EVOLUTION-MANAGER
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} </style> </head> <body> <h1 class="title toc-ignore">Lazyeval: a new approach to NSE</h1> <h4 class="date"><em>2019-03-15</em></h4> <p>This document outlines my previous approach to non-standard evaluation (NSE). You should avoid it unless you are working with an older version of dplyr or tidyr.</p> <p>There are three key ideas:</p> <ul> <li><p>Instead of using <code>substitute()</code>, use <code>lazyeval::lazy()</code> to capture both expression and environment. (Or use <code>lazyeval::lazy_dots(...)</code> to capture promises in <code>...</code>)</p></li> <li><p>Every function that uses NSE should have a standard evaluation (SE) escape hatch that does the actual computation. The SE-function name should end with <code>_</code>.</p></li> <li><p>The SE-function has a flexible input specification to make it easy for people to program with.</p></li> </ul> <div id="lazy" class="section level2"> <h2><code>lazy()</code></h2> <p>The key tool that makes this approach possible is <code>lazy()</code>, an equivalent to <code>substitute()</code> that captures both expression and environment associated with a function argument:</p> <div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" data-line-number="1"><span class="kw">library</span>(lazyeval)</a> <a class="sourceLine" id="cb1-2" data-line-number="2">f <-<span class="st"> </span><span class="cf">function</span>(<span class="dt">x =</span> a <span class="op">-</span><span class="st"> </span>b) {</a> <a class="sourceLine" id="cb1-3" data-line-number="3"> <span class="kw">lazy</span>(x)</a> <a class="sourceLine" id="cb1-4" data-line-number="4">}</a> <a class="sourceLine" id="cb1-5" data-line-number="5"><span class="kw">f</span>()</a> <a class="sourceLine" id="cb1-6" data-line-number="6"><span class="co">#> <lazy></span></a> <a class="sourceLine" id="cb1-7" data-line-number="7"><span class="co">#> expr: a - b</span></a> <a class="sourceLine" id="cb1-8" data-line-number="8"><span class="co">#> env: <environment: 0x7ff852dfd638></span></a> <a class="sourceLine" id="cb1-9" data-line-number="9"><span class="kw">f</span>(a <span class="op">+</span><span class="st"> </span>b)</a> <a class="sourceLine" id="cb1-10" data-line-number="10"><span class="co">#> <lazy></span></a> <a class="sourceLine" id="cb1-11" data-line-number="11"><span class="co">#> expr: a + b</span></a> <a class="sourceLine" id="cb1-12" data-line-number="12"><span class="co">#> env: <environment: R_GlobalEnv></span></a></code></pre></div> <p>As a complement to <code>eval()</code>, the lazy package provides <code>lazy_eval()</code> that uses the environment associated with the lazy object:</p> <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" data-line-number="1">a <-<span class="st"> </span><span class="dv">10</span></a> <a class="sourceLine" id="cb2-2" data-line-number="2">b <-<span class="st"> </span><span class="dv">1</span></a> <a class="sourceLine" id="cb2-3" data-line-number="3"><span class="kw">lazy_eval</span>(<span class="kw">f</span>())</a> <a class="sourceLine" id="cb2-4" data-line-number="4"><span class="co">#> [1] 9</span></a> <a class="sourceLine" id="cb2-5" data-line-number="5"><span class="kw">lazy_eval</span>(<span class="kw">f</span>(a <span class="op">+</span><span class="st"> </span>b))</a> <a class="sourceLine" id="cb2-6" data-line-number="6"><span class="co">#> [1] 11</span></a></code></pre></div> <p>The second argument to lazy eval is a list or data frame where names should be looked up first:</p> <div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" data-line-number="1"><span class="kw">lazy_eval</span>(<span class="kw">f</span>(), <span class="kw">list</span>(<span class="dt">a =</span> <span class="dv">1</span>))</a> <a class="sourceLine" id="cb3-2" data-line-number="2"><span class="co">#> [1] 0</span></a></code></pre></div> <p><code>lazy_eval()</code> also works with formulas, since they contain the same information as a lazy object: an expression (only the RHS is used by convention) and an environment:</p> <div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" data-line-number="1"><span class="kw">lazy_eval</span>(<span