programming - How to unprotect GeneratingFunction

I'm trying to add custom downvalues for GeneratingFunction, and to do so I thought I just had to Unprotect it. However, that doesn't work:

Unprotect[GeneratingFunction]

{"GeneratingFunction"}

GeneratingFunction[2] = 3

During evaluation of In[3]:= Set::write: Tag GeneratingFunction in 
GeneratingFunction[2] is Protected. >>

 3

GeneratingFunction[2]

During evaluation of In[4]:= GeneratingFunction::argmu: GeneratingFunction
called with 1 argument; 3 or more arguments are expected. >>


GeneratingFunction[2]

I'm running Mathematica 9 64 bit on Linux. What do I need to do to really remove protection from this symbol?

Answer

GeneratingFunction by default is not a function: it is a stub which loads corresponding .mx package. You can see this with the following:

ClearAttributes[GeneratingFunction,{Protected,ReadProtected}]
OwnValues@GeneratingFunction

{HoldPattern[GeneratingFunction] :>
System`Dump`AutoLoad[Hold[GeneratingFunction], Hold[GeneratingFunction, GenerateConditions`TopLevelCode], "Discrete`GeneratingFunction`"] /; System`Dump`TestLoad}

The functions ClearAttributes and OwnValues have Hold* attributes and so the above code does not evaluate GeneratingFunction. After first evaluation it's Attributes and Options are redefined by the loaded package:

GeneratingFunction;
Attributes[GeneratingFunction]
Options[GeneratingFunction]

{Protected, ReadProtected}

{Assumptions :> $Assumptions, GenerateConditions -> False, Method -> Automatic, VerifyConvergence -> True}

I do not know why we can't see any top-level code for GeneratingFunction with Information, but Tracing its evaluation reveals a bunch of top-level functions it uses:

Trace[GeneratingFunction[1, n, x], TraceInternal -> True]

For the original discussion of this issue see this answer by Sasha (Wolfram Research) with comments under it.

Comments

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