(** Dimension reduction: transform multi-dimensional arrays to one-dimensional
    arrays, and pass original array dimensions in function calls. *)

(**
    This phase lowers multi-dimensional arrays to one-dimensional arrays. This
    transformation is done in two steps.

    In the first step, function calls and function parameter lists are modified.
    For function calls, array dimensions are passed as explicit arguments before
    the array argument itself. Naturally, function declarations need to be
    modified accordingly, adding explicit parameters for array dimensions.

    Note that we need not create new variable declarations for array
    declarations here. This is already done during the desugaring phase
    ({!Desug} explains the reason for this).

    In the second step, statements and expressions involving multi-dimensional
    array referencing are transformed such that they reference a one-dimensional
    array. Variable declarations with type [ArrayDims] are transformed into
    variables of type [Array], thus removing the dimensionality information.
    Allocation statements become one-dimensional allocations with a length that
    is the product of all array dimensions. Indexing multi-dimensional arrays is
    changed such that arrays are accessed in row-major order.

{v void foo(int[a, b, c] p) \{
    int n; int m; int k; int[n, m, k] q;  // n, m, k are added during desugaring
    n = 5;
    m = 10;
    k = 3;
    q = __allocate(n, m, k);
    q[x, y, z] = p[x, y, z];
    foo(q);
\} v}

    step 1:

{v void foo(int a, int b, int c, int[] p) \{  // Array parameter
    int n; int m; int k; int[n, m, k] q;
    n = 5;
    m = 10;
    k = 3;
    q = __allocate(n, m, k);
    q[x, y, z] = p[x, y, z];
    foo(n, m, k, q);                      // Array argument
\} v}

    step 2:

{v void foo(int[a, b, c] p) \{
    int n; int m; int k; int[] q;  // Removing dimension information
    n = 5;
    m = 10;
    k = 3;
    q = __allocate(n * m * k);                            // Allocation
    q[((x * m) + y) * k + z] = p[((x * b) + y) * c + z];  // Indexing
    foo(n, m, k, q);
\} v}

    Note that when array dimensions are constant integer values, an array index
    may be simplified to a single constant value during contant propagation.
    *)


(** Main phase function, called by {!Main}. *)
val phase : Main.phase_func