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Create branch ${ searchTerm }
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blag/static/profunctors.ml.html

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Initial commit
7 years ago
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  5. <title>~/Projects/amulet/profunctors.ml.html</title>
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  59. .Operator { color: #C678DD; }
  60. .Type { color: #E5C07B; }
  61. .Include { color: #61AFEF; }
  62. .Special { color: #61AFEF; }
  63. .String { color: #98C379; }
  64. .Float { color: #D19A66; }
  65. .Constant { color: #56B6C2; }
  66. .Keyword { color: #E06C75; }
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  98. <pre id='vimCodeElement'>
  99. <span class="Keyword">external</span> <span class="Keyword">val</span> print <span class="Operator">:</span> <span class="Type">'a</span> <span class="Keyword">-&gt;</span> <span class="Special">unit</span> <span class="Operator">=</span> <span class="String">&quot;print&quot;</span>
  100. 

  101. <span class="Keyword">let</span> id x <span class="Operator">=</span> x
  102. <span class="Keyword">let</span> f <span class="Operator">&lt;&lt;&lt;</span> g <span class="Operator">=</span> <span class="Keyword">fun</span> x <span class="Keyword">-&gt;</span> f <span class="Keyword">(</span>g x<span class="Keyword">)</span>
  103. <span class="Keyword">let</span> const x <span class="Keyword">_</span> <span class="Operator">=</span> x
  104. <span class="Keyword">let</span> x <span class="Operator">|</span><span class="Operator">&gt;</span> f <span class="Operator">=</span> f x
  105. 

  106. <span class="Keyword">let</span> fst <span class="Keyword">(</span>x<span class="Operator">,</span> <span class="Keyword">_</span><span class="Keyword">)</span> <span class="Operator">=</span> x
  107. <span class="Keyword">let</span> snd <span class="Keyword">(</span><span class="Keyword">_</span><span class="Operator">,</span> x<span class="Keyword">)</span> <span class="Operator">=</span> x
  108. <span class="Keyword">let</span> uncurry f <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">)</span> <span class="Operator">=</span> f x y
  109. 

  110. <span class="Keyword">let</span> fork f g x <span class="Operator">=</span> <span class="Keyword">(</span>f x<span class="Operator">,</span> g x<span class="Keyword">)</span>
  111. 

  112. <span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Keyword">begin</span>
  113.   <span class="Keyword">val</span> dimap <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Type">'c</span> <span class="Type">'d</span><span class="Operator">.</span> <span class="Keyword">(</span><span class="Type">'b</span> <span class="Keyword">-&gt;</span> <span class="Type">'a</span><span class="Keyword">)</span> <span class="Keyword">-&gt;</span> <span class="Keyword">(</span><span class="Type">'c</span> <span class="Keyword">-&gt;</span> <span class="Type">'d</span><span class="Keyword">)</span>
  114.               <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'c</span> <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Type">'b</span> <span class="Type">'d</span>
  115. <span class="Keyword">end</span>
  116. 

  117. <span class="Keyword">let</span> lmap g <span class="Operator">=</span> dimap g id
  118. <span class="Keyword">let</span> rmap x <span class="Operator">=</span> dimap id x
  119. 

  120. <span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> strong <span class="Type">'p</span> <span class="Keyword">begin</span>
  121.   <span class="Keyword">val</span> first <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Type">'c</span><span class="Operator">.</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Keyword">(</span><span class="Type">'a</span> <span class="Operator">*</span> <span class="Type">'c</span><span class="Keyword">)</span> <span class="Keyword">(</span><span class="Type">'b</span> <span class="Operator">*</span> <span class="Type">'c</span><span class="Keyword">)</span>
  122.   <span class="Keyword">val</span> second <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Type">'c</span><span class="Operator">.</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Keyword">(</span><span class="Type">'c</span> <span class="Operator">*</span> <span class="Type">'a</span><span class="Keyword">)</span> <span class="Keyword">(</span><span class="Type">'c</span> <span class="Operator">*</span> <span class="Type">'b</span><span class="Keyword">)</span>
  123. <span class="Keyword">end</span>
  124. 

  125. <span class="Keyword">type</span> <span class="Special">either</span> <span class="Type">'l</span> <span class="Type">'r</span> <span class="Operator">=</span> <span class="Constant">Left</span> <span class="Keyword">of</span> <span class="Type">'l</span> <span class="Operator">|</span> <span class="Constant">Right</span> <span class="Keyword">of</span> <span class="Type">'r</span>
  126. 

