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

In the Webel recipe for pseudo classes with ADTs, an ADT-Method is specified using TagSetDelayed UpValues, an approach adapted from a reply on this forum posting by Mathematica expert Leonid Shiffrin and books on Mathematica by Roman Maeder. As explained by Leonid Shiffrin, the choice of UpValues rather than DownValues (as used by the user-contributed MTools for OO) has some advantages, including being looked up before DownValues.

For example, to directly create an ADT-Method for a class ADT$TestString::

ADT$TestString /: stringLength[pattern] := StringLength[$$];

Note the use of the special $$ for the "wrapped" value slot: We haven't seen yet how the signature pattern is used, but looking ahead, the Webel ADT-Signature here is ADT$TestString[$$_String], so the above ATD-Method can be "invoked" or "called" on an "object" using Webel i:/o: notation for Mathematica input and output cells in online code examples:

i: adt$s1 = ADT$TestString["string1"]

i: stringLength[adt$s1]
o: 7

This of course does not read like the syntax of a regular OO language. An infix operator ⊙ for it can be created as explained under:

adt$s1⊙stringLength

An ADT-Method may take additional arguments, but the signature pattern argument MUST come first. Here a convenient take method is defined:

ADT$TestString /: take[pattern,nSpec_] := StringTake[$$,nSpec];

i: take[adt$s1, 3]
o: str  

An ADT-Method can also be generated against a default of injected ADT-signature via an ADT-definer function, which is how reuse through ADT-inheritance is leveraged: