title: What is the name of the monadic "versions" of fmap?
body: <p>Having a background in powershell scripting i first thought it natural to think of function composition in a pipe kind of way. That means the syntax for composition should be <code>fun1 | fun2 | fun3</code> in a psudocode kind of way. (where <code>fun[i]</code> is the <code>i</code>'th function to apply in order). This order of functions is also what you find in haskell monadic binds. <code>fun1 &gt;&gt;= fun2 &gt;&gt;= fun3</code>.</p>
  
  <p>But in other occasions in haskell, the order of functions is more math'y, such as <code>fun3 . fun2 . fun1</code>, or in the functorial setting <code>fmap fun3 . fmap fun2 . fmap fun1</code>.</p>
  
  <p>I am very much aware that the functions have different signature in the two examples, but it puzzles me that the structure is reversed, still. My workaround is to sometimes define a function <code>mmap = flip (&gt;&gt;=)</code> such that I can write <code>mmap fun3 . mmap fun2 . mmap fun1</code>.</p>
  
  <p>So to the question:</p>
  
  <ol>
  <li>Is there a <code>mmap</code> already defined? What is is called?</li>
  <li>Why if bind defined as an operator with arguments in an order that feels backwards?</li>
  </ol>