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Doing the Y-Combinator for a single argument function such as factorial or fibonacci in Clojure is well documented: http://rosettacode.org/wiki/Y_combinator#Clojure

My question is - how do you do it for a two argument function such as this getter for example?

(Assumption here is that I want to solve this problem recursively and this non-idiomatic clojure code is there deliberately for another reason)

[non y-combinator version]

(defn get_ [n lat] (cond (empty? lat) () (= 0 (- n 1)) (first lat) true (get_ (- n 1) (rest lat)))) (get_ 3 '(a b c d e f g h i j))
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  • (= 0 (- n 1)) is really an elaborate way to say (= n 1). Why are the fourth and fifth line indented more than the third, by the way? Commented Aug 14, 2010 at 12:59
  • Is there any specific reason to make this getter 1-based? Commented Aug 14, 2010 at 13:01

2 Answers 2

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4

The number of args doesn't change anything since the args are apply'd. You just need to change the structure of get_:

 (defn get_ [f] (fn [n lat] (cond (empty? lat) () (= 1 n) (first lat) :else (f (dec n) (next lat))))) (defn Y [f] ((fn [x] (x x)) (fn [x] (f (fn [& args] (apply (x x) args)))))) 
 user=> ((Y getf) 3 '(a b c d e f g h i j)) c
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2

It'd be pretty straight forward.

Say you've got a function H:

(def H (fn [x] (fn [x y] (stuff happens))))

Then you apply the same ol' Y-Combinator: 

((Y H) 4 5)

Where 4 and 5 are arguments you want to pass to H.

The combinator is essentially "dealing with" the top-level function in H, not the one that's doing the hard work (the one with arity 2, here).

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