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ghc-fgl-devel-5.4.2.3-1.fc14.i686.rpm

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>Data.Graph.Inductive.Query.Monad</TITLE
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>fgl-5.4.2.3: Martin Erwig's Functional Graph Library</TD
><TD CLASS="topbut"
><A HREF="index.html"
>Contents</A
></TD
><TD CLASS="topbut"
><A HREF="doc-index.html"
>Index</A
></TD
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><FONT SIZE="6"
>Data.Graph.Inductive.Query.Monad</FONT
></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"
>Additional Graph Utilities
</A
></DT
><DT
><A HREF="#2"
>Graph Transformer Monad
</A
></DT
><DT
><A HREF="#3"
>Graph Computations Based on Graph Monads
</A
></DT
><DD
><DL
><DT
><A HREF="#4"
>Monadic Graph Accessing Functions
</A
></DT
><DT
><A HREF="#5"
>Derived Graph Recursion Operators
</A
></DT
></DL
></DD
><DT
><A HREF="#6"
>Examples: Graph Algorithms as Instances of Recursion Operators
</A
></DT
><DD
><DL
><DT
><A HREF="#7"
>Instances of graphRec
</A
></DT
></DL
></DD
><DT
><A HREF="#8"
>Example: Monadic DFS Algorithm(s)
</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"
>Monadic Graph Algorithms
</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"
><A HREF="#v%3AmapFst"
>mapFst</A
> ::  (a -&gt; b) -&gt; (a, c) -&gt; (b, c)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AmapSnd"
>mapSnd</A
> ::  (a -&gt; b) -&gt; (c, a) -&gt; (c, b)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3A%3E%3C"
>(&gt;&lt;)</A
> ::  (a -&gt; b) -&gt; (c -&gt; d) -&gt; (a, c) -&gt; (b, d)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AorP"
>orP</A
> ::  (a -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; (b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; (a, b) -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>data</SPAN
>  <A HREF="#t%3AGT"
>GT</A
> m g a = <A HREF="#v%3AMGT"
>MGT</A
> (m g -&gt; m (a, g))</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Aapply"
>apply</A
> ::  <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m (a, g)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3Aapply%27"
>apply'</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; g -&gt; m (a, g)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AapplyWith"
>applyWith</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (a -&gt; b) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m (b, g)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AapplyWith%27"
>applyWith'</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (a -&gt; b) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; g -&gt; m (b, g)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3ArunGT"
>runGT</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AcondMGT%27"
>condMGT'</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (s -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3ArecMGT%27"
>recMGT'</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (s -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; (a -&gt; b -&gt; b) -&gt; b -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AcondMGT"
>condMGT</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (m s -&gt; m <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3ArecMGT"
>recMGT</A
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (m s -&gt; m <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; (a -&gt; b -&gt; b) -&gt; b -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s b</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgetNode"
>getNode</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
></TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgetContext"
>getContext</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b)</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgetNodes%27"
>getNodes'</A
> :: (<A HREF="Data-Graph-Inductive-Graph.html#t%3AGraph"
>Graph</A
> gr, <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr) =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgetNodes"
>getNodes</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AsucGT"
>sucGT</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
> -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Maybe.html#t%3AMaybe"
>Maybe</A
> [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>])</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AsucM"
>sucM</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
> -&gt; m (gr a b) -&gt; m (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Maybe.html#t%3AMaybe"
>Maybe</A
> [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>])</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphRec"
>graphRec</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c -&gt; (c -&gt; d -&gt; d) -&gt; d -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphRec%27"
>graphRec'</A
> :: (<A HREF="Data-Graph-Inductive-Graph.html#t%3AGraph"
>Graph</A
> gr, <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr) =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c -&gt; (c -&gt; d -&gt; d) -&gt; d -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) d</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphUFold"
