I'm shocked that this is missing from clojure.core:
(defn accum [f init coll]
(loop [x init c coll]
(if (empty? c)
x
(recur (f x (first c)) (rest c)))))
user=> (accum + 0 [1 2 3])
6
user=> (accum + 0 [1 2 3 4 5])
15
This is one of the most basic, useful functions in functional
programming. :)
Here's any triangular number:
(defn tri [n] (accum + 0 (take n (iterate inc 1))))
Here's a lazy seq of them all:
(def *tris* (for [i (iterate inc 1)] (tri i)))
This, however, is more efficient (and demonstrates another case where
super-lazy-seq makes something very compact and readable):
(defn accum-map [f init coll]
(super-lazy-seq [x init c coll]
(if (seq c)
(next-item x (f x (first c)) (rest c)))))
(def *tris* (rest (accum-map + 0 (iterate inc 1))))
Notice how similar the accum-map code is to the accum code? With just
lazy-seq it would not be as clear. :)
The "rest" in the replacement def for *tris* is because accum-map
returns the init value as the first value of the sequence, i.e., it's
equivalent to making a sequence of (tri 0), (tri 1), (tri 2), and so
on.
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