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<title>Data/Number/Symbolic.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>-- | Symbolic number, i.e., these are not numbers at all, but just build</span>
<a name="line-2"></a><span class='hs-comment'>-- a representation of the expressions.</span>
<a name="line-3"></a><span class='hs-comment'>-- This implementation is incomplete in that it allows comnstruction,</span>
<a name="line-4"></a><span class='hs-comment'>-- but not deconstruction of the expressions. It's mainly useful for</span>
<a name="line-5"></a><span class='hs-comment'>-- debugging.</span>
<a name="line-6"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Symbolic</span><span class='hs-layout'>(</span><span class='hs-conid'>Sym</span><span class='hs-layout'>,</span> <span class='hs-varid'>var</span><span class='hs-layout'>,</span> <span class='hs-varid'>con</span><span class='hs-layout'>,</span> <span class='hs-varid'>subst</span><span class='hs-layout'>,</span> <span class='hs-varid'>unSym</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-7"></a>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Char</span><span class='hs-layout'>(</span><span class='hs-varid'>isAlpha</span><span class='hs-layout'>)</span>
<a name="line-9"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span><span class='hs-layout'>(</span><span class='hs-varid'>fromMaybe</span><span class='hs-layout'>)</span>
<a name="line-10"></a>
<a name="line-11"></a><a name="Sym"></a><span class='hs-comment'>-- | Symbolic numbers over some base type for the literals.</span>
<a name="line-12"></a><a name="Sym"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>App</span> <span class='hs-conid'>String</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-keyglyph'>-></span><span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-13"></a>
<a name="line-14"></a><a name="instance%20Eq%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-15"></a> <span class='hs-conid'>Con</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-conid'>Con</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>x'</span>
<a name="line-16"></a> <span class='hs-conid'>App</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>==</span> <span class='hs-conid'>App</span> <span class='hs-varid'>f'</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs'</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-layout'>(</span><span class='hs-varid'>f'</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs'</span><span class='hs-layout'>)</span>
<a name="line-17"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'>==</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-18"></a>
<a name="line-19"></a><a name="instance%20Ord%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Ord</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-20"></a> <span class='hs-conid'>Con</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`compare`</span> <span class='hs-conid'>Con</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`compare`</span> <span class='hs-varid'>x'</span>
<a name="line-21"></a> <span class='hs-conid'>Con</span> <span class='hs-keyword'>_</span> <span class='hs-varop'>`compare`</span> <span class='hs-conid'>App</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LT</span>
<a name="line-22"></a> <span class='hs-conid'>App</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-varop'>`compare`</span> <span class='hs-conid'>Con</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>GT</span>
<a name="line-23"></a> <span class='hs-conid'>App</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>`compare`</span> <span class='hs-conid'>App</span> <span class='hs-varid'>f'</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs'</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>`compare`</span> <span class='hs-layout'>(</span><span class='hs-varid'>f'</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs'</span><span class='hs-layout'>)</span>
<a name="line-24"></a>
<a name="line-25"></a><a name="var"></a><span class='hs-comment'>-- | Create a variable.</span>
<a name="line-26"></a><span class='hs-definition'>var</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span>
<a name="line-27"></a><span class='hs-definition'>var</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>App</span> <span class='hs-varid'>s</span> <span class='hs-varid'>undefined</span> <span class='hs-conid'>[]</span>
<a name="line-28"></a>
<a name="line-29"></a><a name="con"></a><span class='hs-comment'>-- | Create a constant (useful when it is not a literal).</span>
<a name="line-30"></a><span class='hs-definition'>con</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span>
<a name="line-31"></a><span class='hs-definition'>con</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span>
<a name="line-32"></a>
<a name="line-33"></a><a name="subst"></a><span class='hs-comment'>-- | The expression @subst x v e@ substitutes the expression @v@ for each</span>
<a name="line-34"></a><span class='hs-comment'>-- occurence of the variable @x@ in @e@.</span>
<a name="line-35"></a><span class='hs-definition'>subst</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span>
<a name="line-36"></a><span class='hs-definition'>subst</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>e</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span>
<a name="line-37"></a><span class='hs-definition'>subst</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span> <span class='hs-varid'>e</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-varid'>x'</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span>
<a name="line-38"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span>
<a name="line-39"></a><span class='hs-definition'>subst</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-varid'>s</span> <span class='hs-varid'>f</span> <span class='hs-varid'>es</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-40"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>subst</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-varid'>es</span> <span class='hs-keyword'>of</span>
