By the way, once you start looking for conjugation in common code
patterns, you see it everywhere. A less trivial example is the
Schwartzian transform for caching sorting keys:

(defn schwartz [key-fn] #(map (fn [x] [(key-fn x) x]) %))

(def unschwartz #(map second %))

(defn schwartz-sort [key-fn] (conjugate sort (schwartz key-fn) unschwartz))

If you implement first-class support for invertible functions
(surprisingly easy), you can capture important properties such as:

- composing invertible functions gives an invertible function.
- the inverse of an invertible function is an invertible function.

>From this, it follows (with no extra work) that the conjugate
transformation of an invertible function is an invertible function.

-Per

On Thu, Apr 22, 2010 at 10:38 AM, Michał Marczyk
<michal.marc...@gmail.com> wrote:
> On 22 April 2010 03:51, Per Vognsen <per.vogn...@gmail.com> wrote:
>> Yet another variation:
>>
>> [...]
>>
>> Food for thought. :)
>
> This is absolutely beautiful. I feel a tremendous joy now. :-)
>
> Sincerely,
> Michał
>
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