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One strategy is by "tracing" a function call:

https://docs.racket-lang.org/trace/


That doesn't work for mutual recursion, what is quite common in Scheme programs. Besides, tail call optimization is not only useful in recursion.


Tails calls are especially useful in languages with macros. You don't know what context you are in, you just generate the call that makes sense. If the call happens to be in tail-position, you get the benefit of it.

Moreover, you can design cooperating macros that induce and take advantage of tail-position calls.

Here's a simple example that motivates tail-calls that are not tail-recursive:

https://cs.brown.edu/~sk/Publications/Papers/Published/sk-au...


Yeah, absent automatic TCO, we have to do it all, explicitly, by hand... `recur` and `trampoline`.

recur: https://clojuredocs.org/clojure.core/recur

  > Evaluates the exprs in order, then, in parallel, rebinds the bindings of
the recursion point to the values of the exprs.

  (def factorial
    (fn [n]
      (loop [cnt n
             acc 1]
         (if (zero? cnt)
              acc
            (recur (dec cnt) (* acc cnt))
  ; in loop cnt will take the value (dec cnt)
  ; and acc will take the value (* acc cnt)
  ))))
trampoline: https://clojuredocs.org/clojure.core/trampoline

  > trampoline can be used to convert algorithms requiring mutual recursion without stack consumption.
i.e. these emulate TCO, with similar stack consumption properties (they don't implement real TCO).

(edit: formatting)


Thanks for the pointers. Trampolining is an old idea for obtaining tail-calls. It's a kind of folk-wisdom that has been rediscovered many times, as the related work here shows:

https://dl.acm.org/doi/pdf/10.1145/317636.317779

Usually the trampoline is implemented automatically by the language rather than forcing the author to confront it, though I can see why Clojure might have chosen to put the burden on the user.


Yeah, Rich's HOPL lecture covers that ground...

https://clojure.org/about/history

  > Clojure is not the product of traditional research
  > and (as may be evident) writing a paper for this setting 
  > was a different and challenging exercise.
  > I hope the paper provides some insight into why 
  > Clojure is the way it is and the process and people
  > behind its creation and development.


Ah, I didn't know there was a HOPL paper! Some day I will have time to run a course reading HOPL papers. Some day I will have the time to read HOPL papers myself (-:. Thanks for the pointer.


May I quote the first sentences from Scheme's R7RS standard that relates to this topic:

"Programming languages should be designed not by piling feature on top of feature, but by removing the weaknesses and restrictions that make additional features appear necessary. Scheme demonstrates that a very small number of rules for forming expressions, with no restrictions on how they are composed, suffice to form a practical and efficient programming language that is flexible enough to support most of the major programming paradigms in use today."


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