Turning Off Error messages locally

Question

I'm trying to turn Off an error in an expression.

myFunction[x_] = 1/x
myFunction2[x_] = Quiet[1/x]  (*1/x*)
myFunction[0]
myFunction2[0]

I do not want to use :=, I also do not want to Globally turn Off this error. I want it using = such that it looks like:

myFunction3[x_] = TurnedOffError[1/x]  (*TurnedOffError[1/x]*)
myFunction3[0]

Answer 1

This is not an attempt to answer the question exactly as posed, because generally speaking I don't consider it a good idea to subvert Mathematica's evaluation process (e.g. by reaching up the stack and rewriting definitions based on their RHS before they evaluate) just to satisfy arbitrary syntactical preferences.

A better way, if you just want to stop Quiet from evaluating when the definition is made and before the message is actually going to be produced, is to Block it:

Block[{Quiet}, myFunction3[x_] = Quiet[1/x, Power::infy]] (* -> 1/x *)

myFunction3[0] (* -> ComplexInfinity [with no messages] *)

Something that works more similarly to what is described in the question, and still without requiring any awful hacks, is the following:

TurnedOffError /: HoldPattern[
  lhs_ = TurnedOffError[rhs_, msg : _MessageName | {___MessageName} | PatternSequence[]]
 ] := lhs = Unevaluated@Quiet[rhs, msg];

myFunction3[x_] = TurnedOffError[1/x, Power::infy] (* -> 1/x *)

myFunction3[0] (* -> ComplexInfinity [with no messages] *)

But this, of course, only works when TurnedOffError appears directly at level 1 inside Set.