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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types, ScopedTypeVariables,
<a name="line-2"></a> MultiParamTypeClasses, DeriveDataTypeable,
<a name="line-3"></a> GeneralizedNewtypeDeriving, TemplateHaskell, CPP #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# OPTIONS_GHC -fno-warn-incomplete-patterns -fno-warn-name-shadowing #-}</span>
<a name="line-5"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-6"></a><span class='hs-comment'>-- |</span>
<a name="line-7"></a><span class='hs-comment'>-- Module : Data.Param.FSVec</span>
<a name="line-8"></a><span class='hs-comment'>-- Copyright : (c) 2008 Alfonso Acosta, Oleg Kiselyov, Wolfgang Jeltsch</span>
<a name="line-9"></a><span class='hs-comment'>-- and KTH's SAM group </span>
<a name="line-10"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-11"></a><span class='hs-comment'>-- </span>
<a name="line-12"></a><span class='hs-comment'>-- Maintainer : alfonso.acosta@gmail.com</span>
<a name="line-13"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-14"></a><span class='hs-comment'>-- Portability : non-portable</span>
<a name="line-15"></a><span class='hs-comment'>--</span>
<a name="line-16"></a><span class='hs-comment'>-- 'FSVec': Fixed sized vectors. Vectors with numerically parameterized size.</span>
<a name="line-17"></a><span class='hs-comment'>--</span>
<a name="line-18"></a><span class='hs-comment'>-- Tutorial: <<a href="http://www.ict.kth.se/forsyde/files/tutorial/tutorial.html#FSVec">http://www.ict.kth.se/forsyde/files/tutorial/tutorial.html#FSVec</a>></span>
<a name="line-19"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-20"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Param</span><span class='hs-varop'>.</span><span class='hs-conid'>FSVec</span>
<a name="line-21"></a> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span><span class='hs-layout'>,</span> <span class='hs-varid'>empty</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'>singleton</span><span class='hs-layout'>,</span> <span class='hs-varid'>vectorCPS</span><span class='hs-layout'>,</span> <span class='hs-varid'>vectorTH</span><span class='hs-layout'>,</span>
<a name="line-22"></a><span class='hs-comment'>-- #if __GLASGOW_HASKELL__ >= 609</span>
<a name="line-23"></a><span class='hs-comment'>-- v,</span>
<a name="line-24"></a><span class='hs-comment'>-- #endif</span>
<a name="line-25"></a> <span class='hs-varid'>unsafeVector</span><span class='hs-layout'>,</span> <span class='hs-varid'>reallyUnsafeVector</span><span class='hs-layout'>,</span> <span class='hs-varid'>readFSVec</span><span class='hs-layout'>,</span> <span class='hs-varid'>readFSVecCPS</span><span class='hs-layout'>,</span> <span class='hs-varid'>length</span><span class='hs-layout'>,</span>
<a name="line-26"></a> <span class='hs-varid'>genericLength</span><span class='hs-layout'>,</span> <span class='hs-varid'>lengthT</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromVector</span><span class='hs-layout'>,</span> <span class='hs-varid'>null</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'>replace</span><span class='hs-layout'>,</span> <span class='hs-varid'>head</span><span class='hs-layout'>,</span> <span class='hs-varid'>last</span><span class='hs-layout'>,</span>
<a name="line-27"></a> <span class='hs-varid'>init</span><span class='hs-layout'>,</span> <span class='hs-varid'>tail</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'>select</span><span class='hs-layout'>,</span> <span class='hs-varid'>group</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-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>map</span><span class='hs-layout'>,</span> <span class='hs-varid'>zipWith</span><span class='hs-layout'>,</span>
<a name="line-28"></a> <span class='hs-varid'>foldl</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldr</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> <span class='hs-varid'>shiftl</span><span class='hs-layout'>,</span> <span class='hs-varid'>shiftr</span><span class='hs-layout'>,</span> <span class='hs-varid'>rotl</span><span class='hs-layout'>,</span> <span class='hs-varid'>rotr</span><span class='hs-layout'>,</span> <span class='hs-varid'>concat</span><span class='hs-layout'>,</span>
<a name="line-29"></a> <span class='hs-varid'>reverse</span><span class='hs-layout'>,</span> <span class='hs-varid'>iterate</span><span class='hs-layout'>,</span> <span class='hs-varid'>generate</span><span class='hs-layout'>,</span> <span class='hs-varid'>copy</span>
<a name="line-30"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-31"></a>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Num</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-layout'>)</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-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</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-layout'>(</span><span class='hs-varop'><</span><span class='hs-layout'>)</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-layout'>(</span><span class='hs-varop'><=</span><span class='hs-layout'>)</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>
<a name="line-33"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Num</span><span class='hs-varop'>.</span><span class='hs-conid'>Aliases</span><span class='hs-varop'>.</span><span class='hs-conid'>TH</span> <span class='hs-layout'>(</span><span class='hs-varid'>dec2TypeLevel</span><span class='hs-layout'>)</span>
<a name="line-34"></a>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span> <span class='hs-layout'>(</span><span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span><span class='hs-layout'>,</span> <span class='hs-varid'>dataTypeOf</span><span class='hs-layout'>,</span> <span class='hs-varid'>toConstr</span><span class='hs-layout'>,</span> <span class='hs-varid'>gunfold</span><span class='hs-layout'>,</span> <span class='hs-varid'>gfoldl</span><span class='hs-layout'>,</span>
<a name="line-36"></a> <span class='hs-varid'>mkConstr</span><span class='hs-layout'>,</span> <span class='hs-varid'>mkDataType</span><span class='hs-layout'>,</span> <span class='hs-conid'>Fixity</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-37"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Prelude</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>P</span>
<a name="line-38"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span>
<a name="line-39"></a> <span class='hs-varid'>null</span><span class='hs-layout'>,</span> <span class='hs-varid'>length</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'>last</span><span class='hs-layout'>,</span> <span class='hs-varid'>init</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>
<a name="line-40"></a> <span class='hs-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>map</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldl</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldr</span><span class='hs-layout'>,</span>
<a name="line-41"></a> <span class='hs-varid'>zipWith</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-42"></a> <span class='hs-varid'>concat</span><span class='hs-layout'>,</span> <span class='hs-varid'>reverse</span><span class='hs-layout'>,</span> <span class='hs-varid'>iterate</span><span class='hs-layout'>)</span>
<a name="line-43"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>DF</span> <span class='hs-layout'>(</span><span class='hs-conid'>Foldable</span><span class='hs-layout'>,</span> <span class='hs-varid'>foldr</span><span class='hs-layout'>)</span>
<a name="line-44"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>DT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span><span class='hs-layout'>(</span><span class='hs-varid'>traverse</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-45"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Language</span><span class='hs-varop'>.</span><span class='hs-conid'>Haskell</span><span class='hs-varop'>.</span><span class='hs-conid'>TH</span>
