xodarap

Fearless recursion in Clojure!

Why

The JVM puts a hard limit on how deep our functions can recurse without blowing the stack:

;; Ex. 1
;; =====
(defn unsafe-factorial [n]
  (if (< n 2)
    1
    (*' n (unsafe-factorial (dec n)))))

(unsafe-factorial 5000)
;; => StackOverflowError   clojure.lang.Numbers.lt (Numbers.java:3816)

This is a very simple example, and the fn can be defined in a tail-recursive manner to avoid this issue, but we are not always this lucky! Consider:

;; Ex. 2
;; =====
(defn unsafe-ackermann [m n] 
  (cond (zero? m) (inc n)
        (zero? n) (recur (dec m) 1)
        :else (recur (dec m) (unsafe-ackermann m (dec n)))))

(unsafe-ackermann 3 10)
;; => StackOverflowError   clojure.lang.Numbers$LongOps.inc (Numbers.java:545)

Try converting the above to use tail recursion - possible, but not trivial.

... and then there are mutually-recursive functions:

;; Ex. 3
;; =====
(declare is-even?)

(defn is-odd? [n]
  (if (zero? n)
    false
    (is-even? (dec n))))

(defn is-even? [n]
  (if (zero? n)
    true
    (is-odd? (dec n))))

(is-even? 10000)
;; => StackOverflowError   clojure.lang.Numbers$LongOps.isZero (Numbers.java:443)

Clojure's recur form doesn't help us here, so we generally end up using a trampoline.

Is there a general way to recurse safely (ie without blowing up the stack) in all these cases, and without changing the structure of our code?

Usage

(use 'xodarap.core)

;; Ex. 1
;; =====
(defrec factorial [n]
  (if (< n 2)
    1
    (*' n (rec (factorial (dec n))))))

(factorial 5000)
;; => 4228577926605543522201064200233584405390...

Here, we define a safe recursive factorial fn using the defrec form. Note that the recursive call to itself is wrapped in a rec form.

;; Ex. 2
;; =====
(defrec ackermann [m n] 
  (cond (zero? m) (inc n)
        (zero? n) (recur (dec m) 1)
        :else (recur (dec m) (rec (ackermann m (dec n))))))

(ackermann 3 10)
;; => 8189 (after a long pause)

We can crack tougher nuts using the same method.

;; Ex. 3
;; =====
(letrec [(is-odd? [n]
           (if (zero? n)
             false
             (rec (is-even? (dec n)))))
         (is-even? [n]
           (if (zero? n)
             true
             (rec (is-odd? (dec n)))))]
  (is-even? 10000))
;; => true

Here we define mutually recursive functions using letrec.

;; like fn
(recfn fact [n]
  (if (< n 2)
    1
    (*' n (rec (fact (dec n))))))

Similarly, recfn is an alternative to fn.

License

Copyright © 2018 Divyansh Prakash

Distributed under the Eclipse Public License either version 1.0 or (at your option) any later version.