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<title>src/full/Agda/TypeChecking/Coverage/SplitTree.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>{-| Split tree for transforming pattern clauses into case trees.
<a name="line-4"></a>
<a name="line-5"></a>The coverage checker generates a split tree from the clauses.
<a name="line-6"></a>The clause compiler uses it to transform clauses to case trees.
<a name="line-7"></a>
<a name="line-8"></a>The initial problem is a set of clauses. The root node designates
<a name="line-9"></a>on which argument to split and has subtrees for all the constructors.
<a name="line-10"></a>Splitting continues until there is only a single clause left at
<a name="line-11"></a>each leaf of the split tree.
<a name="line-12"></a>
<a name="line-13"></a>-}</span>
<a name="line-14"></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'>Coverage</span><span class='hs-varop'>.</span><span class='hs-conid'>SplitTree</span> <span class='hs-keyword'>where</span>
<a name="line-15"></a>
<a name="line-16"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tree</span>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Test</span><span class='hs-varop'>.</span><span class='hs-conid'>QuickCheck</span>
<a name="line-18"></a>
<a name="line-19"></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-20"></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'>Abstract</span><span class='hs-varop'>.</span><span class='hs-conid'>Name</span>
<a name="line-21"></a>
<a name="line-22"></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'>Monad</span>
<a name="line-23"></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'>Impossible</span>
<a name="line-24"></a><span class='hs-cpp'>#include "../../undefined.h"</span>
<a name="line-25"></a>
<a name="line-26"></a><a name="SplitTree"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>SplitTree</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SplitTree'</span> <span class='hs-conid'>QName</span>
<a name="line-27"></a><a name="SplitTrees"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>SplitTrees</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SplitTrees'</span> <span class='hs-conid'>QName</span>
<a name="line-28"></a>
<a name="line-29"></a><a name="SplitTree'"></a><span class='hs-comment'>-- | Abstract case tree shape.</span>
<a name="line-30"></a><a name="SplitTree'"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>SplitTree'</span> <span class='hs-varid'>a</span>
<a name="line-31"></a> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-- | No more splits coming. We are at a single, all-variable</span>
<a name="line-32"></a> <span class='hs-comment'>-- clause.</span>
<a name="line-33"></a> <span class='hs-conid'>SplittingDone</span>
<a name="line-34"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>splitBindings</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-comment'>-- ^ The number of variables bound in the clause</span>
<a name="line-35"></a> <span class='hs-layout'>}</span>
<a name="line-36"></a> <span class='hs-keyglyph'>|</span> <span class='hs-comment'>-- | A split is necessary.</span>
<a name="line-37"></a> <span class='hs-conid'>SplitAt</span>
<a name="line-38"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>splitArg</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-comment'>-- ^ Arg. no to split at.</span>
<a name="line-39"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>splitTrees</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>SplitTrees'</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^ Sub split trees.</span>
<a name="line-40"></a> <span class='hs-layout'>}</span>
<a name="line-41"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>)</span>
<a name="line-42"></a>
<a name="line-43"></a><a name="SplitTrees'"></a><span class='hs-comment'>-- | Split tree branching. A finite map from constructor names to splittrees</span>
<a name="line-44"></a><a name="SplitTrees'"></a><span class='hs-comment'>-- A list representation seems appropriate, since we are expecting not</span>
<a name="line-45"></a><a name="SplitTrees'"></a><span class='hs-comment'>-- so many constructors per data type, and there is no need for</span>
<a name="line-46"></a><a name="SplitTrees'"></a><span class='hs-comment'>-- random access.</span>
<a name="line-47"></a><a name="SplitTrees'"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>SplitTrees'</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>SplitTree'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-48"></a>
<a name="line-49"></a><span class='hs-comment'>-- * Printing a split tree</span>
<a name="line-50"></a>
<a name="line-51"></a><a name="SplitTreeLabel"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>SplitTreeLabel</span>
<a name="line-52"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>lblConstructorName</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^ 'Nothing' for root of split tree</span>
<a name="line-53"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lblSplitArg</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Maybe</span> <span class='hs-conid'>Int</span>
<a name="line-54"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lblBindings</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Maybe</span> <span class='hs-conid'>Int</span>
<a name="line-55"></a> <span class='hs-layout'>}</span>
<a name="line-56"></a><a name="instance%20Show%20(SplitTreeLabel%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-57"></a> <span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-conid'>Nothing</span> <span class='hs-conid'>Nothing</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"done, "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span> <span class='hs-varop'>++</span> <span class='hs-str'>" bindings"</span>
<a name="line-58"></a> <span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-conid'>Nothing</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"split at "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span>
<a name="line-59"></a> <span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-conid'>Nothing</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>show</span> <span class='hs-varid'>q</span> <span class='hs-varop'>++</span> <span class='hs-str'>" -> done, "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span> <span class='hs-varop'>++</span> <span class='hs-str'>" bindings"</span>
<a name="line-60"></a> <span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>show</span> <span class='hs-varid'>q</span> <span class='hs-varop'>++</span> <span class='hs-str'>" -> split at "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span>
