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Arrays: Overview of multidimensional array RFCs (RFC 203 through RFC 207)
Maintainer: Jeremy Howard <j@howard.fm> Date: 8 Sep 2000 Last Modified: 21 Sep 2000 Mailing List: perl6-language-data@perl.org Number: 202 Version: 2 Status: Frozen
All agreed that multidimensional arrays would be a useful addition to Perl. There was general consensus on this proposed overall approach to multidimensional arrays. RFC 231 is presented as an alternative to RFCs 204 and 205, but since it provides suggested implementation of a subset of interfaces proposed in RFCs 204 and 205, they need not be mutually exclusive. This is discussed further in RFC 205.
Adding multidimensional array syntax to Perl 6 requires a large number of separate but highly connected language and internals changes. Each of these changes has its own RFC. This RFC describes how these changes fit together, and provides a 'reading guide' through the multidimensional array RFCs.
Arrays are data structures that store a series of elements all of the same type in a contiguous area of memory. The elements of an array can most simply be indexed by the count of the number of elements into the array. This style of indexing results in a one dimensional array, also called a vector. A more sophisticated approach allows indexing into a two dimensional plane of elements, where the plane is 'flattened' by laying the rows or columns end on end in order to find the correct offset into the area of memory. Two dimensional arrays are called matrices. Arrays of more than two dimensions follow the same logic, but use coordinate systems of three or more coordinates for their indexing. These arrays mirror the mathematical structures known as tensors.
Perl 5 does not strictly provide a syntax for defining arrays, since the closest equivalent in Perl 5, the list, can contain different types of element within one structure. Using a list in Perl 5 to mirror a one dimensional array leads to a loss of efficiency, because the elements of a list may be of different sizes, and can therefore not be jumped to directly.
Perl 5 does not strictly provide a syntax for indexing arrays of greater than one dimension, however the use of a list of lists (or LOL) allows an approximation, as described in perllol in the Perl 5 documentation. The LOL structure does not guarantee that sub-lists are of equal size, which, with the lack of guarantee that list elements are of equal size, results in a loss of efficiency. Furthermore, the syntax for indexing LOLs:
$scalar = $lol[$i][$j][$k];
does not allow multiple elements to be accessed in a way that takes advantage of the coordinate system (such as taking all elements that are one plane of a three dimensional array).
The multidimensional array RFCs describe a set of language and internals changes that together provide the two key foundations of arrays:
In addition, the RFCs describe syntax that allows the more rigid structure of an array to be utilised to create more efficient programs.
The following RFCs describe the proposals:
RFC 203 - Arrays: Notation for declaring and creating arrays RFC 204 - Arrays: Use list reference for multidimensional array access RFC 205 - Arrays: New operator ';' for creating array slices RFC 206 - Arrays: @#arr for getting the dimensions of an array RFC 207 - Arrays: Efficient array loops
RFC 203 describes the notation to create data structures that contain elements of the same type stored contiguously in memory. RFC 204 describes the notation to index arrays in multiple dimensions, and RFC 205 describes how to utilise the coordinate nature of indices to index multiple elements easily. These three RFCs provide the core foundation of arrays in Perl 6.
RFC 206 provides the syntax to query arrays to find their structure at runtime.
Finally, RFC 207 provides the means to operate efficiently on multidimensional arrays, bypassing Perl's more flexible but slower generic looping approaches.
The multidimensional array RFCs rely on the lazily generated list generation syntax provided by RFC 81 for creating slices, and on the reduce() builtin provided by RFC 76 for reducing arrays.
None necessary; this is a summary RFC
<perllol> in the Perl 5 documentation
Arrays in Numeric Python: starship.python.net
Arrays in Haskell: haskell.cs.yale.edu
Arrays in Perl Data Language: pdl.sourceforge.net t.html#Perl_Datatypes_and_how_PDL_exten
Arrays in Blitz++ (efficient C++ library): oonumerics.org#l26