Sortal structures are representational structures based on sorts, a concept for representational flexibility. Sorts provide a semi-constructive algebraic formalism for design representations (sortal structures) that enables these to be compared with respect to scope and coverage and that presents a uniform approach to dealing with and manipulating data constructs (sortal descriptions).

The main descriptional elements are sorts, individuals and forms. More on the terminology

• Sorts can be considered as class structures, specifying either a single data type or a composition of other class structures. For instance, data types such as points, labels, and lines all define sorts.
• Individuals are the basic elements of a sort, that is, these are the instances of the class structure. For example, a point is an individual of the sort of points.
• A form is a collection of individuals of the same sort, e.g., a set of points.

The characteristic individual of a primitive sort defines its representational aspect, specifically, the representation of its individuals' data values and behavioral methods. It is specified in its class implementation.
Examples of characteristic individuals

Each characteristic individual is assigned a behavioral category that specifies the operational behavior of forms of corresponding individuals, that is, their behavior under common arithmetic operations, their canonical form, and when a form is part of another form. Examples of behavioral categories

In addition, each characteristic individual is assigned a matching mechanism that governs how one form can be found to match another form even if the former is not a part of the latter, in support of emergence and sortal grammars. Examples of matching mechanisms

The Sortal Description Language (SDL) is an interpretive language for describing sortal representational structures and data constructs. It can be used to store and exchange sortal structures and descriptions.
More on the Sortal Description Language

Last update: 2 December 2019, webmaster @ sortal.org