class="op">~</span><span class="st"> </span>a <span class="op">+</span><span class="st"> </span>b)</a> <a class="sourceLine" id="cb4-2" data-line-number="2"><span class="co">#> [1] 11</span></a> <a class="sourceLine" id="cb4-3" data-line-number="3">h <-<span class="st"> </span><span class="cf">function</span>(i) {</a> <a class="sourceLine" id="cb4-4" data-line-number="4"> <span class="op">~</span><span class="st"> </span><span class="dv">10</span> <span class="op">+</span><span class="st"> </span>i</a> <a class="sourceLine" id="cb4-5" data-line-number="5">}</a> <a class="sourceLine" id="cb4-6" data-line-number="6"><span class="kw">lazy_eval</span>(<span class="kw">h</span>(<span class="dv">1</span>))</a> <a class="sourceLine" id="cb4-7" data-line-number="7"><span class="co">#> [1] 11</span></a></code></pre></div> </div> <div id="standard-evaluation" class="section level2"> <h2>Standard evaluation</h2> <p>Whenever we need a function that does non-standard evaluation, always write the standard evaluation version first. For example, let’s implement our own version of <code>subset()</code>:</p> <div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" data-line-number="1">subset2_ <-<span class="st"> </span><span class="cf">function</span>(df, condition) {</a> <a class="sourceLine" id="cb5-2" data-line-number="2"> r <-<span class="st"> </span><span class="kw">lazy_eval</span>(condition, df)</a> <a class="sourceLine" id="cb5-3" data-line-number="3"> r <-<span class="st"> </span>r <span class="op">&</span><span class="st"> </span><span class="op">!</span><span class="kw">is.na</span>(r)</a> <a class="sourceLine" id="cb5-4" data-line-number="4"> df[r, , drop =<span class="st"> </span><span class="ot">FALSE</span>]</a> <a class="sourceLine" id="cb5-5" data-line-number="5">} </a> <a class="sourceLine" id="cb5-6" data-line-number="6"></a> <a class="sourceLine" id="cb5-7" data-line-number="7"><span class="kw">subset2_</span>(mtcars, <span class="kw">lazy</span>(mpg <span class="op">></span><span class="st"> </span><span class="dv">31</span>))</a> <a class="sourceLine" id="cb5-8" data-line-number="8"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb5-9" data-line-number="9"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb5-10" data-line-number="10"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p><code>lazy_eval()</code> will always coerce it’s first argument into a lazy object, so a variety of specifications will work:</p> <div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" data-line-number="1"><span class="kw">subset2_</span>(mtcars, <span class="op">~</span>mpg <span class="op">></span><span class="st"> </span><span class="dv">31</span>)</a> <a class="sourceLine" id="cb6-2" data-line-number="2"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb6-3" data-line-number="3"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb6-4" data-line-number="4"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a> <a class="sourceLine" id="cb6-5" data-line-number="5"><span class="kw">subset2_</span>(mtcars, <span class="kw">quote</span>(mpg <span class="op">></span><span class="st"> </span><span class="dv">31</span>))</a> <a class="sourceLine" id="cb6-6" data-line-number="6"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb6-7" data-line-number="7"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb6-8" data-line-number="8"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a> <a class="sourceLine" id="cb6-9" data-line-number="9"><span class="kw">subset2_</span>(mtcars, <span class="st">"mpg > 31"</span>)</a> <a class="sourceLine" id="cb6-10" data-line-number="10"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb6-11" data-line-number="11"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb6-12" data-line-number="12"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p>Note that quoted called and strings don’t have environments associated with them, so <code>as.lazy()</code> defaults to using <code>baseenv()</code>. This will work if the expression is self-contained (i.e. doesn’t contain any references to variables in the local environment), and will otherwise fail quickly and robustly.