<a name="line-41"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>e</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>unOp</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span>
<a name="line-42"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>e1</span><span class='hs-layout'>,</span><span class='hs-varid'>e2</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-varid'>e1</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e2</span>
<a name="line-43"></a> <span class='hs-varid'>es'</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>App</span> <span class='hs-varid'>s</span> <span class='hs-varid'>f</span> <span class='hs-varid'>es'</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="unSym"></a><span class='hs-comment'>-- Turn a symbolic number into a regular one if it is a constant,</span>
<a name="line-46"></a><span class='hs-comment'>-- otherwise generate an error.</span>
<a name="line-47"></a><span class='hs-definition'>unSym</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Show</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-48"></a><span class='hs-definition'>unSym</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>c</span>
<a name="line-49"></a><span class='hs-definition'>unSym</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-varop'>$</span> <span class='hs-str'>"unSym called: "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>e</span>
<a name="line-50"></a>
<a name="line-51"></a><a name="instance%20Show%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Show</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-52"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-varid'>c</span>
<a name="line-53"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showString</span> <span class='hs-varid'>s</span>
<a name="line-54"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-varid'>op</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-varid'>c</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>isAlpha</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-55"></a> <span class='hs-varid'>showParen</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-varop'>></span><span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>showsPrec</span> <span class='hs-varid'>ql</span> <span class='hs-varid'>x</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showString</span> <span class='hs-varid'>op</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>qr</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-56"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>ql</span><span class='hs-layout'>,</span> <span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-varid'>qr</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromMaybe</span> <span class='hs-layout'>(</span><span class='hs-num'>9</span><span class='hs-layout'>,</span><span class='hs-num'>9</span><span class='hs-layout'>,</span><span class='hs-num'>9</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>lookup</span> <span class='hs-varid'>op</span> <span class='hs-keyglyph'>[</span>
<a name="line-57"></a> <span class='hs-layout'>(</span><span class='hs-str'>"**"</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>9</span><span class='hs-layout'>,</span><span class='hs-num'>8</span><span class='hs-layout'>,</span><span class='hs-num'>8</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-58"></a> <span class='hs-layout'>(</span><span class='hs-str'>"/"</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>7</span><span class='hs-layout'>,</span><span class='hs-num'>7</span><span class='hs-layout'>,</span><span class='hs-num'>8</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-59"></a> <span class='hs-layout'>(</span><span class='hs-str'>"*"</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>7</span><span class='hs-layout'>,</span><span class='hs-num'>7</span><span class='hs-layout'>,</span><span class='hs-num'>8</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-60"></a> <span class='hs-layout'>(</span><span class='hs-str'>"+"</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>6</span><span class='hs-layout'>,</span><span class='hs-num'>6</span><span class='hs-layout'>,</span><span class='hs-num'>7</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-61"></a> <span class='hs-layout'>(</span><span class='hs-str'>"-"</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-num'>6</span><span class='hs-layout'>,</span><span class='hs-num'>6</span><span class='hs-layout'>,</span><span class='hs-num'>7</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-62"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"negate"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-63"></a> <span class='hs-varid'>showParen</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-varop'>>=</span><span class='hs-num'>6</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>showString</span> <span class='hs-str'>"-"</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec</span> <span class='hs-num'>7</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-64"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-65"></a> <span class='hs-varid'>showParen</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-varop'>></span><span class='hs-num'>10</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>foldl</span> <span class='hs-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>showString</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>showChar</span> <span class='hs-chr'>' '</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec</span> <span class='hs-num'>11</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-66"></a>
