Why does Evaluate[a[[1]]]=0 assign a value to a variable while a[[1]]=0 doesn't?

Question

I'm trying to do a small page counter with Mathematica, for leting me know about my reading progress on some books. I'm stuck on a problem:

Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6}
a[[1]] = 0
v1

With this, I'm trying to give 0 as a value to v1, but it seems that it swaps the v1 for 0 instead. I was expecting the evaluation of v1 to give me 0 as a value, but it still gives me v1, I've managed to partialy solve this with the following addition:

Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6}
Evaluate[a[[1]]] = 0
v1

When the v1 is evaluated, it gives me 0 as output, but it's not working in my program and I have no idea why this is happening.

I've also managed to perform a separate test by evaluation both:

Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6}
Evaluate[a[[1]]] = 0
v1

Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6}
a[[1]] = 0
v1

In this case, it the outputs for both v1's are v1. Why is this happening?

My program(If needed):

Clear["Global`*"]
g = 1; i = 1; l = {}; ln = {}; pi = {}; m = 1;
r1 := AppendTo[l, ToExpression["p" <> ToString[i++]]]
r2 := AppendTo[ln, n]
r3 := Clear[n]
r4 := AppendTo[pi, np] 
r5 := Clear[np]
r6 := Evaluate[l[[m]]] = 0 
r7 := m++

o1 = Button["+1", r1; r2; r3; r4; r5; r6; r7, ImageSize -> {30, 19}];
o2 = InputField[Dynamic[n], String, FieldSize -> {15, 1}];
o3 = InputField[Dynamic[np], Number, FieldSize -> {4, 1}];
o4 = {o1, o2, o3};
o5 = Style["Book", 12];
o6 = Style["Book Title", 12];
o7 = Style["# Pages", 12];
o8 = {o5, o6, o7};

Grid[{o8, o4}, Frame -> True]

t = Table[Button[ToString[x], Delete[l, {x}]], {x, 1, Length[l]}] // 
  Dynamic
l // Dynamic
ln // Dynamic
pi // Dynamic

Answer 1

It is because a[[1]] does not evaluate to v1 in the case of assignment a[[1]] = 0 because Set (=) has attribute HoldFirst:

In[1]:= Set // Attributes

Out[1]= {HoldFirst, Protected, SequenceHold}

So you just reassign the first element of the list a to 0:

In[6]:= Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6};
a[[1]] = 0;
a

Out[9]= {0, v2, v3, v4, v5, v6}

In the case of assignment Evaluate[a[[1]]] = 0 you override this attribute and assign to the variable v1 (if it is undefined).

The third piece of code in your question works as expected on my machine:

In[13]:= Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6};
Evaluate[a[[1]]] = 0;
v1

Clear["Global`*"]
a = {v1, v2, v3, v4, v5, v6};
a[[1]] = 0;
v1

Out[16]= 0

Out[20]= v1

P.S. You may be interested in this discussion: "Elegant manipulation of the variables list."

Answer 2

Please see Assigning values to a list of variable names, my answer to it, and the four linked questions in the comment below the question. There you will find a better alternative (indexed variables) and a way to work with a list of symbols should you insist.

A brief example:

assign[symbols_, idx_, val_] := symbols[[{idx}]] /. _[x_] :> (x = val)

a = Hold[v1, v2, v3, v4, v5, v6];

assign[a, 1, 0];

v1

0