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<title>src/full/Agda/TypeChecking/Rules/LHS/Problem.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Rules</span><span class='hs-varop'>.</span><span class='hs-conid'>LHS</span><span class='hs-varop'>.</span><span class='hs-conid'>Problem</span> <span class='hs-keyword'>where</span>
<a name="line-3"></a>
<a name="line-4"></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>
<a name="line-5"></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-6"></a>
<a name="line-7"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Common</span>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Literal</span>
<a name="line-9"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Position</span>
<a name="line-10"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span>
<a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Pattern</span>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span><span class='hs-varop'>.</span><span class='hs-conid'>Abstract</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>A</span>
<a name="line-13"></a>
<a name="line-14"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Substitute</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>S</span>
<a name="line-15"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeChecking</span><span class='hs-varop'>.</span><span class='hs-conid'>Pretty</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Permutation</span>
<a name="line-18"></a>
<a name="line-19"></a><span class='hs-comment'>{- UNUSED
<a name="line-20"></a>#include "../../../undefined.h"
<a name="line-21"></a>import Agda.Utils.Impossible
<a name="line-22"></a>-}</span>
<a name="line-23"></a>
<a name="line-24"></a><a name="Substitution"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Substitution</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Maybe</span> <span class='hs-conid'>Term</span><span class='hs-keyglyph'>]</span>
<a name="line-25"></a><a name="FlexibleVars"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>FlexibleVars</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Nat</span><span class='hs-keyglyph'>]</span>
<a name="line-26"></a>
<a name="line-27"></a><a name="Problem'"></a><span class='hs-comment'>-- | State of typechecking a LHS; input to 'split'.</span>
<a name="line-28"></a><a name="Problem'"></a><span class='hs-comment'>-- [Ulf Norell's PhD, page. 35]</span>
<a name="line-29"></a><a name="Problem'"></a><span class='hs-comment'>--</span>
<a name="line-30"></a><a name="Problem'"></a><span class='hs-comment'>-- In @Problem ps p delta@,</span>
<a name="line-31"></a><a name="Problem'"></a><span class='hs-comment'>-- @ps@ are the user patterns of supposed type @delta@.</span>
<a name="line-32"></a><a name="Problem'"></a><span class='hs-comment'>-- @p@ is the pattern resulting from the splitting.</span>
<a name="line-33"></a><a name="Problem'"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Problem'</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Problem</span> <span class='hs-layout'>{</span> <span class='hs-varid'>problemInPat</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>NamedArg</span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Pattern</span><span class='hs-keyglyph'>]</span>
<a name="line-34"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>problemOutPat</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>p</span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>problemTel</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Telescope</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>problemRest</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ProblemRest</span>
<a name="line-37"></a> <span class='hs-layout'>}</span>
<a name="line-38"></a>
<a name="line-39"></a><a name="ProblemRest"></a><span class='hs-comment'>-- | User patterns that could not be given a type yet.</span>
<a name="line-40"></a><a name="ProblemRest"></a><span class='hs-comment'>--</span>
<a name="line-41"></a><a name="ProblemRest"></a><span class='hs-comment'>-- Example:</span>
<a name="line-42"></a><a name="ProblemRest"></a><span class='hs-comment'>-- @</span>
<a name="line-43"></a><a name="ProblemRest"></a><span class='hs-comment'>-- f : (b : Bool) -> if b then Nat else Nat -> Nat</span>
<a name="line-44"></a><a name="ProblemRest"></a><span class='hs-comment'>-- f true = zero</span>
<a name="line-45"></a><a name="ProblemRest"></a><span class='hs-comment'>-- f false zero = zero</span>
<a name="line-46"></a><a name="ProblemRest"></a><span class='hs-comment'>-- f false (suc n) = n</span>
<a name="line-47"></a><a name="ProblemRest"></a><span class='hs-comment'>-- @</span>
<a name="line-48"></a><a name="ProblemRest"></a><span class='hs-comment'>-- In this sitation, for clause 2, we construct an initial problem</span>
<a name="line-49"></a><a name="ProblemRest"></a><span class='hs-comment'>-- @</span>
<a name="line-50"></a><a name="ProblemRest"></a><span class='hs-comment'>-- problemInPat = [false]</span>
<a name="line-51"></a><a name="ProblemRest"></a><span class='hs-comment'>-- problemTel = (b : Bool)</span>
<a name="line-52"></a><a name="ProblemRest"></a><span class='hs-comment'>-- problemRest.restPats = [zero]</span>
