Object-Oriented Design Patterns in Mathematica


In this blog post I would like to proclaim a recent completion of the first version of a document describing how to implement the most important (in my view) Object-Oriented Programming Designed Patterns by GoF.

Here is the link to the document in MathematicaForPrediction at GitHub:

“Implementation of Object-Oriented Programming Design Patterns in Mathematica”  , [1].

That document presents a particular style of programming in Mathematica (Wolfram Language) that allows the application of the Object-Oriented Programming (OOP) paradigm. The approach does not require the use of preliminary implementations, packages, or extra code. Using the OOP paradigm is achieved by following a specific programming style and conventions with native, fundamental programming constructs in Mathematica’s programming language.

A side product of working on this document is a Mathematica package for creating UML diagrams proclaimed in previous post, “UML diagram creation and generation”.

Below are several topics I consider most important not covered or briefly considered in that document.

Related presentation

Here is a video recording of my presentation “Object Oriented Design Patterns” at the Wolfram Technology Conference 2015. The presentation recording is also uploaded at YouTube.

Here is link to the presentation notebook : “Object-Oriented Design Patterns with Wolfram Language”.

Why use design patterns in Mathematica

For large development projects it is a good idea to use the well established, understood, and documented Design Patterns. Design Patterns help overcome limitations of programming languages, give higher level abstractions for program design, and provide design transformation guidance. Because of extensive documentation and examples, Design Patterns help knowledge transfer and communication between developers.

Because of these observations it is much better to emulate OOP in Mathematica through Design Patterns than through emulation of OOP objects. (The latter is done in all other approaches and projects I have seen.)

As it was said above the proposed method is minimalistic: native language features of Mathematica are used.

The larger context of Design Patterns

This diagram shows the large context of patterns:

VennDiagramForPatternsInGeneral-smallThe Mathematica implementations discussed in [1]  are for “Design Patterns by GoF”. One of the design patterns “Interpreter” is extended with the package FunctionalParsers.m that uses the so called “monadic programming”. (Hence the overlap of “Design Patterns by GoF” with “Functional programming patterns”.)

In order to provide a feel for the larger context in the diagram I have referenced the book “Go Rin no Sho”(“The book of five scrolls”) by Miyamoto Musashi. We can say that the book contains patterns applicable in antagonistic conflicts. It presents the patterns in abstract forms applicable to person-to-person fights, battles between armies, or other antagonistic settings. Another interesting idea in this book is that if you practice the explained strategy with a samurai sword you will become capable applying that strategy when leading an army.

Personal experiences with design patterns

I was introduced to OOP Design Patterns in the conferences ECOOP’99. At the time I was working on my Ph.D. in the field of large scale air pollution simulations.

Air pollution simulations over continents, like Europe, are grand challenge problems that encompass several scientific sub-cultures: computational fluid dynamics, computational chemistry, computational geometry, and parallel programming. I did not want to just a produce an OOP framework for addressing this problem — I wanted to produce the best OOP framework for the set of adopted methods to solve these kind of problems.

One way to design such a framework is to use Design Patterns and did so using C++. Because I wanted to bring sound arguments during my Ph.D. defense that I derived one of the best possible designs, I had to use some formal method for judging the designs made with Design Patterns. I introduced the relational algebra of the Database theory into the OOP Design Patterns, and I was able to come up with some sort of proof why the framework written is designed well. More practically this was proven by developing, running, and obtaining results with different numerical methods for the air-pollution problems.

In my Ph.D. thesis I showed how to prove that Design Patterns provide robust code construction through the theory Relational Databases, [2].

Justifying Design Patterns with the theory of Relational Databases

One of the key concepts and goals in OOP is reuse. In OOP when developing software we do not want changes in one functional part to bring domino effect changes in other parts. Design Patterns help with that. Relational Databases were developed with similar goals in mind — we want the data changes to be confined to only one relevant place. We can view OOP code as a database, the signatures of the functions being the identifiers and the function bodies being the data. If we bring that code-database into a third normal form we are going to achieve the stability in respect to changes desired in OOP. We can interpret the individual Design Patterns as bringing the code into such third normal forms for the satisfaction of different types of anticipated code changes.


[1] Anton Antonov, “Implementation of Object-Oriented Programming Design Patterns in Mathematica”, (2016), MathematicaForPrediction project at GitHub.

[2] Anton Antonov, Object-oriented framework for large scale air pollution models, 2001. Ph.D. thesis, Informatics and Mathematical Modelling, Technical University of Denmark, DTU.