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

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This universal base class ADT is also called "the All". Example:

adt$def$ADT[
  class_Symbol,
  $usage_String,
  pattern_,
  isAllSuper:(True|False):False
] := Module[{ ...},
...
  class /: get[pattern] := $$;
  class /: head[pattern] := Head[$$];
...
  pattern
];
Every ADT sub-class 'definer' MUST directly or indirectly call adt$def$ADT, passing its pseudo ADT class name Symbol, a $usage String, its unique signature pattern, and whether it is isSuperAll (has ADT as direct super class)

Its definer can be used on-the-fly to create new ADT sub-classes:


pattern = adt$def$ADT[MY$ADT$String,
  "An ADT that carries a String",
  MY$ADT$String[$$_String],
  True
];
MY$ADT$String /: stringLength[pattern] := StringLength[$$]; 

my$adt$s = MY$ADT$String["string1"];

stringLength[my$adt$s]

7
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