  127. <span class="Keyword">let</span> <span class="Special">either</span> f g <span class="Operator">=</span> <span class="Keyword">function</span>
  128.   <span class="Operator">|</span> <span class="Constant">Left</span> x <span class="Keyword">-&gt;</span> f x
  129.   <span class="Operator">|</span> <span class="Constant">Right</span> y <span class="Keyword">-&gt;</span> g y
  130. 

  131. <span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> choice <span class="Type">'p</span> <span class="Keyword">begin</span>
  132.   <span class="Keyword">val</span> left <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Type">'c</span><span class="Operator">.</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span>
  133.               <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Keyword">(</span><span class="Special">either</span> <span class="Type">'a</span> <span class="Type">'c</span><span class="Keyword">)</span> <span class="Keyword">(</span><span class="Special">either</span> <span class="Type">'b</span> <span class="Type">'c</span><span class="Keyword">)</span>
  134.   <span class="Keyword">val</span> right <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Type">'c</span><span class="Operator">.</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span>
  135.               <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Keyword">(</span><span class="Special">either</span> <span class="Type">'c</span> <span class="Type">'a</span><span class="Keyword">)</span> <span class="Keyword">(</span><span class="Special">either</span> <span class="Type">'c</span> <span class="Type">'b</span><span class="Keyword">)</span>
  136. <span class="Keyword">end</span>
  137. 

  138. <span class="Keyword">class</span> monoid <span class="Type">'m</span> <span class="Keyword">begin</span>
  139.   <span class="Keyword">val</span> <span class="Keyword">(</span><span class="Operator">&lt;&gt;</span><span class="Keyword">)</span> <span class="Operator">:</span> <span class="Type">'m</span> <span class="Keyword">-&gt;</span> <span class="Type">'m</span> <span class="Keyword">-&gt;</span> <span class="Type">'m</span>
  140.   <span class="Keyword">val</span> zero <span class="Operator">:</span> <span class="Type">'m</span>
  141. <span class="Keyword">end</span>
  142. 

  143. <span class="Keyword">type</span> forget <span class="Type">'r</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">of</span> <span class="Type">'a</span> <span class="Keyword">-&gt;</span> <span class="Type">'r</span>
  144. <span class="Keyword">let</span> remember <span class="Keyword">(</span><span class="Constant">Forget</span> r<span class="Keyword">)</span> <span class="Operator">=</span> r
  145. 

  146. <span class="Keyword">instance</span> profunctor <span class="Keyword">(</span><span class="Keyword">-&gt;</span><span class="Keyword">)</span>
  147.   <span class="Keyword">let</span> dimap f g h <span class="Operator">=</span> g <span class="Operator">&lt;&lt;&lt;</span> h <span class="Operator">&lt;&lt;&lt;</span> f
  148. 

  149. <span class="Keyword">instance</span> strong <span class="Keyword">(</span><span class="Keyword">-&gt;</span><span class="Keyword">)</span>
  150.   <span class="Keyword">let</span> first f <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Keyword">(</span>f x<span class="Operator">,</span> y<span class="Keyword">)</span>
  151.   <span class="Keyword">let</span> second f <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Keyword">(</span>x<span class="Operator">,</span> f y<span class="Keyword">)</span>
  152. 

  153. <span class="Keyword">instance</span> choice <span class="Keyword">(</span><span class="Keyword">-&gt;</span><span class="Keyword">)</span>
  154.   <span class="Keyword">let</span> left f <span class="Operator">=</span> <span class="Special">either</span> <span class="Keyword">(</span><span class="Constant">Left</span> <span class="Operator">&lt;&lt;&lt;</span> f<span class="Keyword">)</span> <span class="Constant">Right</span>
  155.   <span class="Keyword">let</span> right f <span class="Operator">=</span> <span class="Special">either</span> <span class="Constant">Left</span> <span class="Keyword">(</span><span class="Constant">Right</span> <span class="Operator">&lt;&lt;&lt;</span> f<span class="Keyword">)</span>
  156. 

