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<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module : Data.Ranged.Boundaries</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright : (c) Paul Johnson 2006</span>
<a name="line-5"></a><span class='hs-comment'>-- License : BSD-style</span>
<a name="line-6"></a><span class='hs-comment'>-- Maintainer : paul@cogito.org.uk</span>
<a name="line-7"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-8"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-9"></a><span class='hs-comment'>--</span>
<a name="line-10"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-11"></a>
<a name="line-12"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Ranged</span><span class='hs-varop'>.</span><span class='hs-conid'>Boundaries</span> <span class='hs-layout'>(</span>
<a name="line-13"></a> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-14"></a> <span class='hs-varid'>enumAdjacent</span><span class='hs-layout'>,</span>
<a name="line-15"></a> <span class='hs-varid'>boundedAdjacent</span><span class='hs-layout'>,</span>
<a name="line-16"></a> <span class='hs-varid'>boundedBelow</span><span class='hs-layout'>,</span>
<a name="line-17"></a> <span class='hs-conid'>Boundary</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-18"></a> <span class='hs-varid'>above</span><span class='hs-layout'>,</span>
<a name="line-19"></a> <span class='hs-layout'>(</span><span class='hs-varop'>/>/</span><span class='hs-layout'>)</span>
<a name="line-20"></a><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Ratio</span>
<a name="line-23"></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-24"></a>
<a name="line-25"></a><span class='hs-keyword'>infix</span> <span class='hs-num'>4</span> <span class='hs-varop'>/>/</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='hs-comment'>{- |
<a name="line-28"></a>Distinguish between dense and sparse ordered types. A dense type is
<a name="line-29"></a>one in which any two values @v1 < v2@ have a third value @v3@ such that
<a name="line-30"></a>@v1 < v3 < v2@.
<a name="line-31"></a>
<a name="line-32"></a>In theory the floating types are dense, although in practice they can only have
<a name="line-33"></a>finitely many values. This class treats them as dense.
<a name="line-34"></a>
<a name="line-35"></a>Tuples up to 4 members are declared as instances. Larger tuples may be added
<a name="line-36"></a>if necessary.
<a name="line-37"></a>
<a name="line-38"></a>Most values of sparse types have an @adjacentBelow@, such that, for all x:
<a name="line-39"></a>
<a name="line-40"></a>> case adjacentBelow x of
<a name="line-41"></a>> Just x1 -> adjacent x1 x
<a name="line-42"></a>> Nothing -> True
<a name="line-43"></a>
<a name="line-44"></a>The exception is for bounded types when @x == lowerBound@. For dense types
<a name="line-45"></a>@adjacentBelow@ always returns 'Nothing'.
<a name="line-46"></a>
<a name="line-47"></a>This approach was suggested by Ben Rudiak-Gould on comp.lang.functional.
<a name="line-48"></a>-}</span>
<a name="line-49"></a>
<a name="line-50"></a><a name="DiscreteOrdered"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-51"></a> <span class='hs-comment'>-- | Two values @x@ and @y@ are adjacent if @x < y@ and there does not</span>
<a name="line-52"></a> <span class='hs-comment'>-- exist a third value between them. Always @False@ for dense types.</span>
<a name="line-53"></a> <span class='hs-varid'>adjacent</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-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-54"></a> <span class='hs-comment'>-- | The value immediately below the argument, if it can be determined.</span>
<a name="line-55"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span>
<a name="line-56"></a>
<a name="line-57"></a>
<a name="line-58"></a><span class='hs-comment'>-- Implementation note: the precise rules about unbounded enumerated vs</span>
<a name="line-59"></a><span class='hs-comment'>-- bounded enumerated types are difficult to express using Haskell 98, so</span>
<a name="line-60"></a><span class='hs-comment'>-- the prelude types are listed individually here.</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="instance%20DiscreteOrdered%20Bool"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Bool</span> <span class='hs-keyword'>where</span>
<a name="line-63"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedAdjacent</span>
<a name="line-64"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedBelow</span>
<a name="line-65"></a>
<a name="line-66"></a><a name="instance%20DiscreteOrdered%20Ordering"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Ordering</span> <span class='hs-keyword'>where</span>
<a name="line-67"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedAdjacent</span>
<a name="line-68"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedBelow</span>
<a name="line-69"></a>
<a name="line-70"></a><a name="instance%20DiscreteOrdered%20Char"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Char</span> <span class='hs-keyword'>where</span>
<a name="line-71"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedAdjacent</span>
<a name="line-72"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedBelow</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="instance%20DiscreteOrdered%20Int"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Int</span> <span class='hs-keyword'>where</span>
<a name="line-75"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedAdjacent</span>
<a name="line-76"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>boundedBelow</span>
<a name="line-77"></a>
<a name="line-78"></a><a name="instance%20DiscreteOrdered%20Integer"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Integer</span> <span class='hs-keyword'>where</span>
<a name="line-79"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>enumAdjacent</span>
<a name="line-80"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pred</span>
<a name="line-81"></a>
<a name="line-82"></a><a name="instance%20DiscreteOrdered%20Double"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Double</span> <span class='hs-keyword'>where</span>
