(a) Modern programming languages would automatically transform a non-tail-recursive func- tion to its equivalent tail-recursive implementation or loop variant which is more efficient in terms of both space and time, compared to a non-tail-recursive equivalent function. Give explanations as to how the following efficiencies are obtained: 1. space efficiency 2. time efficiency

briefly answer the following questions:
(a) Modern programming languages would automatically transform a non-tail-recursive func-
tion to its equivalent tail-recursive implementation or loop variant which is more efficient in terms
of both space and time, compared to a non-tail-recursive equivalent function. Give explanations as
to how the following efficiencies are obtained:
1. space efficiency
2. time efficiency
(b) In early implementations of FORTRAN language, a compiler may choose to use static
allocation (i.e., allocation in the static area) for local variables and parameters, effectively arranging
for the variables of different invocations to share the same locations, and thereby avoiding
any run-time overhead for creation and destruction of stack frames. However, such an implemen-
tation changes the meaning of recursive function calls.
Provide a simple example and explain how its meaning changes under the “FORTRAN” semantics
as stated above, compared with standard semantics found in languages like C, Python, and Java.