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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-Active.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">active-0.2.0.8: Abstractions for animation</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Copyright</th><td>(c) 2011 Brent Yorgey</td></tr><tr><th>License</th><td>BSD-style (see LICENSE)</td></tr><tr><th>Maintainer</th><td>byorgey@cis.upenn.edu</td></tr><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">Data.Active</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Representing time</a><ul><li><a href="#g:2">Time and duration</a></li><li><a href="#g:3">Eras</a></li></ul></li><li><a href="#g:4">Dynamic values</a></li><li><a href="#g:5">Active values</a></li><li><a href="#g:6">Combinators</a><ul><li><a href="#g:7">Special active values</a></li><li><a href="#g:8">Transforming active values</a></li><li><a href="#g:9">Working with values outside the era</a></li><li><a href="#g:10">Composing active values</a></li></ul></li><li><a href="#g:11">Discretization</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Inspired by the work of Kevin Matlage and Andy Gill (<em>Every</em>
<em>Animation Should Have a Beginning, a Middle, and an End</em>, Trends
in Functional Programming,
2010. <a href="http://ittc.ku.edu/csdl/fpg/node/46">http://ittc.ku.edu/csdl/fpg/node/46</a>), this module defines a
simple abstraction for working with time-varying values. A value
of type <code>Active a</code> is either a constant value of type <code>a</code>, or a
time-varying value of type <code>a</code> (<em>i.e.</em> a function from time to
<code>a</code>) with specific start and end times. Since active values
have start and end times, they can be aligned, sequenced,
stretched, or reversed.</p><p>In a sense, this is sort of like a stripped-down version of
functional reactive programming (FRP), without the reactivity.</p><p>The original motivating use for this library is to support making
animations with the diagrams framework
(<a href="http://projects.haskell.org/diagrams">http://projects.haskell.org/diagrams</a>), but the hope is that it
may find more general utility.</p><p>There are two basic ways to create an <code>Active</code> value. The first is
to use <code><a href="Data-Active.html#v:mkActive">mkActive</a></code> to create one directly, by specifying a start and
end time and a function of time. More indirectly, one can use the
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> instance together with the unit interval <code><a href="Data-Active.html#v:ui">ui</a></code>, which
takes on values from the unit interval from time 0 to time 1, or
<code><a href="Data-Active.html#v:interval">interval</a></code>, which creates an active over an arbitrary interval.</p><p>For example, to create a value of type <code>Active Double</code> which
represents one period of a sine wave starting at time 0 and ending
at time 1, we could write</p><pre>mkActive 0 1 (\t -> sin (fromTime t * tau))</pre><p>or</p><pre>(sin . (*tau)) <$> ui</pre><p><code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code> can also be used to create <code>Active</code> values which are
constant and have no start or end time. For example,</p><pre>mod <$> (floor <$> interval 0 100) <*> pure 7</pre><p>cycles repeatedly through the numbers 0-6.</p><p>Note that the "idiom bracket" notation supported by the SHE
preprocessor (<a href="http://personal.cis.strath.ac.uk/~conor/pub/she/">http://personal.cis.strath.ac.uk/~conor/pub/she/</a>,
<a href="http://hackage.haskell.org/package/she">http://hackage.haskell.org/package/she</a>) can make for somewhat
more readable <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> code. For example, the above example
can be rewritten using SHE as</p><pre>{-# OPTIONS_GHC -F -pgmF she #-}
... (| mod (| floor (interval 0 100) |) ~7 |)</pre><p>There are many functions for transforming and composing active
values; see the documentation below for more details.</p><p>With careful handling, this module should be suitable to generating
deep embeddings if <code><a href="Data-Active.html#t:Active">Active</a></code> values.</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:Time">Time</a> n</li><li class="src short"><a href="#v:toTime">toTime</a> :: n -> <a href="Data-Active.html#t:Time">Time</a> n</li><li class="src short"><a href="#v:fromTime">fromTime</a> :: <a href="Data-Active.html#t:Time">Time</a> n -> n</li><li class="src short"><span class="keyword">data</span> <a href="#t:Duration">Duration</a> n</li><li class="src short"><a href="#v:toDuration">toDuration</a> :: n -> <a href="Data-Active.html#t:Duration">Duration</a> n</li><li class="src short"><a href="#v:fromDuration">fromDuration</a> :: <a href="Data-Active.html#t:Duration">Duration</a> n -> n</li><li class="src short"><span class="keyword">data</span> <a href="#t:Era">Era</a> n</li><li class="src short"><a href="#v:mkEra">mkEra</a> :: <a href="Data-Active.html#t:Time">Time</a> n -> <a href="Data-Active.html#t:Time">Time</a> n -> <a href="Data-Active.html#t:Era">Era</a> n</li><li class="src short"><a href="#v:start">start</a> :: <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Time">Time</a> n</li><li class="src short"><a href="#v:end">end</a> :: <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Time">Time</a> n</li><li class="src short"><a href="#v:duration">duration</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Duration">Duration</a> n</li><li class="src short"><span class="keyword">data</span> <a href="#t:Dynamic">Dynamic</a> a = <a href="#v:Dynamic">Dynamic</a> {<ul class="subs"><li><a href="#v:era">era</a> :: <a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a></li><li><a href="#v:runDynamic">runDynamic</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a</li></ul>}</li><li