 Moschovakis (2001) objects that the intuitive notion of algorithm is not captured in full by abstract machines. Given a general recursive function f: ℕ → ℕ defined on natural numbers, there are usually many different algorithms computing it; “essential, implementation-independent properties” are not captured by abstract machines, but rather by a system of recursive equations. Consider the algorithm mergesort for sorting lists; there are many different abstract machines for mergesort, and the question arises which one is to be chosen as the mergesort algorithm. The mergesort algorithm is instead the system of recursive equations specifying the involved function, whereas abstract machines for the mergesort procedure are different implementations of the same algorithm. Two questions are put forward by Moschovakis’ formal analysis: different implementations of the same algorithm should be equivalent implementations, and yet, an equivalence relation among algorithm implementations is to be formally defined. Furthermore, it remains to be clarified what the intuitive notion of algorithm formalized by systems of recursive equations amounts to.