<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <!--Rendered using the Haskell Html Library v0.2--> <HTML ><HEAD ><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8" ><TITLE >Control.Applicative</TITLE ><LINK HREF="haddock.css" REL="stylesheet" TYPE="text/css" ><SCRIPT SRC="haddock-util.js" TYPE="text/javascript" ></SCRIPT ><SCRIPT TYPE="text/javascript" >window.onload = function () {setSynopsis("mini_Control-Applicative.html")};</SCRIPT ></HEAD ><BODY ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="topbar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><IMG SRC="haskell_icon.gif" WIDTH="16" HEIGHT="16" ALT=" " ></TD ><TD CLASS="title" >base-4.1.0.0: Basic libraries</TD ><TD CLASS="topbut" ><A HREF="index.html" >Contents</A ></TD ><TD CLASS="topbut" ><A HREF="doc-index.html" >Index</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="modulebar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><FONT SIZE="6" >Control.Applicative</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" >Applicative functors </A ></DT ><DT ><A HREF="#2" >Alternatives </A ></DT ><DT ><A HREF="#3" >Instances </A ></DT ><DT ><A HREF="#4" >Utility functions </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 >This module describes a structure intermediate between a functor and a monad: it provides pure expressions and sequencing, but no binding. (Technically, a strong lax monoidal functor.) For more details, see <EM >Applicative Programming with Effects</EM >, by Conor McBride and Ross Paterson, online at <A HREF="http://www.soi.city.ac.uk/~ross/papers/Applicative.html" >http://www.soi.city.ac.uk/~ross/papers/Applicative.html</A >. </P ><P >This interface was introduced for parsers by Niklas Röjemo, because it admits more sharing than the monadic interface. The names here are mostly based on recent parsing work by Doaitse Swierstra. </P ><P >This class is also useful with instances of the Data.Traversable.Traversable class. </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="Control-Monad.html#t%3AFunctor" >Functor</A > f => <A HREF="#t%3AApplicative" >Applicative</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%3Apure" >pure</A > :: a -> f a</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%2A%3E" >(<*>)</A > :: f (a -> b) -> f a -> f b</TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => <A HREF="#t%3AAlternative" >Alternative</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%3Aempty" >empty</A > :: f a</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%7C%3E" >(<|>)</A > :: f a -> f a -> f a</TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >newtype</SPAN > <A HREF="#t%3AConst" >Const</A > a b = <A HREF="#v%3AConst" >Const</A > {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="recfield" ><A HREF="#v%3AgetConst" >getConst</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%3AWrappedMonad" >WrappedMonad</A > m a = <A HREF="#v%3AWrapMonad" >WrapMonad</A > {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="recfield" ><A HREF="#v%3AunwrapMonad" >unwrapMonad</A > :: m a</TD ></TR ></TABLE >}</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >newtype</SPAN > <A HREF="#t%3AWrappedArrow" >WrappedArrow</A > a b c = <A HREF="#v%3AWrapArrow" >WrapArrow</A > {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="recfield" ><A HREF="#v%3AunwrapArrow" >unwrapArrow</A > :: a b c</TD ></TR ></TABLE >}</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >newtype</SPAN > <A HREF="#t%3AZipList" >ZipList</A > a = <A HREF="#v%3AZipList" >ZipList</A > {<TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="recfield" ><A HREF="#v%3AgetZipList" >getZipList</A > :: [a]</TD ></TR ></TABLE >}</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%24%3E" >(<$>)</A > :: <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > f => (a -> b) -> f a -> f b</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%24" >(<$)</A > :: <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > f => a -> f b -> f a</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%2A%3E" >(*>)</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f b -> f b</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%2A" >(<*)</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f b -> f a</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%2A%2A%3E" >(<**>)</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f (a -> b) -> f b</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AliftA" >liftA</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b) -> f a -> f b</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AliftA2" >liftA2</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b -> c) -> f a -> f b -> f c</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AliftA3" >liftA3</A > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Aoptional" >optional</A > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f (<A HREF="Data-Maybe.html#t%3AMaybe" >Maybe</A > a)</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Asome" >some</A > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f [a]</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Amany" >many</A > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f [a]</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" >Applicative functors </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > f => <A NAME="t:Applicative" ><A NAME="t%3AApplicative" ></A ></A ><B >Applicative</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 >A functor with application. </P ><P >Instances should satisfy the following laws: </P ><DL ><DT ><EM >identity</EM ></DT ><DD > <TT ><TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > <TT ><A HREF="Control-Category.html#v%3Aid" >id</A ></TT > <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > v = v</TT > </DD ><DT ><EM >composition</EM ></DT ><DD > <TT ><TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > (.) <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > u <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > v <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > w = u <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > (v <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > w)</TT > </DD ><DT ><EM >homomorphism</EM ></DT ><DD > <TT ><TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > f <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > <TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > x = <TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > (f x)</TT > </DD ><DT ><EM >interchange</EM ></DT ><DD > <TT >u <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > <TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > y = <TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > (<TT ><A HREF="Prelude.html#v%3A%24" >$</A ></TT > y) <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > u</TT > </DD ></DL ><P >The <TT ><A HREF="Control-Monad.html#t%3AFunctor" >Functor</A ></TT > instance should satisfy </P ><PRE > <TT ><A HREF="Control-Monad.html#v%3Afmap" >fmap</A ></TT > f x = <TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > f <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > x </PRE ><P >If <TT >f</TT > is also a <TT ><A HREF="Control-Monad.html#t%3AMonad" >Monad</A ></TT >, define <TT ><TT ><A HREF="Control-Applicative.html#v%3Apure" >pure</A ></TT > = <TT ><A HREF="Control-Monad.html#v%3Areturn" >return</A ></TT ></TT > and <TT >(<TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT >) = <TT ><A HREF="Control-Monad.html#v%3Aap" >ap</A ></TT ></TT >. </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:pure" ><A NAME="v%3Apure" ></A ></A ><B >pure</B > :: a -> f a</TD ></TR ><TR ><TD CLASS="doc" >Lift a value. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<*>" ><A NAME="v%3A%3C%2A%3E" ></A ></A ><B >(<*>)</B > :: f (a -> b) -> f a -> f b</TD ></TR ><TR ><TD CLASS="doc" >Sequential application. </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:Applicative')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Applicative" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > []</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > <A HREF="System-IO.html#t%3AIO" >IO</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > <A HREF="Data-Maybe.html#t%3AMaybe" >Maybe</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > <A HREF="Control-Applicative.html#t%3AZipList" >ZipList</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > Id</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > ((->) a)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Monoid.html#t%3AMonoid" >Monoid</A > a => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</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.html#t%3AMonad" >Monad</A > m => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (<A HREF="Control-Applicative.html#t%3AWrappedMonad" >WrappedMonad</A > m)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Monoid.html#t%3AMonoid" >Monoid</A > m => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (<A HREF="Control-Applicative.html#t%3AConst" >Const</A > m)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (StateR s)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (StateL s)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Arrow.html#t%3AArrow" >Arrow</A > a => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</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="section1" ><A NAME="2" ><A NAME="2" >Alternatives </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => <A NAME="t:Alternative" ><A NAME="t%3AAlternative" ></A ></A ><B >Alternative</B > f <SPAN CLASS="keyword" >where</SPAN ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >A monoid on applicative functors. </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:empty" ><A NAME="v%3Aempty" ></A ></A ><B >empty</B > :: f a</TD ></TR ><TR ><TD CLASS="doc" >The identity of <TT ><A HREF="Control-Applicative.html#v%3A%3C%7C%3E" ><|></A ></TT > </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<|>" ><A NAME="v%3A%3C%7C%3E" ></A ></A ><B >(<|>)</B > :: f a -> f a -> f a</TD ></TR ><TR ><TD CLASS="doc" >An associative binary operation </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:Alternative')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Alternative" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > []</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > <A HREF="Data-Maybe.html#t%3AMaybe" >Maybe</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Monad.html#t%3AMonadPlus" >MonadPlus</A > m => <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > (<A HREF="Control-Applicative.html#t%3AWrappedMonad" >WrappedMonad</A > m)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Control-Arrow.html#t%3AArrowZero" >ArrowZero</A > a, <A HREF="Control-Arrow.html#t%3AArrowPlus" >ArrowPlus</A > a) => <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</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="section1" ><A NAME="3" ><A NAME="3" >Instances </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >newtype</SPAN > <A NAME="t:Const" ><A NAME="t%3AConst" ></A ></A ><B >Const</B > a b </TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><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:Const" ><A NAME="v%3AConst" ></A ></A ><B >Const</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:getConst" ><A NAME="v%3AgetConst" ></A ></A ><B >getConst</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:Const')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Const" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > (<A HREF="Control-Applicative.html#t%3AConst" >Const</A > m)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-Monoid.html#t%3AMonoid" >Monoid</A > m => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (<A HREF="Control-Applicative.html#t%3AConst" >Const</A > m)</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:WrappedMonad" ><A NAME="t%3AWrappedMonad" ></A ></A ><B >WrappedMonad</B > m a </TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><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:WrapMonad" ><A NAME="v%3AWrapMonad" ></A ></A ><B >WrapMonad</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:unwrapMonad" ><A NAME="v%3AunwrapMonad" ></A ></A ><B >unwrapMonad</B > :: m 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:WrappedMonad')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:WrappedMonad" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Monad.html#t%3AMonad" >Monad</A > m => <A HREF="Control-Monad.