  157. <span class="Keyword">instance</span> profunctor <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
  158.   <span class="Keyword">let</span> dimap f <span class="Keyword">_</span> <span class="Keyword">(</span><span class="Constant">Forget</span> g<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">(</span>g <span class="Operator">&lt;&lt;&lt;</span> f<span class="Keyword">)</span>
  159. 

  160. <span class="Keyword">instance</span> monoid <span class="Type">'r</span> <span class="Operator">=</span><span class="Operator">&gt;</span> choice <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
  161.   <span class="Keyword">let</span> left <span class="Keyword">(</span><span class="Constant">Forget</span> z<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">(</span><span class="Special">either</span> z <span class="Keyword">(</span>const zero<span class="Keyword">))</span>
  162.   <span class="Keyword">let</span> right <span class="Keyword">(</span><span class="Constant">Forget</span> z<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">(</span><span class="Special">either</span> <span class="Keyword">(</span>const zero<span class="Keyword">)</span> z<span class="Keyword">)</span>
  163. 

  164. <span class="Keyword">instance</span> strong <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
  165.   <span class="Keyword">let</span> first <span class="Keyword">(</span><span class="Constant">Forget</span> z<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">(</span>z <span class="Operator">&lt;&lt;&lt;</span> fst<span class="Keyword">)</span>
  166.   <span class="Keyword">let</span> second <span class="Keyword">(</span><span class="Constant">Forget</span> z<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Constant">Forget</span> <span class="Keyword">(</span>z <span class="Operator">&lt;&lt;&lt;</span> snd<span class="Keyword">)</span>
  167. 

  168. <span class="Keyword">let</span> lens get set <span class="Operator">=</span>
  169.   dimap <span class="Keyword">(</span>fork get id<span class="Keyword">)</span> <span class="Keyword">(</span>uncurry set<span class="Keyword">)</span> <span class="Operator">&lt;&lt;&lt;</span> first
  170. 

  171. <span class="Keyword">let</span> view l <span class="Operator">=</span> remember <span class="Keyword">(</span>l <span class="Keyword">(</span><span class="Constant">Forget</span> id<span class="Keyword">))</span>
  172. <span class="Keyword">let</span> over f <span class="Operator">=</span> f
  173. <span class="Keyword">let</span> set l b <span class="Operator">=</span> over l <span class="Keyword">(</span>const b<span class="Keyword">)</span>
  174. 

  175. <span class="Keyword">let</span> x <span class="Operator">^.</span> l <span class="Operator">=</span> view l x
  176. <span class="Keyword">let</span> l <span class="Operator">^</span><span class="Operator">~</span> f <span class="Operator">=</span> over l f
  177. 

  178. <span class="Keyword">type</span> pair <span class="Type">'a</span> <span class="Type">'b</span> <span class="Operator">=</span> <span class="Constant">Pair</span> <span class="Keyword">of</span> <span class="Type">'a</span> <span class="Operator">*</span> <span class="Type">'b</span>
  179. <span class="Keyword">let</span> fst' <span class="Keyword">(</span><span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> <span class="Keyword">_</span><span class="Keyword">))</span> <span class="Operator">=</span> x
  180. <span class="Keyword">let</span> snd' <span class="Keyword">(</span><span class="Constant">Pair</span> <span class="Keyword">(</span><span class="Keyword">_</span><span class="Operator">,</span> x<span class="Keyword">))</span> <span class="Operator">=</span> x
  181. 

  182. <span class="Keyword">let</span> first' x <span class="Operator">=</span> lens fst' <span class="Keyword">(fun</span> x <span class="Keyword">(</span><span class="Constant">Pair</span> <span class="Keyword">(</span><span class="Keyword">_</span><span class="Operator">,</span> y<span class="Keyword">))</span> <span class="Keyword">-&gt;</span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
  183. <span class="Keyword">let</span> second' x <span class="Operator">=</span> lens snd' <span class="Keyword">(fun</span> y <span class="Keyword">(</span><span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> <span class="Keyword">_</span><span class="Keyword">))</span> <span class="Keyword">-&gt;</span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
  184. 

  185. <span class="Keyword">type</span> proxy <span class="Type">'a</span> <span class="Operator">=</span> <span class="Constant">Proxy</span>
  186. 

  187. <span class="Keyword">type</span> optic <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'s</span> <span class="Operator">&lt;-</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'a</span> <span class="Keyword">-&gt;</span> <span class="Type">'p</span> <span class="Type">'s</span> <span class="Type">'s</span>
  188. 