class="src short"><a href="#v:mkDynamic">mkDynamic</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a</li><li class="src short"><a href="#v:onDynamic">onDynamic</a> :: (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> b) -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> b</li><li class="src short"><a href="#v:shiftDynamic">shiftDynamic</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a</li><li class="src short"><span class="keyword">data</span> <a href="#t:Active">Active</a> a</li><li class="src short"><a href="#v:mkActive">mkActive</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:fromDynamic">fromDynamic</a> :: <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:isConstant">isConstant</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:isDynamic">isDynamic</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a></li><li class="src short"><a href="#v:onActive">onActive</a> :: (a -> b) -> (<a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> b) -> <a href="Data-Active.html#t:Active">Active</a> a -> b</li><li class="src short"><a href="#v:modActive">modActive</a> :: (a -> b) -> (<a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> b) -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> b</li><li class="src short"><a href="#v:runActive">runActive</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a</li><li class="src short"><a href="#v:activeEra">activeEra</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a>)</li><li class="src short"><a href="#v:setEra">setEra</a> :: <a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:atTime">atTime</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:activeStart">activeStart</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> a</li><li class="src short"><a href="#v:activeEnd">activeEnd</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> a</li><li class="src short"><a href="#v:ui">ui</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:interval">interval</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:stretch">stretch</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:stretchTo">stretchTo</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:during">during</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:shift">shift</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:backwards">backwards</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:snapshot">snapshot</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:clamp">clamp</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:clampBefore">clampBefore</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:clampAfter">clampAfter</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:trim">trim</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:trimBefore">trimBefore</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:trimAfter">trimAfter</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:after">after</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:-45--62--62-">(->>)</a> :: <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:-124--62--62-">(|>>)</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:movie">movie</a> :: [<a href="Data-Active.html#t:Active">Active</a> a] -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:discrete">discrete</a> :: [a] -> <a href="Data-Active.html#t:Active">Active</a> a</li><li class="src short"><a href="#v:simulate">simulate</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> [a]</li></ul></div><div id="interface"><h1 id="g:1">Representing time</h1><h2 id="g:2">Time and duration</h2><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Time" class="def">Time</a> n <a href="src/Data-Active.html#Time" class="link">Source</a></p><div class="doc"><p>An abstract type for representing <em>points in time</em>. Note that
literal numeric values may be used as <code>Time</code>s, thanks to the the
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> and <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> instances.</p></div><div class="subs instances"><p id="control.i:Time" class="caption collapser" onclick="toggleSection('i:Time')">Instances</p><div id="section.i:Time" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> <a href="Data-Active.html#t:Time">Time</a></span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-linear-doc/html/Linear-Affine.html#t:Affine">Affine</a> <a href="Data-Active.html#t:Time">Time</a></span> <a href="src/Data-Active.html#line-182" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Enum">Enum</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Enum">Enum</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Real">Real</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Real">Real</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:RealFrac">RealFrac</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:RealFrac">RealFrac</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-170" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Wrapped">Wrapped</a> (<a href="Data-Active.html#t:Time">Time</a> n)</span> <a href="src/Data-Active.html#line-172" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * (<a href="Data-Active.html#t:Time">Time</a> n1) t0 => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Rewrapped">Rewrapped</a> (<a href="Data-Active.html#t:Time">Time</a> n) t</span> <a href="src/Data-Active.html#line-172" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-linear-doc/html/Linear-Affine.html#t:Diff">Diff</a> <a href="Data-Active.html#t:Time">Time</a> = <a href="Data-Active.html#t:Duration">Duration</a></span> <a href="src/Data-Active.html#line-183" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Unwrapped">Unwrapped</a> (<a href="Data-Active.html#t:Time">Time</a> n0) = n0</span> <a href="src/Data-Active.html#line-172" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:toTime" class="def">toTime</a> :: n -> <a href="Data-Active.html#t:Time">Time</a> n <a href="src/Data-Active.html#toTime" class="link">Source</a></p><div class="doc"><p>A convenient wrapper function to convert a numeric value into a time.</p></div></div><div class="top"><p class="src"><a name="v:fromTime" class="def">fromTime</a> :: <a href="Data-Active.html#t:Time">Time</a> n -> n <a href="src/Data-Active.html#fromTime" class="link">Source</a></p><div class="doc"><p>A convenient unwrapper function to turn a time into a numeric value.</p></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Duration" class="def">Duration</a> n <a href="src/Data-Active.html#Duration" class="link">Source</a></p><div class="doc"><p>An abstract type representing <em>elapsed time</em> between two points
