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blag/static/profunctor-impredicative.ml...

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7 years ago
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  63. .Include { color: #61AFEF; }
  64. .Special { color: #61AFEF; }
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  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="Operator">-&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">&amp;</span> g <span class="Operator">=</span> <span class="Keyword">fun</span> x <span class="Operator">-&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="Operator">-&gt;</span> <span class="Type">'a</span><span class="Keyword">)</span> <span class="Operator">-&gt;</span> <span class="Keyword">(</span><span class="Type">'c</span> <span class="Operator">-&gt;</span> <span class="Type">'d</span><span class="Keyword">)</span>
  114.               <span class="Operator">-&gt;</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'c</span> <span class="Operator">-&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="Operator">-&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="Operator">-&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="Operator">-&gt;</span> f x
  129.   <span class="Operator">|</span> <span class="Constant">Right</span> y <span class="Operator">-&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="Operator">-&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="Operator">-&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="Operator">-&gt;</span> <span class="Type">'m</span> <span class="Operator">-&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="Operator">-&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="Operator">-&gt;</span><span class="Keyword">)</span>
  147.   <span class="Keyword">let</span> dimap f g h <span class="Operator">=</span> g <span class="Operator">&amp;</span> h <span class="Operator">&amp;</span> f
  148. 

  149. <span class="Keyword">instance</span> strong <span class="Keyword">(</span><span class="Operator">-&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="Operator">-&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">&amp;</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">&amp;</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">&amp;</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">&amp;</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">&amp;</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">&amp;</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">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>
  176. <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
  177. <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
  178. 

  179. <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="Operator">-&gt;</span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
  180. <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="Operator">-&gt;</span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
  181. 

  182. <span class="Keyword">type</span> proxy <span class="Type">'a</span> <span class="Operator">=</span> <span class="Constant">Proxy</span>
  183. 

  184. <span class="Keyword">type</span> lens <span class="Type">'s</span> <span class="Type">'t</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Operator">&lt;-</span> <span class="Keyword">forall</span> <span class="Type">'p</span><span class="Operator">.</span> strong <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Operator">-&gt;</span> <span class="Type">'p</span> <span class="Type">'s</span> <span class="Type">'t</span>
  185. <span class="Keyword">type</span> lens' <span class="Type">'s</span> <span class="Type">'a</span> <span class="Operator">&lt;-</span> lens <span class="Type">'s</span> <span class="Type">'s</span> <span class="Type">'a</span> <span class="Type">'a</span>
  186. 

  187. <span class="Keyword">class</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> <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> <span class="Operator">|</span> <span class="Type">'key</span> <span class="Type">'new</span> <span class="Operator">-&gt;</span> <span class="Type">'record</span> <span class="Type">'type</span> <span class="Keyword">begin</span>
  188.   <span class="Keyword">val</span> rlens <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'p</span><span class="Operator">.</span> strong <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> proxy <span class="Type">'key</span> <span class="Operator">-&gt;</span> <span class="Type">'p</span> <span class="Type">'type</span> <span class="Type">'type</span> <span class="Operator">-&gt;</span> <span class="Type">'p</span> <span class="Type">'new</span> <span class="Type">'new</span>
  189. <span class="Keyword">end</span>
  190. 

  191. <span class="Keyword">instance</span> <span class="Include">Amc</span>.known_string <span class="Type">'key</span> <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> <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> <span class="Keyword">begin</span>
  192.   <span class="Keyword">let</span> rlens <span class="Keyword">_</span> <span class="Operator">=</span>
  193.     <span class="Keyword">let</span> view r <span class="Operator">=</span>
  194.       <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
  195.       x
  196.     <span class="Keyword">let</span> set x r <span class="Operator">=</span>
  197.       <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
  198.       <span class="Include">Amc</span>.extend_row <span class="Operator">@</span><span class="Type">'key</span> x r'
  199.     lens view set
  200. <span class="Keyword">end</span>
  201. 

  202. <span class="Keyword">let</span> r <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'key</span> <span class="Operator">-&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> <span class="Include">Amc</span>.known_string <span class="Type">'key</span> <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> <span class="Operator">*</span> strong <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">&gt;</span> <span class="Type">'p</span> <span class="Type">'type</span> <span class="Type">'type</span> <span class="Operator">-&gt;</span> <span class="Type">'p</span> <span class="Type">'new</span> <span class="Type">'new</span> <span class="Operator">=</span>
  203.   <span class="Keyword">fun</span> x <span class="Operator">-&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
  204. 

  205. <span class="Keyword">let</span> x <span class="Operator">::</span> xs <span class="Operator">=</span> <span class="Constant">Cons</span> <span class="Keyword">(</span>x<span class="Operator">,</span> xs<span class="Keyword">)</span>
  206. <span class="Keyword">let</span> lens_list <span class="Constant">()</span> <span class="Operator">=</span> <span class="Keyword">(fun</span> x <span class="Operator">-&gt;</span> r <span class="Operator">@</span><span class="String">&quot;foo&quot;</span> x<span class="Keyword">)</span> <span class="Operator">::</span> <span class="Keyword">(fun</span> x <span class="Operator">-&gt;</span> r <span class="Operator">@</span><span class="String">&quot;bar&quot;</span> x<span class="Keyword">)</span> <span class="Operator">::</span> <span class="Constant">Nil</span> <span class="Operator">@</span><span class="Keyword">(</span>lens' <span class="Keyword">_</span> <span class="Keyword">_</span><span class="Keyword">)</span>
  207. 

  208. <span class="Keyword">let</span> map f xs <span class="Operator">=</span> <span class="Keyword">[</span> f x <span class="Operator">|</span> <span class="Keyword">with</span> x <span class="Operator">&lt;-</span> xs <span class="Keyword">]</span>
  209. 

  210. <span class="Keyword">let</span> x <span class="Operator">=</span> <span class="Keyword">{</span> foo <span class="Operator">=</span> <span class="Float">1</span><span class="Operator">,</span> bar <span class="Operator">=</span> <span class="Float">2</span> <span class="Keyword">}</span>
  211. <span class="Keyword">let</span> xs <span class="Operator">=</span> map <span class="Keyword">(</span>`view` x<span class="Keyword">)</span> <span class="Keyword">(</span>lens_list <span class="Constant">()</span><span class="Keyword">)</span>
  212. </pre>
  213. </body>
  214. </html>
  215. <!-- vim: set foldmethod=manual : -->