  189. <span class="Keyword">class</span>
  190.      <span class="Include">Amc</span>.row_cons <span class="Type">'r</span> <span class="Type">'k</span> <span class="Type">'t</span> <span class="Type">'n</span>
  191.   <span class="Operator">=</span><span class="Operator">&gt;</span> has_lens <span class="Type">'r</span> <span class="Type">'k</span> <span class="Type">'t</span> <span class="Type">'n</span>
  192.   <span class="Operator">|</span> <span class="Type">'k</span> <span class="Type">'n</span> <span class="Keyword">-&gt;</span> <span class="Type">'r</span> <span class="Type">'t</span>
  193. <span class="Keyword">begin</span>
  194.   <span class="Keyword">val</span> rlens <span class="Operator">:</span> strong <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> proxy <span class="Type">'k</span> <span class="Keyword">-&gt;</span> optic <span class="Type">'p</span> <span class="Type">'t</span> <span class="Type">'n</span>
  195. <span class="Keyword">end</span>
  196. 

  197. <span class="Keyword">instance</span>
  198.     <span class="Include">Amc</span>.known_string <span class="Type">'key</span>
  199.   <span class="Operator">*</span> <span class="Include">Amc</span>.row_cons <span class="Type">'record</span> <span class="Type">'key</span> <span class="Type">'type</span> <span class="Type">'new</span>
  200.   <span class="Operator">=</span><span class="Operator">&gt;</span> has_lens <span class="Type">'record</span> <span class="Type">'key</span> <span class="Type">'type</span> <span class="Type">'new</span>
  201. <span class="Keyword">begin</span>
  202.   <span class="Keyword">let</span> rlens <span class="Keyword">_</span> <span class="Operator">=</span>
  203.     <span class="Keyword">let</span> view r <span class="Operator">=</span>
  204.       <span class="Keyword">let</span> <span class="Keyword">(</span>x<span class="Operator">,</span> <span class="Keyword">_</span><span class="Keyword">)</span> <span class="Operator">=</span> <span class="Include">Amc</span>.restrict_row <span class="Operator">@</span><span class="Type">'key</span> r
  205.       x
  206.     <span class="Keyword">let</span> set x r <span class="Operator">=</span>
  207.       <span class="Keyword">let</span> <span class="Keyword">(</span><span class="Keyword">_</span><span class="Operator">,</span> r'<span class="Keyword">)</span> <span class="Operator">=</span> <span class="Include">Amc</span>.restrict_row <span class="Operator">@</span><span class="Type">'key</span> r
  208.       <span class="Include">Amc</span>.extend_row <span class="Operator">@</span><span class="Type">'key</span> x r'
  209.     lens view set
  210. <span class="Keyword">end</span>
  211. 

  212. <span class="Keyword">let</span> r
  213.   <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'key</span> <span class="Keyword">-&gt;</span> <span class="Keyword">forall</span> <span class="Type">'record</span> <span class="Type">'type</span> <span class="Type">'new</span> <span class="Type">'p</span><span class="Operator">.</span>
  214.      <span class="Include">Amc</span>.known_string <span class="Type">'key</span>
  215.    <span class="Operator">*</span> has_lens <span class="Type">'record</span> <span class="Type">'key</span> <span class="Type">'type</span> <span class="Type">'new</span>
  216.    <span class="Operator">*</span> strong <span class="Type">'p</span>
  217.   <span class="Operator">=</span><span class="Operator">&gt;</span> optic <span class="Type">'p</span> <span class="Type">'type</span> <span class="Type">'new</span> <span class="Operator">=</span>
  218.   <span class="Keyword">fun</span> x <span class="Keyword">-&gt;</span> rlens <span class="Operator">@</span><span class="Type">'record</span> <span class="Keyword">(</span><span class="Constant">Proxy</span> <span class="Operator">:</span> proxy <span class="Type">'key</span><span class="Keyword">)</span> x
  219. 

  220. <span class="Keyword">let</span> succ <span class="Operator">=</span> <span class="Keyword">(</span><span class="Operator">+</span> <span class="Float">1</span><span class="Keyword">)</span>
  221. </pre>
  222. </body>
  223. </html>
  224. <!-- vim: set foldmethod=manual : -->