Final answer:
The stack implementation where it grows down toward high memory addresses and the stack pointer points to the first empty space is termed a top-of-stack implementation.
Step-by-step explanation:
The type of stack implementation described in the program, where the stack grows down toward high memory addresses, and the stack pointer points to the first free empty space on the stack, is known as a top-of-stack implementation. This design is commonly used in computer architecture because it allows for easy increment and decrement operations, which are fundamental for effectively managing the call and return from subroutine operations in programming. A stack that grows in the opposite direction, towards lower memory addresses, would be a growing-up stack.