title: Evaluate beyond one level within Hold in Mathematica
body: <p>The mathematica documentation on Evaluate at possible issues says:</p>
  
  <blockquote>
    <p>Evaluate works only on the first
    level, directly inside a held function</p>
  </blockquote>
  
  <p>Why does Mathematica have this limitation? So if I have an expression with more than one level take this simplified example: </p>
  
  <p>Hold[Plus[Plus[2, 2], 2]]]</p>
  
  <p>Now suppose I want to see what the answer is to the the second Plus, without evaluating anything on levels below it. I've tried different things such as:</p>
  
  <pre><code>In[290]:= Hold[Plus[Evaluate[Plus[2, 2]], 2]]
  Out[290]= Hold[Evaluate[2+2]+2]
  
  In[287]:= Hold[Plus[ReleaseHold[Hold[Plus[2, 2]]], 2]]
  Out[287]= Hold[ReleaseHold[Hold[2+2]]+2]
  </code></pre>
  
  <p>The first Hold keeps everything unevaluated at and beyond the first level in this case.
  The goal is to control evaluation of an expression at each stage from the most inner nested function to the outer one using successive Hold, ReleaseHold and Evaluate functions to achieve that. I know I could use trace to see what happens beyond level one in an expression but that is different and sometimes complex to read with longer expressions.</p>
  
  <p>It seems like the only way is to extract and totally dismantle the expression into lists using Extract, Part or Level; evaluate part of the expression that I want; then reconstruct and re-map the expression back together for each stage. Are there any other approaches or functions for achieving this I could consider?</p>
  
  <p>Edit: This might be a better example to look at the approach of releasing the first hold. With the expression: </p>
  
  <pre><code>Hold[Plus[Plus[2, Plus[2,2]], 2]]]
  </code></pre>
  
  <p>If you release the first hold and place a hold on a higher level in a expression at the third Plus, to look like this:    </p>
  
  <pre><code>in = Plus[Plus[2, Hold[Plus[2,2]]], 2]]]
  out = Hold[2+2]+4
  </code></pre>
  
  <p>You find that Mathematica will evaluate lower levels in the background when you really want it to wait. </p>