in time. Note that durations can be negative. Literal numeric
values may be used as <code>Duration</code>s thanks to the <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a></code> and
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a></code> instances.</p></div><div class="subs instances"><p id="control.i:Duration" class="caption collapser" onclick="toggleSection('i:Duration')">Instances</p><div id="section.i:Duration" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> <a href="Data-Active.html#t:Duration">Duration</a></span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> <a href="Data-Active.html#t:Duration">Duration</a></span> <a href="src/Data-Active.html#line-208" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-linear-doc/html/Linear-Vector.html#t:Additive">Additive</a> <a href="Data-Active.html#t:Duration">Duration</a></span> <a href="src/Data-Active.html#line-212" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Enum">Enum</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Enum">Enum</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Real">Real</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Real">Real</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:RealFrac">RealFrac</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:RealFrac">RealFrac</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-196" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-218" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-215" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Wrapped">Wrapped</a> (<a href="Data-Active.html#t:Duration">Duration</a> n)</span> <a href="src/Data-Active.html#line-198" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * (<a href="Data-Active.html#t:Duration">Duration</a> n1) t0 => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Rewrapped">Rewrapped</a> (<a href="Data-Active.html#t:Duration">Duration</a> n) t</span> <a href="src/Data-Active.html#line-198" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Unwrapped">Unwrapped</a> (<a href="Data-Active.html#t:Duration">Duration</a> n0) = n0</span> <a href="src/Data-Active.html#line-198" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:toDuration" class="def">toDuration</a> :: n -> <a href="Data-Active.html#t:Duration">Duration</a> n <a href="src/Data-Active.html#toDuration" class="link">Source</a></p><div class="doc"><p>A convenient wrapper function to convert a numeric value into a duration.</p></div></div><div class="top"><p class="src"><a name="v:fromDuration" class="def">fromDuration</a> :: <a href="Data-Active.html#t:Duration">Duration</a> n -> n <a href="src/Data-Active.html#fromDuration" class="link">Source</a></p><div class="doc"><p>A convenient unwrapper function to turn a duration into a numeric value.</p></div></div><h2 id="g:3">Eras</h2><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Era" class="def">Era</a> n <a href="src/Data-Active.html#Era" class="link">Source</a></p><div class="doc"><p>An <code>Era</code> is a concrete span of time, that is, a pair of times
representing the start and end of the era. <code>Era</code>s form a
semigroup: the combination of two <code>Era</code>s is the smallest <code>Era</code>
which contains both. They do not form a <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code>, since there is
no <code>Era</code> which acts as the identity with respect to this
combining operation.</p><p><code>Era</code> is abstract. To construct <code>Era</code> values, use <code><a href="Data-Active.html#v:mkEra">mkEra</a></code>; to
deconstruct, use <code><a href="Data-Active.html#v:start">start</a></code> and <code><a href="Data-Active.html#v:end">end</a></code>.</p></div><div class="subs instances"><p id="control.i:Era" class="caption collapser" onclick="toggleSection('i:Era')">Instances</p><div id="section.i:Era" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> n => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Data-Active.html#t:Era">Era</a> n)</span> <a href="src/Data-Active.html#line-232" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> n => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Data-Active.html#t:Era">Era</a> n)</span> <a href="src/Data-Active.html#line-232" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:mkEra" class="def">mkEra</a> :: <a href="Data-Active.html#t:Time">Time</a> n -> <a href="Data-Active.html#t:Time">Time</a> n -> <a href="Data-Active.html#t:Era">Era</a> n <a href="src/Data-Active.html#mkEra" class="link">Source</a></p><div class="doc"><p>Create an <code><a href="Data-Active.html#t:Era">Era</a></code> by specifying start and end <code><a href="Data-Active.html#t:Time">Time</a></code>s.