<a name="line-53"></a><a name="ProblemRest"></a><span class='hs-comment'>-- problemRest.restType = if b then Nat else Nat -> Nat</span>
<a name="line-54"></a><a name="ProblemRest"></a><span class='hs-comment'>-- @</span>
<a name="line-55"></a><a name="ProblemRest"></a><span class='hs-comment'>-- As we instantiate @b@ to @false@, the 'restType' reduces to</span>
<a name="line-56"></a><a name="ProblemRest"></a><span class='hs-comment'>-- @Nat -> Nat@ and we can move pattern @zero@ over to @problemInPat@.</span>
<a name="line-57"></a><a name="ProblemRest"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>ProblemRest</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ProblemRest</span>
<a name="line-58"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>restPats</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>NamedArg</span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Pattern</span><span class='hs-keyglyph'>]</span> <span class='hs-comment'>-- ^ non-empty list of user patterns which could not yet be typed</span>
<a name="line-59"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>restType</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Type</span> <span class='hs-comment'>-- ^ type eliminated by 'restPats'</span>
<a name="line-60"></a> <span class='hs-layout'>}</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="Focus"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Focus</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Focus</span> <span class='hs-layout'>{</span> <span class='hs-varid'>focusCon</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>QName</span>
<a name="line-63"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusConArgs</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>NamedArg</span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Pattern</span><span class='hs-keyglyph'>]</span>
<a name="line-64"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusRange</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Range</span>
<a name="line-65"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusOutPat</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>OneHolePatterns</span>
<a name="line-66"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusHoleIx</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-comment'>-- ^ Index of focused variable in the out patterns.</span>
<a name="line-67"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusDatatype</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>QName</span>
<a name="line-68"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusParams</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Arg</span> <span class='hs-conid'>Term</span><span class='hs-keyglyph'>]</span>
<a name="line-69"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusIndices</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Arg</span> <span class='hs-conid'>Term</span><span class='hs-keyglyph'>]</span>
<a name="line-70"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>focusType</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Type</span> <span class='hs-comment'>-- ^ Type of variable we are splitting, kept for record patterns.</span>
<a name="line-71"></a> <span class='hs-layout'>}</span>
<a name="line-72"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>LitFocus</span> <span class='hs-conid'>Literal</span> <span class='hs-conid'>OneHolePatterns</span> <span class='hs-conid'>Int</span> <span class='hs-conid'>Type</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="SplitProblem"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>SplitProblem</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Split</span> <span class='hs-conid'>ProblemPart</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Name</span><span class='hs-keyglyph'>]</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arg</span> <span class='hs-conid'>Focus</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Abs</span> <span class='hs-conid'>ProblemPart</span><span class='hs-layout'>)</span>
<a name="line-75"></a> <span class='hs-comment'>-- ^ the [Name]s give the as-bindings for the focus</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="SplitError"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>SplitError</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NothingToSplit</span>
<a name="line-78"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>SplitPanic</span> <span class='hs-conid'>String</span>
<a name="line-79"></a>
<a name="line-80"></a><a name="Problem"></a><span class='hs-comment'>-- | The permutation should permute @allHoles@ of the patterns to correspond to</span>
<a name="line-81"></a><a name="Problem"></a><span class='hs-comment'>-- the abstract patterns in the problem.</span>
