<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html> <head> <!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ --> <title>Data/Stream.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <pre><a name="line-1"></a><span class='hs-comment'>-- | Streams are infinite lists. Most operations on streams are</span> <a name="line-2"></a><span class='hs-comment'>-- completely analogous to the definition in Data.List.</span> <a name="line-3"></a> <a name="line-4"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Stream</span> <a name="line-5"></a> <span class='hs-layout'>(</span> <a name="line-6"></a> <span class='hs-comment'>-- * The type of streams</span> <a name="line-7"></a> <span class='hs-conid'>Stream</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span> <a name="line-8"></a> <span class='hs-comment'>-- * Basic functions</span> <a name="line-9"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'><:></span><span class='hs-layout'>)</span> <a name="line-10"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>head</span> <a name="line-11"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>tail</span> <a name="line-12"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>inits</span> <a name="line-13"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>tails</span> <a name="line-14"></a> <span class='hs-comment'>-- * Stream transformations</span> <a name="line-15"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>map</span> <a name="line-16"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>intersperse</span> <a name="line-17"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>interleave</span> <a name="line-18"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>scan</span> <a name="line-19"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>scan'</span> <a name="line-20"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>scan1</span> <a name="line-21"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>scan1'</span> <a name="line-22"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>transpose</span> <a name="line-23"></a> <span class='hs-comment'>-- * Building streams</span> <a name="line-24"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>iterate</span> <a name="line-25"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>repeat</span> <a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cycle</span> <a name="line-27"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>unfold</span> <a name="line-28"></a> <span class='hs-comment'>-- * Extracting sublists</span> <a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>take</span> <a name="line-30"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>drop</span> <a name="line-31"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>splitAt</span> <a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>takeWhile</span> <a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>dropWhile</span> <a name="line-34"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>span</span> <a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>break</span> <a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>filter</span> <a name="line-37"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>partition</span> <a name="line-38"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>group</span> <a name="line-39"></a> <span class='hs-comment'>-- * Sublist predicates</span> <a name="line-40"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>isPrefixOf</span> <a name="line-41"></a> <span class='hs-comment'>-- * Indexing streams</span> <a name="line-42"></a> <span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>!!</span><span class='hs-layout'>)</span> <a name="line-43"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>elemIndex</span> <a name="line-44"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>elemIndices</span> <a name="line-45"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>findIndex</span> <a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>findIndices</span> <a name="line-47"></a> <span class='hs-comment'>-- * Zipping and unzipping streams</span> <a name="line-48"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>zip</span> <a name="line-49"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>zipWith</span> <a name="line-50"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>unzip</span> <a name="line-51"></a> <span class='hs-comment'>-- * Functions on streams of characters</span> <a name="line-52"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>words</span> <a name="line-53"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>unwords</span> <a name="line-54"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lines</span> <a name="line-55"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>unlines</span> <a name="line-56"></a> <span class='hs-comment'>-- * Converting to and from an infinite list</span> <a name="line-57"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>toList</span> <a name="line-58"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>fromList</span> <a name="line-59"></a> <span class='hs-layout'>)</span> <a name="line-60"></a> <span class='hs-keyword'>where</span> <a name="line-61"></a> <a name="line-62"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span><span class='hs-layout'>,</span> <span class='hs-varid'>tail</span><span class='hs-layout'>,</span> <span class='hs-varid'>map</span><span class='hs-layout'>,</span> <span class='hs-varid'>scanl</span><span class='hs-layout'>,</span> <span class='hs-varid'>scanl1</span><span class='hs-layout'>,</span> <a name="line-63"></a> <span class='hs-varid'>iterate</span><span class='hs-layout'>,</span> <span class='hs-varid'>take</span><span class='hs-layout'>,</span> <span class='hs-varid'>drop</span><span class='hs-layout'>,</span> <span class='hs-varid'>takeWhile</span><span class='hs-layout'>,</span> <a name="line-64"></a> <span class='hs-varid'>dropWhile</span><span class='hs-layout'>,</span> <span class='hs-varid'>repeat</span><span class='hs-layout'>,</span> <span class='hs-varid'>cycle</span><span class='hs-layout'>,</span> <span class='hs-varid'>filter</span><span class='hs-layout'>,</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'>zip</span><span class='hs-layout'>,</span> <span class='hs-varid'>unzip</span><span