</p></div></div><div class="top"><p class="src"><a name="v:start" class="def">start</a> :: <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Time">Time</a> n <a href="src/Data-Active.html#start" class="link">Source</a></p><div class="doc"><p>Get the start <code><a href="Data-Active.html#t:Time">Time</a></code> of an <code><a href="Data-Active.html#t:Era">Era</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:end" class="def">end</a> :: <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Time">Time</a> n <a href="src/Data-Active.html#end" class="link">Source</a></p><div class="doc"><p>Get the end <code><a href="Data-Active.html#t:Time">Time</a></code> of an <code><a href="Data-Active.html#t:Era">Era</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:duration" class="def">duration</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Num">Num</a> n => <a href="Data-Active.html#t:Era">Era</a> n -> <a href="Data-Active.html#t:Duration">Duration</a> n <a href="src/Data-Active.html#duration" class="link">Source</a></p><div class="doc"><p>Compute the <code><a href="Data-Active.html#t:Duration">Duration</a></code> of an <code><a href="Data-Active.html#t:Era">Era</a></code>.</p></div></div><h1 id="g:4">Dynamic values</h1><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Dynamic" class="def">Dynamic</a> a <a href="src/Data-Active.html#Dynamic" class="link">Source</a></p><div class="doc"><p>A <code>Dynamic a</code> can be thought of as an <code>a</code> value that changes over
the course of a particular <code><a href="Data-Active.html#t:Era">Era</a></code>. It's envisioned that <code>Dynamic</code>
will be mostly an internal implementation detail and that
<code><a href="Data-Active.html#t:Active">Active</a></code> will be most commonly used. But you never know what
uses people might find for things.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:Dynamic" class="def">Dynamic</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:era" class="def">era</a> :: <a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a></dt><dd class="doc empty"> </dd><dt class="src"><a name="v:runDynamic" class="def">runDynamic</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a</dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></div><div class="subs instances"><p id="control.i:Dynamic" class="caption collapser" onclick="toggleSection('i:Dynamic')">Instances</p><div id="section.i:Dynamic" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> <a href="Data-Active.html#t:Dynamic">Dynamic</a></span> <a href="src/Data-Active.html#line-264" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> <a href="Data-Active.html#t:Dynamic">Dynamic</a></span> <a href="src/Data-Active.html#line-275" class="link">Source</a></td><td class="doc"><p><code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> is an instance of <code><a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a></code> (<em>i.e.</em> <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> without
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code>): a time-varying function is applied to a time-varying
value pointwise; the era of the result is the combination of the
function and value eras. Note, however, that <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> is <em>not</em>
an instance of <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> since there is no way to implement
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code>: the era would have to be empty, but there is no such
thing as an empty era (that is, <code><a href="Data-Active.html#t:Era">Era</a></code> is not an instance of
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code>).</p></td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> a => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Data-Active.html#t:Dynamic">Dynamic</a> a)</span> <a href="src/Data-Active.html#line-282" class="link">Source</a></td><td class="doc"><p><code><code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> a</code> is a <code><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a></code> whenever <code>a</code> is: the eras are
combined according to their semigroup structure, and the values
of type <code>a</code> are combined pointwise. Note that <code><code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> a</code> cannot
be an instance of <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> since <code><a href="Data-Active.html#t:Era">Era</a></code> is not.</p></td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:mkDynamic" class="def">mkDynamic</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a <a href="src/Data-Active.html#mkDynamic" class="link">Source</a></p><div class="doc"><p>Create a <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> from a start time, an end time, and a
time-varying value.</p></div></div><div class="top"><p class="src"><a name="v:onDynamic" class="def">onDynamic</a> :: (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> b) -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> b <a href="src/Data-Active.html#onDynamic" class="link">Source</a></p><div class="doc"><p>Fold for <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:shiftDynamic" class="def">shiftDynamic</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a <a href="src/Data-Active.html#shiftDynamic" class="link">Source</a></p><div class="doc"><p>Shift a <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> value by a certain duration.</p></div></div><h1 id="g:5">Active values</h1><div class="doc"><p>For working with time-varying values, it is convenient to have an
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> instance: <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:-60--42--62-"><*></a></code> lets us apply time-varying
functions to time-varying values; <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code> allows treating constants
as time-varying values which do not vary. However, as explained in
its documentation, <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> cannot be made an instance of
