with bounds declares an array class.
The number of bounds is called the dimension of the array class. The
dimension is part of the type defined by the array class. The bounds
are transformed into readonly attribute declarations readonly
m: INT; readonly n: INT,.... These attributes are initialized
whenever a new object of the type is created by a type constructor
# 
.
In case of the predefined class ROW [asize] (T)
the attribute asize is constant and its value is part of the
type.
An array class declaration D may inherit an array class C taking over C's bounds including their names. This is indicated by supplying the symbol * in the inheritance as parameter for the index bounds to be taken over. The number of stars must match the dimension of D. The class must not inherit multiply in this way.
Every array class should define the procedures aget and aset with the appropriate number and types of parameters.
The replacements of a[i,j] by a.aget(i,j) or a.aset(i,j,v) described in 4.5 are made in any case, also if a does not belong to an array class. The correct number of indices in a[i,j] is determined by the (method) types of aget and aset respectively.
A class specifier must give values to all its bounds when it is used as a type constructor or when it is of the form ROW[asize](T). In all other cases some bounds may be replaced by stars. In case of an assignment a:= b to a variable declared by a: C[10,*] it is checked that the first bound of b has the value 10 whereas the second bound is not checked.
Hint: Since for value types v:V is equivalent to v:#V
which is short for v:V:=#V, and since an explicit size must be
given for ARR creation, a specification a:ARR[*]; is legal for
method parameters only. 
The built-in classes for handling arrays are:
: Generic value class. Objects
of type ROW[n] (T) are fixed size one dimensional arrays of
elements of type T indexed by 
. The class supplies
the procedures aset 
and aget 
as explained in 4.5 for
accessing the elements, and the constant asize giving its
length. asize must be known to the compiler and is part of the
row type, i.e., it is illegal to specify a row-type by
ROW[*](T). No class may inherit from ROW.
, ..., asize 
] : This
generic value class is defined for every dimension k > 0. It
supplies dynamic k-dimensional arrays of size
. The bounds carry
the names asize0, asize1, ... up to the dimension of the
array. It defines the procedures aget 
and aset 
.
The length is not part of the type. Whenever a type constructor
# ARR 
is evaluated then the
will be evaluated and determine the length of the array
which is then fixed. A type constructor # ARR 
for a k-dimensional array must be
followed by an aggregate consisting of unnamed expressions. The
number of these expressions determines asize . If k>1 then
the
expressions must each be aggregates for (k-1)-dimensional arrays. Otherwise
objects of an ARR-type have the same properties as rows. , ..., asize ] :
This generic reference class is defined for every dimension k > 0.
It supplies k-dimensional arrays of size
. The bounds carry
the names asize0, asize1, ... up to the dimension of the
array. It defines
the procedures aget and
aset . An aggregate for an
array consists of a list of the values of the elements of the array
or row. In case of multidimensional arrays the rows are given by
substructures.ARR[ 
and ARRAY[ are not
user-definable because it exists for any number k of
dimensions.
No class may transitiveley inherit from ARR more than once.
. String denotations "abracadabra" are
denotations for
# STR 
'a','b','r','a','c','a','d','a','b','r','a' 
. When
declaring a quantity of type STR with an initializing string
denotation then the size of the string denotation may determine the
size of the quantity. For convenience STR[*] may be abbreviated
to STR. . Otherwise it has the same properties as STR.
For convenience STRING[*] may be abbreviated to STRING.
.