</p> </div> <div id="non-standard-evaluation" class="section level2"> <h2>Non-standard evaluation</h2> <p>With the SE version in hand, writing the NSE version is easy. We just use <code>lazy()</code> to capture the unevaluated expression and corresponding environment:</p> <div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" data-line-number="1">subset2 <-<span class="st"> </span><span class="cf">function</span>(df, condition) {</a> <a class="sourceLine" id="cb7-2" data-line-number="2"> <span class="kw">subset2_</span>(df, <span class="kw">lazy</span>(condition))</a> <a class="sourceLine" id="cb7-3" data-line-number="3">}</a> <a class="sourceLine" id="cb7-4" data-line-number="4"><span class="kw">subset2</span>(mtcars, mpg <span class="op">></span><span class="st"> </span><span class="dv">31</span>)</a> <a class="sourceLine" id="cb7-5" data-line-number="5"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb7-6" data-line-number="6"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb7-7" data-line-number="7"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p>This standard evaluation escape hatch is very important because it allows us to implement different NSE approaches. For example, we could create a subsetting function that finds all rows where a variable is above a threshold:</p> <div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" data-line-number="1">above_threshold <-<span class="st"> </span><span class="cf">function</span>(df, var, threshold) {</a> <a class="sourceLine" id="cb8-2" data-line-number="2"> cond <-<span class="st"> </span><span class="kw">interp</span>(<span class="op">~</span><span class="st"> </span>var <span class="op">></span><span class="st"> </span>x, <span class="dt">var =</span> <span class="kw">lazy</span>(var), <span class="dt">x =</span> threshold)</a> <a class="sourceLine" id="cb8-3" data-line-number="3"> <span class="kw">subset2_</span>(df, cond)</a> <a class="sourceLine" id="cb8-4" data-line-number="4">}</a> <a class="sourceLine" id="cb8-5" data-line-number="5"><span class="kw">above_threshold</span>(mtcars, mpg, <span class="dv">31</span>)</a> <a class="sourceLine" id="cb8-6" data-line-number="6"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb8-7" data-line-number="7"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb8-8" data-line-number="8"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p>Here we’re using <code>interp()</code> to modify a formula. We use the value of <code>threshold</code> and the expression in by <code>var</code>.</p> </div> <div id="scoping" class="section level2"> <h2>Scoping</h2> <p>Because <code>lazy()</code> captures the environment associated with the function argument, we automatically avoid a subtle scoping bug present in <code>subset()</code>:</p> <div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" data-line-number="1">x <-<span class="st"> </span><span class="dv">31</span></a> <a class="sourceLine" id="cb9-2" data-line-number="2">f1 <-<span class="st"> </span><span class="cf">function</span>(...) {</a> <a class="sourceLine" id="cb9-3" data-line-number="3"> x <-<span class="st"> </span><span class="dv">30</span></a> <a class="sourceLine" id="cb9-4" data-line-number="4"> <span class="kw">subset</span>(mtcars, ...)</a> <a class="sourceLine" id="cb9-5" data-line-number="5">}</a> <a class="sourceLine" id="cb9-6" data-line-number="6"><span class="co"># Uses 30 instead of 31</span></a> <a class="sourceLine" id="cb9-7" data-line-number="7"><span class="kw">f1</span>(mpg <span class="op">></span><span class="st"> </span>x)</a> <a class="sourceLine" id="cb9-8" data-line-number="8"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb9-9" data-line-number="9"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb9-10" data-line-number="10"><span class="co">#> 19 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2</span></a> <a class="sourceLine" id="cb9-11" data-line-number="11"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a> <a class="sourceLine" id="cb9-12" data-line-number="12"><span class="co">#> 28 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2</span></a> <a class="sourceLine" id="cb9-13" data-line-number="13"></a> <a class="sourceLine" id="cb9-14" data-line-number="14">f2 <-<span class="st"> </span><span class="cf">function</span>(...) {</a> <a class="sourceLine" id="cb9-15" data-line-number="15"> x <-<span class="st"> </span><span class="dv">30</span></a> <a class="sourceLine" id="cb9-16" data-line-number="16"> <span class="kw">subset2</span>(mtcars, ...)