Fully Typed Checked at Compile Time

Question

I am having a hard time understanding the answers to this question.

Giving the following code:

int: size, size2, j;
float: x;
array[1:30] of int: nums;

For each assignment statement below, circle can or cannot to say whether it can or cannot be fully type-checked at compile time. Assume that an array’s subscript range is considered part of its type. Assume that numeric overflow is not considered a type-error.

 A. size = size2 + 1; --> Answer: CAN
 B. x = size; --> Answer: CAN
 C. nums[j] = 33; --> Answer: CANNOT
 D. nums[3] = nums[4]; --> Answer: CAN
 E. nums[j] = nums[j+1]--> Answer: CANNOT

Now, compile time errors occur when the program is being converted into machine code where run time errors occur during a program's execution. I have also read up on the following stack overflow question regarding compile vs run time errors: Runtime vs Compile time. After researching both topics, I am still confused how the following answers were derived. Any help would be much appreciated.

Answer 1

I believe the question asks if the type checker "can"/"cannot" catch the logic error at compile time.

The type checker knows for sure A, D are valid and B is invalid (assuming no implicit conversion), so the type checker CAN determine the validity of these three statements.

However, for C and E the validity depends on the actual value of j (e.g. they are valid when j == 1 and invalid when j == 100). So the type checker CANNOT determine if C and E are valid (because "an array's subscript range is considered part of its type").

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Note that these answers are based on the assumption that the type checker is unable to determine / does not care about the value range of j. Some languages like Ada and Pascal support the "range" type, so those type checkers could in principle statically check if C (requiring j having type int range 1:30) and E (requiring j having type int range 1:29) are valid.