class='hs-layout'>,</span> <a name="line-65"></a> <span class='hs-varid'>zipWith</span><span class='hs-layout'>,</span><span class='hs-varid'>words</span><span class='hs-layout'>,</span><span class='hs-varid'>unwords</span><span class='hs-layout'>,</span><span class='hs-varid'>lines</span><span class='hs-layout'>,</span><span class='hs-varid'>unlines</span><span class='hs-layout'>,</span> <span class='hs-varid'>break</span><span class='hs-layout'>,</span> <span class='hs-varid'>span</span><span class='hs-layout'>,</span> <span class='hs-varid'>splitAt</span><span class='hs-layout'>)</span> <a name="line-66"></a> <a name="line-67"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span> <a name="line-68"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-varid'>liftM2</span><span class='hs-layout'>)</span> <a name="line-69"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span><span class='hs-layout'>)</span> <a name="line-70"></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'>isSpace</span><span class='hs-layout'>)</span> <a name="line-71"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Test</span><span class='hs-varop'>.</span><span class='hs-conid'>QuickCheck</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arbitrary</span><span class='hs-layout'>,</span> <span class='hs-conid'>CoArbitrary</span><span class='hs-layout'>,</span> <span class='hs-varid'>arbitrary</span><span class='hs-layout'>,</span> <span class='hs-varid'>coarbitrary</span><span class='hs-layout'>)</span> <a name="line-72"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Test</span><span class='hs-varop'>.</span><span class='hs-conid'>LazySmallCheck</span> <span class='hs-layout'>(</span><span class='hs-conid'>Serial</span><span class='hs-layout'>,</span> <span class='hs-varid'>series</span><span class='hs-layout'>,</span> <span class='hs-varid'>cons2</span><span class='hs-layout'>)</span> <a name="line-73"></a> <a name="line-74"></a><span class='hs-comment'>-- | An infinite sequence.</span> <a name="line-75"></a><span class='hs-comment'>--</span> <a name="line-76"></a><span class='hs-comment'>-- /Beware/: If you use any function from the @ Eq @ or @ Ord @</span> <a name="line-77"></a><span class='hs-comment'>-- class to compare two equal streams, these functions will diverge.</span> <a name="line-78"></a> <a name="line-79"></a><a name="Stream"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span><span class='hs-layout'>)</span> <a name="line-80"></a> <a name="line-81"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>5</span> <span class='hs-varop'>`Cons`</span> <a name="line-82"></a> <a name="line-83"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>Stream</span> <span class='hs-keyword'>where</span> <a name="line-84"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-85"></a> <a name="line-86"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-conid'>Stream</span> <span class='hs-keyword'>where</span> <a name="line-87"></a> <span class='hs-varid'>pure</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>repeat</span> <a name="line-88"></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'>zipWith</span> <span class='hs-layout'>(</span><span class='hs-varop'>$</span><span class='hs-layout'>)</span> <a name="line-89"></a> <a name="line-90"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-conid'>Stream</span> <span class='hs-keyword'>where</span> <a name="line-91"></a> <span class='hs-varid'>return</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>repeat</span> <a name="line-92"></a> <span class='hs-varid'>xs</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>join</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-93"></a> <span class='hs-keyword'>where</span> <a name="line-94"></a> <span class='hs-varid'>join</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-95"></a> <span class='hs-varid'>join</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>xss</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>tail</span> <span class='hs-varid'>xss</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-96"></a> <a name="line-97"></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'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-98"></a> <span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftM2</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>arbitrary</span> <span class='hs-varid'>arbitrary</span> <a name="line-99"></a> <a name="line-100"></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'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-101"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>gen</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <a name="line-102"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>arbitrary</span> <a name="line-103"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-varid'>take</span> <span class='hs-layout'>(</span><span class='hs-varid'>abs</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>gen</span> <a name="line-104"></a> <a name="line-105"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Serial</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Serial</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-106"></a> <span class='hs-varid'>series</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cons2</span> <span class='hs-conid'>Cons</span> <a name="line-107"></a> <a name="line-108"></a><span class='hs-comment'>-- | A Show instance for Streams that takes the right associativity into</span> <a name="line-109"></a><span class='hs-comment'>-- account and so doesn't put parenthesis around the tail of the Stream.</span> <a name="line-110"></a><span class='hs-comment'>-- Note that 'show' returns an infinite 'String'.</span> <a name="line-111"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-112"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-113"></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'>consPrecedence</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <a name="line-114"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-layout'>(</span><span class='hs-varid'>consPrecedence</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-varop'>.</span> <a name="line-115"></a> <span class='hs-varid'>showString</span> <span class='hs-str'>" <:> "</span> <span class='hs-varop'>.