<a name="line-46"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Language</span><span class='hs-varop'>.</span><span class='hs-conid'>Haskell</span><span class='hs-varop'>.</span><span class='hs-conid'>TH</span><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lift</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-47"></a><span class='hs-comment'>-- #if __GLASGOW_HASKELL__ >= 609</span>
<a name="line-48"></a><span class='hs-comment'>-- import Language.Haskell.TH.Quote</span>
<a name="line-49"></a><span class='hs-comment'>-- #endif</span>
<a name="line-50"></a>
<a name="line-51"></a>
<a name="line-52"></a><a name="FSVec"></a><span class='hs-comment'>-- | Fixed-Sized Vector data type, indexed with type-level naturals, the </span>
<a name="line-53"></a><a name="FSVec"></a><span class='hs-comment'>-- first index for all vectors is 0</span>
<a name="line-54"></a><a name="FSVec"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-layout'>{</span><span class='hs-varid'>unFSVec</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-layout'>}</span>
<a name="line-55"></a> <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'>Typeable</span><span class='hs-layout'>)</span>
<a name="line-56"></a>
<a name="line-57"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Data</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Data</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-58"></a> <span class='hs-varid'>dataTypeOf</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>tFSVec</span>
<a name="line-59"></a> <span class='hs-varid'>toConstr</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cFSVec</span>
<a name="line-60"></a> <span class='hs-varid'>gunfold</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-conid'>FSVec</span><span class='hs-layout'>)</span>
<a name="line-61"></a> <span class='hs-varid'>gfoldl</span> <span class='hs-varid'>k</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>a1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>z</span> <span class='hs-conid'>FSVec</span> <span class='hs-varop'>`k`</span> <span class='hs-varid'>a1</span><span class='hs-layout'>)</span>
<a name="line-62"></a><a name="cFSVec"></a><span class='hs-definition'>cFSVec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkConstr</span> <span class='hs-varid'>tFSVec</span> <span class='hs-str'>"FSVec"</span> <span class='hs-keyglyph'>[</span><span class='hs-str'>"unFSVec"</span><span class='hs-keyglyph'>]</span> <span class='hs-conid'>Prefix</span>
<a name="line-63"></a><a name="tFSVec"></a><span class='hs-definition'>tFSVec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkDataType</span> <span class='hs-str'>"Data.Param.FSVec"</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>cFSVec</span><span class='hs-keyglyph'>]</span>
<a name="line-64"></a>
<a name="line-65"></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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-66"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showV</span><span class='hs-varop'>.</span><span class='hs-varid'>unFSVec</span>
<a name="line-67"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>showV</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showString</span> <span class='hs-str'>"<>"</span>
<a name="line-68"></a> <span class='hs-varid'>showV</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-varid'>showChar</span> <span class='hs-chr'>'<'</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shows</span> <span class='hs-varid'>x</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showl</span> <span class='hs-varid'>xs</span>
<a name="line-69"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>showl</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showChar</span> <span class='hs-chr'>'>'</span>
<a name="line-70"></a> <span class='hs-varid'>showl</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-varid'>showChar</span> <span class='hs-chr'>','</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shows</span> <span class='hs-varid'>x</span> <span class='hs-varop'>.</span>
<a name="line-71"></a> <span class='hs-varid'>showl</span> <span class='hs-varid'>xs</span>
<a name="line-72"></a>
<a name="line-73"></a><span class='hs-comment'>-------------------------</span>
<a name="line-74"></a><span class='hs-comment'>-- Constructing functions</span>
<a name="line-75"></a><span class='hs-comment'>-------------------------</span>
<a name="line-76"></a>
<a name="line-77"></a><a name="empty"></a><span class='hs-definition'>empty</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FSVec</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>a</span>
<a name="line-78"></a><span class='hs-definition'>empty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-conid'>[]</span>
<a name="line-79"></a>
<a name="line-80"></a><a name="+>"></a><span class='hs-comment'>-- | Cons operator, note it's not a constructor</span>
<a name="line-81"></a><span class='hs-layout'>(</span><span class='hs-varop'>+></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-conid'>Succ</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s'</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-82"></a><a name="x"></a><span class='hs-definition'>x</span> <span class='hs-varop'>+></span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</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>
<a name="line-83"></a>
<a name="line-84"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>5</span> <span class='hs-varop'>+></span>
<a name="line-85"></a>
<a name="line-86"></a>
<a name="line-87"></a><a name="singleton"></a><span class='hs-comment'>-- | A FSVec with a single element</span>
<a name="line-88"></a><span class='hs-definition'>singleton</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>a</span>
<a name="line-89"></a><span class='hs-definition'>singleton</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>+></span> <span class='hs-varid'>empty</span>
<a name="line-90"></a>
<a name="line-91"></a>
<a name="line-92"></a><a name="vectorCPS"></a><span class='hs-comment'>-- | Build a vector from a list (CPS style)</span>
<a name="line-93"></a><span class='hs-definition'>vectorCPS</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-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span>
<a name="line-94"></a><span class='hs-definition'>vectorCPS</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsafeVectorCPS</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>length</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="vectorTH"></a><span class='hs-comment'>-- | Build a vector from a list (using Template Haskell)</span>
<a name="line-97"></a><span class='hs-definition'>vectorTH</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Lift</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'>ExpQ</span>
<a name="line-98"></a><span class='hs-definition'>vectorTH</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>vectorCPS</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>lift</span>
<a name="line-99"></a>
<a name="line-100"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 609</span>
<a name="line-101"></a><span class='hs-comment'>-- -- | Vector quasiquoter</span>
<a name="line-102"></a><span class='hs-comment'>-- v :: QuasiQuoter</span>
<a name="line-103"></a><span class='hs-comment'>-- v = undefined</span>
<a name="line-104"></a><span class='hs-comment'>-- -- v = QuasiQuoter (fst.parseFSVecExp) parseFSVecPat</span>
<a name="line-105"></a><span class='hs-comment'>-- </span>
<a name="line-106"></a><span class='hs-comment'>-- -- Build a vector using quasiquotation</span>
<a name="line-107"></a><span class='hs-comment'>-- -- Not possible in the general case! It is feasible, though, when only </span>
<a name="line-108"></a><span class='hs-comment'>-- -- allowing monomorphic vectors. For example, in the case of Ints:</span>
<a name="line-109"></a><span class='hs-comment'>-- -- parseFSVecExp :: String -> ExpQ</span>
<a name="line-110"></a><span class='hs-comment'>-- -- parseFSVecExp str = (readFSVec str) (lift :: Nat s => FSVec s Int -> ExpQ)</span>
<a name="line-111"></a><span class='hs-comment'>-- parseFSVecExp :: forall a . String -> (ExpQ, a)</span>
