Definition:Collation

Definition
A collation is a structured alignment with certain placeholders that underpins the construction of formal languages.

These placeholders may be replaced by elements of an alphabet $\mathcal A$ under consideration.

A collation in $\mathcal A$ is one where all placeholders are replaced by symbols from $\mathcal A$.

For example, if we take $\square$ to denote a placeholder, then $\square\square\square\square\square$ represents the collation "a word of length $5$".

We can see that then the word "sheep" is an instance of the collation "a word of length $5$" in the English alphabet, as is "axiom".

Typical examples of collations encountered in mathematics are words or structured graphics like labeled trees.

Examples
The concept of collation being a very fundamental and abstract one, it is helpful to discuss some examples.


 * Any word in natural language is a collation in the standard alphabet;
 * Any number is a collation in the alphabet of digits;
 * Any sentence is a collation in the alphabet of all words;
 * Any sentence is a collation in the alphabet of letters and punctuation marks;
 * Any movie is a collation in the alphabet of stills;
 * Any Lego construction is a collation in the alphabet of Lego bricks;
 * Any labeled tree is a collation.

We see that unique readability is typically ensured by:


 * Position on the paper (or any other 2D carrier);
 * Position in time;
 * Position in the real world (or any other 3D environment).