How do contexts work exactly? Is there anything special about Private` or Internal` context?

Question

Suppose I begin a package:

BeginPackage["MyPackage`"];

Before running this command in a fresh kernel, the context and path were:

$ContextPath->$Context

{"System`", "Global`"} -> "Global`"

and afterward:

{"MyPackage`", "System`"} -> "MyPackage`"

Now if I were to declare a function Fun1:

Fun1::"usage" = "Fun1[]";

The context of Fun1 is obviously Context[Fun1]:

"MyPackage`"

Now if I begin a subcontext inside this context:

Begin["`Private`"];

Now my context and path are:

{"MyPackage`", "System`"} -> "MyPackage`Private`"

Now if I try to define a new function with the same name Fun1 here in the subcontext:

Fun1[arg_] := 1 + 1;

It gets defined in "MyPackage`" context whilst clearly the current context right now was "MyPackage`Private`".

If I were to use a different name say Fun2 here then it gets defined in the subcontext as expected:

Fun2[arg_] := 1 + 2;

Why is that? I am trying to understand the rules governing this. Does it mean if you are in a subcontext and there is a symbol with the same name existing in the outer context then the current context given by $Context is ignored if you define without using full context name?

MyPackage`Private`Fun1[arg_] := 1 + 3;

was the effect I was expecting. Is this rule general in terms of how deeply nested the current context is compared to where the symbol with the same name exists in the outer context?

---

I have a second question regarding BeginPackage second argument:

BeginPackage["MyPackage`",{"Package1`","Package2`"}]

is this the same as:

Needs["Package1`"];
Needs["Package2`"];
BeginPackage["MyPackage`"];

or

BeginPackage["MyPackage`"];
Needs["Package1`"];
Needs["Package2`"];

Also are there any cases where in a multipackage paclet, these can produce different results, i.e. the order in which Needs are called relative to BeginPackage matters?

Also, does these do something different?

Needs["`MyPackage`"];
BeginPackage["`MyPackage`"];

Answer 1

"BeginPackage" does 2 things. It defines a new context and it puts the new context on the ContextPath. "Begin" only defines a new context.

A new symbol is only defined if no symbol with this name is found.

Consider the following:

Remove["pack1`*"];
$ContextPath = {"System`"};

BeginPackage["pack1`"];
Print["in pack1"]
fun1[x_] = "fun1"; Print[fun1[x]];
Print["$ContextPath= ", $ContextPath];
Print["Symbols in context pack1:", Information["pack1`*"]];

Begin["`pack2`"];
Print["in pack2"];
fun1[x_] = "fun2"; Print[fun1[x]];
newVariable = 1;
Print["$ContextPath= ", $ContextPath];
Print["Symbols in context pack1`pack2:", Information["pack1`pack2`*"]];
End[]

Print["outside pack2: fun1[x]=", fun1[x]];
Print["$ContextPath= ", $ContextPath];
EndPackage[];
$ContextPath

with output:

As you can see, the second definition of "fun1" does not define a new symbol, it merely redefines the symbol in pack1. Only "newVAriable is defined in "pack1pack2"