<a name="line-82"></a><a name="Problem"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Problem</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Problem'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Permutation</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Arg</span> <span class='hs-conid'>Pattern</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-83"></a><a name="ProblemPart"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>ProblemPart</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Problem'</span> <span class='hs-conid'>()</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="DotPatternInst"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>DotPatternInst</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>DPI</span> <span class='hs-conid'>A</span><span class='hs-varop'>.</span><span class='hs-conid'>Expr</span> <span class='hs-conid'>Term</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dom</span> <span class='hs-conid'>Type</span><span class='hs-layout'>)</span>
<a name="line-86"></a><a name="AsBinding"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>AsBinding</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>AsB</span> <span class='hs-conid'>Name</span> <span class='hs-conid'>Term</span> <span class='hs-conid'>Type</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="LHSState"></a><span class='hs-comment'>-- | State worked on during the main loop of checking a lhs.</span>
<a name="line-89"></a><a name="LHSState"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>LHSState</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LHSState</span>
<a name="line-90"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>lhsProblem</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Problem</span>
<a name="line-91"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lhsSubst</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>S</span><span class='hs-varop'>.</span><span class='hs-conid'>Substitution</span>
<a name="line-92"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lhsDPI</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>DotPatternInst</span><span class='hs-keyglyph'>]</span>
<a name="line-93"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lhsAsB</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>AsBinding</span><span class='hs-keyglyph'>]</span>
<a name="line-94"></a> <span class='hs-layout'>}</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="instance%20Subst%20ProblemRest"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Subst</span> <span class='hs-conid'>ProblemRest</span> <span class='hs-keyword'>where</span>
<a name="line-97"></a> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>p</span> <span class='hs-layout'>{</span> <span class='hs-varid'>restType</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-varop'>$</span> <span class='hs-varid'>restType</span> <span class='hs-varid'>p</span> <span class='hs-layout'>}</span>
<a name="line-98"></a>
<a name="line-99"></a><a name="instance%20Subst%20(Problem'%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Subst</span> <span class='hs-layout'>(</span><span class='hs-conid'>Problem'</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-100"></a> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>p</span> <span class='hs-layout'>{</span> <span class='hs-varid'>problemTel</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-varop'>$</span> <span class='hs-varid'>problemTel</span> <span class='hs-varid'>p</span>
<a name="line-101"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>problemRest</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-varop'>$</span> <span class='hs-varid'>problemRest</span> <span class='hs-varid'>p</span> <span class='hs-layout'>}</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="instance%20Subst%20DotPatternInst"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Subst</span> <span class='hs-conid'>DotPatternInst</span> <span class='hs-keyword'>where</span>
<a name="line-104"></a> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-layout'>(</span><span class='hs-conid'>DPI</span> <span class='hs-varid'>e</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uncurry</span> <span class='hs-layout'>(</span><span class='hs-conid'>DPI</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-105"></a>
<a name="line-106"></a><a name="instance%20Subst%20AsBinding"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Subst</span> <span class='hs-conid'>AsBinding</span> <span class='hs-keyword'>where</span>
<a name="line-107"></a> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-layout'>(</span><span class='hs-conid'>AsB</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uncurry</span> <span class='hs-layout'>(</span><span class='hs-conid'>AsB</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>applySubst</span> <span class='hs-varid'>rho</span> <span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-108"></a>
<a name="line-109"></a><a name="instance%20PrettyTCM%20DotPatternInst"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PrettyTCM</span> <span class='hs-conid'>DotPatternInst</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-varid'>prettyTCM</span> <span class='hs-layout'>(</span><span class='hs-conid'>DPI</span> <span class='hs-varid'>e</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sep</span>
<a name="line-111"></a> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>prettyA</span> <span class='hs-varid'>e</span> <span class='hs-varop'><+></span> <span class='hs-varid'>text</span> <span class='hs-str'>"="</span>