</span> <a name="line-116"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>consPrecedence</span> <span class='hs-varid'>xs</span> <a name="line-117"></a> <span class='hs-keyword'>where</span> <a name="line-118"></a> <span class='hs-varid'>consPrecedence</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>5</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <a name="line-119"></a> <a name="line-120"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>5</span> <span class='hs-varop'><:></span> <a name="line-121"></a><a name="%3c:%3e"></a><span class='hs-comment'>-- | The @ \<:\> @ operator is an infix version of the 'Cons'</span> <a name="line-122"></a><span class='hs-comment'>-- constructor.</span> <a name="line-123"></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'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-124"></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'>Cons</span> <a name="line-125"></a> <a name="line-126"></a><a name="head"></a><span class='hs-comment'>-- | Extract the first element of the sequence.</span> <a name="line-127"></a><span class='hs-definition'>head</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <a name="line-128"></a><span class='hs-definition'>head</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <a name="line-129"></a> <a name="line-130"></a><a name="tail"></a><span class='hs-comment'>-- | Extract the sequence following the head of the stream.</span> <a name="line-131"></a><span class='hs-definition'>tail</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-132"></a><span class='hs-definition'>tail</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xs</span> <a name="line-133"></a> <a name="line-134"></a><span class='hs-comment'>-- | The 'inits' function takes a stream @xs@ and returns all the</span> <a name="line-135"></a><span class='hs-comment'>-- finite prefixes of @xs@.</span> <a name="line-136"></a><span class='hs-comment'>--</span> <a name="line-137"></a><span class='hs-comment'>-- Note that this 'inits' is lazier then @Data.List.inits@:</span> <a name="line-138"></a><span class='hs-comment'>--</span> <a name="line-139"></a><span class='hs-comment'>-- > inits _|_ = [] ::: _|_</span> <a name="line-140"></a><span class='hs-comment'>--</span> <a name="line-141"></a><span class='hs-comment'>-- while for @Data.List.inits@:</span> <a name="line-142"></a><span class='hs-comment'>--</span> <a name="line-143"></a><span class='hs-comment'>-- > inits _|_ = _|_</span> <a name="line-144"></a> <a name="line-145"></a><a name="inits"></a><span class='hs-definition'>inits</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</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-layout'>)</span> <a name="line-146"></a><span class='hs-definition'>inits</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span> <span class='hs-varid'>xs</span> <span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>inits</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-147"></a> <a name="line-148"></a><a name="tails"></a><span class='hs-comment'>-- | The 'tails' function takes a stream @xs@ and returns all the</span> <a name="line-149"></a><span class='hs-comment'>-- suffixes of @xs@.</span> <a name="line-150"></a><span class='hs-definition'>tails</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-151"></a><span class='hs-definition'>tails</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>tails</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-152"></a> <a name="line-153"></a><a name="map"></a><span class='hs-comment'>-- | Apply a function uniformly over all elements of a sequence.</span> <a name="line-154"></a><span class='hs-definition'>map</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'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span> <a name="line-155"></a><span class='hs-definition'>map</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-156"></a> <a name="line-157"></a><a name="intersperse"></a><span class='hs-comment'>-- | 'intersperse' @y@ @xs@ creates an alternating stream of</span> <a name="line-158"></a><span class='hs-comment'>-- elements from @xs@ and @y@.</span> <a name="line-159"></a><span class='hs-definition'>intersperse</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-160"></a><span class='hs-definition'>intersperse</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>y</span> <span class='hs-layout'>(</span><span class='hs-varid'>intersperse</span> <span class='hs-varid'>y</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-161"></a> <a name="line-162"></a><a name="interleave"></a><span class='hs-comment'>-- | Interleave two Streams @xs@ and @ys@, alternating elements</span> <a name="line-163"></a><span class='hs-comment'>-- from each list.</span> <a name="line-164"></a><span class='hs-comment'>--</span> <a name="line-165"></a><span class='hs-comment'>-- > [x1,x2,...] `interleave` [y1,y2,...] == [x1,y1,x2,y2,...]</span> <a name="line-166"></a><span class='hs-definition'>interleave</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-167"></a><span class='hs-definition'>interleave</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>interleave</span> <span class='hs-varid'>ys</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-168"></a> <a name="line-169"></a><a name="scan"></a><span class='hs-comment'>-- | 'scan' yields a stream of successive reduced values from:</span> <a name="line-170"></a><span class='hs-comment'>--</span> <a name="line-171"></a><span class='hs-comment'>-- > scan f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]</span> <a name="line-172"></a><span class='hs-definition'>scan</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'>b</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-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-173"></a><span class='hs-definition'>scan</span> <span class='hs-varid'>f</span> <span class='hs-varid'>z</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>z</span> <span class='hs-varop'><:></span> <span class='hs-varid'>scan</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>z</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <a name="line-174"></a> <a name="line-175"></a><a name="scan'"></a><span class='hs-comment'>-- | @scan'@ is a strict scan.</span> <a name="line-176"></a><span class='hs-definition'>scan'</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'>b</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-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-177"></a><span class='hs-definition'>scan'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>z</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>z</span> <span class='hs-varop'><:></span> <span class='hs-layout'>(</span><span class='hs-varid'>scan'</span> <span class='hs-varid'>f</span> <span class='hs-varop'>$!</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-178"></a> <a name="line-179"></a><a name="scan1"></a><span class='hs-comment'>-- | 'scan1' is a variant of 'scan' that has no starting value argument:</span> <a name="line-180"></a><span class='hs-comment'>--</span> <a name="line-181"></a><span class='hs-comment'>-- > scan1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]</span> <a name="line-182"></a><span class='hs-definition'>scan1</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'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-183"></a><span class='hs-definition'>scan1</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>scan</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <a name="line-184"></a> <a name="line-185"></a><a name="scan1'"></a><span class='hs-comment'>-- | @scan1'@ is a strict scan that has no starting value.</span> <a name="line-186"></a><span class='hs-definition'>scan1'</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'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-187"></a><span class='hs-definition'>scan1'</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>scan'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <a name="line-188"></a> <a name="line-189"></a><a name="transpose"></a><span class='hs-comment'>-- | 'transpose' computes the transposition of a stream of streams.</span> <a name="line-190"></a><span class='hs-definition'>transpose</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-191"></a><span class='hs-definition'>transpose</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>yss</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-192"></a> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><:></span> <span class='hs-varid'>map</span> <span class='hs-varid'>head</span> <span class='hs-varid'>yss</span><span class='hs-layout'>)</span> <span class='hs-varop'><:></span> <span class='hs-varid'>transpose</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span> <span class='hs-varop'><:></span> <span class='hs-varid'>map</span> <span class='hs-varid'>tail</span> <span class='hs-varid'>yss</span><span class='hs-layout'>)</span> <a name="line-193"></a> <a name="line-194"></a><a name="iterate"></a><span class='hs-comment'>-- | 'iterate' @f@ @x@ function produces the infinite sequence</span> <a name="line-195"></a><span class='hs-comment'>-- of repeated applications of @f@ to @x@.</span> <a name="line-196"></a><span class='hs-comment'>--</span> <a name="line-197"></a><span class='hs-comment'>-- > iterate f x = [x, f x, f (f x), ..]</span> <a name="line-198"></a><span class='hs-definition'>iterate</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-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-199"></a><span class='hs-definition'>iterate</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>iterate</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-200"></a> <a name="line-201"></a><a name="repeat"></a><span class='hs-comment'>-- | 'repeat' @x@ returns a constant stream, where all elements are</span> <a name="line-202"></a><span class='hs-comment'>-- equal to @x@.</span> <a name="line-203"></a><span class='hs-definition'>repeat</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-204"></a><span class='hs-definition'>repeat</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>repeat</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <a name="line-205"></a> <a name="line-206"></a><a name="cycle"></a><span class='hs-comment'>-- | 'cycle' @xs@ returns the infinite repetition of @xs@:</span> <a name="line-207"></a><span class='hs-comment'>--</span> <a name="line-208"></a><span class='hs-comment'>-- > cycle [1,2,3] = Cons 1 (Cons 2 (Cons 3 (Cons 1 (Cons 2 ...</span> <a name="line-209"></a><span class='hs-definition'>cycle</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-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-210"></a><span class='hs-definition'>cycle</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>cycle</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <a name="line-211"></a> <a name="line-212"></a><a name="unfold"></a><span class='hs-comment'>-- | The unfold function is similar to the unfold for lists. Note</span> <a name="line-213"></a><span class='hs-comment'>-- there is no base case: all streams must be infinite.</span> <a name="line-214"></a><span class='hs-definition'>unfold</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-215"></a><span class='hs-definition'>unfold</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <a name="line-216"></a> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>c</span> <a name="line-217"></a> <span class='hs-keyword'>in</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>unfold</span> <span class='hs-varid'>f</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <a name="line-218"></a> <a name="line-219"></a><a name="take"></a><span class='hs-comment'>-- | 'take' @n@ @xs@ returns the first @n@ elements of @xs@.</span> <a name="line-220"></a><span class='hs-comment'>--</span> <a name="line-221"></a><span class='hs-comment'>-- /Beware/: passing a negative integer as the first argument will</span> <a name="line-222"></a><span class='hs-comment'>-- cause an error.</span> <a name="line-223"></a><span class='hs-definition'>take</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <a name="line-224"></a><span class='hs-definition'>take</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-225"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span> <a name="line-226"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-layout'>(</span><span class='hs-varid'>take</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-227"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Stream.take: negative argument."</span> <a name="line-228"></a> <a name="line-229"></a><a name="drop"></a><span class='hs-comment'>-- | 'drop' @n@ @xs@ drops the first @n@ elements off the front of</span> <a name="line-230"></a><span class='hs-comment'>-- the sequence @xs@.</span> <a name="line-231"></a><span class='hs-comment'>--</span> <a name="line-232"></a><span class='hs-comment'>-- /Beware/: passing a negative integer as the first argument will</span> <a name="line-233"></a><span class='hs-comment'>-- cause an error.</span> <a name="line-234"></a><span class='hs-definition'>drop</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-235"></a><span class='hs-definition'>drop</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <a name="line-236"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xs</span> <a name="line-237"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>drop</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-238"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Stream.drop: negative argument."</span> <a name="line-239"></a> <a name="line-240"></a><a name="splitAt"></a><span class='hs-comment'>-- | The 'splitAt' function takes an integer @n@ and a stream @xs@</span> <a name="line-241"></a><span class='hs-comment'>-- and returns a pair consisting of the prefix of @xs@ of length</span> <a name="line-242"></a><span class='hs-comment'>-- @n@ and the remaining stream immediately following this prefix.</span> <a name="line-243"></a><span class='hs-comment'>--</span> <a name="line-244"></a><span class='hs-comment'>-- /Beware/: passing a negative integer as the first argument will</span> <a name="line-245"></a><span class='hs-comment'>-- cause an error.</span> <a name="line-246"></a><span class='hs-definition'>splitAt</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></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-layout'>,</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-247"></a><span class='hs-definition'>splitAt</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <a name="line-248"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-249"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>prefix</span><span class='hs-layout'>,</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>splitAt</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-250"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-varid'>head</span> <span class='hs-varid'>xs</span> <span class='hs-conop'>:</span> <span class='hs-varid'>prefix</span><span class='hs-layout'>,</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <a name="line-251"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Stream.splitAt negative argument."</span> <a name="line-252"></a> <a name="line-253"></a><a name="takeWhile"></a><span class='hs-comment'>-- | 'takeWhile' @p@ @xs@ returns the longest prefix of the stream</span> <a name="line-254"></a><span class='hs-comment'>-- @xs@ for which the predicate @p@ holds.</span> <a name="line-255"></a><span class='hs-definition'>takeWhile</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <a name="line-256"></a><span class='hs-definition'>takeWhile</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-257"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>takeWhile</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <a name="line-258"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span> <a name="line-259"></a> <a name="line-260"></a><a name="dropWhile"></a><span class='hs-comment'>-- | 'dropWhile' @p@ @xs@ returns the suffix remaining after</span> <a name="line-261"></a><span class='hs-comment'>-- 'takeWhile' @p@ @xs@.</span> <a name="line-262"></a><span class='hs-comment'>--</span> <a name="line-263"></a><span class='hs-comment'>-- /Beware/: this function may diverge if every element of @xs@</span> <a name="line-264"></a><span class='hs-comment'>-- satisfies @p@, e.g. @dropWhile even (repeat 0)@ will loop.</span> <a name="line-265"></a><span class='hs-definition'>dropWhile</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-266"></a><span class='hs-definition'>dropWhile</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-267"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dropWhile</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <a name="line-268"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <a name="line-269"></a> <a name="line-270"></a><a name="span"></a><span class='hs-comment'>-- | 'span' @p@ @xs@ returns the longest prefix of @xs@ that satisfies</span> <a name="line-271"></a><span class='hs-comment'>-- @p@, together with the remainder of the stream.</span> <a name="line-272"></a><span class='hs-definition'>span</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></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-layout'>,</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-273"></a><span class='hs-definition'>span</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-274"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>trues</span><span class='hs-layout'>,</span> <span class='hs-varid'>falses</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>span</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <a name="line-275"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>trues</span><span class='hs-layout'>,</span> <span class='hs-varid'>falses</span><span class='hs-layout'>)</span> <a name="line-276"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-277"></a> <a name="line-278"></a><a name="break"></a><span class='hs-comment'>-- | The 'break' @p@ function is equivalent to 'span' @not . p@.</span> <a name="line-279"></a><span class='hs-definition'>break</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></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-layout'>,</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-280"></a><span class='hs-definition'>break</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>span</span> <span class='hs-layout'>(</span><span class='hs-varid'>not</span> <span class='hs-varop'>.</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <a name="line-281"></a> <a name="line-282"></a><a name="filter"></a><span class='hs-comment'>-- | 'filter' @p@ @xs@, removes any elements from @xs@ that do not satisfy @p@.</span> <a name="line-283"></a><span class='hs-comment'>--</span> <a name="line-284"></a><span class='hs-comment'>-- /Beware/: this function may diverge if there is no element of</span> <a name="line-285"></a><span class='hs-comment'>-- @xs@ that satisfies @p@, e.g. @filter odd (repeat 0)@ will loop.