<a name="line-61"></a> <span class='hs-varid'>show</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-sel'>__IMPOSSIBLE__</span>
<a name="line-62"></a>
<a name="line-63"></a><a name="toTree"></a><span class='hs-comment'>-- | Convert a split tree into a 'Data.Tree' (for printing).</span>
<a name="line-64"></a><span class='hs-definition'>toTree</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>SplitTree'</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Tree</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-65"></a><span class='hs-definition'>toTree</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>t</span> <span class='hs-keyword'>of</span>
<a name="line-66"></a> <span class='hs-conid'>SplittingDone</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Node</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-conid'>Nothing</span> <span class='hs-conid'>Nothing</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-conid'>[]</span>
<a name="line-67"></a> <span class='hs-conid'>SplitAt</span> <span class='hs-varid'>n</span> <span class='hs-varid'>ts</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Node</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-conid'>Nothing</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>toTrees</span> <span class='hs-varid'>ts</span>
<a name="line-68"></a>
<a name="line-69"></a><a name="toTrees"></a><span class='hs-definition'>toTrees</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>SplitTrees'</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Forest</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-70"></a><span class='hs-definition'>toTrees</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-layout'>(</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>setCons</span> <span class='hs-varid'>c</span> <span class='hs-varop'>$</span> <span class='hs-varid'>toTree</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-71"></a> <span class='hs-keyword'>where</span>
<a name="line-72"></a> <span class='hs-varid'>setCons</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Tree</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Tree</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTreeLabel</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-73"></a> <span class='hs-varid'>setCons</span> <span class='hs-varid'>c</span> <span class='hs-layout'>(</span><span class='hs-conid'>Node</span> <span class='hs-varid'>l</span> <span class='hs-varid'>ts</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Node</span> <span class='hs-layout'>(</span><span class='hs-varid'>l</span> <span class='hs-layout'>{</span> <span class='hs-varid'>lblConstructorName</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>c</span> <span class='hs-layout'>}</span><span class='hs-layout'>)</span> <span class='hs-varid'>ts</span>
<a name="line-74"></a>
<a name="line-75"></a><a name="instance%20Show%20(SplitTree'%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTree'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>show</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>drawTree</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>show</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toTree</span>
<a name="line-77"></a>
<a name="line-78"></a><span class='hs-comment'>-- * Generating random split trees for testing</span>
<a name="line-79"></a>
<a name="line-80"></a><a name="instance%20Arbitrary%20(SplitTree'%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Arbitrary</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Arbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTree'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-81"></a> <span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>frequency</span>
<a name="line-82"></a> <span class='hs-keyglyph'>[</span> <span class='hs-layout'>(</span><span class='hs-num'>5</span><span class='hs-layout'>,</span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>SplittingDone</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span>
<a name="line-83"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>3</span><span class='hs-layout'>,</span> <span class='hs-conid'>SplitAt</span> <span class='hs-varop'><$></span> <span class='hs-varid'>choose</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span><span class='hs-layout'>,</span><span class='hs-num'>5</span><span class='hs-layout'>)</span> <span class='hs-varop'><*></span> <span class='hs-layout'>(</span><span class='hs-varid'>take</span> <span class='hs-num'>3</span> <span class='hs-varop'><$></span> <span class='hs-varid'>listOf1</span> <span class='hs-varid'>arbitrary</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-84"></a> <span class='hs-keyglyph'>]</span>
<a name="line-85"></a>
<a name="line-86"></a><span class='hs-comment'>-- * Testing the printer</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="CName"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>CName</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>CName</span> <span class='hs-conid'>String</span>
<a name="line-89"></a><a name="instance%20Show%20CName"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>CName</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-conid'>CName</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>s</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="instance%20Arbitrary%20CName"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Arbitrary</span> <span class='hs-conid'>CName</span> <span class='hs-keyword'>where</span>
<a name="line-93"></a> <span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>CName</span> <span class='hs-varop'><$></span> <span class='hs-varid'>elements</span>
<a name="line-94"></a> <span class='hs-keyglyph'>[</span> <span class='hs-str'>"zero"</span><span class='hs-layout'>,</span> <span class='hs-str'>"suc"</span><span class='hs-layout'>,</span> <span class='hs-str'>"nil"</span><span class='hs-layout'>,</span> <span class='hs-str'>"cons"</span><span class='hs-layout'>,</span> <span class='hs-str'>"left"</span><span class='hs-layout'>,</span> <span class='hs-str'>"right"</span><span class='hs-layout'>,</span> <span class='hs-str'>"just"</span><span class='hs-layout'>,</span> <span class='hs-str'>"nothing"</span> <span class='hs-keyglyph'>]</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="testSplitTreePrinting"></a><span class='hs-definition'>testSplitTreePrinting</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sample</span> <span class='hs-layout'>(</span><span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Gen</span> <span class='hs-layout'>(</span><span class='hs-conid'>SplitTree'</span> <span class='hs-conid'>CName</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
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