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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-Functor-Day.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">contravariant-0.6.1.1: Contravariant functors and Day convolution</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>portable</td></tr><tr><th>Stability</th><td>provisional</td></tr><tr><th>Maintainer</th><td>Edward Kmett <ekmett@gmail.com></td></tr><tr><th>Safe Haskell</th><td>None</td></tr></table><p class="caption">Data.Functor.Day</p></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Eitan Chatav first introduced me to this construction
</p><p>The Day convolution of two covariant functors is a covariant functor.
</p><p>Day convolution is usually defined in terms of contravariant functors,
however, it just needs a monoidal category, and Hask^op is also monoidal.
</p><p>Day convolution can be used to nicely describe monoidal functors as monoid
objects w.r.t this product.
</p><p><a href="http://ncatlab.org/nlab/show/Day+convolution">http://ncatlab.org/nlab/show/Day+convolution</a>
</p></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">data</span> <a href="#t:Day">Day</a> f g a = <span class="keyword">forall</span> b c . <a href="#v:Day">Day</a> (f b) (g c) (b -> c -> a)</li><li class="src short"><a href="#v:day">day</a> :: f (a -> b) -> g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f g b</li><li class="src short"><a href="#v:dap">dap</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> f f a -> f a</li><li class="src short"><a href="#v:assoc">assoc</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> f (<a href="Data-Functor-Day.html#t:Day">Day</a> g h) a -> <a href="Data-Functor-Day.html#t:Day">Day</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g) h a</li><li class="src short"><a href="#v:disassoc">disassoc</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g) h a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f (<a href="Data-Functor-Day.html#t:Day">Day</a> g h) a</li><li class="src short"><a href="#v:swapped">swapped</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> f g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> g f a</li><li class="src short"><a href="#v:intro1">intro1</a> :: f a -> <a href="Data-Functor-Day.html#t:Day">Day</a> <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> f a</li><li class="src short"><a href="#v:intro2">intro2</a> :: f a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> a</li><li class="src short"><a href="#v:elim1">elim1</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> f a -> f a</li><li class="src short"><a href="#v:elim2">elim2</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> f <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> a -> f a</li><li class="src short"><a href="#v:trans1">trans1</a> :: (<span class="keyword">forall</span> x. f x -> g x) -> <a href="Data-Functor-Day.html#t:Day">Day</a> f h a -> <a href="Data-Functor-Day.html#t:Day">Day</a> g h a</li><li class="src short"><a href="#v:trans2">trans2</a> :: (<span class="keyword">forall</span> x. g x -> h x) -> <a href="Data-Functor-Day.html#t:Day">Day</a> f g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f h a</li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Day" class="def">Day</a> f g a <a href="src/Data-Functor-Day.html#Day" class="link">Source</a></p><div class="doc"><p>The Day convolution of two covariant functors.
</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><span class="keyword">forall</span> b c . <a name="v:Day" class="def">Day</a> (f b) (g c) (b -> c -> a)</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Day" class="caption collapser" onclick="toggleSection('i:Day')">Instances</p><div id="section.i:Day" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> f, <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> g) => <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Typeable-Internal.html#t:Typeable1">Typeable1</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:day" class="def">day</a> :: f (a -> b) -> g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f g b<a href="src/Data-Functor-Day.html#day" class="link">Source</a></p><div class="doc"><p>Construct the Day convolution
</p></div></div><div class="top"><p class="src"><a name="v:dap" class="def">dap</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#t:Applicative">Applicative</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> f f a -> f a<a href="src/Data-Functor-Day.html#dap" class="link">Source</a></p><div class="doc"><p>Collapse via a monoidal functor.
</p><pre>
<code><a href="Data-Functor-Day.html#v:dap">dap</a></code> (<code><a href="Data-Functor-Day.html#v:day">day</a></code> f g) = f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Applicative.html#v:-60--42--62-"><*></a></code> g
</pre></div></div><div class="top"><p class="src"><a name="v:assoc" class="def">assoc</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> f (<a href="Data-Functor-Day.html#t:Day">Day</a> g h) a -> <a href="Data-Functor-Day.html#t:Day">Day</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g) h a<a href="src/Data-Functor-Day.html#assoc" class="link">Source</a></p><div class="doc"><p>Day convolution provides a monoidal product. The associativity
of this monoid is witnessed by <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> and <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code>.
</p><pre>
<code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> . <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> . <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> = <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f
</pre></div></div><div class="top"><p class="src"><a name="v:disassoc" class="def">disassoc</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> (<a href="Data-Functor-Day.html#t:Day">Day</a> f g) h a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f (<a href="Data-Functor-Day.html#t:Day">Day</a> g h) a<a href="src/Data-Functor-Day.html#disassoc" class="link">Source</a></p><div class="doc"><p>Day convolution provides a monoidal product. The associativity
of this monoid is witnessed by <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> and <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code>.