</span> <a name="line-286"></a><span class='hs-definition'>filter</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-287"></a><span class='hs-definition'>filter</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-288"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>filter</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-289"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>filter</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <a name="line-290"></a> <a name="line-291"></a><a name="partition"></a><span class='hs-comment'>-- | The 'partition' function takes a predicate @p@ and a stream</span> <a name="line-292"></a><span class='hs-comment'>-- @xs@, and returns a pair of streams. The first stream corresponds</span> <a name="line-293"></a><span class='hs-comment'>-- to the elements of @xs@ for which @p@ holds; the second stream</span> <a name="line-294"></a><span class='hs-comment'>-- corresponds to the elements of @xs@ for which @p@ does not hold.</span> <a name="line-295"></a><span class='hs-comment'>--</span> <a name="line-296"></a><span class='hs-comment'>-- /Beware/: One of the elements of the tuple may be undefined. For</span> <a name="line-297"></a><span class='hs-comment'>-- example, @fst (partition even (repeat 0)) == repeat 0@; on the</span> <a name="line-298"></a><span class='hs-comment'>-- other hand @snd (partition even (repeat 0))@ is undefined.</span> <a name="line-299"></a><span class='hs-definition'>partition</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-300"></a><span class='hs-definition'>partition</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-301"></a> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>trues</span><span class='hs-layout'>,</span><span class='hs-varid'>falses</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>partition</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <a name="line-302"></a> <span class='hs-keyword'>in</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyword'>then</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>trues</span><span class='hs-layout'>,</span> <span class='hs-varid'>falses</span><span class='hs-layout'>)</span> <a name="line-303"></a> <span class='hs-keyword'>else</span> <span class='hs-layout'>(</span><span class='hs-varid'>trues</span><span class='hs-layout'>,</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>falses</span><span class='hs-layout'>)</span> <a name="line-304"></a> <a name="line-305"></a><a name="group"></a><span class='hs-comment'>-- | The 'group' function takes a stream and returns a stream of</span> <a name="line-306"></a><span class='hs-comment'>-- lists such that flattening the resulting stream is equal to the</span> <a name="line-307"></a><span class='hs-comment'>-- argument. Moreover, each sublist in the resulting stream</span> <a name="line-308"></a><span class='hs-comment'>-- contains only equal elements. For example,</span> <a name="line-309"></a><span class='hs-comment'>--</span> <a name="line-310"></a><span class='hs-comment'>-- > group $ cycle "Mississippi" = "M" ::: "i" ::: "ss" ::: "i" ::: "ss" ::: "i" ::: "pp" ::: "i" ::: "M" ::: "i" ::: ...</span> <a name="line-311"></a><span class='hs-definition'>group</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <a name="line-312"></a><span class='hs-definition'>group</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>span</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>y</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'>ys</span> <a name="line-313"></a> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'><:></span> <span class='hs-varid'>group</span> <span class='hs-varid'>zs</span> <a name="line-314"></a> <a name="line-315"></a><a name="isPrefixOf"></a><span class='hs-comment'>-- | The 'isPrefix' function returns @True@ if the first argument is</span> <a name="line-316"></a><span class='hs-comment'>-- a prefix of the second.</span> <a name="line-317"></a><span class='hs-definition'>isPrefixOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span> <a name="line-318"></a><span class='hs-definition'>isPrefixOf</span> <span class='hs-conid'>[]</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span> <a name="line-319"></a><span class='hs-definition'>isPrefixOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-conop'>:</span><span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-320"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>y</span> <span class='hs-varop'>==</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isPrefixOf</span> <span class='hs-varid'>ys</span> <span class='hs-varid'>xs</span> <a name="line-321"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span> <a name="line-322"></a> <a name="line-323"></a><a name="!!"></a><span class='hs-comment'>-- | @xs !! n@ returns the element of the stream @xs@ at index</span> <a name="line-324"></a><span class='hs-comment'>-- @n@. Note that the head of the stream has index 0.</span> <a name="line-325"></a><span class='hs-comment'>--</span> <a name="line-326"></a><span class='hs-comment'>-- /Beware/: passing a negative integer as the first argument will cause</span> <a name="line-327"></a><span class='hs-comment'>-- an error.</span> <a name="line-328"></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'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <a name="line-329"></a><span class='hs-layout'>(</span><span class='hs-varop'>!!</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>n</span> <a name="line-330"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <a name="line-331"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>></span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>!!</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <a name="line-332"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Stream.!! negative argument"</span> <a name="line-333"></a> <a name="line-334"></a><a name="elemIndex"></a><span class='hs-comment'>-- | The 'elemIndex' function returns the index of the first element</span> <a name="line-335"></a><span class='hs-comment'>-- in the given stream which is equal (by '==') to the query element,</span> <a name="line-336"></a><span class='hs-comment'>--</span> <a name="line-337"></a><span class='hs-comment'>-- /Beware/: 'elemIndex' @x@ @xs@ will diverge if none of the elements</span> <a name="line-338"></a><span class='hs-comment'>-- of @xs@ equal @x@.