<code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> since there is no way to implement <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#v:pure">pure</a></code>. The
problem is that all <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code> values must have a finite start and
end time. The solution is to adjoin a special constructor for
pure/constant values with no start or end time, giving us <code><a href="Data-Active.html#t:Active">Active</a></code>.</p></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:Active" class="def">Active</a> a <a href="src/Data-Active.html#Active" class="link">Source</a></p><div class="doc"><p>There are two types of <code>Active</code> values:</p><ul><li>An <code><a href="Data-Active.html#t:Active">Active</a></code> can simply be a <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code>, that is, a time-varying
value with start and end times.</li><li>An <code><a href="Data-Active.html#t:Active">Active</a></code> value can also be a constant: a single value,
constant across time, with no start and end times.</li></ul><p>The addition of constant values enable <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a></code> and <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code>
instances for <code><a href="Data-Active.html#t:Active">Active</a></code>.</p></div><div class="subs instances"><p id="control.i:Active" class="caption collapser" onclick="toggleSection('i:Active')">Instances</p><div id="section.i:Active" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> <a href="Data-Active.html#t:Active">Active</a></span> <a href="src/Data-Active.html#line-329" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a> <a href="Data-Active.html#t:Active">Active</a></span> <a href="src/Data-Active.html#line-329" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:Apply">Apply</a> <a href="Data-Active.html#t:Active">Active</a></span> <a href="src/Data-Active.html#line-329" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(<a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a, <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> a) => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> (<a href="Data-Active.html#t:Active">Active</a> a)</span> <a href="src/Data-Active.html#line-355" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> a => <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> (<a href="Data-Active.html#t:Active">Active</a> a)</span> <a href="src/Data-Active.html#line-340" class="link">Source</a></td><td class="doc"><p>Active values over a type with a <code><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a></code> instance are also an
instance of <code><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a></code>. Two active values are combined
pointwise; the resulting value is constant iff both inputs are.</p></td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Wrapped">Wrapped</a> (<a href="Data-Active.html#t:Active">Active</a> a)</span> <a href="src/Data-Active.html#line-331" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left">(~) * (<a href="Data-Active.html#t:Active">Active</a> a1) t0 => <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Rewrapped">Rewrapped</a> (<a href="Data-Active.html#t:Active">Active</a> a) t</span> <a href="src/Data-Active.html#line-331" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-lens-doc/html/Control-Lens-Wrapped.html#t:Unwrapped">Unwrapped</a> (<a href="Data-Active.html#t:Active">Active</a> a0) = <a href="file:///usr/share/doc/libghc-semigroupoids-doc/html/Data-Functor-Apply.html#t:MaybeApply">MaybeApply</a> <a href="Data-Active.html#t:Dynamic">Dynamic</a> a0</span> <a href="src/Data-Active.html#line-331" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:mkActive" class="def">mkActive</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> (<a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a) -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#mkActive" class="link">Source</a></p><div class="doc"><p>Create a dynamic <code><a href="Data-Active.html#t:Active">Active</a></code> from a start time, an end time, and a
time-varying value.</p></div></div><div class="top"><p class="src"><a name="v:fromDynamic" class="def">fromDynamic</a> :: <a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#fromDynamic" class="link">Source</a></p><div class="doc"><p>Create an <code><a href="Data-Active.html#t:Active">Active</a></code> value from a <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:isConstant" class="def">isConstant</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Data-Active.html#isConstant" class="link">Source</a></p><div class="doc"><p>Test whether an <code><a href="Data-Active.html#t:Active">Active</a></code> value is constant.</p></div></div><div class="top"><p class="src"><a name="v:isDynamic" class="def">isDynamic</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Bool.html#t:Bool">Bool</a> <a href="src/Data-Active.html#isDynamic" class="link">Source</a></p><div class="doc"><p>Test whether an <code><a href="Data-Active.html#t:Active">Active</a></code> value is <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:onActive" class="def">onActive</a> :: (a -> b) -> (<a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> b) -> <a href="Data-Active.html#t:Active">Active</a> a -> b <a href="src/Data-Active.html#onActive" class="link">Source</a></p><div class="doc"><p>Fold for <code><a href="Data-Active.html#t:Active">Active</a></code>s. Process an 'Active a', given a function to
apply if it is a pure (constant) value, and a function to apply if
it is a <code><a href="Data-Active.html#t:Dynamic">Dynamic</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:modActive" class="def">modActive</a> :: (a -> b) -> (<a href="Data-Active.html#t:Dynamic">Dynamic</a> a -> <a href="Data-Active.html#t:Dynamic">Dynamic</a> b) -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> b <a href="src/Data-Active.html#modActive" class="link">Source</a></p><div class="doc"><p>Modify an <code><a href="Data-Active.html#t:Active">Active</a></code> value using a case analysis to see whether it
is constant or dynamic.</p></div></div><div class="top"><p class="src"><a name="v:runActive" class="def">runActive</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> a <a href="src/Data-Active.html#runActive" class="link">Source</a></p><div class="doc"><p>Interpret an <code><a href="Data-Active.html#t:Active">Active</a></code> value as a function from time.</p></div></div><div class="top"><p class="src"><a name="v:activeEra" class="def">activeEra</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#t:Maybe">Maybe</a> (<a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a>) <a href="src/Data-Active.html#activeEra" class="link">Source</a></p><div class="doc"><p>Get the <code><a href="Data-Active.html#t:Era">Era</a></code> of an <code><a href="Data-Active.html#t:Active">Active</a></code> value (or <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Maybe.html#v:Nothing">Nothing</a></code> if it is
a constant/pure value).</p></div></div><div class="top"><p class="src"><a name="v:setEra" class="def">setEra</a> :: <a href="Data-Active.html#t:Era">Era</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#setEra" class="link">Source</a></p><div class="doc"><p>Set the era of an <code><a href="Data-Active.html#t:Active">Active</a></code> value. Note that this will change a
constant <code><a href="Data-Active.html#t:Active">Active</a></code> into a dynamic one which happens to have the
same value at all times.</p></div></div><div class="top"><p class="src"><a name="v:atTime" class="def">atTime</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#atTime" class="link">Source</a></p><div class="doc"><p><code>atTime t a</code> is an active value with the same behavior as <code>a</code>,
shifted so that it starts at time <code>t</code>. If <code>a</code> is constant it is
returned unchanged.</p></div></div><div class="top"><p class="src"><a name="v:activeStart" class="def">activeStart</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> a <a href="src/Data-Active.html#activeStart" class="link">Source</a></p><div class="doc"><p>Get the value of an <code>Active a</code> at the beginning of its era.</p></div></div><div class="top"><p class="src"><a name="v:activeEnd" class="def">activeEnd</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> a <a href="src/Data-Active.html#activeEnd" class="link">Source</a></p><div class="doc"><p>Get the value of an <code>Active a</code> at the end of its era.</p></div></div><h1 id="g:6">Combinators</h1><h2 id="g:7">Special active values</h2><div class="top"><p class="src"><a name="v:ui" class="def">ui</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#ui" class="link">Source</a></p><div class="doc"><p><code>ui</code> represents the <em>unit interval</em>, which takes on the value <code>t</code>
at time <code>t</code>, and has as its era <code>[0,1]</code>. It is equivalent to
<code><code><a href="Data-Active.html#v:interval">interval</a></code> 0 1</code>, and can be visualized as follows:</p><p><img src="diagrams/src_Data_Active_uiDia.svg#diagram=uiDia&width=200" /></p><p>On the x-axis is time, and the value that <code>ui</code> takes on is on the
y-axis. The shaded portion represents the era. Note that the
value of <code>ui</code> (as with any active) is still defined outside its
era, and this can make a difference when it is combined with
other active values with different eras. Applying a function
with <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#v:fmap">fmap</a></code> affects all values, both inside and outside the era.
To manipulate values outside the era specifically, see <code><a href="Data-Active.html#v:clamp">clamp</a></code>
and <code><a href="Data-Active.html#v:trim">trim</a></code>.</p><p>To alter the <em>values</em> that <code>ui</code> takes on without altering its
era, use its <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a></code> and <code><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Control-Applicative.html#t:Applicative">Applicative</a></code> instances. For example,
<code>(*2) <$> ui</code> varies from <code>0</code> to <code>2</code> over the era <code>[0,1]</code>. To
alter the era, you can use <code><a href="Data-Active.html#v:stretch">stretch</a></code> or <code><a href="Data-Active.html#v:shift">shift</a></code>.</p></div></div><div class="top"><p class="src"><a name="v:interval" class="def">interval</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Fractional">Fractional</a> a => <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#interval" class="link">Source</a></p><div class="doc"><p><code>interval a b</code> is an active value starting at time <code>a</code>, ending at
time <code>b</code>, and taking the value <code>t</code> at time <code>t</code>.</p></div></div><h2 id="g:8">Transforming active values</h2><div class="top"><p class="src"><a name="v:stretch" class="def">stretch</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#stretch" class="link">Source</a></p><div class="doc"><p><code>stretch s act</code> "stretches" the active <code>act</code> so that it takes
<code>s</code> times as long (retaining the same start time).</p></div></div><div class="top"><p class="src"><a name="v:stretchTo" class="def">stretchTo</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#stretchTo" class="link">Source</a></p><div class="doc"><p><code>stretchTo d</code> <code><a href="Data-Active.html#v:stretch">stretch</a></code>es an <code><a href="Data-Active.html#t:Active">Active</a></code> so it has duration <code>d</code>.
