Name Sample  

Substitutions  ( x^2+x/(1+x) where x=(exp(y+sin(z)) ) 
Partial Descriptions 

Enumerated types
 
Inequality  Two notations: x!=y(C), x<>y (Pascal) 
Both forms bind values to abbreviations in a small area of text only.
becomes
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then we can quote as facts.
It is convenient to allow these to be valid input into a documentation system:
A described term is always the name of a set of possibilities and so can have many descriptions. It must satisfy them all. If t::=S&... then t represents the largest subset S that is a subset of all other descriptions. A term with a definition can be quoted as a description. If declared, then a term that is described as a set of type S must be declared as type @S. TBD provides the semantics of definitions in general.
It is best to start from a specific, easily understood subset of the problem and progress to more general forms[Botting 84b]. The development of error handling is an ubiquitous example:
So is that of a compiler:
Thus given that
then we can quote the following
Again it should be possible to input a series of additional alternatives into a documentation processor, and have them, checked, appended, etc.
Formally a set of additional alternatives are combined into a single definition where the term is defined as the union of the separate alternatives.
It is incorrect to use more than one ellipsis on the same term.
These notations are conveniences. Formally they do not exist. They become a set of definitions that are created by either the intersection or union of all the descriptions.
When a term has several alternative meaning and they overlap then the first one defined takes priority??
An incomplete argument is called an enthymeme[Aristotle?]. In MATHS it is an argument with any contiguous set of steps replace by the ellipsis (...) symbol (see Chapter 5). Similarly the ellipsis can be used inside any set of documentation to hide a piece of irrelevant documentation from the reader/user. Online the three dots could react to being selected by expanding to show the details.
A third form of incompleteness occurs when part of a sequence is left out. Similar  but much more informal  is the use of the ellipsis "..." in mathematical expressions :
as in the design of bin.p above. These can only be verified if they are accompanied with a formal expression that makes clear what is meantSubstitutions
Finally, if the class of a structured object is given (C) and a tight enough condition(P) specified, then missing attributes can be predicted that make the object fit the class. Formally, suppose that C is a class with structure N and P a boolean expression containing variable of N then:
Similarly if C has identifers k and data d (C : @N(k)>(d)) then
The following syntax is a natural alternative:
(the B with L) ::= the{ x:set B  L }
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direction::={east,north, west, south).implies
direction::Sets.
east::direction.
north::direction.
west::direction.
south::direction.
 direction = {east,north, west, south).In general a defition of a new type as a set of new variables, implicitly declares the variables.
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Proofs follow a natural deduction style that start with assumptions ("Let") and continue to a consequence ("Close Let") and then discard the assumptions and deduce a conclusion. Look here [ Block Structure in logic_25_Proofs ] for more on the structure and rules.
The notation also allows you to create a new network of variables and constraints. A "Net" has a number of variables (including none) and a number of properties (including none) that connect variables. You can give them a name and then reuse them. The schema, formal system, or an elementary piece of documentation starts with "Net" and finishes "End of Net". For more, see [ notn_13_Docn_Syntax.html ] for these ways of defining and reusing pieces of logic and algebra in your documents. A quick example: a circle might be described by Net{radius:Positive Real, center:Point, area:=π*radius^2, ...}.
For a complete listing of pages in this part of my site by topic see [ home.html ]
For a more rigorous description of the standard notations see