</span> <a name="line-339"></a><span class='hs-definition'>elemIndex</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</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'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <a name="line-340"></a><span class='hs-definition'>elemIndex</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>findIndex</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>y</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> <a name="line-341"></a> <a name="line-342"></a><a name="elemIndices"></a><span class='hs-comment'>-- | The 'elemIndices' function extends 'elemIndex', by returning the</span> <a name="line-343"></a><span class='hs-comment'>-- indices of all elements equal to the query element, in ascending order.</span> <a name="line-344"></a><span class='hs-comment'>--</span> <a name="line-345"></a><span class='hs-comment'>-- /Beware/: 'elemIndices' @x@ @xs@ will diverge if any suffix of</span> <a name="line-346"></a><span class='hs-comment'>-- @xs@ does not contain @x@.</span> <a name="line-347"></a><span class='hs-definition'>elemIndices</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</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'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Int</span> <a name="line-348"></a><span class='hs-definition'>elemIndices</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>findIndices</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <a name="line-349"></a> <a name="line-350"></a> <a name="line-351"></a><a name="findIndex"></a><span class='hs-comment'>-- | The 'findIndex' function takes a predicate and a stream and returns</span> <a name="line-352"></a><span class='hs-comment'>-- the index of the first element in the stream that satisfies the predicate,</span> <a name="line-353"></a><span class='hs-comment'>--</span> <a name="line-354"></a><span class='hs-comment'>-- /Beware/: 'findIndex' @p@ @xs@ will diverge if none of the elements of</span> <a name="line-355"></a><span class='hs-comment'>-- @xs@ satisfy @p@.</span> <a name="line-356"></a><span class='hs-definition'>findIndex</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span> <a name="line-357"></a><span class='hs-definition'>findIndex</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>indexFrom</span> <span class='hs-num'>0</span> <a name="line-358"></a> <span class='hs-keyword'>where</span> <a name="line-359"></a> <span class='hs-varid'>indexFrom</span> <span class='hs-varid'>ix</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-360"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ix</span> <a name="line-361"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>indexFrom</span> <span class='hs-varop'>$!</span> <span class='hs-layout'>(</span><span class='hs-varid'>ix</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <a name="line-362"></a> <a name="line-363"></a><a name="findIndices"></a><span class='hs-comment'>-- | The 'findIndices' function extends 'findIndex', by returning the</span> <a name="line-364"></a><span class='hs-comment'>-- indices of all elements satisfying the predicate, in ascending</span> <a name="line-365"></a><span class='hs-comment'>-- order.</span> <a name="line-366"></a><span class='hs-comment'>--</span> <a name="line-367"></a><span class='hs-comment'>-- /Beware/: 'findIndices' @p@ @xs@ will diverge if all the elements</span> <a name="line-368"></a><span class='hs-comment'>-- of any suffix of @xs@ fails to satisfy @p@.</span> <a name="line-369"></a><span class='hs-definition'>findIndices</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-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Int</span> <a name="line-370"></a><span class='hs-definition'>findIndices</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>indicesFrom</span> <span class='hs-num'>0</span> <a name="line-371"></a> <span class='hs-keyword'>where</span> <a name="line-372"></a> <span class='hs-varid'>indicesFrom</span> <span class='hs-varid'>ix</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-373"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>ixs</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>indicesFrom</span> <span class='hs-varop'>$!</span> <span class='hs-layout'>(</span><span class='hs-varid'>ix</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <a name="line-374"></a> <span class='hs-keyword'>in</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>ix</span> <span class='hs-varid'>ixs</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>ixs</span> <a name="line-375"></a> <a name="line-376"></a><a name="zip"></a><span class='hs-comment'>-- | The 'zip' function takes two streams and returns a list of</span> <a name="line-377"></a><span class='hs-comment'>-- corresponding pairs.</span> <a name="line-378"></a><span class='hs-definition'>zip</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</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-379"></a><span class='hs-definition'>zip</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>y</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>zip</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <a name="line-380"></a> <a name="line-381"></a><a name="zipWith"></a><span class='hs-comment'>-- | The 'zipWith' function generalizes 'zip'. Rather than tupling</span> <a name="line-382"></a><span class='hs-comment'>-- the functions, the elements are combined using the function</span> <a name="line-383"></a><span class='hs-comment'>-- passed as the first argument to 'zipWith'.</span> <a name="line-384"></a><span class='hs-definition'>zipWith</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'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>c</span> <a name="line-385"></a><span class='hs-definition'>zipWith</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>y</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</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> <span class='hs-layout'>(</span><span class='hs-varid'>zipWith</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <a name="line-386"></a> <a name="line-387"></a><a name="unzip"></a><span class='hs-comment'>-- | The 'unzip' function is the inverse of the 'zip' function.