Changes

==Computational representation==

==Computational representation==

The parse graphs that we've been looking at so far bring us one step closer to the pointer graphs that it takes to make these trees live in computer memory, but they are still a couple of steps too abstract to detail the concrete species of dynamic data structures that we need.  The time has come to flesh out the skeleton that we've drawn up to this point.

The parse graphs that we've been looking at so far bring us one step closer to the pointer graphs that it takes to make these maps and trees live in computer memory, but they are still a couple of steps too abstract to detail the concrete species of dynamic data structures that we need.  The time has come to flesh out the skeletons that we've drawn up to this point.

Nodes in a graph represent ''records'' in computer memory.  A record is a collection of data that can be conceived to reside at a specific ''address''.  The address of a record is analogous to a demonstrative pronoun, a word like ''this'' or ''that'', on which account programmers commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

Nodes in a graph represent ''records'' in computer memory.  A record is a collection of data that can be conceived to reside at a specific ''address''.  The address of a record is analogous to a demonstrative pronoun, on which account programmers commonly describe it as a ''pointer'' and semioticians recognize it as a type of sign called an ''index''.

At the next level of concreteness, a pointer→record data structure can be represented as follows:

At the next level of concreteness, a pointer→record data structure can be represented as follows:

<center><p><math>datum_1, datum_2, datum_3, \ldots,\!</math> and so on.</p></center>

<center><p><math>datum_1, datum_2, datum_3, \ldots,\!</math> and so on.</p></center>

What makes it possible to represent graph-theoretical structures as data structures in computer memory is the fact that an address is just another datum, and so we can have a circumstance like this:

What makes it possible to represent graph-theoretical structures as data structures in computer memory is the fact that an address is just another datum, and so we may have a state of affairs like this:

<pre>

<p>[[Image:Logical_Graph_Figure_12.jpg|center]]</p>

          | datum_1 datum_2 ... index_1 index_2 ... |       

          |                                                

</pre>

Back at the abstract level, it takes three nodes to represent the three data records, with a root node connected to two other nodes.  The ordinary bits of data are then treated as labels on the nodes:

Back at the abstract level, it takes three nodes to represent the three data records, with a root node connected to two other nodes.  The ordinary bits of data are then treated as labels on the nodes: