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>Data.Monoid</TITLE
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>base-4.1.0.0: Basic libraries</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
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>Index</A
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><TD CLASS="modulebar"
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><FONT SIZE="6"
>Data.Monoid</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"
>experimental</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
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="section4"
><B
>Contents</B
></TD
></TR
><TR
><TD
><DL
><DT
><A HREF="#1"
>Monoid typeclass
</A
></DT
><DT
><A HREF="#2"
>Bool wrappers
</A
></DT
><DT
><A HREF="#3"
>Num wrappers
</A
></DT
><DT
><A HREF="#4"
>Maybe wrappers
</A
></DT
></DL
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
>Description</TD
></TR
><TR
><TD CLASS="doc"
><P
>The Monoid class with various general-purpose instances.
</P
><P
>Inspired by the paper
    /Functional Programming with Overloading and
        Higher-Order Polymorphism/,
      Mark P Jones (<A HREF="http://citeseer.ist.psu.edu/jones95functional.html"
>http://citeseer.ist.psu.edu/jones95functional.html</A
>)
        Advanced School of Functional Programming, 1995.
</P
></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%3AMonoid"
>Monoid</A
> a  <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%3Amempty"
>mempty</A
> :: a</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Amappend"
>mappend</A
> :: a -&gt; a -&gt; a</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Amconcat"
>mconcat</A
> :: [a] -&gt; a</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3ADual"
>Dual</A
> a = <A HREF="#v%3ADual"
>Dual</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetDual"
>getDual</A
> :: a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AEndo"
>Endo</A
> a = <A HREF="#v%3AEndo"
>Endo</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AappEndo"
>appEndo</A
> :: a -&gt; a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AAll"
>All</A
>  = <A HREF="#v%3AAll"
>All</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetAll"
>getAll</A
> :: <A HREF="../ghc-prim/GHC-Bool.html#t%3ABool"
>Bool</A
></TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AAny"
>Any</A
>  = <A HREF="#v%3AAny"
>Any</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetAny"
>getAny</A
> :: <A HREF="../ghc-prim/GHC-Bool.html#t%3ABool"
>Bool</A
></TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3ASum"
>Sum</A
> a = <A HREF="#v%3ASum"
>Sum</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetSum"
>getSum</A
> :: a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AProduct"
>Product</A
> a = <A HREF="#v%3AProduct"
>Product</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetProduct"
>getProduct</A
> :: a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3AFirst"
>First</A
> a = <A HREF="#v%3AFirst"
>First</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetFirst"
>getFirst</A
> :: <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
> a</TD
></TR
></TABLE
>}</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A HREF="#t%3ALast"
>Last</A
> a = <A HREF="#v%3ALast"
>Last</A
> {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="recfield"
><A HREF="#v%3AgetLast"
>getLast</A
> :: <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
> a</TD
></TR
></TABLE
>}</TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="1"
><A NAME="1"
>Monoid typeclass
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>class</SPAN
>  <A NAME="t:Monoid"
><A NAME="t%3AMonoid"
></A
></A
><B
>Monoid</B
> a  <SPAN CLASS="keyword"
>where</SPAN
></TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>The monoid class.
 A minimal complete definition must supply <TT
><A HREF="Data-Monoid.html#v%3Amempty"
>mempty</A
></TT
> and <TT
><A HREF="Data-Monoid.html#v%3Amappend"
>mappend</A
></TT
>,
 and these should satisfy the monoid laws.
</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:mempty"
><A NAME="v%3Amempty"
></A
></A
><B
>mempty</B
> :: a</TD
></TR
><TR
><TD CLASS="doc"
>Identity of <TT
><A HREF="Data-Monoid.html#v%3Amappend"
>mappend</A
></TT
>
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mappend"
><A NAME="v%3Amappend"
></A
></A
><B
>mappend</B
> :: a -&gt; a -&gt; a</TD
></TR
><TR
><TD CLASS="doc"
>An associative operation
</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mconcat"
><A NAME="v%3Amconcat"
></A
></A
><B
>mconcat</B
> :: [a] -&gt; a</TD
></TR
><TR
><TD CLASS="doc"
>Fold a list using the monoid.
