Mathematica: POLICY NOTES for the Webel Abstract Data Type (ADT) pseudo classes with inheritance for the Wolfram Language

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Dr Darren of Webel IT Australia makes the case for better object-orientation for Mathematica using pseudo class ADTs without losing the super-functional power of the Wolfram Language

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Webel: Programmers who can count higher than one (1) know that you don't have to choose exclusively between object-orientation (and classes) and functional programming. You can have your cake and eat it. It's not XOR!

And Dr Darren of Webel IT Australia will show exactly how! There are now some dedicated technical slide trail sections on this topic:

SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

This page collates some of the main policies behind the Webel recipe for stateless pseudo-classes using (so-called) Abstract Data Types (ADTs), which blend brilliantly with the "super functional" capabilities of the Wolfram Language for Mathematica. The entire recipe is also modelled in Systems Modeling Language v1 (SysML^®).

The Policy Note pages linked below are cross-referenced from many examples in the above slide trail, or you can access the slides from the policy notes pages.

Webel ADT recipe Policy Note pages

Mathematica: Webel ADT: The term 'Abstract Data Types (ADT)' is used informally (the Webel ADTs do not always adhere to strict definitions of ADTs). Please just think of it here as meaning a strong type or stateless "pseudo class".

Mathematica: Webel ADT pseudo classes: POLICY: The expression '$$' is reserved as the primary named parameter for the defining pattern of all ADT classes that extend the universal base 'ADT' class.

Mathematica: Webel ADT pseudo classes: The ADT⊙get method may be used to access the '$$' wrapped primary. This is intended for development and testing purposes only (not for regular use by clients) since it BREAKS ENCAPSULATION!

Mathematica: Webel ADT pseudo classes: The SysMLv1 models are supported by custom stereotypes with icons. Some of these indicate OO-similar use of ADT-Methods and departures from formal Abstract Data Type (ADT) definitions.

Mathematica: Webel ADT pseudo classes: POLICY: The Abstract Data Types (ADTs) are stateless functional (although inheritance and overrides are supported), with no caching by default (although there is nice optional caching using CreateUUID[] and Once[]).

Mathematica: Webel ADT pseudo classes: POLICY: The ADT-Methods of an ADT-Class are created as TagSetDelayed UpValues using the 'signature' of the ADT-Class and its defining 'pattern' as 1st argument

Mathematica: Webel ADT pseudo classes: POLICY: Every named concrete Abstract Data Type (ADT) has a ONE unique "signature" (which is the pattern passed to the "definer" functions). To vary a signature, define another unique ADT name.

Mathematica: Webel ADT pseudo classes: DEFINITION/CONVENTION: Functions that populate ADTs with reusable ADT-method UpValues are called 'definers' and include '$def' in the name after a Package scope indicator: Example: adt$def$ADT, my$def$MY$CleverList

Mathematica: Webel ADT pseudo classes: POLICY: Definer functions MUST return the self-declared or injected 'pattern' that determines the unique "ADT-signature" of the defined ADT class.

Mathematica: Webel ADT pseudo classes: There is an 'ADT' universal base that has no supers. It "blesses" every other sub-class ADT by populating it with some common ADT-Method UpValues against a signature pattern via the 'adt$def$All[]' definer function.

Mathematica: Webel ADT pseudo classes: NAMING CONVENTION: An UpValue that can be invoked on an ADT accepting its unique 'signature' pattern as (at least) 1st argument is called an 'ADT-Method'. They are NOT methods in the general object-oriented sense!

Mathematica: Webel ADT pseudo classes: ADTs that define membership of ADT-classes in a domain package have ADT-signature MemberInterface[$$:None] and MUST NOT populate ADT-method UpValues in their definers.

Mathematica: Webel ADT pseudo classes: POLICY: Multiple inheritance is supported via ONE (only) ADT-Class and one or more ADT-MemberInterfaces (which have no ADT-Method UpValues)

Mathematica: Webel ADT pseudo classes: A tricky POLICY & CONVENTION: Client packages MUST access the special "wrapped" primary '$$' via $ContextAliases! The recommended alias is "A`" (which stands of course for ADT).

Mathematica: Webel ADT pseudo classes: Webel ADT-Methods support Wolfram Language Options[] as TagSetDelayed UpValues (but there are some pros and cons). Webel ADT-Methods work with the Webel HelpO` class/method registry, including rich help on options.

Mathematica: Webel ADT pseudo classes: The validity of the type of a wrapped '$$' value of an EX$Val may be checked in ADT "constructors" which have type checking utility support. This strategy has been chosen over sub-types of EX$Val.

Mathematica: Webel ADT pseudo classes: An EX$Val has concise methods for testing the type of its wrapped '$$' value: isR, isI, isB, isQ, isS. These may be used in ADT "constructor" type tests.

Mathematica: Webel ADT pseudo classes: 'Q: Do I have to use these EX$Val scalar "atom" thingies and the EX$Row, EX$RowList, and EX$RowMap? Can't I just use Wolfram Language Lists and Associations?' A: Of course you can also use the basic Wolfram Language!

Mathematica: Webel ADT pseudo classes: TIP: Prefer the Decorator Pattern over multiple inheritance of ADT-Method UpValues! (But not because "inheritance is evil" per se, it isn't.) The base ADT libraries make heavy (and very useful) use in inheritance.

Mathematica: Webel ADT pseudo classes: POLICY/DEFINITION: Every "hard coded" definer or defining client of a definer has a corresponding ADT ArchetypeClass. Example ("hard coded"): The definer 'my$def$MY$SmartList' has ArchetypeClass 'MY$SmartList'.

Mathematica: Webel ADT pseudo classes: POLICY: Where an ADT-Method uses UUID-driven Once[] caching the trigger argument is a String '$uuid' which MUST have a default None and MUST be the first argument that has a default.

Mathematica: Webel ADT pseudo classes: There does not seem to be a way to register ::usage specific to a Webel ADT-Method (TagSetDelayed UpValue). The Webel libraries offer method documentation support via the HelpO` class/method registry.

Mathematica: Webel ADT pseudo classes: CONVENTION: PROVISIONAL: The infix operator for calling ADT-Methods on ADT "objects" is the CircleDot (⊙ in Notebooks). ISSUE: \[CircleDot] is NOT GOOD FOR USE IN IDEs!

Background on ADTs and strong types for Mathematica

You may wish to also read this forum posting answer by the ever helpful Mathematica expert Leonid Shiffrin, or any of the books on Mathematica by Roman Maeder

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Dr Darren of Webel IT Australia makes the case for better object-orientation for Mathematica using pseudo class ADTs without losing the super-functional power of the Wolfram Language

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If you want to navigate the entire tutorial including the additional explanatory text, click on the title link of the first slide to view the full slide page, then use the next links to move through the slides pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in the tutorial trail.

Dr Darren of Webel IT Australia makes the case for better object-orientation for Mathematica using pseudo class ADTs without losing the super-functional power of the Wolfram Language