[elbenshira]

That article was what inspired me to write this blog post.

In short, the key insight of the blog post is this (via untested javascript):

You can define transforming functions like map and filter via reduce (e.g. foldleft or, for Ruby, inject) instead. For example,

  map([...], function (x) { return x + 1; });

Can be written as:

  // append (x + 1) to the result collection
  reduce([...], [], function (result, x) { return append(result, plusOne(x)); });

But notice that, above, we explicitly chose `plusOne` and `append`. If we allow a user to pass in any function instead, then we have a higher-order function:

  function mapping(f) {
    return function (reducing) {
      return function (result, input) {
        return reducing(result, f(input));
      }
    };
  }

Now we can do:

  var xform = mapping(plusOne)(append);
  
  reduce([...], [], xform);

`xform` is a transducer.