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If an object is compared with a number or string, JavaScript attempts to return the default value for the object. An object is converted to a primitive String or Number value, using the .valueOf() or .toString() methods of the object.
The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final. If an object is both initial and terminal, it is called a zero object or null object.
Universal morphisms can also be thought more abstractly as initial or terminal objects of a comma category (see § Connection with comma categories, below). Universal properties occur almost everywhere in mathematics, and the use of the concept allows the use of general properties of universal properties for easily proving some properties that ...
Let C be a category with finite products and a terminal object 1. A list object over an object A of C is: an object L A, a morphism o A : 1 → L A, and; a morphism s A : A × L A → L A; such that for any object B of C with maps b : 1 → B and t : A × B → B, there exists a unique f : L A → B such that the following diagram commutes:
The expression objects are composed recursively into a composite/tree structure that is called abstract syntax tree (see Composite pattern). The Interpreter pattern doesn't describe how to build an abstract syntax tree. This can be done either manually by a client or automatically by a parser. See also the UML class and object diagram below.
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The idea of using an initial property is to set up the problem in terms of some auxiliary category E, so that the problem at hand corresponds to finding an initial object of E. This has an advantage that the optimization —the sense that the process finds the most efficient solution—means something rigorous and recognisable, rather like the ...
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