</a> <a class="sourceLine" id="cb9-17" data-line-number="17">}</a> <a class="sourceLine" id="cb9-18" data-line-number="18"><span class="co"># Correctly uses 31</span></a> <a class="sourceLine" id="cb9-19" data-line-number="19"><span class="kw">f2</span>(mpg <span class="op">></span><span class="st"> </span>x)</a> <a class="sourceLine" id="cb9-20" data-line-number="20"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb9-21" data-line-number="21"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb9-22" data-line-number="22"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p><code>lazy()</code> has another advantage over <code>substitute()</code> - by default, it follows promises across function invocations. This simplifies the casual use of NSE.</p> <div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" data-line-number="1">x <-<span class="st"> </span><span class="dv">31</span></a> <a class="sourceLine" id="cb10-2" data-line-number="2">g1 <-<span class="st"> </span><span class="cf">function</span>(comp) {</a> <a class="sourceLine" id="cb10-3" data-line-number="3"> x <-<span class="st"> </span><span class="dv">30</span></a> <a class="sourceLine" id="cb10-4" data-line-number="4"> <span class="kw">subset</span>(mtcars, comp)</a> <a class="sourceLine" id="cb10-5" data-line-number="5">}</a> <a class="sourceLine" id="cb10-6" data-line-number="6"><span class="kw">g1</span>(mpg <span class="op">></span><span class="st"> </span>x)</a> <a class="sourceLine" id="cb10-7" data-line-number="7"><span class="co">#> Error: object 'mpg' not found</span></a></code></pre></div> <div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" data-line-number="1">g2 <-<span class="st"> </span><span class="cf">function</span>(comp) {</a> <a class="sourceLine" id="cb11-2" data-line-number="2"> x <-<span class="st"> </span><span class="dv">30</span></a> <a class="sourceLine" id="cb11-3" data-line-number="3"> <span class="kw">subset2</span>(mtcars, comp)</a> <a class="sourceLine" id="cb11-4" data-line-number="4">}</a> <a class="sourceLine" id="cb11-5" data-line-number="5"><span class="kw">g2</span>(mpg <span class="op">></span><span class="st"> </span>x)</a> <a class="sourceLine" id="cb11-6" data-line-number="6"><span class="co">#> mpg cyl disp hp drat wt qsec vs am gear carb</span></a> <a class="sourceLine" id="cb11-7" data-line-number="7"><span class="co">#> 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1</span></a> <a class="sourceLine" id="cb11-8" data-line-number="8"><span class="co">#> 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1</span></a></code></pre></div> <p>Note that <code>g2()</code> doesn’t have a standard-evaluation escape hatch, so it’s not suitable for programming with in the same way that <code>subset2_()</code> is.</p> </div> <div id="chained-promises" class="section level2"> <h2>Chained promises</h2> <p>Take the following example:</p> <div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" data-line-number="1"><span class="kw">library</span>(lazyeval)</a> <a class="sourceLine" id="cb12-2" data-line-number="2">f1 <-<span class="st"> </span><span class="cf">function</span>(x) <span class="kw">lazy</span>(x)</a> <a class="sourceLine" id="cb12-3" data-line-number="3">g1 <-<span class="st"> </span><span class="cf">function</span>(y) <span class="kw">f1</span>(y)</a> <a class="sourceLine" id="cb12-4" data-line-number="4"></a> <a class="sourceLine" id="cb12-5" data-line-number="5"><span class="kw">g1</span>(a <span class="op">+</span><span class="st"> </span>b)</a> <a class="sourceLine" id="cb12-6" data-line-number="6"><span class="co">#> <lazy></span></a> <a class="sourceLine" id="cb12-7" data-line-number="7"><span class="co">#> expr: a + b</span></a> <a class="sourceLine" id="cb12-8" data-line-number="8"><span class="co">#> env: <environment: R_GlobalEnv></span></a></code></pre></div> <p><code>lazy()</code> returns <code>a + b</code> because it always tries to find the top-level promise.