</p><pre>
<code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> . <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> . <code><a href="Data-Functor-Day.html#v:assoc">assoc</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> = <code><a href="Data-Functor-Day.html#v:disassoc">disassoc</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f
</pre></div></div><div class="top"><p class="src"><a name="v:swapped" class="def">swapped</a> :: <a href="Data-Functor-Day.html#t:Day">Day</a> f g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> g f a<a href="src/Data-Functor-Day.html#swapped" class="link">Source</a></p><div class="doc"><p>The monoid for <code><a href="Data-Functor-Day.html#t:Day">Day</a></code> convolution on the cartesian monoidal structure is symmetric.
</p><pre>
<code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:swapped">swapped</a></code> = <code><a href="Data-Functor-Day.html#v:swapped">swapped</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f
</pre></div></div><div class="top"><p class="src"><a name="v:intro1" class="def">intro1</a> :: f a -> <a href="Data-Functor-Day.html#t:Day">Day</a> <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> f a<a href="src/Data-Functor-Day.html#intro1" class="link">Source</a></p><div class="doc"><p><code><a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a></code> is the unit of <code><a href="Data-Functor-Day.html#t:Day">Day</a></code> convolution
</p><pre>
<code><a href="Data-Functor-Day.html#v:intro1">intro1</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:elim1">elim1</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:elim1">elim1</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:intro1">intro1</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:intro2" class="def">intro2</a> :: f a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> a<a href="src/Data-Functor-Day.html#intro2" class="link">Source</a></p><div class="doc"><p><code><a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a></code> is the unit of <code><a href="Data-Functor-Day.html#t:Day">Day</a></code> convolution
</p><pre>
<code><a href="Data-Functor-Day.html#v:intro2">intro2</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:elim2">elim2</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:elim2">elim2</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:intro2">intro2</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:elim1" class="def">elim1</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> f a -> f a<a href="src/Data-Functor-Day.html#elim1" class="link">Source</a></p><div class="doc"><p><code><a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a></code> is the unit of <code><a href="Data-Functor-Day.html#t:Day">Day</a></code> convolution
</p><pre>
<code><a href="Data-Functor-Day.html#v:intro1">intro1</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:elim1">elim1</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:elim1">elim1</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:intro1">intro1</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:elim2" class="def">elim2</a> :: <a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#t:Functor">Functor</a> f => <a href="Data-Functor-Day.html#t:Day">Day</a> f <a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a> a -> f a<a href="src/Data-Functor-Day.html#elim2" class="link">Source</a></p><div class="doc"><p><code><a href="/usr/share/doc/libghc-transformers-doc/html/Data-Functor-Identity.html#t:Identity">Identity</a></code> is the unit of <code><a href="Data-Functor-Day.html#t:Day">Day</a></code> convolution
</p><pre>
<code><a href="Data-Functor-Day.html#v:intro2">intro2</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:elim2">elim2</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
<code><a href="Data-Functor-Day.html#v:elim2">elim2</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:intro2">intro2</a></code> = <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:id">id</a></code>
</pre></div></div><div class="top"><p class="src"><a name="v:trans1" class="def">trans1</a> :: (<span class="keyword">forall</span> x. f x -> g x) -> <a href="Data-Functor-Day.html#t:Day">Day</a> f h a -> <a href="Data-Functor-Day.html#t:Day">Day</a> g h a<a href="src/Data-Functor-Day.html#trans1" class="link">Source</a></p><div class="doc"><p>Apply a natural transformation to the left-hand side of a Day convolution.
</p><p>This respects the naturality of the natural transformation you supplied:
</p><pre>
<code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:trans1">trans1</a></code> fg = <code><a href="Data-Functor-Day.html#v:trans1">trans1</a></code> fg <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f
</pre></div></div><div class="top"><p class="src"><a name="v:trans2" class="def">trans2</a> :: (<span class="keyword">forall</span> x. g x -> h x) -> <a href="Data-Functor-Day.html#t:Day">Day</a> f g a -> <a href="Data-Functor-Day.html#t:Day">Day</a> f h a<a href="src/Data-Functor-Day.html#trans2" class="link">Source</a></p><div class="doc"><p>Apply a natural transformation to the right-hand side of a Day convolution.
</p><p>This respects the naturality of the natural transformation you supplied:
</p><pre>
<code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="Data-Functor-Day.html#v:trans2">trans2</a></code> fg = <code><a href="Data-Functor-Day.html#v:trans2">trans2</a></code> fg <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Prelude.html#v:.">.</a></code> <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Control-Monad.html#v:fmap">fmap</a></code> f
</pre></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
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