Has no effect if (1) <code>d</code> is non-positive, or (2) the <code><a href="Data-Active.html#t:Active">Active</a></code>
value is constant, or (3) the <code><a href="Data-Active.html#t:Active">Active</a></code> value has zero duration.
[AJG: conditions (1) and (3) no longer true: to consider changing]</p></div></div><div class="top"><p class="src"><a name="v:during" class="def">during</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#during" class="link">Source</a></p><div class="doc"><p><code>a1 `during` a2</code> <code><a href="Data-Active.html#v:stretch">stretch</a></code>es and <code><a href="Data-Active.html#v:shift">shift</a></code>s <code>a1</code> so that it has the
same era as <code>a2</code>. Has no effect if either of <code>a1</code> or <code>a2</code> are constant.</p></div></div><div class="top"><p class="src"><a name="v:shift" class="def">shift</a> :: <a href="Data-Active.html#t:Duration">Duration</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#shift" class="link">Source</a></p><div class="doc"><p><code>shift d act</code> shifts the start time of <code>act</code> by duration <code>d</code>.
Has no effect on constant values.</p></div></div><div class="top"><p class="src"><a name="v:backwards" class="def">backwards</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#backwards" class="link">Source</a></p><div class="doc"><p>Reverse an active value so the start of its era gets mapped to
the end and vice versa. For example, <code>backwards <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be
visualized as</p><p><img src="diagrams/src_Data_Active_backwardsDia.svg#diagram=backwardsDia&width=200" /></p></div></div><div class="top"><p class="src"><a name="v:snapshot" class="def">snapshot</a> :: <a href="Data-Active.html#t:Time">Time</a> <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#snapshot" class="link">Source</a></p><div class="doc"><p>Take a "snapshot" of an active value at a particular time,
resulting in a constant value.</p></div></div><h2 id="g:9">Working with values outside the era</h2><div class="top"><p class="src"><a name="v:clamp" class="def">clamp</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#clamp" class="link">Source</a></p><div class="doc"><p>"Clamp" an active value so that it is constant before and after
its era. Before the era, <code>clamp a</code> takes on the value of <code>a</code> at
the start of the era. Likewise, after the era, <code>clamp a</code> takes
on the value of <code>a</code> at the end of the era. <code>clamp</code> has no effect
on constant values.</p><p>For example, <code>clamp <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_clampDia.svg#diagram=clampDia&width=200" /></p><p>See also <code><a href="Data-Active.html#v:clampBefore">clampBefore</a></code> and <code><a href="Data-Active.html#v:clampAfter">clampAfter</a></code>, which clamp only before
or after the era, respectively.</p></div></div><div class="top"><p class="src"><a name="v:clampBefore" class="def">clampBefore</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#clampBefore" class="link">Source</a></p><div class="doc"><p>"Clamp" an active value so that it is constant before the start
of its era. For example, <code>clampBefore <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_clampBeforeDia.svg#diagram=clampBeforeDia&width=200" /></p><p>See the documentation of <code><a href="Data-Active.html#v:clamp">clamp</a></code> for more information.</p></div></div><div class="top"><p class="src"><a name="v:clampAfter" class="def">clampAfter</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#clampAfter" class="link">Source</a></p><div class="doc"><p>"Clamp" an active value so that it is constant after the end
of its era. For example, <code>clampBefore <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_clampAfterDia.svg#diagram=clampAfterDia&width=200" /></p><p>See the documentation of <code><a href="Data-Active.html#v:clamp">clamp</a></code> for more information.</p></div></div><div class="top"><p class="src"><a name="v:trim" class="def">trim</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#trim" class="link">Source</a></p><div class="doc"><p>"Trim" an active value so that it is empty outside its era.
<code>trim</code> has no effect on constant values.</p><p>For example, <code>trim <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_trimDia.svg#diagram=trimDia&width=200" /></p><p>Actually, <code>trim ui</code> is not well-typed, since it is not guaranteed
that <code>ui</code>'s values will be monoidal (and usually they won't be)!
