Set on symbol with OwnValues skips UpValues

Question

Can anyone provide insight on what's going on here?

First I define a new Set behavior for a symbol:

mySym /: Set[mySym[f_], v_] := v

mySym[1] = 2

(* Out *) 2

mySym[1]

(* Out *) mySym[1]

Works great

But if we provide an alias for this symbol the UpValues never get called:

ms = mySym;

ms[1] = 2

(* Out *) 2

mySym[1]

(* Out *) 2

Even more, if we pre-Evaluate that ms we still have an issue:

Evaluate[ms][1] = 3

(* Out *) 3

mySym[1]

(* Out *) 3

Although With does the appropriate thing:

With[{m = ms},
 m[1] = 4
 ]

(* Out *) 4

mySym[1]

(* Out *) 3

What's the cause of that? It's single-handedly nixed an OO implementation I was working on.

Answer 1

But if we provide an alias for this symbol the UpValues never get called:

Set is HoldFirst. That means that its first argument does not get evaluated before it is passed to Set. ms[1] = 2 never gets transformed to mySym[1] = 2.

It is true that internally Set will examine its first argument and will evaluate it sometimes. That is why in this case the definition mySym[1] = 2 gets created. But that happens internally within Set. The expression mySym[1] = 2, which could trigger the UpValues rule, never materializes.

Even more, if we pre-Evaluate that ms we still have an issue:

Evaluate works only at level 1 within a held expression.

Hold[Evaluate[1 + 1]]
(* Hold[2] *)

Hold[{Evaluate[1 + 1]}]
(* Hold[{Evaluate[1 + 1]}] *)

Whenever the evaluator encounters a symbol with a Hold* attribute, it will check for any Evaluate within the first level only, and act accordingly.