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.html#t%3AMonadPlus" >MonadPlus</A > m => <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > (<A HREF="Control-Applicative.html#t%3AWrappedMonad" >WrappedMonad</A > m)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Monad.html#t%3AMonad" >Monad</A > m => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > (<A HREF="Control-Applicative.html#t%3AWrappedMonad" >WrappedMonad</A > m)</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:WrappedArrow" ><A NAME="t%3AWrappedArrow" ></A ></A ><B >WrappedArrow</B > a b c </TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><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:WrapArrow" ><A NAME="v%3AWrapArrow" ></A ></A ><B >WrapArrow</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:unwrapArrow" ><A NAME="v%3AunwrapArrow" ></A ></A ><B >unwrapArrow</B > :: a b c</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:WrappedArrow')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:WrappedArrow" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Arrow.html#t%3AArrow" >Arrow</A > a => <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > (<A HREF="Control-Applicative.html#t%3AWrappedArrow" >WrappedArrow</A > a b)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Control-Arrow.html#t%3AArrowZero" >ArrowZero</A > a, <A HREF="Control-Arrow.html#t%3AArrowPlus" >ArrowPlus</A > a) => <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > (<A HREF="Control-Applicative.html#t%3AWrappedArrow" >WrappedArrow</A > a b)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Arrow.html#t%3AArrow" >Arrow</A > a => <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</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" >newtype</SPAN > <A NAME="t:ZipList" ><A NAME="t%3AZipList" ></A ></A ><B >ZipList</B > a </TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" ><P >Lists, but with an <TT ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A ></TT > functor based on zipping, so that </P ><PRE >f <TT ><A HREF="Control-Applicative.html#v%3A%3C%24%3E" ><$></A ></TT > <TT ><A HREF="Control-Applicative.html#t%3AZipList" >ZipList</A ></TT > xs1 <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > ... <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > <TT ><A HREF="Control-Applicative.html#t%3AZipList" >ZipList</A ></TT > xsn = <TT ><A HREF="Control-Applicative.html#t%3AZipList" >ZipList</A ></TT > (zipWithn f xs1 ... xsn)</PRE ></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:ZipList" ><A NAME="v%3AZipList" ></A ></A ><B >ZipList</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:getZipList" ><A NAME="v%3AgetZipList" ></A ></A ><B >getZipList</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:ZipList')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:ZipList" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > <A HREF="Control-Applicative.html#t%3AZipList" >ZipList</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > <A HREF="Control-Applicative.html#t%3AZipList" >ZipList</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" >Utility functions </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<$>" ><A NAME="v%3A%3C%24%3E" ></A ></A ><B >(<$>)</B > :: <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > f => (a -> b) -> f a -> f b</TD ></TR ><TR ><TD CLASS="doc" >A synonym for <TT ><A HREF="Control-Monad.html#v%3Afmap" >fmap</A ></TT >. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<$" ><A NAME="v%3A%3C%24" ></A ></A ><B >(<$)</B > :: <A HREF="Control-Monad.html#t%3AFunctor" >Functor</A > f => a -> f b -> f a</TD ></TR ><TR ><TD CLASS="doc" >Replace the value. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:*>" ><A NAME="v%3A%2A%3E" ></A ></A ><B >(*>)</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f b -> f b</TD ></TR ><TR ><TD CLASS="doc" >Sequence actions, discarding the value of the first argument. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<*" ><A NAME="v%3A%3C%2A" ></A ></A ><B >(<*)</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f b -> f a</TD ></TR ><TR ><TD CLASS="doc" >Sequence actions, discarding the value of the second argument. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:<**>" ><A NAME="v%3A%3C%2A%2A%3E" ></A ></A ><B >(<**>)</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => f a -> f (a -> b) -> f b</TD ></TR ><TR ><TD CLASS="doc" >A variant of <TT ><A HREF="Control-Applicative.html#v%3A%3C%2A%3E" ><*></A ></TT > with the arguments reversed. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:liftA" ><A NAME="v%3AliftA" ></A ></A ><B >liftA</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b) -> f a -> f b</TD ></TR ><TR ><TD CLASS="doc" >Lift a function to actions. This function may be used as a value for <TT ><A HREF="Control-Monad.html#v%3Afmap" >fmap</A ></TT > in a <TT ><A HREF="Control-Monad.html#t%3AFunctor" >Functor</A ></TT > instance. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:liftA2" ><A NAME="v%3AliftA2" ></A ></A ><B >liftA2</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b -> c) -> f a -> f b -> f c</TD ></TR ><TR ><TD CLASS="doc" >Lift a binary function to actions. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:liftA3" ><A NAME="v%3AliftA3" ></A ></A ><B >liftA3</B > :: <A HREF="Control-Applicative.html#t%3AApplicative" >Applicative</A > f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d</TD ></TR ><TR ><TD CLASS="doc" >Lift a ternary function to actions. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:optional" ><A NAME="v%3Aoptional" ></A ></A ><B >optional</B > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f (<A HREF="Data-Maybe.html#t%3AMaybe" >Maybe</A > a)</TD ></TR ><TR ><TD CLASS="doc" >One or none. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:some" ><A NAME="v%3Asome" ></A ></A ><B >some</B > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f [a]</TD ></TR ><TR ><TD CLASS="doc" >One or more. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="decl" ><A NAME="v:many" ><A NAME="v%3Amany" ></A ></A ><B >many</B > :: <A HREF="Control-Applicative.html#t%3AAlternative" >Alternative</A > f => f a -> f [a]</TD ></TR ><TR ><TD CLASS="doc" >Zero or more. </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 ></TR ></TABLE ></BODY ></HTML >