<a name="line-112"></a><span class='hs-comment'>-- parseFSVecExp str = ((readFSVec str) (lift :: (Nat s, Lift a) => FSVec s a -> ExpQ), undefined) </span>
<a name="line-113"></a><span class='hs-comment'>-- </span>
<a name="line-114"></a><span class='hs-comment'>-- -- Pattern match a vector using quasiquotation</span>
<a name="line-115"></a><span class='hs-comment'>-- parseFSVecPat :: String -> PatQ</span>
<a name="line-116"></a><span class='hs-comment'>-- parseFSVecPat = error "Data.Param.FSVec: quasiquoting paterns not supported"</span>
<a name="line-117"></a><span class='hs-comment'>-- </span>
<a name="line-118"></a><span class='hs-comment'>-- -- __GLASGOW_HASKELL__</span>
<a name="line-119"></a><span class='hs-cpp'>#endif </span>
<a name="line-120"></a>
<a name="line-121"></a><a name="unsafeVector"></a><span class='hs-comment'>-- | Build a vector from a list (unsafe version: The static/dynamic size of </span>
<a name="line-122"></a><span class='hs-comment'>-- the list is checked to match at runtime)</span>
<a name="line-123"></a><span class='hs-definition'>unsafeVector</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-124"></a><span class='hs-definition'>unsafeVector</span> <span class='hs-varid'>l</span> <span class='hs-varid'>xs</span>
<a name="line-125"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>toNum</span> <span class='hs-varid'>l</span> <span class='hs-varop'>/=</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>length</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span>
<a name="line-126"></a> <span class='hs-varid'>error</span> <span class='hs-layout'>(</span><span class='hs-varid'>show</span> <span class='hs-chr'>'</span><span class='hs-varid'>unsafeVector</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-str'>": dynamic/static length mismatch"</span><span class='hs-layout'>)</span>
<a name="line-127"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span>
<a name="line-128"></a>
<a name="line-129"></a><a name="reallyUnsafeVector"></a><span class='hs-comment'>-- | Build a vector from a list. </span>
<a name="line-130"></a><span class='hs-comment'>-- </span>
<a name="line-131"></a><span class='hs-comment'>-- Unlike unsafeVector, reallyunsafeVector doesn't have access to the </span>
<a name="line-132"></a><span class='hs-comment'>-- static size of the list and thus cannot not check it against its</span>
<a name="line-133"></a><span class='hs-comment'>-- dynamic size (which saves traversing the list at runtime to obtain </span>
<a name="line-134"></a><span class='hs-comment'>-- the dynamic length).</span>
<a name="line-135"></a><span class='hs-comment'>--</span>
<a name="line-136"></a><span class='hs-comment'>-- Therefore, reallyUnsafeVector (the name is that long on purspose)</span>
<a name="line-137"></a><span class='hs-comment'>-- can be used to gain some performance but may break the consistency</span>
<a name="line-138"></a><span class='hs-comment'>-- of the size parameter if not handled with care (i.e. the size</span>
<a name="line-139"></a><span class='hs-comment'>-- parameter can nolonger be checked statically and the fullfilment of</span>
<a name="line-140"></a><span class='hs-comment'>-- function constraints is left to the programmers judgement).</span>
<a name="line-141"></a><span class='hs-comment'>-- </span>
<a name="line-142"></a><span class='hs-comment'>-- Do not use reallyUnsafeVector unless you know what you're doing!</span>
<a name="line-143"></a><span class='hs-definition'>reallyUnsafeVector</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-144"></a><span class='hs-definition'>reallyUnsafeVector</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span>
<a name="line-145"></a>
<a name="line-146"></a><a name="readFSVec"></a><span class='hs-comment'>-- | Read a vector (Note the the size of </span>
<a name="line-147"></a><span class='hs-comment'>-- the vector string is checked to match the resulting type at runtime)</span>
<a name="line-148"></a><span class='hs-definition'>readFSVec</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Read</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-149"></a><span class='hs-definition'>readFSVec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>read</span>
<a name="line-150"></a>
<a name="line-151"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Read</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Read</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-152"></a> <span class='hs-varid'>readsPrec</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>str</span>
<a name="line-153"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>all</span> <span class='hs-varid'>fitsLength</span> <span class='hs-varid'>posibilities</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>map</span> <span class='hs-varid'>toReadS</span> <span class='hs-varid'>posibilities</span>
<a name="line-154"></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-layout'>(</span><span class='hs-varid'>fName</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-str'>": string/dynamic length mismatch"</span><span class='hs-layout'>)</span>
<a name="line-155"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>fName</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"Data.Param.FSVec.read"</span>
<a name="line-156"></a> <span class='hs-varid'>expectedL</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-157"></a> <span class='hs-varid'>posibilities</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>readFSVecList</span> <span class='hs-varid'>str</span>
<a name="line-158"></a> <span class='hs-varid'>fitsLength</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span> <span class='hs-varid'>l</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>l</span> <span class='hs-varop'>==</span> <span class='hs-varid'>expectedL</span>
<a name="line-159"></a> <span class='hs-varid'>toReadS</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</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-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span>
<a name="line-160"></a>
<a name="line-161"></a><a name="readFSVecCPS"></a><span class='hs-comment'>-- | Read a vector, CPS version.</span>
<a name="line-162"></a><span class='hs-definition'>readFSVecCPS</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Read</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span>
<a name="line-163"></a><span class='hs-definition'>readFSVecCPS</span> <span class='hs-varid'>str</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsafeVectorCPS</span> <span class='hs-varid'>l</span> <span class='hs-varid'>xs</span>
<a name="line-164"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>fName</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>show</span> <span class='hs-chr'>'</span><span class='hs-varid'>readFSVecCPS</span>
<a name="line-165"></a> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>l</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'>readFSVecList</span> <span class='hs-varid'>str</span><span class='hs-layout'>,</span>
<a name="line-166"></a> <span class='hs-layout'>(</span><span class='hs-str'>""</span><span class='hs-layout'>,</span><span class='hs-str'>""</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>rest</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>of</span>
<a name="line-167"></a> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span>
<a name="line-168"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>error</span> <span class='hs-layout'>(</span><span class='hs-varid'>fName</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-str'>": no parse"</span><span class='hs-layout'>)</span>
<a name="line-169"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>error</span> <span class='hs-layout'>(</span><span class='hs-varid'>fName</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-str'>": ambiguous parse"</span><span class='hs-layout'>)</span>
<a name="line-170"></a>
<a name="line-171"></a><span class='hs-comment'>----------------------</span>
<a name="line-172"></a><span class='hs-comment'>-- Observing functions</span>
