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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances, Rank2Types, FlexibleInstances, MultiParamTypeClasses #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-4"></a><span class='hs-comment'>-- |</span>
<a name="line-5"></a><span class='hs-comment'>-- Module : Control.Monad.Logic</span>
<a name="line-6"></a><span class='hs-comment'>-- Copyright : (c) Dan Doel</span>
<a name="line-7"></a><span class='hs-comment'>-- License : BSD3</span>
<a name="line-8"></a><span class='hs-comment'>--</span>
<a name="line-9"></a><span class='hs-comment'>-- Maintainer : dan.doel@gmail.com</span>
<a name="line-10"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-11"></a><span class='hs-comment'>-- Portability : non-portable (multi-parameter type classes)</span>
<a name="line-12"></a><span class='hs-comment'>--</span>
<a name="line-13"></a><span class='hs-comment'>-- A backtracking, logic programming monad.</span>
<a name="line-14"></a><span class='hs-comment'>--</span>
<a name="line-15"></a><span class='hs-comment'>-- Adapted from the paper</span>
<a name="line-16"></a><span class='hs-comment'>-- /Backtracking, Interleaving, and Terminating</span>
<a name="line-17"></a><span class='hs-comment'>-- Monad Transformers/, by</span>
<a name="line-18"></a><span class='hs-comment'>-- Oleg Kiselyov, Chung-chieh Shan, Daniel P. Friedman, Amr Sabry</span>
<a name="line-19"></a><span class='hs-comment'>-- (<<a href="http://www.cs.rutgers.edu/~ccshan/logicprog/LogicT-icfp2005.pdf">http://www.cs.rutgers.edu/~ccshan/logicprog/LogicT-icfp2005.pdf</a>>).</span>
<a name="line-20"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Logic</span> <span class='hs-layout'>(</span>
<a name="line-23"></a> <span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Logic</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span><span class='hs-layout'>,</span>
<a name="line-24"></a> <span class='hs-comment'>-- * The Logic monad</span>
<a name="line-25"></a> <span class='hs-conid'>Logic</span><span class='hs-layout'>,</span>
<a name="line-26"></a> <span class='hs-varid'>logic</span><span class='hs-layout'>,</span>
<a name="line-27"></a> <span class='hs-varid'>runLogic</span><span class='hs-layout'>,</span>
<a name="line-28"></a> <span class='hs-varid'>observe</span><span class='hs-layout'>,</span>
<a name="line-29"></a> <span class='hs-varid'>observeMany</span><span class='hs-layout'>,</span>
<a name="line-30"></a> <span class='hs-varid'>observeAll</span><span class='hs-layout'>,</span>
<a name="line-31"></a> <span class='hs-comment'>-- * The LogicT monad transformer</span>
<a name="line-32"></a> <span class='hs-conid'>LogicT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-33"></a> <span class='hs-varid'>runLogicT</span><span class='hs-layout'>,</span>
<a name="line-34"></a> <span class='hs-varid'>observeT</span><span class='hs-layout'>,</span>
<a name="line-35"></a> <span class='hs-varid'>observeManyT</span><span class='hs-layout'>,</span>
<a name="line-36"></a> <span class='hs-varid'>observeAllT</span><span class='hs-layout'>,</span>
<a name="line-37"></a> <span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-layout'>,</span>
<a name="line-38"></a> <span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span>
<a name="line-39"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-40"></a>
<a name="line-41"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-42"></a>
<a name="line-43"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-44"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Identity</span>
<a name="line-45"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span>
<a name="line-46"></a>
<a name="line-47"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Reader</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-48"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>State</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-49"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Error</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-50"></a>
<a name="line-51"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-varid'>mappend</span><span class='hs-layout'>,</span> <span class='hs-varid'>mempty</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-52"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>F</span>
<a name="line-53"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>T</span>
<a name="line-54"></a>
<a name="line-55"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Logic</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-56"></a>
<a name="line-57"></a><a name="LogicT"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-58"></a><a name="LogicT"></a><span class='hs-comment'>-- | A monad transformer for performing backtracking computations</span>
<a name="line-59"></a><a name="LogicT"></a><span class='hs-comment'>-- layered over another monad 'm'</span>
<a name="line-60"></a><a name="LogicT"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span>
<a name="line-61"></a> <span class='hs-conid'>LogicT</span> <span class='hs-layout'>{</span> <span class='hs-varid'>unLogicT</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-layout'>}</span>
<a name="line-62"></a>
<a name="line-63"></a><a name="observeT"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-64"></a><span class='hs-comment'>-- | Extracts the first result from a LogicT computation,</span>
<a name="line-65"></a><span class='hs-comment'>-- failing otherwise.</span>
<a name="line-66"></a><span class='hs-definition'>observeT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-67"></a><span class='hs-definition'>observeT</span> <span class='hs-varid'>lt</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>lt</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fail</span> <span class='hs-str'>"No answer."</span><span class='hs-layout'>)</span>
<a name="line-68"></a>
<a name="line-69"></a><a name="observeAllT"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-70"></a><span class='hs-comment'>-- | Extracts all results from a LogicT computation.</span>
<a name="line-71"></a><span class='hs-definition'>observeAllT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-72"></a><span class='hs-definition'>observeAllT</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>liftM</span> <span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="observeManyT"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-75"></a><span class='hs-comment'>-- | Extracts up to a given number of results from a LogicT computation.</span>
<a name="line-76"></a><span class='hs-definition'>observeManyT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-77"></a><span class='hs-definition'>observeManyT</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span>
<a name="line-78"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'><=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-conid'>[]</span>
<a name="line-79"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-80"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unLogicT</span> <span class='hs-layout'>(</span><span class='hs-varid'>msplit</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>sk</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-81"></a> <span class='hs-keyword'>where</span>