<a name="line-112"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>nest</span> <span class='hs-num'>2</span> <span class='hs-varop'>$</span> <span class='hs-varid'>prettyTCM</span> <span class='hs-varid'>v</span> <span class='hs-varop'><+></span> <span class='hs-varid'>text</span> <span class='hs-str'>":"</span>
<a name="line-113"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>nest</span> <span class='hs-num'>2</span> <span class='hs-varop'>$</span> <span class='hs-varid'>prettyTCM</span> <span class='hs-varid'>a</span>
<a name="line-114"></a> <span class='hs-keyglyph'>]</span>
<a name="line-115"></a>
<a name="line-116"></a><a name="instance%20PrettyTCM%20AsBinding"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>PrettyTCM</span> <span class='hs-conid'>AsBinding</span> <span class='hs-keyword'>where</span>
<a name="line-117"></a> <span class='hs-varid'>prettyTCM</span> <span class='hs-layout'>(</span><span class='hs-conid'>AsB</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-118"></a> <span class='hs-varid'>sep</span> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>prettyTCM</span> <span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>text</span> <span class='hs-str'>"@"</span> <span class='hs-varop'><></span> <span class='hs-varid'>parens</span> <span class='hs-layout'>(</span><span class='hs-varid'>prettyTCM</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span>
<a name="line-119"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>nest</span> <span class='hs-num'>2</span> <span class='hs-varop'>$</span> <span class='hs-varid'>text</span> <span class='hs-str'>":"</span> <span class='hs-varop'><+></span> <span class='hs-varid'>prettyTCM</span> <span class='hs-varid'>a</span>
<a name="line-120"></a> <span class='hs-keyglyph'>]</span>
<a name="line-121"></a>
<a name="line-122"></a><a name="instance%20Error%20SplitError"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Error</span> <span class='hs-conid'>SplitError</span> <span class='hs-keyword'>where</span>
<a name="line-123"></a> <span class='hs-varid'>noMsg</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>NothingToSplit</span>
<a name="line-124"></a> <span class='hs-varid'>strMsg</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SplitPanic</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="instance%20Monoid%20ProblemRest"></a><span class='hs-comment'>-- | 'ProblemRest' is a right dominant monoid.</span>
<a name="line-127"></a><a name="instance%20Monoid%20ProblemRest"></a><span class='hs-comment'>-- @pr1 \`mappend\` pr2 = pr2@ unless @pr2 = mempty@, then it is @pr1@.</span>
<a name="line-128"></a><a name="instance%20Monoid%20ProblemRest"></a><span class='hs-comment'>-- Basically, this means that the left 'ProblemRest' is discarded, so</span>
<a name="line-129"></a><a name="instance%20Monoid%20ProblemRest"></a><span class='hs-comment'>-- use it wisely!</span>
<a name="line-130"></a><a name="instance%20Monoid%20ProblemRest"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-conid'>ProblemRest</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ProblemRest</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>typeDontCare</span>
<a name="line-132"></a> <span class='hs-varid'>mappend</span> <span class='hs-varid'>pr</span> <span class='hs-layout'>(</span><span class='hs-conid'>ProblemRest</span> <span class='hs-conid'>[]</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pr</span>
<a name="line-133"></a> <span class='hs-varid'>mappend</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>pr</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pr</span>
<a name="line-134"></a>
<a name="line-135"></a><a name="instance%20Monoid%20(Problem'%20p)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Problem'</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-136"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Problem</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>mempty</span> <span class='hs-conid'>EmptyTel</span> <span class='hs-varid'>mempty</span>
<a name="line-137"></a> <span class='hs-conid'>Problem</span> <span class='hs-varid'>ps1</span> <span class='hs-varid'>qs1</span> <span class='hs-varid'>tel1</span> <span class='hs-varid'>pr1</span> <span class='hs-varop'>`mappend`</span> <span class='hs-conid'>Problem</span> <span class='hs-varid'>ps2</span> <span class='hs-varid'>qs2</span> <span class='hs-varid'>tel2</span> <span class='hs-varid'>pr2</span> <span class='hs-keyglyph'>=</span>
<a name="line-138"></a> <span class='hs-conid'>Problem</span> <span class='hs-layout'>(</span><span class='hs-varid'>ps1</span> <span class='hs-varop'>++</span> <span class='hs-varid'>ps2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span> <span class='hs-varid'>qs1</span> <span class='hs-varid'>qs2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>abstract</span> <span class='hs-varid'>tel1</span> <span class='hs-varid'>tel2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span> <span class='hs-varid'>pr1</span> <span class='hs-varid'>pr2</span><span class='hs-layout'>)</span>
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