<a name="line-67"></a><a name="instance%20Num%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Num</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-68"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-str'>"+"</span> <span class='hs-varid'>y</span>
<a name="line-69"></a> <span class='hs-varid'>x</span> <span class='hs-comment'>-</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-str'>"-"</span> <span class='hs-varid'>y</span>
<a name="line-70"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-varid'>y</span>
<a name="line-71"></a> <span class='hs-varid'>negate</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>negate</span> <span class='hs-str'>"negate"</span> <span class='hs-varid'>x</span>
<a name="line-72"></a> <span class='hs-varid'>abs</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>abs</span> <span class='hs-str'>"abs"</span> <span class='hs-varid'>x</span>
<a name="line-73"></a> <span class='hs-varid'>signum</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>signum</span> <span class='hs-str'>"signum"</span> <span class='hs-varid'>x</span>
<a name="line-74"></a> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-75"></a>
<a name="line-76"></a><a name="instance%20Fractional%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Fractional</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-77"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>/</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-varop'>/</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>y</span>
<a name="line-78"></a> <span class='hs-varid'>fromRational</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromRational</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-79"></a>
<a name="line-80"></a><a name="binOp"></a><span class='hs-comment'>-- Assume the numbers are a field and simplify a little</span>
<a name="line-81"></a><span class='hs-definition'>binOp</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</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'>a</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span>
<a name="line-82"></a><span class='hs-definition'>binOp</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-83"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"+"</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-84"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-num'>0</span> <span class='hs-str'>"+"</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-85"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"+"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"+"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>z</span>
<a name="line-86"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"+"</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isCon</span> <span class='hs-varid'>y</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>isCon</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>y</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x</span>
<a name="line-87"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"+"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"negate"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-comment'>-</span> <span class='hs-varid'>y</span>
<a name="line-88"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"-"</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-89"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"-"</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-90"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"-"</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>isCon</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x</span>
<a name="line-91"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-str'>"*"</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-92"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-93"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-varid'>x</span>
<a name="line-94"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-num'>0</span> <span class='hs-str'>"*"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-95"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-num'>1</span> <span class='hs-str'>"*"</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-96"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-str'>"*"</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-varid'>x</span>
<a name="line-97"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"*"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varop'>*</span> <span class='hs-varid'>z</span>
<a name="line-98"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isCon</span> <span class='hs-varid'>y</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>isCon</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>y</span> <span class='hs-varop'>*</span> <span class='hs-varid'>x</span>
<a name="line-99"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"*"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>App</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-keyglyph'>]</span>
<a name="line-100"></a><span class='hs-comment'>{-
<a name="line-101"></a>binOp _ x "*" (App "+" _ [y, z]) = x*y + x*z
<a name="line-102"></a>binOp _ (App "+" _ [y, z]) "*" x = y*x + z*x
<a name="line-103"></a>-}</span>
<a name="line-104"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"/"</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-105"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"/"</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-varid'>x</span>
<a name="line-106"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>x'</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1</span>
<a name="line-107"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-str'>"/"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>App</span> <span class='hs-str'>"/"</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>z</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span>