</span> <a name="line-388"></a><span class='hs-definition'>unzip</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</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-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <a name="line-389"></a><span class='hs-definition'>unzip</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>xys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>fst</span> <span class='hs-layout'>(</span><span class='hs-varid'>unzip</span> <span class='hs-varid'>xys</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <a name="line-390"></a> <span class='hs-conid'>Cons</span> <span class='hs-varid'>y</span> <span class='hs-layout'>(</span><span class='hs-varid'>snd</span> <span class='hs-layout'>(</span><span class='hs-varid'>unzip</span> <span class='hs-varid'>xys</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-391"></a> <a name="line-392"></a><a name="words"></a><span class='hs-comment'>-- | The 'words' function breaks a stream of characters into a</span> <a name="line-393"></a><span class='hs-comment'>-- stream of words, which were delimited by white space.</span> <a name="line-394"></a><span class='hs-comment'>--</span> <a name="line-395"></a><span class='hs-comment'>-- /Beware/: if the stream of characters @xs@ does not contain white</span> <a name="line-396"></a><span class='hs-comment'>-- space, accessing the tail of @words xs@ will loop.</span> <a name="line-397"></a><span class='hs-definition'>words</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Char</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>String</span> <a name="line-398"></a><span class='hs-definition'>words</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span><span class='hs-layout'>,</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>break</span> <span class='hs-varid'>isSpace</span> <span class='hs-varid'>xs</span> <a name="line-399"></a> <span class='hs-keyword'>in</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>words</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <a name="line-400"></a> <a name="line-401"></a><a name="unwords"></a><span class='hs-comment'>-- | The 'unwords' function is an inverse operation to 'words'. It</span> <a name="line-402"></a><span class='hs-comment'>-- joins words with separating spaces.</span> <a name="line-403"></a><span class='hs-definition'>unwords</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Char</span> <a name="line-404"></a><span class='hs-definition'>unwords</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-chr'>' '</span> <span class='hs-layout'>(</span><span class='hs-varid'>unwords</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <a name="line-405"></a> <a name="line-406"></a><a name="lines"></a><span class='hs-comment'>-- | The 'lines' function breaks a stream of characters into a list</span> <a name="line-407"></a><span class='hs-comment'>-- of strings at newline characters. The resulting strings do not</span> <a name="line-408"></a><span class='hs-comment'>-- contain newlines.</span> <a name="line-409"></a><span class='hs-comment'>--</span> <a name="line-410"></a><span class='hs-comment'>-- /Beware/: if the stream of characters @xs@ does not contain</span> <a name="line-411"></a><span class='hs-comment'>-- newline characters, accessing the tail of @lines xs@ will loop.</span> <a name="line-412"></a><span class='hs-definition'>lines</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Char</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>String</span> <a name="line-413"></a><span class='hs-definition'>lines</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-varid'>l</span><span class='hs-layout'>,</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>break</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span> <span class='hs-chr'>'\n'</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span> <a name="line-414"></a> <span class='hs-keyword'>in</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-varid'>lines</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-415"></a> <a name="line-416"></a><a name="unlines"></a><span class='hs-comment'>-- | The 'unlines' function is an inverse operation to 'lines'. It</span> <a name="line-417"></a><span class='hs-comment'>-- joins lines, after appending a terminating newline to each.</span> <a name="line-418"></a><span class='hs-definition'>unlines</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stream</span> <span class='hs-conid'>Char</span> <a name="line-419"></a><span class='hs-definition'>unlines</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-conid'>Cons</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-chr'>'\n'</span> <span class='hs-layout'>(</span><span class='hs-varid'>unlines</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <a name="line-420"></a> <a name="line-421"></a><a name="toList"></a><span class='hs-comment'>-- | The 'toList' converts a stream into an infinite list.</span> <a name="line-422"></a><span class='hs-definition'>toList</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Stream</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <a name="line-423"></a><span class='hs-definition'>toList</span> <span class='hs-layout'>(</span><span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>toList</span> <span class='hs-varid'>xs</span> <a name="line-424"></a> <a name="line-425"></a><a name="fromList"></a><span class='hs-comment'>-- | The 'fromList' converts an infinite list to a</span> <a name="line-426"></a><span class='hs-comment'>-- stream.</span> <a name="line-427"></a><span class='hs-comment'>--</span> <a name="line-428"></a><span class='hs-comment'>-- /Beware/: Passing a finite list, will cause an error.</span> <a name="line-429"></a><span class='hs-definition'>fromList</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-conid'>Stream</span> <span class='hs-varid'>a</span> <a name="line-430"></a><span class='hs-definition'>fromList</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Cons</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <a name="line-431"></a><span class='hs-definition'>fromList</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Stream.fromList applied to finite list"</span> <a name="line-432"></a> </pre></body> </html>