<a name="line-173"></a><span class='hs-comment'>----------------------</span>
<a name="line-174"></a>
<a name="line-175"></a><a name="length"></a><span class='hs-comment'>-- | value-level length of a vector </span>
<a name="line-176"></a><span class='hs-definition'>length</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span>
<a name="line-177"></a><span class='hs-definition'>length</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-178"></a>
<a name="line-179"></a><a name="genericLength"></a><span class='hs-comment'>-- | generic value-level length of a vector </span>
<a name="line-180"></a><span class='hs-definition'>genericLength</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varid'>n</span> <span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>n</span>
<a name="line-181"></a><span class='hs-definition'>genericLength</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toNum</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-182"></a>
<a name="line-183"></a><a name="lengthT"></a><span class='hs-comment'>-- | type-level version of length</span>
<a name="line-184"></a><span class='hs-definition'>lengthT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span>
<a name="line-185"></a><span class='hs-definition'>lengthT</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-186"></a>
<a name="line-187"></a><a name="fromVector"></a><span class='hs-comment'>-- | Transform Vector to a list</span>
<a name="line-188"></a><span class='hs-definition'>fromVector</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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-189"></a><span class='hs-definition'>fromVector</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</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-190"></a>
<a name="line-191"></a><a name="null"></a><span class='hs-comment'>-- | Check if a Vector is empty</span>
<a name="line-192"></a><span class='hs-definition'>null</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FSVec</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-193"></a><span class='hs-definition'>null</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-194"></a><span class='hs-comment'>-- Note: This definition checks the length at _runtime_, we don't want it</span>
<a name="line-195"></a><span class='hs-comment'>-- null (FSVec []) = True</span>
<a name="line-196"></a><span class='hs-comment'>-- null _ = False</span>
<a name="line-197"></a>
<a name="line-198"></a><a name="!"></a><span class='hs-comment'>-- | Access an element of a vector</span>
<a name="line-199"></a><span class='hs-layout'>(</span><span class='hs-varop'>!</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-varid'>i</span> <span class='hs-conop'>:<:</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-200"></a><span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>!</span> <span class='hs-varid'>i</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'>toInt</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-201"></a>
<a name="line-202"></a><span class='hs-comment'>-------------------------</span>
<a name="line-203"></a><span class='hs-comment'>-- Transforming functions</span>
<a name="line-204"></a><span class='hs-comment'>-------------------------</span>
<a name="line-205"></a>
<a name="line-206"></a><a name="replace"></a><span class='hs-comment'>-- | Replace an element of a vector</span>
<a name="line-207"></a><span class='hs-definition'>replace</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-208"></a><span class='hs-comment'>-- alternative, more restrictive type </span>
<a name="line-209"></a><span class='hs-comment'>-- replace :: (Pos s, Nat i, n :<: s) => FSVec s a -> i -> a -> FSVec s a</span>
<a name="line-210"></a><span class='hs-definition'>replace</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>i</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-varop'>$</span> <span class='hs-varid'>replace'</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span>
<a name="line-211"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>replace'</span> <span class='hs-conid'>[]</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-212"></a> <span class='hs-varid'>replace'</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-213"></a> <span class='hs-varid'>replace'</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-varid'>n</span> <span class='hs-varid'>y</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'>replace'</span> <span class='hs-varid'>xs</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'>y</span><span class='hs-layout'>)</span>
<a name="line-214"></a>
<a name="line-215"></a><a name="head"></a><span class='hs-comment'>-- | Take the first element of a vector</span>
<a name="line-216"></a><span class='hs-definition'>head</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-217"></a><span class='hs-definition'>head</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>head</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unFSVec</span>
<a name="line-218"></a>
<a name="line-219"></a><a name="last"></a><span class='hs-comment'>-- | Take the last element of a vector</span>
<a name="line-220"></a><span class='hs-definition'>last</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-221"></a><span class='hs-definition'>last</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>last</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unFSVec</span>
<a name="line-222"></a>
<a name="line-223"></a><a name="tail"></a><span class='hs-comment'>-- | Return all but the first element of a vector</span>
<a name="line-224"></a><span class='hs-definition'>tail</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Succ</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-225"></a><span class='hs-definition'>tail</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>tail</span>
<a name="line-226"></a>
<a name="line-227"></a><a name="init"></a><span class='hs-comment'>-- | Return all but the last element of a vector</span>
<a name="line-228"></a><span class='hs-definition'>init</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Succ</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-229"></a><span class='hs-definition'>init</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>init</span>
<a name="line-230"></a>
<a name="line-231"></a><a name="take"></a><span class='hs-comment'>-- | Take the first i elements of a vector</span>
<a name="line-232"></a><span class='hs-definition'>take</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Min</span> <span class='hs-varid'>s</span> <span class='hs-varid'>i</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-233"></a><span class='hs-definition'>take</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-varop'>$</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>take</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-234"></a>
<a name="line-235"></a><a name="drop"></a><span class='hs-comment'>-- | Drop the first i elements of a vector</span>
<a name="line-236"></a><span class='hs-definition'>drop</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Min</span> <span class='hs-varid'>s</span> <span class='hs-varid'>i</span> <span class='hs-varid'>sm</span><span class='hs-layout'>,</span> <span class='hs-conid'>Sub</span> <span class='hs-varid'>s</span> <span class='hs-varid'>sm</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-237"></a><span class='hs-definition'>drop</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-varop'>$</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>drop</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-238"></a>
<a name="line-239"></a>
<a name="line-240"></a><a name="select"></a><span class='hs-comment'>-- | The function 'select' selects elements in the vector. The first argument</span>
<a name="line-241"></a><span class='hs-comment'>-- gives the initial element, starting from zero, the second argument gives the</span>
<a name="line-242"></a><span class='hs-comment'>-- stepsize between elements and the last argument gives the number of </span>
