expression manipulation - What are the scoping rules for function parameters shadowing System` symbols?

Here are some very contrived code snippets, highly unlikely to appear in real code, but still I am curious why they behave like this:

Function[List, {1, 2, 3}][Hold]
(* Hold[1, 2, 3] *)

Function[Function, Function[Slot[1]]][Hold]
(* Hold[#1] *)


Function[Slot, Function[Slot[1]]][Hold]
(* Hold[1] & *)

Function[Function, Function[x, 1]][Hold]
(* Function[x, 1] *) (* Why not Hold[x, 1]? *)

{Function[Null, Null][1]}
(* {Null} *) (* Why not {1}? *)

I think I understand the first 3 cases.

Could you please explain the last 2 results?

Answer

For the first puzzle, I can only guess. The idea is that Function with named variables is a true lexical scoping construct, in that it cares about the possible name collisions inside the inner scoping constructs, including another Function-s (this is where it is different from Slot- based functions, which are not like that. The price to pay is that Slot-based functions can not be non-trivially nested). This name collision analysis and variable renaming is happening before the variable binding - this is important. Another important point is that generally the renaming is excessive - it is often performed even when not strictly necessary.

So, when you enter

Function[Function, Function[x, 1]][Hold]

the following should (according to my guess) roughly happen:

• The inner scoping constructs are analyzed. The named function Function[x,1] is detected.


• The Function variable in Function[Function,...] is renamed (just in case). We end up with something like Function[$Function,Function[x,1]][Hold].



• The variable binding is performed. Effectively we have now a constant function that returns Function[x,1] regardless of the input. This happens because the renaming of Function (as a variable) to $Function happened before the binding stage, and therefore did not affect the body (Function[x,1]).


• The resulting function is called on Hold, and returns Function[x,1], as it now should.

Now, here is how you can fool the detection mechanism (just one way out of many):

Function[Function,Function@@Hold[x,1]][Hold]

(* Hold[x,1] *)

Now the inner Function is not detected as a scoping construct, renaming is not performed, then the Function as a variable is lexically bound to the Function in the body, and we get the expected result.

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The second case is simpler. Note that there is an undocumented way to enter Slot-based functions, such as:

Function[Null, body]

which is interpreted as body&. This form is needed to be able to define Slot-based pure functions with attributes, such as

Function[Null, #=1,HoldAll]

Now, in your case, your function is interpreted as Null&, so it will return Null on all inputs.