If you rearrange the arguments of your proposed three-argument iterate:

(defn iterate
  ...
  ([f n x]
   (if (zero? n)
     x
     (recur f (f x) (dec n))))

it supports partial application of the multiply-composed function to
different arguments more easily, which suggests redefinition as:

(defn ncomp [f n]
  (loop [g identity n n]
    (if (zero? n)
       g
       (recur (comp g f) (dec n)))))

This seems to come closer to matching what's desired from the
three-argument iterate without confusingly (as you note) overloading
"iterate": you want f applied n times to x and the stream of intermediate
values isn't really of interest.

On Mon, Nov 16, 2015 at 12:37 PM, Jason Felice <jason.m.fel...@gmail.com>
wrote:

>
> I *frequently* see:
>
> (nth (iterate foo bar) n)
>
> And:
>
> (->> (iterate foo bar)
>    (drop n)
>    first)
>
> I've also coded this in `avi` after being surprised no such thing exists:
>
> (defn n-times
>   [thing n a-fn]
>   (reduce
>     (fn [thing n]
>       (a-fn thing))
>     thing
>     (range n)))
>
> (which is kind of a bad implementation, now that I think of it):
>
> Would it be useful to file a ticket for a new arity for iterate?:
>
> (defn iterate
>   ...
>   ([f x n]
>    (if (zero? n)
>      x
>      (recur f (f x) (dec n))))
>
> There's a little bit of weirdness - this returns a single value, while the
> other arity returns a lazy sequence.  However, I think it's the correct
> name (and the original arity might  have better been named "iterations" for
> symmetry with "reduce" and "reductions").  But ah well.
>
> Thoughts?
>
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-- 
Ben Wolfson
"Human kind has used its intelligence to vary the flavour of drinks, which
may be sweet, aromatic, fermented or spirit-based. ... Family and social
life also offer numerous other occasions to consume drinks for pleasure."
[Larousse, "Drink" entry]

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