</p> <p>In this case the process looks like this:</p> <ol style="list-style-type: decimal"> <li>Find the object that <code>x</code> is bound to.</li> <li>It’s a promise, so find the expr it’s bound to (<code>y</code>, a symbol) and the environment in which it should be evaluated (the environment of <code>g()</code>).</li> <li>Since <code>x</code> is bound to a symbol, look up its value: it’s bound to a promise.</li> <li>That promise has expression <code>a + b</code> and should be evaluated in the global environment.</li> <li>The expression is not a symbol, so stop.</li> </ol> <p>Occasionally, you want to avoid this recursive behaviour, so you can use <code>follow_symbol = FALSE</code>:</p> <div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" data-line-number="1">f2 <-<span class="st"> </span><span class="cf">function</span>(x) <span class="kw">lazy</span>(x, <span class="dt">.follow_symbols =</span> <span class="ot">FALSE</span>)</a> <a class="sourceLine" id="cb13-2" data-line-number="2">g2 <-<span class="st"> </span><span class="cf">function</span>(y) <span class="kw">f2</span>(y)</a> <a class="sourceLine" id="cb13-3" data-line-number="3"></a> <a class="sourceLine" id="cb13-4" data-line-number="4"><span class="kw">g2</span>(a <span class="op">+</span><span class="st"> </span>b)</a> <a class="sourceLine" id="cb13-5" data-line-number="5"><span class="co">#> <lazy></span></a> <a class="sourceLine" id="cb13-6" data-line-number="6"><span class="co">#> expr: x</span></a> <a class="sourceLine" id="cb13-7" data-line-number="7"><span class="co">#> env: <environment: 0x7ff853abd7f8></span></a></code></pre></div> <p>Either way, if you evaluate the lazy expression you’ll get the same result:</p> <div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" data-line-number="1">a <-<span class="st"> </span><span class="dv">10</span></a> <a class="sourceLine" id="cb14-2" data-line-number="2">b <-<span class="st"> </span><span class="dv">1</span></a> <a class="sourceLine" id="cb14-3" data-line-number="3"></a> <a class="sourceLine" id="cb14-4" data-line-number="4"><span class="kw">lazy_eval</span>(<span class="kw">g1</span>(a <span class="op">+</span><span class="st"> </span>b))</a> <a class="sourceLine" id="cb14-5" data-line-number="5"><span class="co">#> [1] 11</span></a> <a class="sourceLine" id="cb14-6" data-line-number="6"><span class="kw">lazy_eval</span>(<span class="kw">g2</span>(a <span class="op">+</span><span class="st"> </span>b))</a> <a class="sourceLine" id="cb14-7" data-line-number="7"><span class="co">#> [1] 11</span></a></code></pre></div> <p>Note that the resolution of chained promises only works with unevaluated objects. This is because R deletes the information about the environment associated with a promise when it has been forced, so that the garbage collector is allowed to remove the environment from memory in case it is no longer used. <code>lazy()</code> will fail with an error in such situations.</p> <div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" data-line-number="1">var <-<span class="st"> </span><span class="dv">0</span></a> <a class="sourceLine" id="cb15-2" data-line-number="2"></a> <a class="sourceLine" id="cb15-3" data-line-number="3">f3 <-<span class="st"> </span><span class="cf">function</span>(x) {</a> <a class="sourceLine" id="cb15-4" data-line-number="4"> <span class="kw">force</span>(x)</a> <a class="sourceLine" id="cb15-5" data-line-number="5"> <span class="kw">lazy</span>(x)</a> <a class="sourceLine" id="cb15-6" data-line-number="6">}</a> <a class="sourceLine" id="cb15-7" data-line-number="7"></a> <a class="sourceLine" id="cb15-8" data-line-number="8"><span class="kw">f3</span>(var)</a> <a class="sourceLine" id="cb15-9" data-line-number="9"><span class="co">#> Error in lazy(x): Promise has already been forced</span></a></code></pre></div> </div> <!-- dynamically load mathjax for compatibility with self-contained --> <script> (function () { var script = document.createElement("script"); script.type = "text/javascript"; script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"; document.getElementsByTagName("head")[0].appendChild(script); })(); </script> </body> </html>