Question

Suppose I have the following clojure functions:

(defn a [x] (* x x))

(def b (fn [x] (* x x)))

(def c (eval (read-string "(defn d [x] (* x x))")))

Is there a way to test for the equality of the function expression – some equivalent of

(eqls a b)

returns true?

Answer 1

I agree with the above answers in regards to Clojure not having a built in ability to determine the equivalence of two functions and that it has been proven that you can not test programs functionally (also known as black box testing) to determine equality due to the halting problem (unless the input set is finite and defined).

I would like to point out that it is possible to algebraically determine the equivalence of two functions, even if they have different forms (different byte code).

The method for proving the equivalence algebraically was developed in the 1930’s by Alonzo Church and is know as beta reduction in Lambda Calculus. This method is certainly applicable to the simple forms in your question (which would also yield the same byte code) and also for more complex forms that would yield different byte codes.