Outside the topic of admittedly really cool delcont stuff:<p>The way you refer to the value and the CPS&#x27;d value as the same is by referring to their effects in stack machine semantics as the same. This makes your intuition non-transferrable to other semantics (lacking a clear CS example off the top of my head, I&#x27;ll just throw out the usual trick of asking: does this work the same on a GPU? I&#x27;m confident there&#x27;s a Yoneda analogue there).<p>Studying CT is completely extra-curricular as far as I&#x27;m concerned and I could never recommend it as a way to implement or use CPS, but <i>understanding</i>, for certain rather aggressive values of &quot;understand&quot; I feel comes from nearly no other pathway. It&#x27;s entirely too beautiful and <i>simple</i> (for certain mathematical values of &quot;simple&quot;) to escape.<p>Also the commutative diagrams are pretty much exactly the same as the chemistry ones you&#x27;re talking about. Both are just ways of writing down systems of equations that are quite hairy to write out &quot;long form&quot;.