<a name="line-243"></a><span class='hs-comment'>-- elements.</span>
<a name="line-244"></a><span class='hs-definition'>select</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>f</span> <span class='hs-conop'>:<:</span> <span class='hs-varid'>i</span><span class='hs-layout'>,</span> <span class='hs-comment'>{- f + s * n <= i -}</span>
<a name="line-245"></a> <span class='hs-conid'>Mul</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-varid'>smn</span><span class='hs-layout'>,</span> <span class='hs-conid'>Add</span> <span class='hs-varid'>f</span> <span class='hs-varid'>smn</span> <span class='hs-varid'>fasmn</span><span class='hs-layout'>,</span> <span class='hs-varid'>fasmn</span> <span class='hs-conop'>:<=:</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-246"></a> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span>
<a name="line-247"></a><span class='hs-definition'>select</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-varid'>select'</span> <span class='hs-varid'>f'</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>n'</span><span class='hs-layout'>)</span>
<a name="line-248"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>f'</span><span class='hs-layout'>,</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-varid'>n'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-249"></a> <span class='hs-varid'>select'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>selectFirst0</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-varop'>.</span><span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>drop</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-250"></a> <span class='hs-comment'>-- list version of select assuming 0 is the index for the first element</span>
<a name="line-251"></a> <span class='hs-varid'>selectFirst0</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</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-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-252"></a> <span class='hs-varid'>selectFirst0</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-varid'>l</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span>
<a name="line-253"></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-varid'>selectFirst0</span> <span class='hs-varid'>s</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-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>drop</span> <span class='hs-varid'>s</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span>
<a name="line-254"></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-255"></a> <span class='hs-varid'>selectFirst0</span> <span class='hs-keyword'>_</span> <span class='hs-num'>0</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-256"></a>
<a name="line-257"></a><a name="group"></a><span class='hs-comment'>-- | break a vector into subvectors of size n.</span>
<a name="line-258"></a><span class='hs-definition'>group</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pos</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Div</span> <span class='hs-varid'>s</span> <span class='hs-varid'>n</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-259"></a> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-260"></a><span class='hs-definition'>group</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-varid'>group'</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-261"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>group'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</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-keyglyph'>[</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-262"></a> <span class='hs-varid'>group'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>splitAtM</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyword'>of</span>
<a name="line-263"></a> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
<a name="line-264"></a> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>ls</span><span class='hs-layout'>,</span> <span class='hs-varid'>rs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>ls</span> <span class='hs-conop'>:</span> <span class='hs-varid'>group'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rs</span>
<a name="line-265"></a>
<a name="line-266"></a><a name="<+"></a><span class='hs-comment'>-- | add an element at the end of a vector. (Inverse of '(+>)') </span>
<a name="line-267"></a><span class='hs-layout'>(</span><span class='hs-varop'><+</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s'</span><span class='hs-layout'>,</span> <span class='hs-conid'>Succ</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-268"></a><span class='hs-comment'>-- This should work, but it doesn't because</span>
<a name="line-269"></a><span class='hs-comment'>-- "Could not deduce (Data.TypeLevel.Num.Ops.Add' s D1 s')</span>
<a name="line-270"></a><span class='hs-comment'>-- from the context (Nat s, Pos s', Succ s s')"</span>
<a name="line-271"></a><span class='hs-comment'>-- xs <+ x = xs Data.Param.FSVec.++ (singleton x)</span>
<a name="line-272"></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'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-273"></a>
<a name="line-274"></a><a name="++"></a><span class='hs-comment'>-- | Concatenate two vectors</span>
<a name="line-275"></a><span class='hs-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s1</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s2</span><span class='hs-layout'>,</span> <span class='hs-conid'>Add</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>s2</span> <span class='hs-varid'>s3</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-276"></a> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s2</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s3</span> <span class='hs-varid'>a</span>
<a name="line-277"></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'>liftV2</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.++</span><span class='hs-layout'>)</span>
<a name="line-278"></a>
<a name="line-279"></a><span class='hs-keyword'>infixl</span> <span class='hs-num'>5</span> <span class='hs-varop'><+</span>
<a name="line-280"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>5</span> <span class='hs-varop'>++</span>
<a name="line-281"></a>
<a name="line-282"></a><a name="map"></a><span class='hs-comment'>-- | Apply a function on all elements of a vector</span>
<a name="line-283"></a><span class='hs-definition'>map</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span>
<a name="line-284"></a><span class='hs-definition'>map</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>map</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-285"></a>
<a name="line-286"></a><a name="zipWith"></a><span class='hs-comment'>-- | Applies function pairwise on two vectors</span>
<a name="line-287"></a><span class='hs-definition'>zipWith</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>c</span>
<a name="line-288"></a><span class='hs-definition'>zipWith</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV2</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>zipWith</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-289"></a>
<a name="line-290"></a><a name="foldl"></a><span class='hs-comment'>-- | Folds a function from the right to the left over a vector using an</span>
<a name="line-291"></a><span class='hs-comment'>-- initial value.</span>
<a name="line-292"></a><span class='hs-definition'>foldl</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-293"></a><span class='hs-definition'>foldl</span> <span class='hs-varid'>f</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>foldl</span> <span class='hs-varid'>f</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unFSVec</span>
<a name="line-294"></a>
<a name="line-295"></a><a name="foldr"></a><span class='hs-comment'>-- | Folds a function from the left to the right over a vector using an </span>
<a name="line-296"></a><span class='hs-comment'>-- initial value.</span>
