References and Data Structures

Analytica User GuideReferences and Data Structures

A reference is an indirect link to a value, an atom or an array. A variable can contain a single reference to a value, or it can contain an array of references. Variables and arrays can themselves contain references, nested to any depth. This lets you create complex data structures, such as linked lists, trees, and non-rectangular structures. Use of references is provided by two operators:

\e is the reference operation. It creates a reference to the value of expression e.
#e is the dereference operation. It obtains the value referred to by e. If e is not a reference, it issues a warning and returns Null.

An example: Variable M Definition: 100

Variable Ref_to_M Definition: \ M

The result of Ref_to_M looks like this:

You can double-click the cell containing «ref» to view the value referenced, in this case:

You can also create an array of references. Suppose:

Index K Definition: 1..5

Variable Ksquare Definition: K^2

Ksquare →

Variable Ref_to_Ksquare Definition: \ Ksquare

Ref_to_Ksquare →

If you click the «ref» cell, it opens:

You can also create an array of references from an array, for example:

Variable Ref_Ksquare_array Definition: \ [] Ksquare Ksquare →

The empty square brackets [ ] specify that the values referred to have no indexes, i.e., they are atoms. You can now click any of these cells to see what it refers to.

Clicking the third cell, for example, gives:

Managing indexes of referenced subarrays: \[i, j,...] e

More generally, you can list in the square brackets any indexes of e that you want to be indexes of each subarray referenced by the result. The other indexes of e (if any) are used as indexes for the referencing array. Thus, in the example above, since there were no indexes in square brackets, the index K was used as an index of the reference array. If instead we write:

\ [K] Ksquare →

It creates a similar result to \ Ksquare, since K is the only index of Ksquare.

To summarize:

\ e	Creates a reference to the value of expression e, whether it is an atom or an array.
\ [] e	Creates an array indexed by all indexes of e containing references to all atoms from e.
\ [i] e	Creates an array indexed by any indexes of e other than i of references to subarrays of e each indexed by i.
\ [i, j…] e	Creates an array indexed by any indexes of e other than i, j … of references to subarrays of e each indexed by i, j ….

In general, it is better to include the square brackets after the reference operator, and avoid the unadorned reference operator, as in the first row of the table. Being explicit about which indexes to include generally leads to expressions that array abstract as intended.