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215 lines
40 KiB
215 lines
40 KiB
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<title>~/Projects/amulet/profunctor-impredicative.ml.html</title>
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<pre id='vimCodeElement'>
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<span class="Keyword">external</span> <span class="Keyword">val</span> print <span class="Operator">:</span> <span class="Type">'a</span> <span class="Operator">-></span> <span class="Special">unit</span> <span class="Operator">=</span> <span class="String">"print"</span>
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<span class="Keyword">let</span> id x <span class="Operator">=</span> x
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<span class="Keyword">let</span> f <span class="Operator">&</span> g <span class="Operator">=</span> <span class="Keyword">fun</span> x <span class="Operator">-></span> f <span class="Keyword">(</span>g x<span class="Keyword">)</span>
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<span class="Keyword">let</span> const x <span class="Keyword">_</span> <span class="Operator">=</span> x
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<span class="Keyword">let</span> x <span class="Operator">|</span><span class="Operator">></span> f <span class="Operator">=</span> f x
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<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
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<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
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<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
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<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>
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<span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Keyword">begin</span>
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<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">-></span> <span class="Type">'a</span><span class="Keyword">)</span> <span class="Operator">-></span> <span class="Keyword">(</span><span class="Type">'c</span> <span class="Operator">-></span> <span class="Type">'d</span><span class="Keyword">)</span>
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<span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'c</span> <span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'b</span> <span class="Type">'d</span>
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<span class="Keyword">end</span>
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<span class="Keyword">let</span> lmap g <span class="Operator">=</span> dimap g id
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<span class="Keyword">let</span> rmap x <span class="Operator">=</span> dimap id x
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<span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">></span> strong <span class="Type">'p</span> <span class="Keyword">begin</span>
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<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">-></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>
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<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">-></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>
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<span class="Keyword">end</span>
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<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>
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<span class="Keyword">let</span> <span class="Special">either</span> f g <span class="Operator">=</span> <span class="Keyword">function</span>
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<span class="Operator">|</span> <span class="Constant">Left</span> x <span class="Operator">-></span> f x
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<span class="Operator">|</span> <span class="Constant">Right</span> y <span class="Operator">-></span> g y
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<span class="Keyword">class</span> profunctor <span class="Type">'p</span> <span class="Operator">=</span><span class="Operator">></span> choice <span class="Type">'p</span> <span class="Keyword">begin</span>
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<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>
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<span class="Operator">-></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>
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<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>
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<span class="Operator">-></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>
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<span class="Keyword">end</span>
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<span class="Keyword">class</span> monoid <span class="Type">'m</span> <span class="Keyword">begin</span>
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<span class="Keyword">val</span> <span class="Keyword">(</span><span class="Operator"><></span><span class="Keyword">)</span> <span class="Operator">:</span> <span class="Type">'m</span> <span class="Operator">-></span> <span class="Type">'m</span> <span class="Operator">-></span> <span class="Type">'m</span>
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<span class="Keyword">val</span> zero <span class="Operator">:</span> <span class="Type">'m</span>
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<span class="Keyword">end</span>
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<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">-></span> <span class="Type">'r</span>
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<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
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<span class="Keyword">instance</span> profunctor <span class="Keyword">(</span><span class="Operator">-></span><span class="Keyword">)</span>
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<span class="Keyword">let</span> dimap f g h <span class="Operator">=</span> g <span class="Operator">&</span> h <span class="Operator">&</span> f
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<span class="Keyword">instance</span> strong <span class="Keyword">(</span><span class="Operator">-></span><span class="Keyword">)</span>
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<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>
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<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>
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<span class="Keyword">instance</span> choice <span class="Keyword">(</span><span class="Operator">-></span><span class="Keyword">)</span>
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<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">&</span> f<span class="Keyword">)</span> <span class="Constant">Right</span>
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<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">&</span> f<span class="Keyword">)</span>
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<span class="Keyword">instance</span> profunctor <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
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<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">&</span> f<span class="Keyword">)</span>
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<span class="Keyword">instance</span> monoid <span class="Type">'r</span> <span class="Operator">=</span><span class="Operator">></span> choice <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
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<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>
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<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>
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<span class="Keyword">instance</span> strong <span class="Keyword">(</span>forget <span class="Type">'r</span><span class="Keyword">)</span>
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<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">&</span> fst<span class="Keyword">)</span>
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<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">&</span> snd<span class="Keyword">)</span>
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<span class="Keyword">let</span> lens get set <span class="Operator">=</span>
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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">&</span> first
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<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>
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<span class="Keyword">let</span> over f <span class="Operator">=</span> f
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<span class="Keyword">let</span> set l b <span class="Operator">=</span> over l <span class="Keyword">(</span>const b<span class="Keyword">)</span>
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<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>
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<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
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<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
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<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">-></span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
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<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">-></span> <span class="Constant">Pair</span> <span class="Keyword">(</span>x<span class="Operator">,</span> y<span class="Keyword">))</span> x
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<span class="Keyword">type</span> proxy <span class="Type">'a</span> <span class="Operator">=</span> <span class="Constant">Proxy</span>
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<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"><-</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">></span> <span class="Type">'p</span> <span class="Type">'a</span> <span class="Type">'b</span> <span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'s</span> <span class="Type">'t</span>
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<span class="Keyword">type</span> lens' <span class="Type">'s</span> <span class="Type">'a</span> <span class="Operator"><-</span> lens <span class="Type">'s</span> <span class="Type">'s</span> <span class="Type">'a</span> <span class="Type">'a</span>
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<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">></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">-></span> <span class="Type">'record</span> <span class="Type">'type</span> <span class="Keyword">begin</span>
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<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">></span> proxy <span class="Type">'key</span> <span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'type</span> <span class="Type">'type</span> <span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'new</span> <span class="Type">'new</span>
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<span class="Keyword">end</span>
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<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">></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>
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<span class="Keyword">let</span> rlens <span class="Keyword">_</span> <span class="Operator">=</span>
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<span class="Keyword">let</span> view r <span class="Operator">=</span>
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<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
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x
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<span class="Keyword">let</span> set x r <span class="Operator">=</span>
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<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
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<span class="Include">Amc</span>.extend_row <span class="Operator">@</span><span class="Type">'key</span> x r'
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lens view set
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<span class="Keyword">end</span>
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<span class="Keyword">let</span> r <span class="Operator">:</span> <span class="Keyword">forall</span> <span class="Type">'key</span> <span class="Operator">-></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">></span> <span class="Type">'p</span> <span class="Type">'type</span> <span class="Type">'type</span> <span class="Operator">-></span> <span class="Type">'p</span> <span class="Type">'new</span> <span class="Type">'new</span> <span class="Operator">=</span>
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<span class="Keyword">fun</span> x <span class="Operator">-></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
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<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>
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<span class="Keyword">let</span> lens_list <span class="Constant">()</span> <span class="Operator">=</span> <span class="Keyword">(fun</span> x <span class="Operator">-></span> r <span class="Operator">@</span><span class="String">"foo"</span> x<span class="Keyword">)</span> <span class="Operator">::</span> <span class="Keyword">(fun</span> x <span class="Operator">-></span> r <span class="Operator">@</span><span class="String">"bar"</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>
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<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"><-</span> xs <span class="Keyword">]</span>
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<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>
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<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>
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</pre>
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</body>
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