
><A NAME="v%3A%3E%3E%3D"
></A
></A
><B
>(&gt;&gt;=)</B
> :: <SPAN CLASS="keyword"
>forall</SPAN
> a b.  m a -&gt; (a -&gt; m b) -&gt; m b</TD
></TR
><TR
><TD CLASS="doc"
>Sequentially compose two actions, passing any value produced
 by the first as an argument to the second.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:>>"
><A NAME="v%3A%3E%3E"
></A
></A
><B
>(&gt;&gt;)</B
> :: <SPAN CLASS="keyword"
>forall</SPAN
> a b.  m a -&gt; m b -&gt; m b</TD
></TR
><TR
><TD CLASS="doc"
>Sequentially compose two actions, discarding any value produced
 by the first, like sequencing operators (such as the semicolon)
 in imperative languages.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:return"
><A NAME="v%3Areturn"
></A
></A
><B
>return</B
> ::  a -&gt; m a</TD
></TR
><TR
><TD CLASS="doc"
>Inject a value into the monadic type.
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:fail"
><A NAME="v%3Afail"
></A
></A
><B
>fail</B
> ::  <A HREF="Data-Char.html#t%3AString"
>String</A
> -&gt; m a</TD
></TR
><TR
><TD CLASS="doc"
>Fail with a message.  This operation is not part of the
 mathematical definition of a monad, but is invoked on pattern-match
 failure in a <TT
>do</TT
> expression.
</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Monad')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Monad" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> []</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> <A HREF="System-IO.html#t%3AIO"
>IO</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> [::]</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> <A HREF="Text-ParserCombinators-ReadP.html#t%3AReadP"
>ReadP</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> P</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> <A HREF="Text-ParserCombinators-ReadPrec.html#t%3AReadPrec"
>ReadPrec</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> <A HREF="GHC-Conc.html#t%3ASTM"
>STM</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> ((-&gt;) r)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Monad-ST.html#t%3AST"
>ST</A
> s)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Arrow.html#t%3AArrowApply"
>ArrowApply</A
> a =&gt; <A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Arrow.html#t%3AArrowMonad"
>ArrowMonad</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Control-Monad-Instances.html#t%3AMonad"
>Monad</A
> (<A HREF="Control-Monad-ST-Lazy.html#t%3AST"
>ST</A
> s)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="botbar"
>Produced by <A HREF="http://www.haskell.org/haddock/"
>Haddock</A
> version 2.4.2</TD
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