What do array subscripts mean in C?

C array subscripts can be understood via pointer arithmetic.

#include <stdio.h>
int main(void) {
  int vals[10];
  printf("%d\n", vals[3]);
  return 0;
}

What does vals[3] mean here? It means “take the pointer vals, shift it up to the fourth element in the array, and dereference that pointer”. We can write this out as *(vals + 3).

This is in fact the definition of the array subscript operator in C: a[b] means *(a+b).

The Standard says

For addition, either both operands shall have arithmetic type, or one operand shall be a pointer to an object type and the other shall have integer type. (Incrementing is equivalent to adding 1.)

Above, we are in the latter case: “one operand shall be a pointer to an object type and the other shall have integer type”. vals has type int*, and 3 has integer type.

When an expression that has integer type is added to or subtracted from a pointer, the result has the type of the pointer operand.

So the expression vals+3 has type int*.

the result points to an element offset from the original element such that the difference of the subscripts of the resulting and original array elements equals the integer expression.

That is, if we consider that vals actually points to some arr[n], then vals+3 points to arr[n+3].

Note that this definition is commutative: 3+vals also points to arr[n+3].

This has the funny consequence that a[b] is actually the same as b[a]!