ANSI/AIM Code 39 for VB.NET B.5 Boolean in .NET Display Code 128 Code Set B in .NET B.5 Boolean

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B.5 Boolean using none toinclude none for web,windows code 39 Only operators defined using none none the postfix dot notation may take additional parameters, as in Rectangle.contains(Point) : Boolean. This notation is the same as that used for object navigation expressions and message-sending.

The following operator precedence rules apply, from highest to lowest, to all expressions (including those involving objects): non-alphabetic unary prefix; non-alphabetic unary postfix; alphabetic unary prefix; alphabetic unary postfix (dot notation with no parameters); infix binary multiplicative ( ,/, ); / infix binary additive (+, , , ); + other infix binary (=, <, , , etc.); = dot notation with parameters; other non-alphabetic infix ( e.g.

(), , ). , Parentheses ( ) may be used to override these rules, in the normal way. When operators of the same precedence appear unbracketed together, the left-most takes precedence.

. QR Code Features B.5 Boolean B.5.1 Literals {true, false}. B.5.2 Type specification Boolean not Boolean : Boolean Boolean none none Boolean : Boolean Boolean Boolean : Boolean Boolean Boolean : Boolean Boolean Boolean : Boolean Boolean Boolean , Boolean : Boolean Invariants: value (true p , q) = p (false p , q) = q not p = (p false , true) p q = (p q , false) p q = (p true , q) (p q) = (p q , true) (p q) = (p q , not q). We do not expect a type recta ngle specifying Boolean to appear in type diagrams; nevertheless it is useful for illustrative purposes because the type is finite and simple.. Value types There are two parts to the sp ecification: the list of operations, with their signatures, and the list of invariants. The statements in the Invariants: section give the rules which govern the meanings of the operations, using the logic defined in appendix A1. In this case we have defined all the operations in terms of the , (if-then-else) operation.

Note that an invariant , such as (true p,q) = p should, strictly speaking, be written as p,q: Boolean ((true p,q) = p). We normally omit the universal quantification over unbound variables whenever the types of these variables can be inferred from the context, as in this case. It would be perfectly correct to include the quantification for clarity, or to disambiguate ambiguous cases.

. B.6 Number B.6.1 Literals {1.0, 1.1, 123456789.

98765432 none none 1,. etc.}, that is, arbitrary-precision rational numbers specified using decimal notat none for none ion. Note that {0, 1, 2, etc.} are Integer literals, see below: Integer is a sub-type of Number, so these literals also denote Number values.

Note that Number values can also be denoted by dividing two Integer values, for example 22/7.. B.6.2 Type specification Number - Number : Number Number + Nu mber : Number Number Number : Number Number Number : Number Number / Number : Number Number < Number : Boolean Number > Number : Boolean Number Number : Boolean Number Number : Boolean Number = Number : Boolean abs Number : Number Number.min(Number) : Number Number.max(Number) : Number Invariants: value a+b = b+a a+(b+c) = (a+b)+c a-b+b = a a+(-a) = a-a a*b = b*a a*(b*c) = (a*b)*c (a/b)*b = a a*(b+c) = a*b+a*c abs n = (n<0) -n, n a a (a b) (b a) (a=b) (a b) (b c) (a c) (a b) (b a) (a b) not (b<a) (a b) (b a) (a<b) (b>a) (a b) (a.

min(b) = a) (a b) (a.max(b) = b) (a b) (a.min(b) = b) (a b) (a.

max(b) = a). may seem like circular reason none none ing to use logic to define the meaning of Boolean. Nevertheless, we have to start somewhere, and as this is not a book about logic, this is where we start..

B.8 Integer sub-ranges These invariants are sufficient to do quite a lot of reasoning about Number values..

B.7 Integer B.7.1 Literals {0,1,2,3,. etc.} : the normal integer numerals. B.7.2 Type specification Integer is a sub-type of Number. This none none means that an Integer value can be used wherever a Number value is expected. This has the following implications:.

The set of Integer values is a subset of the Number values. The Number operations are inherited or overridden by Integer. Any operation overridden by Integer agrees, in the sense that the result obtained by applying it to Integer values is the same result as obtained by applying the overridden version to Number values.

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