This is maybe as good a time as any to discuss the usual alternative presentation of transducers that I find is a far gentler introduction.

A transducer is simply a function of the form `a -> List<b>`. Yes this is fully polymorphic, i.e. it holds even for transducers that only operate over just lists.

In this case `mapping` is just

This lens views a transducer through the lens of the `eduction` function as a more souped up `map`. Whereas with a normal `map` you only get to use a function `a -> b`, which means you can't change the underlying structure, with `eduction` you get to use `a -> List<b>` (again a transducer), where you "keep" any elements that are in the output list and you "discard" any elements not in the output list.

So e.g. `mapping` would be:

    (defn mapping [f] (fn [x] [(f x)]))

or in Python

    def mapping(f):
        return lambda x: [f(x)]

and `filtering` would be:

    (defn filtering [f] (fn [x] [if (f x) [x] []]))

or in Python

    def filtering(f):
        return lambda x: [x] if f(x) else []

In my opinion way clearer and easier!

For more details on the full equivalence see https://news.ycombinator.com/item?id=27778423

The current presentation of transducers has always felt like a wart in Clojure.