Index: doc/theses/mike_brooks_MMath/array.tex
===================================================================
--- doc/theses/mike_brooks_MMath/array.tex	(revision 80e83b6c70ab292c8a3da65fc7273607cea987b3)
+++ doc/theses/mike_brooks_MMath/array.tex	(revision 4904b0516ef6e24899be795ccffb6835533284bc)
@@ -1782,5 +1782,5 @@
 m@[0][1]@ = 3;   // subscript
 \end{cfa}
-The alternative \CFA syntax is a comma separated list.
+The alternative \CFA syntax is a comma separated list:
 \begin{cfa}
 int m@[2, 3]@;   // dimension
@@ -1788,13 +1788,13 @@
 \end{cfa}
 which should be intuitive to C programmers and is used in mathematics $M_{i,j}$ and other programing languages, \eg PL/I, Fortran.
-With respect to the dimension expressions, C only allows an assignment expression.
+With respect to the dimension expressions, C only allows an assignment expression, not a comma expression.
 \begin{cfa}
 	a[i, j];
 test.c:3:16: error: expected ']' before ',' token
 \end{cfa}
-However, there is an ambiguity for a single dimension array, where the syntax for old and new arrays are the same.
+However, there is an ambiguity for a single dimension array, where the syntax for old and new arrays are the same, @int ar[10]@.
 The solution is to use a terminating comma to denote a \CFA-style single-dimension array.
 \begin{cfa}
-int m[2$\Huge\color{red},$];  // single dimension
+int ar[2$\Huge\color{red},$];  // single dimension new array
 \end{cfa}
 This syntactic form is also used for the (rare) singleton tuple @[y@{\Large\color{red},}@]@.
@@ -1804,8 +1804,9 @@
 With respect to the subscript expression, the comma expression is allowed.
 However, a comma expression in this context is rare, and is most commonly a (silent) mistake: subscripting a matrix with @m[i, j]@ instead of @m[i][j]@ selects the @j@th row not the @i, j@ element.
-Finally, it is possible to write @m[(i, j)]@ in the new syntax to achieve the equivalent of the old @m[i, j]@.
+It is still possible to write @m[(i, j)]@ in the new syntax to achieve the equivalent of the old @m[i, j]@.
+Internally, the compiler must de-sugar @[i, j, k]@ into @[i][j][k]@ to match with three calls to subscript operators.
 Note, there is no ambiguity for subscripting a single dimensional array, as the subscript operator selects the correct form from the array type.
-Currently, @array@ supports the old amd new subscript syntax \see{\VRef{f:ovhd-treat-src}}, including combinations of new and old, @arr[1, 2][3]@.
-Finally, the new syntax is trivially lowered to C-style dimension and subscripting.
+Currently, @array@ supports the old and new subscript syntax \see{\VRef[Figure]{f:ovhd-treat-src}}, including combinations of new and old, @arr[1, 2][3]@.
+The new subscript syntax can be extended to C arrays for uniformity, but requires the non-compatible removal of the (rare) comma-expression as a subscript.