<a name="line-108"></a><span class='hs-definition'>binOp</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"**"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-str'>"**"</span> <span class='hs-varid'>z</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-str'>"**"</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-varop'>*</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span>
<a name="line-109"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-str'>"**"</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>1</span>
<a name="line-110"></a><span class='hs-definition'>binOp</span> <span class='hs-keyword'>_</span> <span class='hs-num'>0</span> <span class='hs-str'>"**"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-111"></a><span class='hs-definition'>binOp</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>op</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>App</span> <span class='hs-varid'>op</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>]</span>
<a name="line-112"></a>
<a name="line-113"></a><a name="unOp"></a><span class='hs-definition'>unOp</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</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'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span>
<a name="line-114"></a><span class='hs-definition'>unOp</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-115"></a><span class='hs-definition'>unOp</span> <span class='hs-keyword'>_</span> <span class='hs-str'>"negate"</span> <span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"negate"</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-116"></a><span class='hs-definition'>unOp</span> <span class='hs-keyword'>_</span> <span class='hs-str'>"abs"</span> <span class='hs-varid'>e</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"abs"</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span>
<a name="line-117"></a><span class='hs-definition'>unOp</span> <span class='hs-keyword'>_</span> <span class='hs-str'>"signum"</span> <span class='hs-varid'>e</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>App</span> <span class='hs-str'>"signum"</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>e</span>
<a name="line-118"></a><span class='hs-definition'>unOp</span> <span class='hs-varid'>f</span> <span class='hs-varid'>op</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>App</span> <span class='hs-varid'>op</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="isCon"></a><span class='hs-definition'>isCon</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-121"></a><span class='hs-definition'>isCon</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-122"></a><span class='hs-definition'>isCon</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-123"></a>
<a name="line-124"></a>
<a name="line-125"></a><a name="instance%20Integral%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Integral</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-126"></a> <span class='hs-varid'>quot</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>quot</span> <span class='hs-varid'>x</span> <span class='hs-str'>"quot"</span> <span class='hs-varid'>y</span>
<a name="line-127"></a> <span class='hs-varid'>rem</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>rem</span> <span class='hs-varid'>x</span> <span class='hs-str'>"rem"</span> <span class='hs-varid'>y</span>
<a name="line-128"></a> <span class='hs-varid'>quotRem</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>quot</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>rem</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-129"></a> <span class='hs-varid'>div</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>div</span> <span class='hs-varid'>x</span> <span class='hs-str'>"div"</span> <span class='hs-varid'>y</span>
<a name="line-130"></a> <span class='hs-varid'>mod</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>mod</span> <span class='hs-varid'>x</span> <span class='hs-str'>"mod"</span> <span class='hs-varid'>y</span>
<a name="line-131"></a> <span class='hs-varid'>toInteger</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInteger</span> <span class='hs-varid'>c</span>
<a name="line-132"></a>
<a name="line-133"></a><a name="instance%20Enum%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Enum</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Enum</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-134"></a> <span class='hs-varid'>toEnum</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toEnum</span>
<a name="line-135"></a> <span class='hs-varid'>fromEnum</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromEnum</span> <span class='hs-varid'>a</span>
<a name="line-136"></a>
<a name="line-137"></a><a name="instance%20Real%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Real</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Real</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-138"></a> <span class='hs-varid'>toRational</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toRational</span> <span class='hs-varid'>c</span>
<a name="line-139"></a>
<a name="line-140"></a><a name="instance%20RealFrac%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>RealFrac</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RealFrac</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-141"></a> <span class='hs-varid'>properFraction</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-conid'>Con</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>properFraction</span> <span class='hs-varid'>c</span>
<a name="line-142"></a>
<a name="line-143"></a><a name="instance%20Floating%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Floating</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-144"></a> <span class='hs-varid'>pi</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>var</span> <span class='hs-str'>"pi"</span>
<a name="line-145"></a> <span class='hs-varid'>exp</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>exp</span> <span class='hs-str'>"exp"</span>