<a name="line-297"></a><span class='hs-definition'>foldr</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</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-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-298"></a><span class='hs-definition'>foldr</span> <span class='hs-varid'>f</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>foldr</span> <span class='hs-varid'>f</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unFSVec</span>
<a name="line-299"></a>
<a name="line-300"></a><span class='hs-comment'>-- 'filter' takes a predicate function and a vector and creates a new vector </span>
<a name="line-301"></a><span class='hs-comment'>-- with the elements for which the predicate is true. </span>
<a name="line-302"></a><span class='hs-comment'>-- filterV :: (a -> Bool) -> Vector a -> Vector a</span>
<a name="line-303"></a><span class='hs-comment'>-- FIXME: </span>
<a name="line-304"></a><span class='hs-comment'>-- Imposible to define, the result does not have a predictable static size</span>
<a name="line-305"></a>
<a name="line-306"></a>
<a name="line-307"></a><a name="zip"></a><span class='hs-comment'>-- | zip two vectors into a vector of tuples.</span>
<a name="line-308"></a><span class='hs-definition'>zip</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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-309"></a><span class='hs-definition'>zip</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV2</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>zip</span>
<a name="line-310"></a>
<a name="line-311"></a><a name="unzip"></a><span class='hs-comment'>-- | unzip a vector of tuples into two vectors.</span>
<a name="line-312"></a><span class='hs-definition'>unzip</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-313"></a><span class='hs-definition'>unzip</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</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'>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-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>unzip</span> <span class='hs-varid'>xs</span> <span class='hs-keyword'>in</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-314"></a>
<a name="line-315"></a><a name="shiftl"></a><span class='hs-comment'>-- | shift a value from the left into a vector. </span>
<a name="line-316"></a><span class='hs-definition'>shiftl</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-317"></a><span class='hs-comment'>-- This doesn't work</span>
<a name="line-318"></a><span class='hs-comment'>-- shiftl xs x = x +> init xs</span>
<a name="line-319"></a><span class='hs-definition'>shiftl</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>init</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-320"></a>
<a name="line-321"></a><a name="shiftr"></a><span class='hs-comment'>-- | shift a value from the left into a vector. </span>
<a name="line-322"></a><span class='hs-definition'>shiftr</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Pos</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-323"></a><span class='hs-comment'>-- This doesn't work</span>
<a name="line-324"></a><span class='hs-comment'>-- shiftr xs x = tail xs <+ x</span>
<a name="line-325"></a><span class='hs-definition'>shiftr</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>tail</span> <span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.++</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-326"></a>
<a name="line-327"></a><a name="rotl"></a><span class='hs-comment'>-- | Rotate a vector to the left. Note that this fuctions does not change the </span>
<a name="line-328"></a><span class='hs-comment'>-- size of a vector.</span>
<a name="line-329"></a><span class='hs-definition'>rotl</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-330"></a><span class='hs-comment'>-- This doesn't work (it's highly inneficient anyway)</span>
<a name="line-331"></a><span class='hs-comment'>-- rotl [] = []</span>
<a name="line-332"></a><span class='hs-comment'>-- rotl vs = lastV vs +> initV vs </span>
<a name="line-333"></a><span class='hs-definition'>rotl</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-varid'>rotl'</span>
<a name="line-334"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>vl</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-335"></a> <span class='hs-varid'>rotl'</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-336"></a> <span class='hs-varid'>rotl'</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'>i</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>l</span><span class='hs-keyglyph'>]</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'>vl</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-337"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>l</span> <span class='hs-conop'>:</span> <span class='hs-varid'>i</span>
<a name="line-338"></a>
<a name="line-339"></a><a name="rotr"></a><span class='hs-comment'>-- | Rotate a vector to the left. Note that this fuctions does not change the </span>
<a name="line-340"></a><span class='hs-comment'>-- size of a vector.</span>
<a name="line-341"></a><span class='hs-definition'>rotr</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-342"></a><span class='hs-comment'>-- This doesn't work </span>
<a name="line-343"></a><span class='hs-comment'>-- rotr [] = []</span>
<a name="line-344"></a><span class='hs-comment'>-- rotr vs = tailV vs <: headV vs</span>
<a name="line-345"></a><span class='hs-definition'>rotr</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-varid'>rotr'</span>
<a name="line-346"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>rotr'</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-347"></a> <span class='hs-varid'>rotr'</span> <span class='hs-varid'>l</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>tail</span> <span class='hs-varid'>l</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span>
<a name="line-348"></a>
<a name="line-349"></a>
<a name="line-350"></a><a name="concat"></a><span class='hs-comment'>-- | flatten a vector of vectors to a single vector</span>
<a name="line-351"></a><span class='hs-definition'>concat</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Nat</span> <span class='hs-varid'>s1</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s2</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s3</span><span class='hs-layout'>,</span> <span class='hs-conid'>Mul</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>s2</span> <span class='hs-varid'>s3</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-352"></a> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s1</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s2</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s3</span> <span class='hs-varid'>a</span>
<a name="line-353"></a><span class='hs-comment'>-- this won't work: </span>
<a name="line-354"></a><span class='hs-comment'>-- concat = foldr (++) empty</span>
<a name="line-355"></a><span class='hs-definition'>concat</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>foldr</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.++</span><span class='hs-layout'>)</span><span class='hs-varop'>.</span><span class='hs-varid'>unFSVec</span><span class='hs-layout'>)</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-356"></a>
<a name="line-357"></a><a name="reverse"></a><span class='hs-comment'>-- | reverse a vector</span>
<a name="line-358"></a><span class='hs-definition'>reverse</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-359"></a><span class='hs-definition'>reverse</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftV</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>reverse</span>
<a name="line-360"></a>
<a name="line-361"></a>
<a name="line-362"></a><a name="iterate"></a><span class='hs-comment'>-- | generate a vector with a given number of elements starting from an </span>
<a name="line-363"></a><span class='hs-comment'>-- initial element using a supplied function for the generation of elements. </span>
<a name="line-364"></a><span class='hs-comment'>--</span>
<a name="line-365"></a><span class='hs-comment'>-- > FSVec> iterate d5 (+1) 1</span>
<a name="line-366"></a><span class='hs-comment'>--</span>
<a name="line-367"></a><span class='hs-comment'>-- > <1,2,3,4,5> :: Num a => FSVec D5 a</span>