 For most types, the default definition for <TT
><A HREF="Data-Monoid.html#v%3Amconcat"
>mconcat</A
></TT
> will be
 used, but the function is included in the class definition so
 that an optimized version can be provided for specific types.
</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:Monoid')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Monoid" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="../ghc-prim/GHC-Ordering.html#t%3AOrdering"
>Ordering</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="../ghc-prim/GHC-Unit.html#t%3A%28%29"
>()</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> ([] a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ANum"
>Num</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ANum"
>Num</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AEndo"
>Endo</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> b =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (a -&gt; b)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> b) =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="../ghc-prim/GHC-Tuple.html#t%3A%28%2C%29"
>(,)</A
> a b)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> b, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> c) =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="../ghc-prim/GHC-Tuple.html#t%3A%28%2C%2C%29"
>(,,)</A
> a b c)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> b, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> c, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> d) =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="../ghc-prim/GHC-Tuple.html#t%3A%28%2C%2C%2C%29"
>(,,,)</A
> a b c d)</TD
></TR
><TR
><TD CLASS="decl"
>(<A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> b, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> c, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> d, <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> e) =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="../ghc-prim/GHC-Tuple.html#t%3A%28%2C%2C%2C%2C%29"
>(,,,,)</A
> a b c d e)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Dual"
><A NAME="t%3ADual"
></A
></A
><B
>Dual</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>The dual of a monoid, obtained by swapping the arguments of <TT
><A HREF="Data-Monoid.html#v%3Amappend"
>mappend</A
></TT
>.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Dual"
><A NAME="v%3ADual"
></A
></A
><B
>Dual</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getDual"
><A NAME="v%3AgetDual"
></A
></A
><B
>getDual</B
> :: a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Dual')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Dual" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> a =&gt; <A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> a =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ADual"
>Dual</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Endo"
><A NAME="t%3AEndo"
></A
></A
><B
>Endo</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>The monoid of endomorphisms under composition.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Endo"
><A NAME="v%3AEndo"
></A
></A
><B
>Endo</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:appEndo"
><A NAME="v%3AappEndo"
></A
></A
><B
>appEndo</B
> :: a -&gt; a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Endo')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Endo" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AEndo"
>Endo</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="2"
><A NAME="2"
>Bool wrappers
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:All"
><A NAME="t%3AAll"
></A
></A
><B
>All</B
>  </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Boolean monoid under conjunction.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:All"
><A NAME="v%3AAll"
></A
></A
><B
>All</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getAll"
><A NAME="v%3AgetAll"
></A
></A
><B
>getAll</B
> :: <A HREF="../ghc-prim/GHC-Bool.html#t%3ABool"
>Bool</A
></TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:All')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:All" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="Data-Monoid.html#t%3AAll"
>All</A
></TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Any"
><A NAME="t%3AAny"
></A
></A
><B
>Any</B
>  </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Boolean monoid under disjunction.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Any"
><A NAME="v%3AAny"
></A
></A
><B
>Any</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getAny"
><A NAME="v%3AgetAny"
></A
></A
><B
>getAny</B
> :: <A HREF="../ghc-prim/GHC-Bool.html#t%3ABool"
>Bool</A
></TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Any')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Any" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> <A HREF="Data-Monoid.html#t%3AAny"
>Any</A
></TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="3"
><A NAME="3"
>Num wrappers
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Sum"
><A NAME="t%3ASum"
></A
></A
><B
>Sum</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Monoid under addition.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Sum"
