Is it important to understand continuations conceptually?

Here I asked:

I get the feeling that it is important to understand continuations
conceptually, and specifically not in terms of their implementation.
The TSPL book, for example, does so; and I often see it quoted word
for word in explanations of continuations.
However, the number of articles that describe continuations in terms
of the stack far outweigh explaining them conceptually.
Does describing them in terms of their implementation serve as a
disservice? Will it be an impediment later on?

Here was one reply:

Grant, you're correct in that an understanding of one particular
implementation technique for a linguistic construct causes huge and
ubiquitous misunderstandings.
Procedures and procedure calls are the examples that come to mind.
Those things were explained via a stack-based implementation in the
1950s and 1960s although [&] abstract explanations in terms of 8th
grade algebra all the way to Lambda Calculus had been around for, oh,
a while. [*] As a result, procedure calls had been considered
expensive and a thing to be avoided. Steele pointed out our
misunderstanding of this issue AND YET, to this day, people don't
implement procedures and procedure calls properly and we are still
suffering from this perception. People still write huge procedures to
avoid another call, and people still want to see complete stack
traces in their debuggers for their function calls. So the sentence
labeled with [*] uses the incorrect tense. It should use "have been
and are" instead. It is one sad state of affairs. Of course, this
just refers back to the sentence with [&]: people who design and
implement programming languages do not wish to study mathematical
models of PLs, can't and won't. But they sure want credit on all
fronts. That's why the problem is pervasive.
Continuation objects in Scheme are special-purpose procedures. That
is, they are procedural representations of the 'rest of the
computation with respect to some expression evaluation.' So the story
is related but fortunately (or whatever) doesn't have as much of an
impact. Continuations aren't as useful as procedure. Yes, there are
kids out there who think that if you don't implement continuations
with fast code etc your Scheme implementation isn't worth much. But
those are just mislead.
Continuations can be implemented with at least four basic techniques
that I can remember right now. Clinger et al (a nice scientific paper
from the 80s revised in the 90s) lays out a beautiful and well-
presented comparison of such techniques. I recommend reading it. And
of course Dybvig/Hieb's lazy stack copy technique in the original
paper. Of course in SML/NJ callcc = cons. So that's that.
Continuations can be understood as all kinds of abstract beasts, with
little more knowledge than 8th grade algebra or Lambda Calculus. But
that is just an abstract form of 'how'. I have spent a good deal of
time on this question.
Finally, continuations can be understood from a 'pragmatic'
perspective ('what are they useful for, and how are they used'). For
this question, I recommend two books and a paper:
  -- Shriram's PLAI
  -- Friedman and Springers, "Art and Scheme"
  -- Friedman's POPL talk from 1988 on "Applications of Continuations"
Good luck -- Matthias

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