>graphUFold</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; c -&gt; c) -&gt; c -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphNodesM0"
>graphNodesM0</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphNodesM"
>graphNodesM</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphNodes"
>graphNodes</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphFilterM"
>graphFilterM</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphFilter"
>graphFilter</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AdfsGT"
>dfsGT</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AdfsM"
>dfsM</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AdfsM%27"
>dfsM'</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AdffM"
>dffM</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphDff"
>graphDff</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; m (gr a b) -&gt; m [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s8"
></TD
></TR
><TR
><TD CLASS="decl"
><A HREF="#v%3AgraphDff%27"
>graphDff'</A
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</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"
>Additional Graph Utilities
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mapFst"
><A NAME="v%3AmapFst"
></A
></A
><B
>mapFst</B
> ::  (a -&gt; b) -&gt; (a, c) -&gt; (b, c)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:mapSnd"
><A NAME="v%3AmapSnd"
></A
></A
><B
>mapSnd</B
> ::  (a -&gt; b) -&gt; (c, a) -&gt; (c, b)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:><"
><A NAME="v%3A%3E%3C"
></A
></A
><B
>(&gt;&lt;)</B
> ::  (a -&gt; b) -&gt; (c -&gt; d) -&gt; (a, c) -&gt; (b, d)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:orP"
><A NAME="v%3AorP"
></A
></A
><B
>orP</B
> ::  (a -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; (b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; (a, b) -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="2"
><A NAME="2"
>Graph Transformer Monad
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><SPAN CLASS="keyword"
>data</SPAN
>  <A NAME="t:GT"
><A NAME="t%3AGT"
></A
></A
><B
>GT</B
> m g 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="1" CELLPADDING="0"
><TR
><TD CLASS="arg"
><A NAME="v:MGT"
><A NAME="v%3AMGT"
></A
></A
><B
>MGT</B
> (m g -&gt; m (a, g))</TD
><TD CLASS="rdoc"
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="section4"
><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:GT')" ALT="show/hide"
> Instances</TD
></TR
><TR
><TD CLASS="body"
><DIV ID="i:GT" STYLE="display:block;"
><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0"
><TR
><TD CLASS="decl"
><A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> (<A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g)</TD
></TR
></TABLE
></DIV
></TD
></TR
></TABLE
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:apply"
><A NAME="v%3Aapply"
></A
></A
><B
>apply</B
> ::  <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m (a, g)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:apply'"
><A NAME="v%3Aapply%27"
></A
></A
><B
>apply'</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; g -&gt; m (a, g)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:applyWith"
><A NAME="v%3AapplyWith"
></A
></A
><B
>applyWith</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (a -&gt; b) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m (b, g)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:applyWith'"
><A NAME="v%3AapplyWith%27"
></A
></A
><B
>applyWith'</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (a -&gt; b) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; g -&gt; m (b, g)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:runGT"
><A NAME="v%3ArunGT"
></A
></A
><B
>runGT</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m g a -&gt; m g -&gt; m a</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:condMGT'"
><A NAME="v%3AcondMGT%27"
></A
></A
><B
>condMGT'</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (s -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:recMGT'"
><A NAME="v%3ArecMGT%27"
></A
></A
><B
>recMGT'</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (s -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; (a -&gt; b -&gt; b) -&gt; b -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s b</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:condMGT"
><A NAME="v%3AcondMGT"
></A
></A
><B
>condMGT</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (m s -&gt; m <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:recMGT"
><A NAME="v%3ArecMGT"
></A
></A
><B
>recMGT</B
> :: <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Control-Monad.html#t%3AMonad"
>Monad</A
> m =&gt; (m s -&gt; m <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s a -&gt; (a -&gt; b -&gt; b) -&gt; b -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m s b</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="3"
><A NAME="3"
>Graph Computations Based on Graph Monads
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section2"
><A NAME="4"
><A NAME="4"
>Monadic Graph Accessing Functions
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:getNode"
><A NAME="v%3AgetNode"
></A
></A
><B
>getNode</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:getContext"
><A NAME="v%3AgetContext"
></A
></A