<a name="line-368"></a><span class='hs-definition'>iterate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-369"></a><span class='hs-definition'>iterate</span> <span class='hs-varid'>s</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>s'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>in</span> <span class='hs-conid'>FSVec</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>take</span> <span class='hs-varid'>s'</span> <span class='hs-varop'>$</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>iterate</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-370"></a>
<a name="line-371"></a>
<a name="line-372"></a><a name="generate"></a><span class='hs-comment'>-- | 'generate' behaves in the same way as 'iterate', but starts with the </span>
<a name="line-373"></a><span class='hs-comment'>-- application of the supplied function to the supplied value. </span>
<a name="line-374"></a><span class='hs-comment'>--</span>
<a name="line-375"></a><span class='hs-comment'>-- > FSVec> generate d5 (+1) 1</span>
<a name="line-376"></a><span class='hs-comment'>-- </span>
<a name="line-377"></a><span class='hs-comment'>-- > <2,3,4,5,6> :: Num a => FSVec D5 a</span>
<a name="line-378"></a><span class='hs-definition'>generate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>s</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'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-379"></a><span class='hs-definition'>generate</span> <span class='hs-varid'>s</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>s'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>in</span> <span class='hs-conid'>FSVec</span> <span class='hs-layout'>(</span><span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>take</span> <span class='hs-varid'>s'</span> <span class='hs-varop'>$</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>tail</span> <span class='hs-varop'>$</span> <span class='hs-conid'>P</span><span class='hs-varop'>.</span><span class='hs-varid'>iterate</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-380"></a>
<a name="line-381"></a>
<a name="line-382"></a><a name="copy"></a><span class='hs-comment'>-- | generates a vector with a given number of copies of the same element. </span>
<a name="line-383"></a><span class='hs-comment'>--</span>
<a name="line-384"></a><span class='hs-comment'>-- > FSVec> copy d7 5 </span>
<a name="line-385"></a><span class='hs-comment'>-- </span>
<a name="line-386"></a><span class='hs-comment'>-- > <5,5,5,5,5,5,5> :: FSVec D7 Integer</span>
<a name="line-387"></a><span class='hs-definition'>copy</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-388"></a><span class='hs-definition'>copy</span> <span class='hs-varid'>s</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iterate</span> <span class='hs-varid'>s</span> <span class='hs-varid'>id</span> <span class='hs-varid'>x</span>
<a name="line-389"></a>
<a name="line-390"></a><span class='hs-comment'>------------</span>
<a name="line-391"></a><span class='hs-comment'>-- Instances</span>
<a name="line-392"></a><span class='hs-comment'>------------</span>
<a name="line-393"></a>
<a name="line-394"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DF</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-395"></a> <span class='hs-varid'>foldr</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span>
<a name="line-396"></a>
<a name="line-397"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-398"></a> <span class='hs-varid'>fmap</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span>
<a name="line-399"></a>
<a name="line-400"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>DT</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-401"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-conid'>FSVec</span><span class='hs-layout'>)</span><span class='hs-varop'>.</span><span class='hs-layout'>(</span><span class='hs-conid'>DT</span><span class='hs-varop'>.</span><span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span><span class='hs-varop'>.</span><span class='hs-varid'>unFSVec</span>
<a name="line-402"></a>
<a name="line-403"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lift</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Lift</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-404"></a> <span class='hs-varid'>lift</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>unsafeFSVecCoerce</span> <span class='hs-varop'>$</span><span class='hs-layout'>(</span><span class='hs-varid'>undefSigE</span> <span class='hs-varid'>lengthType</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-405"></a> <span class='hs-keyword'>where</span> <span class='hs-comment'>-- Get the vector length in a type-level decimal</span>
<a name="line-406"></a> <span class='hs-varid'>lengthType</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TypeQ</span>
<a name="line-407"></a> <span class='hs-varid'>lengthType</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dec2TypeLevel</span> <span class='hs-varop'>$</span> <span class='hs-varid'>toInt</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-408"></a>
<a name="line-409"></a><span class='hs-comment'>---------------------</span>
<a name="line-410"></a><span class='hs-comment'>-- Internal functions</span>
<a name="line-411"></a><span class='hs-comment'>---------------------</span>
<a name="line-412"></a>
<a name="line-413"></a><a name="liftV"></a><span class='hs-comment'>-- the FSVec equivalent of liftM</span>
<a name="line-414"></a><span class='hs-comment'>-- note it is unsafe and shouldn't be exported</span>
<a name="line-415"></a><span class='hs-definition'>liftV</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-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>b</span>
<a name="line-416"></a><span class='hs-definition'>liftV</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>unFSVec</span>
<a name="line-417"></a>
<a name="line-418"></a><a name="liftV2"></a><span class='hs-comment'>-- the FSVec equivalent of liftM</span>
<a name="line-419"></a><span class='hs-comment'>-- note it is unsafe and shouldn't be exported</span>
<a name="line-420"></a><span class='hs-definition'>liftV2</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-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s2</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s3</span> <span class='hs-varid'>c</span>
<a name="line-421"></a><span class='hs-definition'>liftV2</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FSVec</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>unFSVec</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>unFSVec</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-422"></a>
<a name="line-423"></a><a name="splitAtM"></a><span class='hs-comment'>-- version of splitAt which checks if the list contains enough elements</span>
<a name="line-424"></a><span class='hs-definition'>splitAtM</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</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'>Maybe</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-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-425"></a><span class='hs-definition'>splitAtM</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>splitAtM'</span> <span class='hs-varid'>n</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>xs</span>
<a name="line-426"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>splitAtM'</span> <span class='hs-num'>0</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-427"></a> <span class='hs-varid'>splitAtM'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</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-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'>do</span>
<a name="line-428"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ls</span><span class='hs-layout'>,</span><span class='hs-varid'>rs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>splitAtM'</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-varid'>ys</span>