<a name="line-82"></a> <span class='hs-varid'>sk</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-conid'>[]</span>
<a name="line-83"></a> <span class='hs-varid'>sk</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>m'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-varop'>`liftM`</span> <span class='hs-varid'>observeManyT</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>m'</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="runLogicT"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-86"></a><span class='hs-comment'>-- | Runs a LogicT computation with the specified initial success and</span>
<a name="line-87"></a><span class='hs-comment'>-- failure continuations.</span>
<a name="line-88"></a><span class='hs-definition'>runLogicT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span>
<a name="line-89"></a><span class='hs-definition'>runLogicT</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unLogicT</span>
<a name="line-90"></a>
<a name="line-91"></a><a name="Logic"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-92"></a><a name="Logic"></a><span class='hs-comment'>-- | The basic Logic monad, for performing backtracking computations</span>
<a name="line-93"></a><a name="Logic"></a><span class='hs-comment'>-- returning values of type 'a'</span>
<a name="line-94"></a><a name="Logic"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Logic</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-conid'>Identity</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="logic"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-97"></a><span class='hs-comment'>-- | A smart constructor for Logic computations.</span>
<a name="line-98"></a><span class='hs-definition'>logic</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Logic</span> <span class='hs-varid'>a</span>
<a name="line-99"></a><span class='hs-definition'>logic</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Identity</span> <span class='hs-varop'>.</span>
<a name="line-100"></a> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Identity</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span>
<a name="line-101"></a> <span class='hs-varid'>runIdentity</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="observe"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-104"></a><span class='hs-comment'>-- | Extracts the first result from a Logic computation.</span>
<a name="line-105"></a><span class='hs-definition'>observe</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Logic</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-106"></a><span class='hs-definition'>observe</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>observeT</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="observeAll"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-109"></a><span class='hs-comment'>-- | Extracts all results from a Logic computation.</span>
<a name="line-110"></a><span class='hs-definition'>observeAll</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Logic</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-111"></a><span class='hs-definition'>observeAll</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>observeAllT</span>
<a name="line-112"></a>
<a name="line-113"></a><a name="observeMany"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-114"></a><span class='hs-comment'>-- | Extracts up to a given number of results from a Logic computation.</span>
<a name="line-115"></a><span class='hs-definition'>observeMany</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Logic</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-116"></a><span class='hs-definition'>observeMany</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>observeManyT</span> <span class='hs-varid'>i</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="runLogic"></a><span class='hs-comment'>-------------------------------------------------------------------------</span>
<a name="line-119"></a><span class='hs-comment'>-- | Runs a Logic computation with the specified initial success and</span>
<a name="line-120"></a><span class='hs-comment'>-- failure continuations.</span>
<a name="line-121"></a><span class='hs-definition'>runLogic</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Logic</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span>
<a name="line-122"></a><span class='hs-definition'>runLogic</span> <span class='hs-varid'>l</span> <span class='hs-varid'>s</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>l</span> <span class='hs-varid'>si</span> <span class='hs-varid'>fi</span>
<a name="line-123"></a> <span class='hs-keyword'>where</span>
<a name="line-124"></a> <span class='hs-varid'>si</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varop'>.</span> <span class='hs-varid'>s</span>
<a name="line-125"></a> <span class='hs-varid'>fi</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Identity</span> <span class='hs-varid'>f</span>
<a name="line-126"></a>
<a name="line-127"></a><a name="instance%20Functor%20(LogicT%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-128"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>lt</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>lt</span> <span class='hs-layout'>(</span><span class='hs-varid'>sk</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>fk</span>
<a name="line-129"></a>
<a name="line-130"></a><a name="instance%20Applicative%20(LogicT%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>sk</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fk</span>
<a name="line-132"></a> <span class='hs-varid'>f</span> <span class='hs-varop'><*></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>g</span> <span class='hs-varid'>fk'</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>sk</span> <span class='hs-varop'>.</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-varid'>fk'</span><span class='hs-layout'>)</span> <span class='hs-varid'>fk</span>
<a name="line-133"></a>
<a name="line-134"></a><a name="instance%20Alternative%20(LogicT%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Alternative</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-135"></a> <span class='hs-varid'>empty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fk</span>
<a name="line-136"></a> <span class='hs-varid'>f1</span> <span class='hs-varop'><|></span> <span class='hs-varid'>f2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>f1</span> <span class='hs-varid'>sk</span> <span class='hs-layout'>(</span><span class='hs-varid'>unLogicT</span> <span class='hs-varid'>f2</span> <span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span><span class='hs-layout'>)</span>
<a name="line-137"></a>
<a name="line-138"></a><a name="instance%20Monad%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-139"></a> <span class='hs-varid'>return</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>sk</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fk</span>
