Copying one symbol into another

Question

I would like to know how can I completely copy one Symbol to another. When I say copy, a refer to UpValues, DownValues, FormatValues.. and so on.

I created this function to do that, but I don't know if it's a good practice.

SetAttributes[copy,HoldFirst];
copy[new_Symbol,org_Symbol]:=Module[{},
    ClearAll@new;
    UpValues@new=UpValues@org/.org:> new;
    DownValues@new=DownValues@org/.org:> new;
    FormatValues@new=FormatValues@org/.org:> new;
    SetAttributes[new,Attributes[org]];
]

So I can copy some symbol b into a using a~copy~b.

There is a simpler way to do that? Or this approach is ok?

---

Update

Thanks for all comments. This is the evolution of the function above:

SetAttributes[copy,HoldFirst];
new_~copy~org_:=With[{prop={Attributes,UpValues, OwnValues, DownValues, SubValues, NValues, FormatValues, Messages,Options}},
    ClearAll@new;
    Set[#@new,#@org/.HoldPattern@org:>new]&~Scan~prop;
]

Answer 1

Update It turns out that the correct way is to use ExtendedDefinition, not ExtendedFullDefinition. Please see the answer by @jkuczm for a detailed explanation.

---

This is a simplification of your solution:

Language`ExtendedFullDefinition[new] = 
 Language`ExtendedFullDefinition[old] /. HoldPattern[old] :> new

I believe Language`ExtendedFullDefinition is used in transferring definitions between the main kernel and subkernels. Also note the HoldPattern on the LHS of the rule which ensures that OwnValues will work.

---

One thing to think about is: what should happen if old refers back to itself? Should new keep referring to old, or to itself? This solution, like yours, replaces the old in the definition as well.

Answer 2

Adding to Szabolcs's answer, it's better to use ExtendedDefinition instead of ExtendedFullDefinition.

In situation in which old symbol (the one that we want to copy), depends on anotherSymbol and anotherSymbol has old symbol somewhere in it's ...Values e.g.:

ClearAll[new, old, anotherSymbol]
old = anotherSymbol
anotherSymbol[] := 2 old

Full definition of old includes definition of anotherSymbol:

Language`ExtendedFullDefinition[old]
(* Language`DefinitionList[
    old -> {
        OwnValues -> HoldPattern[old] :> anotherSymbol, SubValues -> {},
        UpValues -> {}, DownValues -> {}, NValues -> {}, FormatValues -> {},
        DefaultValues -> {}, Messages -> {}, Attributes -> {}
    },
    anotherSymbol -> {
        OwnValues -> {}, SubValues -> {}, UpValues -> {},
        DownValues -> {HoldPattern[anotherSymbol[]] :> 2 old},
        NValues -> {}, FormatValues -> {}, DefaultValues -> {},
        Messages -> {}, Attributes -> {}
    }
] *)

Assignment using ExtendedFullDefinition:

Language`ExtendedFullDefinition[new] =
    Language`ExtendedFullDefinition[old] /. HoldPattern[old] :> new
(* Language`DefinitionList[
    new -> {
        OwnValues -> HoldPattern[new] :> anotherSymbol, SubValues -> {},
        UpValues -> {}, DownValues -> {}, NValues -> {}, FormatValues -> {},
        DefaultValues -> {}, Messages -> {}, Attributes -> {}
    },
    anotherSymbol -> {
        OwnValues -> {}, SubValues -> {}, UpValues -> {},
        DownValues -> {HoldPattern[anotherSymbol[]] :> 2 new},
        NValues -> {}, FormatValues -> {}, DefaultValues -> {},
        Messages -> {}, Attributes -> {}
    }
] *)

has a side effect. As we can see above, rule HoldPattern[old] :> new changes not only possible self references of old, discussed in Szabolcs's answer, but also references to old in definition of anotherSymbol.

By evaluating above assignment we have changed definition of anotherSymbol:

?? anotherSymbol
(* Global`anotherSymbol
anotherSymbol[]:=2 new *)

Language`ExtendedDefinition, in contrast to "Full" variant, returns and assigns only definition of symbol passed to it as argument.

ClearAll[new, old, anotherSymbol]
old = anotherSymbol
anotherSymbol[] := 2 old

Language`ExtendedDefinition[old]
(* Language`DefinitionList[
    old -> {
        OwnValues -> HoldPattern[old] :> anotherSymbol, SubValues -> {},
        UpValues -> {}, DownValues -> {}, NValues -> {}, FormatValues -> {},
        DefaultValues -> {}, Messages -> {}, Attributes -> {}
    }
] *)

Assignment to ExtendedDefinition:

Language`ExtendedDefinition[new] = 
    Language`ExtendedDefinition[old] /. HoldPattern[old] :> new
(* Language`DefinitionList[
    new -> {
        OwnValues -> HoldPattern[new] :> anotherSymbol, SubValues -> {},
        UpValues -> {}, DownValues -> {}, NValues -> {}, FormatValues -> {},
        DefaultValues -> {}, Messages -> {}, Attributes -> {}
    }
] *)

is free of side effect of ExtendedFullDefinition:

?? anotherSymbol
(* Global`anotherSymbol
anotherSymbol[]:=2 old *)

and of course correctly copies definition of old to new:

?? new
(* Global`new
new=anotherSymbol *)