A list of operators in the For cycle

Question

I'm pretty sure that analogous questions have been asked here a zillion of times, but...

I think it is pretty straightforward from the code what I expect it to give:

oplist[] := Module[{op, list = {}, k},
   For[k = 1, k <= 3, k++,
    AppendTo[list, Function[x, x^k]];
    ];
   For[k = 4, k <= 5, k++,
    AppendTo[list, Function[x, x^k]];
    ];
   Return[list];
   ];
list = oplist[];
For[k = 1, k <= Length[list], k++,
  Print[list[[k]][a]];
 ];

Instead of a, a^2, a^3... I have a^6, a^6, a^6... I guess, it's something about pointers/links/evaluating at the moment when smth is called.

I tried replacing x^k with x^Evaluate[k], but this does not help either.

Answer 1

Attributes[Function]

{HoldAll, Protected}

That is, all arguments to Function are to be maintained in an unevaluated form. So x^k in Function[x, x^k] is not evaluated unless it is wrapped with Evaluate:

ClearAll[k, x, a, oplist]
oplist[] :=  Module[{op, list = {}, k}, 
   For[k = 1, k <= 3, k++, 
    AppendTo[list, Function[x, Evaluate[x^k]]];];
   For[k = 4, k <= 5, k++, 
    AppendTo[list, Function[x, Evaluate[x^k]]];];
   Return[list];];

list = oplist[];
For[k = 1, k <= Length[list], k++, Print[list[[k]][a]];];

Alternatively, use With[{j = k}, AppendTo[list, Function[x, x^j]]] in place of AppendTo[list, Function[x, Evaluate[x^k]]].

Answer 2

just remove k from

 Module[{op, list = {}, k}

this will get it right. no other changes in your code

oplist[] := 
Module[{op, list = {}}, 
For[k = 1, k <= 3, k++, AppendTo[list, Function[x, x^k]]];
For[k = 4, k <= 5, k++, AppendTo[list, Function[x, x^k]]];
Return[list]]
list = oplist[]
For[k = 1, k <= Length[list], k++, Print[list[[k]][a]];];