<a name="line-146"></a> <span class='hs-varid'>sqrt</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>sqrt</span> <span class='hs-str'>"sqrt"</span>
<a name="line-147"></a> <span class='hs-varid'>log</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>log</span> <span class='hs-str'>"log"</span>
<a name="line-148"></a> <span class='hs-varid'>x</span> <span class='hs-varop'>**</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-layout'>(</span><span class='hs-varop'>**</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-str'>"**"</span> <span class='hs-varid'>y</span>
<a name="line-149"></a> <span class='hs-varid'>logBase</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>logBase</span> <span class='hs-varid'>x</span> <span class='hs-str'>"logBase"</span> <span class='hs-varid'>y</span>
<a name="line-150"></a> <span class='hs-varid'>sin</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>sin</span> <span class='hs-str'>"sin"</span>
<a name="line-151"></a> <span class='hs-varid'>tan</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>tan</span> <span class='hs-str'>"tan"</span>
<a name="line-152"></a> <span class='hs-varid'>cos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>cos</span> <span class='hs-str'>"cos"</span>
<a name="line-153"></a> <span class='hs-varid'>asin</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>asin</span> <span class='hs-str'>"asin"</span>
<a name="line-154"></a> <span class='hs-varid'>atan</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>atan</span> <span class='hs-str'>"atan"</span>
<a name="line-155"></a> <span class='hs-varid'>acos</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>acos</span> <span class='hs-str'>"acos"</span>
<a name="line-156"></a> <span class='hs-varid'>sinh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>sinh</span> <span class='hs-str'>"sinh"</span>
<a name="line-157"></a> <span class='hs-varid'>tanh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>tanh</span> <span class='hs-str'>"tanh"</span>
<a name="line-158"></a> <span class='hs-varid'>cosh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>cosh</span> <span class='hs-str'>"cosh"</span>
<a name="line-159"></a> <span class='hs-varid'>asinh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>asinh</span> <span class='hs-str'>"asinh"</span>
<a name="line-160"></a> <span class='hs-varid'>atanh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>atanh</span> <span class='hs-str'>"atanh"</span>
<a name="line-161"></a> <span class='hs-varid'>acosh</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unOp</span> <span class='hs-varid'>acosh</span> <span class='hs-str'>"acosh"</span>
<a name="line-162"></a>
<a name="line-163"></a><a name="instance%20RealFloat%20(Sym%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>RealFloat</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RealFloat</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sym</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-164"></a> <span class='hs-varid'>floatRadix</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatRadix</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unSym</span>
<a name="line-165"></a> <span class='hs-varid'>floatDigits</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatDigits</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unSym</span>
<a name="line-166"></a> <span class='hs-varid'>floatRange</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>floatRange</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unSym</span>
<a name="line-167"></a> <span class='hs-varid'>decodeFloat</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>decodeFloat</span> <span class='hs-varid'>c</span>
<a name="line-168"></a> <span class='hs-varid'>encodeFloat</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>encodeFloat</span> <span class='hs-varid'>m</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span>
<a name="line-169"></a> <span class='hs-varid'>exponent</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>exponent</span> <span class='hs-varid'>c</span>
<a name="line-170"></a> <span class='hs-varid'>exponent</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span>
<a name="line-171"></a> <span class='hs-varid'>significand</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>significand</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-172"></a> <span class='hs-varid'>scaleFloat</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Con</span> <span class='hs-layout'>(</span><span class='hs-varid'>scaleFloat</span> <span class='hs-varid'>k</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-173"></a> <span class='hs-varid'>scaleFloat</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-174"></a> <span class='hs-varid'>isNaN</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isNaN</span> <span class='hs-varid'>c</span>
<a name="line-175"></a> <span class='hs-varid'>isInfinite</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isInfinite</span> <span class='hs-varid'>c</span>
<a name="line-176"></a> <span class='hs-varid'>isDenormalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isDenormalized</span> <span class='hs-varid'>c</span>
<a name="line-177"></a> <span class='hs-varid'>isNegativeZero</span> <span class='hs-layout'>(</span><span class='hs-conid'>Con</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isNegativeZero</span> <span class='hs-varid'>c</span>
<a name="line-178"></a> <span class='hs-varid'>isIEEE</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isIEEE</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unSym</span>
<a name="line-179"></a> <span class='hs-varid'>atan2</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>binOp</span> <span class='hs-varid'>atan2</span> <span class='hs-varid'>x</span> <span class='hs-str'>"atan2"</span> <span class='hs-varid'>y</span>
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