<a name="line-140"></a> <span class='hs-varid'>m</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>fk'</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>sk</span> <span class='hs-varid'>fk'</span><span class='hs-layout'>)</span> <span class='hs-varid'>fk</span>
<a name="line-141"></a> <span class='hs-varid'>fail</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fk</span>
<a name="line-142"></a>
<a name="line-143"></a><a name="instance%20MonadPlus%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadPlus</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-144"></a> <span class='hs-varid'>mzero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fk</span>
<a name="line-145"></a> <span class='hs-varid'>m1</span> <span class='hs-varop'>`mplus`</span> <span class='hs-varid'>m2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m1</span> <span class='hs-varid'>sk</span> <span class='hs-layout'>(</span><span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m2</span> <span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span><span class='hs-layout'>)</span>
<a name="line-146"></a>
<a name="line-147"></a><a name="instance%20MonadTrans%20LogicT"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadTrans</span> <span class='hs-conid'>LogicT</span> <span class='hs-keyword'>where</span>
<a name="line-148"></a> <span class='hs-varid'>lift</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varop'>>>=</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>sk</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fk</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="instance%20MonadIO%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadIO</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadIO</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-varid'>liftIO</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>liftIO</span>
<a name="line-152"></a>
<a name="line-153"></a><a name="instance%20MonadLogic%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadLogic</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-154"></a> <span class='hs-varid'>msplit</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-varid'>ssk</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span>
<a name="line-155"></a> <span class='hs-keyword'>where</span>
<a name="line-156"></a> <span class='hs-varid'>ssk</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varid'>lift</span> <span class='hs-varid'>fk</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>reflect</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-157"></a>
<a name="line-158"></a><a name="instance%20F.Foldable%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-159"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>fold</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>liftM</span> <span class='hs-varop'>.</span> <span class='hs-varid'>mappend</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varid'>mempty</span><span class='hs-layout'>)</span>
<a name="line-160"></a>
<a name="line-161"></a><a name="instance%20T.Traversable%20(LogicT%20Identity)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>T</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-conid'>Identity</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-162"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>g</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runLogic</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>ft</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>cons</span> <span class='hs-varop'><$></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ft</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>mzero</span><span class='hs-layout'>)</span>
<a name="line-163"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>cons</span> <span class='hs-varid'>a</span> <span class='hs-varid'>l'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-varid'>a</span> <span class='hs-varop'>`mplus`</span> <span class='hs-varid'>l'</span>
<a name="line-164"></a>
<a name="line-165"></a><a name="instance%20MonadReader%20r%20(LogicT%20m)"></a><span class='hs-comment'>-- Needs undecidable instances</span>
<a name="line-166"></a><a name="instance%20MonadReader%20r%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadReader</span> <span class='hs-varid'>r</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadReader</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-167"></a> <span class='hs-varid'>ask</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varid'>ask</span>
<a name="line-168"></a> <span class='hs-varid'>local</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>local</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>sk</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>local</span> <span class='hs-varid'>f</span> <span class='hs-varid'>fk</span><span class='hs-layout'>)</span>
<a name="line-169"></a>
<a name="line-170"></a><a name="instance%20MonadState%20s%20(LogicT%20m)"></a><span class='hs-comment'>-- Needs undecidable instances</span>
<a name="line-171"></a><a name="instance%20MonadState%20s%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadState</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadState</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-172"></a> <span class='hs-varid'>get</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varid'>get</span>
<a name="line-173"></a> <span class='hs-varid'>put</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>put</span>
<a name="line-174"></a>
<a name="line-175"></a><a name="instance%20MonadError%20e%20(LogicT%20m)"></a><span class='hs-comment'>-- Needs undecidable instances</span>
<a name="line-176"></a><a name="instance%20MonadError%20e%20(LogicT%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadError</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadError</span> <span class='hs-varid'>e</span> <span class='hs-layout'>(</span><span class='hs-conid'>LogicT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-177"></a> <span class='hs-varid'>throwError</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>throwError</span>
<a name="line-178"></a> <span class='hs-varid'>catchError</span> <span class='hs-varid'>m</span> <span class='hs-varid'>h</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LogicT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>let</span>
<a name="line-179"></a> <span class='hs-varid'>handle</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>r</span> <span class='hs-varop'>`catchError`</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>e</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unLogicT</span> <span class='hs-layout'>(</span><span class='hs-varid'>h</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varid'>sk</span> <span class='hs-varid'>fk</span>
<a name="line-180"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>handle</span> <span class='hs-varop'>$</span> <span class='hs-varid'>unLogicT</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>sk</span> <span class='hs-varid'>a</span> <span class='hs-varop'>.</span> <span class='hs-varid'>handle</span><span class='hs-layout'>)</span> <span class='hs-varid'>fk</span>
</pre></body>
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