><A NAME="v%3ASum"
></A
></A
><B
>Sum</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getSum"
><A NAME="v%3AgetSum"
></A
></A
><B
>getSum</B
> :: a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Sum')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Sum" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> a =&gt; <A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> a =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ANum"
>Num</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ASum"
>Sum</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Product"
><A NAME="t%3AProduct"
></A
></A
><B
>Product</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Monoid under multiplication.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Product"
><A NAME="v%3AProduct"
></A
></A
><B
>Product</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getProduct"
><A NAME="v%3AgetProduct"
></A
></A
><B
>getProduct</B
> :: a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Product')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Product" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> a =&gt; <A HREF="Prelude.html#t%3ABounded"
>Bounded</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> a =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Prelude.html#t%3ANum"
>Num</A
> a =&gt; <A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AProduct"
>Product</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="4"
><A NAME="4"
>Maybe wrappers
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="doc"
><P
>To implement <TT
>find</TT
> or <TT
>findLast</TT
> on any Foldable:
</P
><PRE
>
 findLast :: Foldable t =&gt; (a -&gt; Bool) -&gt; t a -&gt; Maybe a
 findLast pred = getLast . foldMap (x -&gt; if pred x
                                            then Last (Just x)
                                            else Last Nothing)
</PRE
><P
>Much of Data.Map's interface can be implemented with
 Data.Map.alter. Some of the rest can be implemented with a new
 <TT
>alterA</TT
> function and either <TT
><A HREF="Data-Monoid.html#t%3AFirst"
>First</A
></TT
> or <TT
><A HREF="Data-Monoid.html#t%3ALast"
>Last</A
></TT
>:
</P
><PRE
> alterA :: (Applicative f, Ord k) =&gt;
           (Maybe a -&gt; f (Maybe a)) -&gt; k -&gt; Map k a -&gt; f (Map k a)

 instance Monoid a =&gt; Applicative ((,) a)  -- from Control.Applicative
</PRE
><PRE
>
 insertLookupWithKey :: Ord k =&gt; (k -&gt; v -&gt; v -&gt; v) -&gt; k -&gt; v
                     -&gt; Map k v -&gt; (Maybe v, Map k v)
 insertLookupWithKey combine key value =
   Arrow.first getFirst . alterA doChange key
   where
   doChange Nothing = (First Nothing, Just value)
   doChange (Just oldValue) =
     (First (Just oldValue),
      Just (combine key value oldValue))
</PRE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:First"
><A NAME="t%3AFirst"
></A
></A
><B
>First</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Maybe monoid returning the leftmost non-Nothing value.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:First"
><A NAME="v%3AFirst"
></A
></A
><B
>First</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getFirst"
><A NAME="v%3AgetFirst"
></A
></A
><B
>getFirst</B
> :: <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
> a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:First')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:First" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> a =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3AFirst"
>First</A
> a)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>newtype</SPAN
>  <A NAME="t:Last"
><A NAME="t%3ALast"
></A
></A
><B
>Last</B
> a </TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0"
><TR
><TD CLASS="ndoc"
>Maybe monoid returning the rightmost non-Nothing value.
</TD
></TR
><TR
><TD CLASS="section4"
>Constructors</TD
></TR
><TR
><TD CLASS="body"
><TABLE CLASS="vanilla" CELLSPACING="5" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:Last"
><A NAME="v%3ALast"
></A
></A
><B
>Last</B
></TD
><TD CLASS="rdoc"
></TD
></TR
><TR
><TD CLASS="body" COLSPAN="2"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:getLast"
><A NAME="v%3AgetLast"
></A
></A
><B
>getLast</B
> :: <A HREF="Data-Maybe.html#t%3AMaybe"
>Maybe</A
> a</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Last')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:Last" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> a =&gt; <A HREF="Data-Eq.html#t%3AEq"
>Eq</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> a =&gt; <A HREF="Data-Ord.html#t%3AOrd"
>Ord</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Read.html#t%3ARead"
>Read</A
> a =&gt; <A HREF="Text-Read.html#t%3ARead"
>Read</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Text-Show.html#t%3AShow"
>Show</A
> a =&gt; <A HREF="Text-Show.html#t%3AShow"
>Show</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</TD
></TR
><TR
><TD CLASS="decl"
><A HREF="Data-Monoid.html#t%3AMonoid"
>Monoid</A
> (<A HREF="Data-Monoid.html#t%3ALast"
>Last</A
> a)</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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