How to handle negative array index in ALGOL?

ALGOL (ALGOrithmic Language) is a high-level programming language that was specifically designed for scientific computations. One common issue when working with ALGOL is handling a negative array index.

In ALGOL, an array is an ordered collection of elements identified by their indices. But in ALGOL, like many other programming languages, arrays are zero-indexed meaning the first element of the array has an index of 0. Therefore, using a negative array index will result in an error, as it falls outside the bounds of the array.

However, there are several ways to handle these situations if the need arises:

Create a Custom Function

Step 1. The first approach is to write a custom function to handle negative indices. This function would take an array and an index as arguments.

Example:

PROCEDURE NegativeIndex (A, INDEX) IS
BEGIN
   IF INDEX < 0 THEN
      RETURN A[A'upper + 1 + INDEX]
   ELSE
      RETURN A[INDEX]
   END IF
END NegativeIndex

In this function, if the index is less than zero (which means it's negative), the function will return the element of an array as located from the end of the array by INDEX distance. If not (the index is zero or positive), it will simply return the INDEX element of the array.

Index transformation

Step 2. Another way to handle negative indices is by transforming the indices so that they fall into the valid array index range.

Example:

INDEX : =  IF INDEX < 0 THEN A'upper + 1 + INDEX ELSE INDEX;
   ARR[INDEX] : = VALUE;

In this case, similarly to the custom function, if an index is lower than 0, it transforms the negative index into a corresponding positive index counting from the end of the array, else it uses the actual index as given.

Remember these are some common ways in managing a negative array index, and you might need to adapt them to fit your exact needs. Moreover, always remember to check the limits and validity of an index before using it to access the array to avoid an index out of range error.
Overall, handling a negative array index in ALGOL, though isn’t built-in into the language but can be managed using a bit of extra code.