<a name="line-83"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-84"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-conid'>Nothing</span>
<a name="line-85"></a>
<a name="line-86"></a><a name="instance%20DiscreteOrdered%20Float"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-conid'>Float</span> <span class='hs-keyword'>where</span>
<a name="line-87"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-88"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-conid'>Nothing</span>
<a name="line-89"></a>
<a name="line-90"></a><a name="instance%20DiscreteOrdered%20(Ratio%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'>DiscreteOrdered</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ratio</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-91"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-92"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-conid'>Nothing</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="instance%20DiscreteOrdered%20%5ba%5d"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>where</span>
<a name="line-95"></a> <span class='hs-varid'>adjacent</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-96"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>const</span> <span class='hs-conid'>Nothing</span>
<a name="line-97"></a>
<a name="line-98"></a><a name="instance%20DiscreteOrdered%20(a,%20b)"></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-conid'>DiscreteOrdered</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-99"></a> <span class='hs-keyword'>where</span>
<a name="line-100"></a> <span class='hs-varid'>adjacent</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-layout'>,</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>adjacent</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span>
<a name="line-101"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-comment'>-- Maybe monad</span>
<a name="line-102"></a> <span class='hs-varid'>x2'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>adjacentBelow</span> <span class='hs-varid'>x2</span>
<a name="line-103"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2'</span><span class='hs-layout'>)</span>
<a name="line-104"></a>
<a name="line-105"></a><a name="instance%20DiscreteOrdered%20(a,%20b,%20c)"></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-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-106"></a> <span class='hs-keyword'>where</span>
<a name="line-107"></a> <span class='hs-varid'>adjacent</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-layout'>,</span> <span class='hs-varid'>y2</span><span class='hs-layout'>,</span> <span class='hs-varid'>y3</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-108"></a> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-layout'>(</span><span class='hs-varid'>x2</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>adjacent</span> <span class='hs-varid'>x3</span> <span class='hs-varid'>y3</span>
<a name="line-109"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-comment'>-- Maybe monad</span>
<a name="line-110"></a> <span class='hs-varid'>x3'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>adjacentBelow</span> <span class='hs-varid'>x3</span>
<a name="line-111"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3'</span><span class='hs-layout'>)</span>
<a name="line-112"></a>
<a name="line-113"></a><a name="instance%20DiscreteOrdered%20(a,%20b,%20c,%20d)"></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-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-114"></a> <span class='hs-conid'>DiscreteOrdered</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span>
<a name="line-115"></a> <span class='hs-keyword'>where</span>
<a name="line-116"></a> <span class='hs-varid'>adjacent</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3</span><span class='hs-layout'>,</span> <span class='hs-varid'>x4</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-layout'>,</span> <span class='hs-varid'>y2</span><span class='hs-layout'>,</span> <span class='hs-varid'>y3</span><span class='hs-layout'>,</span> <span class='hs-varid'>y4</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-117"></a> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-layout'>(</span><span class='hs-varid'>x2</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-layout'>(</span><span class='hs-varid'>x3</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y3</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>adjacent</span> <span class='hs-varid'>x4</span> <span class='hs-varid'>y4</span>
<a name="line-118"></a> <span class='hs-varid'>adjacentBelow</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3</span><span class='hs-layout'>,</span> <span class='hs-varid'>x4</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-comment'>-- Maybe monad</span>
<a name="line-119"></a> <span class='hs-varid'>x4'</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>adjacentBelow</span> <span class='hs-varid'>x4</span>
<a name="line-120"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>x3</span><span class='hs-layout'>,</span> <span class='hs-varid'>x4'</span><span class='hs-layout'>)</span>
<a name="line-121"></a>
<a name="line-122"></a>
<a name="line-123"></a><a name="enumAdjacent"></a><span class='hs-comment'>-- | Check adjacency for sparse enumerated types (i.e. where there</span>
<a name="line-124"></a><span class='hs-comment'>-- is no value between @x@ and @succ x@).</span>
<a name="line-125"></a><span class='hs-definition'>enumAdjacent</span> <span class='hs-keyglyph'>::</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-conid'>Enum</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-126"></a><span class='hs-definition'>enumAdjacent</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'>succ</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-127"></a>
<a name="line-128"></a><a name="boundedAdjacent"></a><span class='hs-comment'>-- | Check adjacency, allowing for case where x = maxBound. Use as the</span>
<a name="line-129"></a><span class='hs-comment'>-- definition of "adjacent" for bounded enumerated types such as Int and Char.</span>
<a name="line-130"></a><span class='hs-definition'>boundedAdjacent</span> <span class='hs-keyglyph'>::</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-conid'>Enum</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-131"></a><span class='hs-definition'>boundedAdjacent</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>x</span> <span class='hs-varop'><</span> <span class='hs-varid'>y</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>succ</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>False</span>
<a name="line-132"></a>
<a name="line-133"></a>
<a name="line-134"></a><a name="boundedBelow"></a><span class='hs-comment'>-- | The usual implementation of 'adjacentBelow' for bounded enumerated types.</span>
<a name="line-135"></a><span class='hs-definition'>boundedBelow</span> <span class='hs-keyglyph'>::</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-conid'>Enum</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bounded</span> <span class='hs-varid'>a</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-conid'>Maybe</span> <span class='hs-varid'>a</span>
<a name="line-136"></a><span class='hs-definition'>boundedBelow</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>minBound</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>Just</span> <span class='hs-varop'>$</span> <span class='hs-varid'>pred</span> <span class='hs-varid'>x</span>
<a name="line-137"></a>
<a name="line-138"></a><span class='hs-comment'>{- |
<a name="line-139"></a>A Boundary is a division of an ordered type into values above
<a name="line-140"></a>and below the boundary. No value can sit on a boundary.
<a name="line-141"></a>
<a name="line-142"></a>Known bug: for Bounded types
<a name="line-143"></a>
<a name="line-144"></a>* @BoundaryAbove maxBound < BoundaryAboveAll@
<a name="line-145"></a>
<a name="line-146"></a>* @BoundaryBelow minBound > BoundaryBelowAll@
<a name="line-147"></a>
<a name="line-148"></a>This is incorrect because there are no possible values in
<a name="line-149"></a>between the left and right sides of these inequalities.
<a name="line-150"></a>-}</span>
<a name="line-151"></a>
<a name="line-152"></a><a name="Boundary"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Boundary</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span>
<a name="line-153"></a> <span class='hs-comment'>-- | The argument is the highest value below the boundary.</span>
<a name="line-154"></a> <span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span>
<a name="line-155"></a> <span class='hs-comment'>-- | The argument is the lowest value above the boundary.</span>
<a name="line-156"></a> <span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span>
<a name="line-157"></a> <span class='hs-comment'>-- | The boundary above all values.</span>
<a name="line-158"></a> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>|</span>
<a name="line-159"></a> <span class='hs-comment'>-- | The boundary below all values.</span>
<a name="line-160"></a> <span class='hs-conid'>BoundaryBelowAll</span>
<a name="line-161"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Show</span><span class='hs-layout'>)</span>
<a name="line-162"></a>
<a name="line-163"></a><a name="above"></a><span class='hs-comment'>-- | True if the value is above the boundary, false otherwise.</span>
<a name="line-164"></a><span class='hs-definition'>above</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Boundary</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-165"></a><span class='hs-definition'>above</span> <span class='hs-layout'>(</span><span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span> <span class='hs-varop'>></span> <span class='hs-varid'>b</span>
<a name="line-166"></a><span class='hs-definition'>above</span> <span class='hs-layout'>(</span><span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>v</span> <span class='hs-varop'>>=</span> <span class='hs-varid'>b</span>
<a name="line-167"></a><span class='hs-definition'>above</span> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-168"></a><span class='hs-definition'>above</span> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-169"></a>
<a name="line-170"></a><a name="/%3e/"></a><span class='hs-comment'>-- | Same as 'above', but with the arguments reversed for more intuitive infix</span>
<a name="line-171"></a><span class='hs-comment'>-- usage.</span>
<a name="line-172"></a><span class='hs-layout'>(</span><span class='hs-varop'>/>/</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Boundary</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-173"></a><span class='hs-layout'>(</span><span class='hs-varop'>/>/</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>above</span>
<a name="line-174"></a>
<a name="line-175"></a><a name="instance%20Eq%20(Boundary%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>DiscreteOrdered</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'>Boundary</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-176"></a> <span class='hs-varid'>b1</span> <span class='hs-varop'>==</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>compare</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span> <span class='hs-varop'>==</span> <span class='hs-conid'>EQ</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="instance%20Ord%20(Boundary%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>DiscreteOrdered</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'>Boundary</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-179"></a> <span class='hs-comment'>-- Comparison alogrithm based on brute force and ignorance:</span>
<a name="line-180"></a> <span class='hs-comment'>-- enumerate all combinations.</span>
<a name="line-181"></a>
<a name="line-182"></a> <span class='hs-varid'>compare</span> <span class='hs-varid'>boundary1</span> <span class='hs-varid'>boundary2</span> <span class='hs-keyglyph'>=</span>
<a name="line-183"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>boundary1</span> <span class='hs-keyword'>of</span>
<a name="line-184"></a> <span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>b1</span> <span class='hs-keyglyph'>-></span>
