Arrays are Pointers?

Let's get the important stuff out of the way first: arrays are not pointers. Array types and pointer types are completely different things and are treated differently by the compiler.

Where the confusion arises is from how C treats array expressions. N1570:

6.3.2.1 Lvalues, arrays, and function designators

...
3 Except when it is the operand of the sizeof operator, the _Alignof operator, or the unary & operator, or is a string literal used to initialize an array, an expression that has type ‘‘array of type’’ is converted to an expression with type ‘‘pointer to type’’ that points to the initial element of the array object and is not an lvalue. If the array object has register storage class, the behavior is undefined.

Let's look at the following declarations:

int arr[10] = {0,1,2,3,4,5,6,7,8,9};
int *parr = arr;

arr is a 10-element array of int; it refers to a contiguous block of memory large enough to store 10 int values. The expression arr in the second declaration is of array type, but since it is not the operand of & or sizeof and it isn't a string literal, the type of the expression becomes "pointer to int", and the value is the address of the first element, or &arr[0].

parr is a pointer to int; it refers to a block of memory large enough to hold the address of a single int object. It is initialized to point to the first element in arr as explained above.

Here's a hypothetical memory map showing the relationship between the two (assuming 16-bit ints and 32-bit addresses):

Object           Address         0x00  0x01  0x02  0x03
------           -------         ----------------------
   arr           0x10008000      0x00  0x00  0x00  0x01
                 0x10008004      0x00  0x02  0x00  0x03
                 0x10008008      0x00  0x04  0x00  0x05
                 0x1000800c      0x00  0x06  0x00  0x07
                 0x10008010      0x00  0x08  0x00  0x09
  parr           0x10008014      0x10  0x00  0x80  0x00

The types matter for things like sizeof and &; sizeof arr == 10 * sizeof (int), which in this case is 20, whereas sizeof parr == sizeof (int *), which in this case is 4. Similarly, the type of the expression &arr is int (*)[10], or a pointer to a 10-element array of int, whereas the type of &parr is int **, or pointer to pointer to int.

Note that the expressions arr and &arr will yield the same value (the address of the first element in arr), but the types of the expressions are different (int * and int (*)[10], respectively). This makes a difference when using pointer arithmetic. For example, given:

int arr[10] = {0,1,2,3,4,5,6,7,8,9};
int *p = arr;
int (*ap)[10] = &arr;

printf("before: arr = %p, p = %p, ap = %p\n", (void *) arr, (void *) p, (void *) ap);
p++;
ap++;
printf("after: arr = %p, p = %p, ap = %p\n", (void *) arr, (void *) p, (void *) ap);

the "before" line should print the same values for all three expressions (in our hypothetical map, 0x10008000). The "after" line should show three different values: 0x10008000, 0x10008002 (base plus sizeof (int)), and 0x10008014 (base plus sizeof (int [10])).

Now let's go back to the second paragraph above: array expressions are converted to pointer types in most circumstances. Let's look at the subscript expression arr[i]. Since the expression arr is not appearing as an operand of either sizeof or &, and since it is not a string literal being used to initialize another array, its type is converted from "10-element array of int" to "pointer to int", and the subscript operation is being applied to this pointer value. Indeed, when you look at the C language definition, you see the following language:

6.5.2.1 Array subscripting
...
2 A postfix expression followed by an expression in square brackets [] is a subscripted designation of an element of an array object. The definition of the subscript operator [] is that E1[E2] is identical to (*((E1)+(E2))). Because of the conversion rules that apply to the binary + operator, if E1 is an array object (equivalently, a pointer to the initial element of an array object) and E2 is an integer, E1[E2] designates the E2-th element of E1 (counting from zero).

In practical terms, this means you can apply the subscript operator to a pointer object as though it were an array. This is why code like

int foo(int *p, size_t size)
{
  int sum = 0;
  int i;
  for (i = 0; i < size; i++)
  {
    sum += p[i];
  }
  return sum;
}

int main(void)
{
  int arr[10] = {0,1,2,3,4,5,6,7,8,9};
  int result = foo(arr, sizeof arr / sizeof arr[0]);
  ...
}

works the way it does. main is dealing with an array of int, whereas foo is dealing with a pointer to int, yet both are able to use the subscript operator as though they were both dealing with an array type.

It also means array subscripting is commutative: assuming a is an array expression and i is an integer expression, a[i] and i[a] are both valid expressions, and both will yield the same value.

Don't know about C++. For C, the c-faq answers much better than I ever could.

Small snippet from c-faq:

6.3 So what is meant by the ``equivalence of pointers and arrays'' in C?

[...]

Specifically, the cornerstone of the equivalence is this key definition:

A reference to an object of type array-of-T which appears in an expression decays (with three exceptions) into a pointer to its first element; the type of the resultant pointer is pointer-to-T.

[...]

In C++ according to the C++ Standard 4.2:

An lvalue or rvalue of type “array of N T” or “array of unknown bound of T” can be converted to an rvalue of type “pointer to T.” The result is a pointer to the first element of the array.