But the above image still provides a good intuitive idea of what
<code>trim</code> is doing. To make this precise we could consider something
like <code>trim (First . Just <a href="$">$</a> ui)</code>.</p><p>See also <code><a href="Data-Active.html#v:trimBefore">trimBefore</a></code> and <code>trimActive</code>, which trim only before or
after the era, respectively.</p></div></div><div class="top"><p class="src"><a name="v:trimBefore" class="def">trimBefore</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#trimBefore" class="link">Source</a></p><div class="doc"><p>"Trim" an active value so that it is empty <em>before</em> the start
of its era. For example, <code>trimBefore <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_trimBeforeDia.svg#diagram=trimBeforeDia&width=200" /></p><p>See the documentation of <code><a href="Data-Active.html#v:trim">trim</a></code> for more details.</p></div></div><div class="top"><p class="src"><a name="v:trimAfter" class="def">trimAfter</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Monoid.html#t:Monoid">Monoid</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#trimAfter" class="link">Source</a></p><div class="doc"><p>"Trim" an active value so that it is empty <em>after</em> the end
of its era. For example, <code>trimAfter <code><a href="Data-Active.html#v:ui">ui</a></code></code> can be visualized as</p><p><img src="diagrams/src_Data_Active_trimAfterDia.svg#diagram=trimAfterDia&width=200" /></p><p>See the documentation of <code><a href="Data-Active.html#v:trim">trim</a></code> for more details.</p></div></div><h2 id="g:10">Composing active values</h2><div class="top"><p class="src"><a name="v:after" class="def">after</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#after" class="link">Source</a></p><div class="doc"><p><code>a1 `after` a2</code> produces an active that behaves like <code>a1</code> but is
shifted to start at the end time of <code>a2</code>. If either <code>a1</code> or <code>a2</code>
are constant, <code>a1</code> is returned unchanged.</p></div></div><div class="top"><p class="src"><a name="v:-45--62--62-" class="def">(->>)</a> :: <a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#t:Semigroup">Semigroup</a> a => <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <span class="fixity">infixr 5</span><span class="rightedge"></span> <a href="src/Data-Active.html#-%3E%3E" class="link">Source</a></p><div class="doc"><p>Sequence/overlay two <code><a href="Data-Active.html#t:Active">Active</a></code> values: shift the second to start
immediately after the first (using <code><a href="Data-Active.html#v:after">after</a></code>), then compose them
(using <code><a href="file:///usr/share/doc/libghc-semigroups-doc/html/Data-Semigroup.html#v:-60--62-"><></a></code>).</p></div></div><div class="top"><p class="src"><a name="v:-124--62--62-" class="def">(|>>)</a> :: <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#%7C%3E%3E" class="link">Source</a></p><div class="doc"><p>"Splice" two <code><a href="Data-Active.html#t:Active">Active</a></code> values together: shift the second to
start immediately after the first (using <code><a href="Data-Active.html#v:after">after</a></code>), and produce
the value which acts like the first up to the common end/start
point, then like the second after that. If both are constant,
return the first.</p></div></div><div class="top"><p class="src"><a name="v:movie" class="def">movie</a> :: [<a href="Data-Active.html#t:Active">Active</a> a] -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#movie" class="link">Source</a></p><div class="doc"><p>Splice together a list of active values using <code><a href="Data-Active.html#v:-124--62--62-">|>></a></code>. The list
must be nonempty.</p></div></div><h1 id="g:11">Discretization</h1><div class="top"><p class="src"><a name="v:discrete" class="def">discrete</a> :: [a] -> <a href="Data-Active.html#t:Active">Active</a> a <a href="src/Data-Active.html#discrete" class="link">Source</a></p><div class="doc"><p>Create an <code>Active</code> which takes on each value in the given list in
turn during the time <code>[0,1]</code>, with each value getting an equal
amount of time. In other words, <code>discrete</code> creates a "slide
show" that starts at time 0 and ends at time 1. The first
element is used prior to time 0, and the last element is used
after time 1.</p><p>It is an error to call <code>discrete</code> on the empty list.</p></div></div><div class="top"><p class="src"><a name="v:simulate" class="def">simulate</a> :: <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Prelude.html#t:Rational">Rational</a> -> <a href="Data-Active.html#t:Active">Active</a> a -> [a] <a href="src/Data-Active.html#simulate" class="link">Source</a></p><div class="doc"><p><code>simulate r act</code> simulates the <code><a href="Data-Active.html#t:Active">Active</a></code> value <code>act</code>, returning a
list of "snapshots" taken at regular intervals from the start
time to the end time. The interval used is determined by the
rate <code>r</code>, which denotes the "frame rate", that is, the number
of snapshots per unit time.</p><p>If the <code><a href="Data-Active.html#t:Active">Active</a></code> value is constant (and thus has no start or end
times), a list of length 1 is returned, containing the constant
value.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.16.1</p></div></body></html>
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