<a name="line-185"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>boundary2</span> <span class='hs-keyword'>of</span>
<a name="line-186"></a> <span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>compare</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span>
<a name="line-187"></a> <span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>-></span>
<a name="line-188"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>b1</span> <span class='hs-varop'><</span> <span class='hs-varid'>b2</span>
<a name="line-189"></a> <span class='hs-keyword'>then</span>
<a name="line-190"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>adjacent</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>EQ</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>LT</span>
<a name="line-191"></a> <span class='hs-keyword'>else</span> <span class='hs-conid'>GT</span>
<a name="line-192"></a> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LT</span>
<a name="line-193"></a> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>GT</span>
<a name="line-194"></a> <span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>b1</span> <span class='hs-keyglyph'>-></span>
<a name="line-195"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>boundary2</span> <span class='hs-keyword'>of</span>
<a name="line-196"></a> <span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>-></span>
<a name="line-197"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>b1</span> <span class='hs-varop'>></span> <span class='hs-varid'>b2</span>
<a name="line-198"></a> <span class='hs-keyword'>then</span>
<a name="line-199"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>adjacent</span> <span class='hs-varid'>b2</span> <span class='hs-varid'>b1</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>EQ</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>GT</span>
<a name="line-200"></a> <span class='hs-keyword'>else</span> <span class='hs-conid'>LT</span>
<a name="line-201"></a> <span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>b2</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>compare</span> <span class='hs-varid'>b1</span> <span class='hs-varid'>b2</span>
<a name="line-202"></a> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LT</span>
<a name="line-203"></a> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>GT</span>
<a name="line-204"></a> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>-></span>
<a name="line-205"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>boundary2</span> <span class='hs-keyword'>of</span>
<a name="line-206"></a> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>EQ</span>
<a name="line-207"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>GT</span>
<a name="line-208"></a> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyglyph'>-></span>
<a name="line-209"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>boundary2</span> <span class='hs-keyword'>of</span>
<a name="line-210"></a> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>EQ</span>
<a name="line-211"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LT</span>
<a name="line-212"></a>
<a name="line-213"></a><span class='hs-comment'>-- QuickCheck Generator</span>
<a name="line-214"></a>
<a name="line-215"></a><a name="instance%20Arbitrary%20(Boundary%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'>Boundary</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-216"></a> <span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>frequency</span> <span class='hs-keyglyph'>[</span>
<a name="line-217"></a> <span class='hs-layout'>(</span><span class='hs-num'>1</span><span class='hs-layout'>,</span> <span class='hs-varid'>return</span> <span class='hs-conid'>BoundaryAboveAll</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-218"></a> <span class='hs-layout'>(</span><span class='hs-num'>1</span><span class='hs-layout'>,</span> <span class='hs-varid'>return</span> <span class='hs-conid'>BoundaryBelowAll</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-219"></a> <span class='hs-layout'>(</span><span class='hs-num'>18</span><span class='hs-layout'>,</span> <span class='hs-keyword'>do</span>
<a name="line-220"></a> <span class='hs-varid'>v</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>arbitrary</span>
<a name="line-221"></a> <span class='hs-varid'>oneof</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>v</span><span class='hs-layout'>,</span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>v</span><span class='hs-keyglyph'>]</span>
<a name="line-222"></a> <span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-223"></a>
<a name="line-224"></a><a name="instance%20CoArbitrary%20(Boundary%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>CoArbitrary</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>CoArbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>Boundary</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-225"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-conid'>BoundaryBelowAll</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>variant</span> <span class='hs-layout'>(</span><span class='hs-num'>0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span><span class='hs-layout'>)</span>
<a name="line-226"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-conid'>BoundaryAboveAll</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>variant</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span><span class='hs-layout'>)</span>
<a name="line-227"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>BoundaryBelow</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>variant</span> <span class='hs-layout'>(</span><span class='hs-num'>2</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>coarbitrary</span> <span class='hs-varid'>v</span>
<a name="line-228"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>BoundaryAbove</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>variant</span> <span class='hs-layout'>(</span><span class='hs-num'>3</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>coarbitrary</span> <span class='hs-varid'>v</span>
<a name="line-229"></a>
</pre></body>
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