<a name="line-429"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-conop'>:</span><span class='hs-varid'>ls</span><span class='hs-layout'>,</span><span class='hs-varid'>rs</span><span class='hs-layout'>)</span>
<a name="line-430"></a> <span class='hs-varid'>splitAtM'</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-431"></a>
<a name="line-432"></a><a name="unsafeFSVecCoerce"></a><span class='hs-comment'>-- Arbitraly coerce the length parameter of a vector</span>
<a name="line-433"></a><span class='hs-definition'>unsafeFSVecCoerce</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s'</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>a</span>
<a name="line-434"></a><span class='hs-definition'>unsafeFSVecCoerce</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>FSVec</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span>
<a name="line-435"></a>
<a name="line-436"></a><a name="undefSigE"></a><span class='hs-comment'>-- Obtain a TH expression of undefined coerced to certain type</span>
<a name="line-437"></a><span class='hs-definition'>undefSigE</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TypeQ</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ExpQ</span>
<a name="line-438"></a><span class='hs-definition'>undefSigE</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sigE</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>t</span>
<a name="line-439"></a>
<a name="line-440"></a><a name="unsafeVectorCPS"></a><span class='hs-comment'>-- unsafely (a trusted length is provided) create a vector using CPS style</span>
<a name="line-441"></a><span class='hs-definition'>unsafeVectorCPS</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span> <span class='hs-varid'>w</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Int</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>
<a name="line-442"></a> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Nat</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FSVec</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span>
<a name="line-443"></a><span class='hs-definition'>unsafeVectorCPS</span> <span class='hs-varid'>l</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>reifyIntegral</span> <span class='hs-varid'>l</span>
<a name="line-444"></a> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>lt</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-conid'>FSVec</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'>FSVec</span> <span class='hs-varid'>lt</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-445"></a>
<a name="line-446"></a><a name="readFSVecList"></a><span class='hs-comment'>-- Modified version of Prelude.readList which accepts < > instead</span>
<a name="line-447"></a><span class='hs-comment'>-- of [ ] to read lists and also provides the list length</span>
<a name="line-448"></a><span class='hs-definition'>readFSVecList</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Read</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>String</span> <span class='hs-keyglyph'>-></span> <span class='hs-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'>Int</span><span class='hs-layout'>,</span> <span class='hs-conid'>String</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-449"></a><span class='hs-definition'>readFSVecList</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>readParen'</span> <span class='hs-conid'>False</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>pr</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-str'>"<"</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>r</span><span class='hs-layout'>,</span>
<a name="line-450"></a> <span class='hs-varid'>pr</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>readl</span> <span class='hs-varid'>s</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-451"></a> <span class='hs-keyword'>where</span>
<a name="line-452"></a> <span class='hs-varid'>readl</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span><span class='hs-num'>0</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-str'>">"</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>s</span><span class='hs-keyglyph'>]</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span>
<a name="line-453"></a> <span class='hs-keyglyph'>[</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-num'>1</span><span class='hs-varop'>+</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>reads</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span>
<a name="line-454"></a> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>readl'</span> <span class='hs-varid'>t</span><span class='hs-keyglyph'>]</span>
<a name="line-455"></a> <span class='hs-varid'>readl'</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span><span class='hs-num'>0</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-str'>">"</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>s</span><span class='hs-keyglyph'>]</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span>
<a name="line-456"></a> <span class='hs-keyglyph'>[</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-num'>1</span><span class='hs-varop'>+</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-str'>","</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lex</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span>
<a name="line-457"></a> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>reads</span> <span class='hs-varid'>t</span><span class='hs-layout'>,</span>
<a name="line-458"></a> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>readl'</span> <span class='hs-varid'>u</span><span class='hs-keyglyph'>]</span>
<a name="line-459"></a> <span class='hs-varid'>readParen'</span> <span class='hs-varid'>b</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>mandatory</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>optional</span>
<a name="line-460"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>optional</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-varid'>r</span> <span class='hs-conid'>P</span><span class='hs-varop'>.++</span> <span class='hs-varid'>mandatory</span> <span class='hs-varid'>r</span>
<a name="line-461"></a> <span class='hs-varid'>mandatory</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-layout'>(</span><span class='hs-str'>"("</span><span class='hs-layout'>,</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>r</span><span class='hs-layout'>,</span>
<a name="line-462"></a> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>optional</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span>
<a name="line-463"></a> <span class='hs-layout'>(</span><span class='hs-str'>")"</span><span class='hs-layout'>,</span><span class='hs-varid'>u</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>lexFSVec</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>]</span>
<a name="line-464"></a>
<a name="line-465"></a><a name="lexFSVec"></a><span class='hs-comment'>-- Custom lexer for FSVecs, we cannot use lex directly because it considers</span>
<a name="line-466"></a><span class='hs-comment'>-- sequences of < and > as unique lexemes, and that breaks nested FSVecs, e.g.</span>
<a name="line-467"></a><span class='hs-comment'>-- <<1,2><3,4>></span>
<a name="line-468"></a><span class='hs-definition'>lexFSVec</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ReadS</span> <span class='hs-conid'>String</span>
<a name="line-469"></a><span class='hs-definition'>lexFSVec</span> <span class='hs-layout'>(</span><span class='hs-chr'>'>'</span><span class='hs-conop'>:</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-str'>">"</span><span class='hs-layout'>,</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-470"></a><span class='hs-definition'>lexFSVec</span> <span class='hs-layout'>(</span><span class='hs-chr'>'<'</span><span class='hs-conop'>:</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-str'>"<"</span><span class='hs-layout'>,</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-471"></a><span class='hs-definition'>lexFSVec</span> <span class='hs-varid'>str</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lex</span> <span class='hs-varid'>str</span>
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