language agnostic - Dynamic Scoping - Deep Binding vs Shallow Binding

Question

I've been trying to get my head around shallow binding and deep binding, wikipedia doesn't do a good job of explaining it properly. Say I have the following code, what would the output be if the language uses dynamic scoping with

a) deep binding

b) shallow binding?

x: integer := 1
y: integer := 2

procedure add
  x := x + y

procedure second(P:procedure)
  x:integer := 2
  P()

procedure first
  y:integer := 3
  second(add)

----main starts here---
first()
write_integer(x)

Answer 1

Deep binding binds the environment at the time the procedure is passed as an argument

Shallow binding binds the environment at the time the procedure is actually called

So for dynamic scoping with deep binding when add is passed into a second the environment is x = 1, y = 3 and the x is the global x so it writes 4 into the global x, which is the one picked up by the write_integer.

Shallow binding just traverses up until it finds the nearest variable that corresponds to the name so the answer would be 1.