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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Control-Category-Cartesian-Closed.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">categories-0.59: categories from category-extras</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>non-portable (class-associated types)</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Maintainer</th><td>Edward Kmett <ekmett@gmail.com></td></tr><tr><th>Safe Haskell</th><td>Safe-Infered</td></tr></table><p class="caption">Control.Category.Cartesian.Closed</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Cartesian Closed Category
</a></li><li><a href="#g:2">Co-(Cartesian Closed Category)
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc empty"> </div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">class</span> (<a href="Control-Category-Cartesian.html#t:Cartesian">Cartesian</a> <=, <a href="Control-Category-Braided.html#t:Symmetric">Symmetric</a> <= (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <=), <a href="Control-Category-Monoidal.html#t:Monoidal">Monoidal</a> <= (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <=)) => <a href="#t:CCC">CCC</a> (<=) <span class="keyword">where</span><ul class="subs"><li><span class="keyword">type</span> <a href="#t:Exp">Exp</a> (<=) :: * -> * -> *</li><li><a href="#v:apply">apply</a> :: <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= (<a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= a b) a <= b</li><li><a href="#v:curry">curry</a> :: (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <= a b <= c) -> a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b c</li><li><a href="#v:uncurry">uncurry</a> :: (a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b c) -> <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= a b <= c</li></ul></li><li class="src short"><a href="#v:unitCCC">unitCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a> <= => a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <= b a)</li><li class="src short"><a href="#v:counitCCC">counitCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a> <= => <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= b (<a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b a) <= a</li><li class="src short"><span class="keyword">class</span> (<a href="Control-Category-Cartesian.html#t:CoCartesian">CoCartesian</a> <=, <a href="Control-Category-Braided.html#t:Symmetric">Symmetric</a> <= (<a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=), <a href="Control-Category-Monoidal.html#t:Comonoidal">Comonoidal</a> <= (<a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=)) => <a href="#t:CoCCC">CoCCC</a> (<=) <span class="keyword">where</span><ul class="subs"><li><span class="keyword">type</span> <a href="#t:Coexp">Coexp</a> (<=) :: * -> * -> *</li><li><a href="#v:coapply">coapply</a> :: b <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= a b) a</li><li><a href="#v:cocurry">cocurry</a> :: (c <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= a b) -> <a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b c <= a</li><li><a href="#v:uncocurry">uncocurry</a> :: (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b c <= a) -> c <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= a b</li></ul></li><li class="src short"><a href="#v:unitCoCCC">unitCoCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CoCCC">CoCCC</a> <= => a <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= b (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b a)</li><li class="src short"><a href="#v:counitCoCCC">counitCoCCC</a> :: (<a href="Control-Category-Cartesian-Closed.html#t:CoCCC">CoCCC</a> <=, subtract ~ <a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <=, + ~ <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=) => subtract b (b + a) <= a</li></ul></div><div id="interface"><h1 id="g:1">Cartesian Closed Category
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Control-Category-Cartesian.html#t:Cartesian">Cartesian</a> <=, <a href="Control-Category-Braided.html#t:Symmetric">Symmetric</a> <= (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <=), <a href="Control-Category-Monoidal.html#t:Monoidal">Monoidal</a> <= (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <=)) => <a name="t:CCC" class="def">CCC</a> (<=) <span class="keyword">where</span><a href="src/Control-Category-Cartesian-Closed.html#CCC" class="link">Source</a></p><div class="doc"><p>A <code><a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a></code> has full-fledged monoidal finite products and exponentials
</p></div><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a name="t:Exp" class="def">Exp</a> (<=) :: * -> * -> *<a href="src/Control-Category-Cartesian-Closed.html#Exp" class="link">Source</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:apply" class="def">apply</a> :: <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= (<a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= a b) a <= b<a href="src/Control-Category-Cartesian-Closed.html#apply" class="link">Source</a></p><p class="src"><a name="v:curry" class="def">curry</a> :: (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <= a b <= c) -> a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b c<a href="src/Control-Category-Cartesian-Closed.html#curry" class="link">Source</a></p><p class="src"><a name="v:uncurry" class="def">uncurry</a> :: (a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b c) -> <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= a b <= c<a href="src/Control-Category-Cartesian-Closed.html#uncurry" class="link">Source</a></p></div><div class="subs instances"><p id="control.i:CCC" class="caption collapser" onclick="toggleSection('i:CCC')">Instances</p><div id="section.i:CCC" class="show"><table><tr><td class="src"><a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a> (->)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:unitCCC" class="def">unitCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a> <= => a <= <a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b (<a href="Control-Category-Cartesian.html#t:Product">Product</a> <= b a)<a href="src/Control-Category-Cartesian-Closed.html#unitCCC" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:counitCCC" class="def">counitCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CCC">CCC</a> <= => <a href="Control-Category-Cartesian.html#t:Product">Product</a> <= b (<a href="Control-Category-Cartesian-Closed.html#t:Exp">Exp</a> <= b a) <= a<a href="src/Control-Category-Cartesian-Closed.html#counitCCC" class="link">Source</a></p></div><h1 id="g:2">Co-(Cartesian Closed Category)
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Control-Category-Cartesian.html#t:CoCartesian">CoCartesian</a> <=, <a href="Control-Category-Braided.html#t:Symmetric">Symmetric</a> <= (<a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=), <a href="Control-Category-Monoidal.html#t:Comonoidal">Comonoidal</a> <= (<a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=)) => <a name="t:CoCCC" class="def">CoCCC</a> (<=) <span class="keyword">where</span><a href="src/Control-Category-Cartesian-Closed.html#CoCCC" class="link">Source</a></p><div class="doc"><p>A Co-CCC has full-fledged comonoidal finite coproducts and coexponentials
</p></div><div class="subs associated-types"><p class="caption">Associated Types</p><p class="src"><span class="keyword">type</span> <a name="t:Coexp" class="def">Coexp</a> (<=) :: * -> * -> *<a href="src/Control-Category-Cartesian-Closed.html#Coexp" class="link">Source</a></p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:coapply" class="def">coapply</a> :: b <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= a b) a<a href="src/Control-Category-Cartesian-Closed.html#coapply" class="link">Source</a></p><p class="src"><a name="v:cocurry" class="def">cocurry</a> :: (c <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= a b) -> <a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b c <= a<a href="src/Control-Category-Cartesian-Closed.html#cocurry" class="link">Source</a></p><p class="src"><a name="v:uncocurry" class="def">uncocurry</a> :: (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b c <= a) -> c <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= a b<a href="src/Control-Category-Cartesian-Closed.html#uncocurry" class="link">Source</a></p></div></div><div class="top"><p class="src"><a name="v:unitCoCCC" class="def">unitCoCCC</a> :: <a href="Control-Category-Cartesian-Closed.html#t:CoCCC">CoCCC</a> <= => a <= <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <= b (<a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <= b a)<a href="src/Control-Category-Cartesian-Closed.html#unitCoCCC" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:counitCoCCC" class="def">counitCoCCC</a> :: (<a href="Control-Category-Cartesian-Closed.html#t:CoCCC">CoCCC</a> <=, subtract ~ <a href="Control-Category-Cartesian-Closed.html#t:Coexp">Coexp</a> <=, + ~ <a href="Control-Category-Cartesian.html#t:Sum">Sum</a> <=) => subtract b (b + a) <= a<a href="src/Control-Category-Cartesian-Closed.html#counitCoCCC" class="link">Source</a></p></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.10.0</p></div></body></html>
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