><B
>getContext</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b)</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:getNodes'"
><A NAME="v%3AgetNodes%27"
></A
></A
><B
>getNodes'</B
> :: (<A HREF="Data-Graph-Inductive-Graph.html#t%3AGraph"
>Graph</A
> gr, <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr) =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:getNodes"
><A NAME="v%3AgetNodes"
></A
></A
><B
>getNodes</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:sucGT"
><A NAME="v%3AsucGT"
></A
></A
><B
>sucGT</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
> -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Maybe.html#t%3AMaybe"
>Maybe</A
> [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>])</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:sucM"
><A NAME="v%3AsucM"
></A
></A
><B
>sucM</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
> -&gt; m (gr a b) -&gt; m (<A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Maybe.html#t%3AMaybe"
>Maybe</A
> [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>])</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section2"
><A NAME="5"
><A NAME="5"
>Derived Graph Recursion Operators
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphRec"
><A NAME="v%3AgraphRec"
></A
></A
><B
>graphRec</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c -&gt; (c -&gt; d -&gt; d) -&gt; d -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) d</TD
></TR
><TR
><TD CLASS="doc"
>encapsulates a simple recursion schema on graphs
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphRec'"
><A NAME="v%3AgraphRec%27"
></A
></A
><B
>graphRec'</B
> :: (<A HREF="Data-Graph-Inductive-Graph.html#t%3AGraph"
>Graph</A
> gr, <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr) =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c -&gt; (c -&gt; d -&gt; d) -&gt; d -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) d</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphUFold"
><A NAME="v%3AgraphUFold"
></A
></A
><B
>graphUFold</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; c -&gt; c) -&gt; c -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) c</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="6"
><A NAME="6"
>Examples: Graph Algorithms as Instances of Recursion Operators
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section2"
><A NAME="7"
><A NAME="7"
>Instances of graphRec
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphNodesM0"
><A NAME="v%3AgraphNodesM0"
></A
></A
><B
>graphNodesM0</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphNodesM"
><A NAME="v%3AgraphNodesM"
></A
></A
><B
>graphNodesM</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphNodes"
><A NAME="v%3AgraphNodes"
></A
></A
><B
>graphNodes</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphFilterM"
><A NAME="v%3AgraphFilterM"
></A
></A
><B
>graphFilterM</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphFilter"
><A NAME="v%3AgraphFilter"
></A
></A
><B
>graphFilter</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; (<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b -&gt; <A HREF="/usr/share/doc/ghc/html/libraries/base-4.2.0.2/Data-Bool.html#t%3ABool"
>Bool</A
>) -&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3AContext"
>Context</A
> a b]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="section1"
><A NAME="8"
><A NAME="8"
>Example: Monadic DFS Algorithm(s)
</A
></A
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:dfsGT"
><A NAME="v%3AdfsGT"
></A
></A
><B
>dfsGT</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="doc"
><P
>Monadic graph algorithms are defined in two steps:
</P
><OL
><LI
> define the (possibly parameterized) graph transformer (e.g., dfsGT)
  (2) run the graph transformer (applied to arguments) (e.g., dfsM)
</LI
></OL
></TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:dfsM"
><A NAME="v%3AdfsM"
></A
></A
><B
>dfsM</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="doc"
>depth-first search yielding number of nodes
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:dfsM'"
><A NAME="v%3AdfsM%27"
></A
></A
><B
>dfsM'</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:dffM"
><A NAME="v%3AdffM"
></A
></A
><B
>dffM</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; <A HREF="Data-Graph-Inductive-Query-Monad.html#t%3AGT"
>GT</A
> m (gr a b) [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="doc"
>depth-first search yielding dfs forest
</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphDff"
><A NAME="v%3AgraphDff"
></A
></A
><B
>graphDff</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; [<A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>] -&gt; m (gr a b) -&gt; m [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
></TR
><TR
><TD CLASS="s15"
></TD
></TR
><TR
><TD CLASS="decl"
><A NAME="v:graphDff'"
><A NAME="v%3AgraphDff%27"
></A
></A
><B
>graphDff'</B
> :: <A HREF="Data-Graph-Inductive-Monad.html#t%3AGraphM"
>GraphM</A
> m gr =&gt; m (gr a b) -&gt; m [<A HREF="/usr/share/doc/ghc/html/libraries/containers-0.3.0.0/Data-Tree.html#t%3ATree"
>Tree</A
> <A HREF="Data-Graph-Inductive-Graph.html#t%3ANode"
>Node</A
>]</TD
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