Cardinal[arbitraryLengthBinary] is the data-format for a counting number of arbitrary size.
For the purposes of human I/O, Cardinals are represented as digit
strings (without decimal
points).
If n is a Cardinal,
Not[n]
represents
negative n. See NegativeCardinal.
If construct is a List, Set, or String,
then...
Cardinal[construct]
...returns the number of elements in
construct.
Expression[Cardinal][expr]
returns the ExpressionSize.
Type[Cardinal][(streamObject/dataType)]
returns the TypeSize.
If n is a Cardinal, then...
...returns a Sequence of Cardinals beginning with 1 and ending with n.
Cardinal[Sequence][n1, n2]
...returns the Cardinal Sequence
between n1 and n2.
If "body" is Loop's body, then...
Cardinal[Loop][body]
...is the same as Loop[body], except the
Cardinal
number of loops
is returned.
Cardinal[Expression][expr]
...evaluates expr and returns the
result followed by the bracketed sequence of cardinal
machine instructions...
result[machinInstr1, machinInstr2, ...,
machinInstrN]
See English definition of "cardinal".
Cardinal is used in counting to indicate quantity but not order.
The Set
of all Cardinalsis zero
plus all
positive integers.
The Cardinal Head
is rarely displayed since a
number's Type
is understood by its numeric
representation.
The Standard ASCII RuleList submerges the
Cardinal Head
of an expression-string composed
of just decimal Digits.
A Character sequence of Digits, unseparated by empty space, is interpreted as a Cardinal Number.
If n is a Cardinal,
its Negative value is
represented
by...
(1)
Not[n]
The above negation is sometimes called the "unary minus".
...evaluates
to Zero
(0).
Zero is the only Cardinal
that is equal to its
negation.
The Set of all Cardinals and their negation comprises the (signed) Integers.
Suppose construct is a List, Set, or String, then...
(2) Cardinal[construct]
...returns the number of elements in
construct.
See Tally.
If n is a Cardinal, then...
(3) Cardinal[Sequence][n]
...returns a Sequence of Cardinals beginning
with 1 and ending with n.
If n is negative, the Sequence begins with Not[1] and ends with Not[n].
If n1 and n2 are both Cardinals, then...
(4) Cardinal[Sequence][n1, n2]
...returns the Cardinal Sequence between n1 and n2.
(5)
Expression[Cardinal][expr]
...where expr is any valid Expression, returns the number of bytes used to store expr.
(6)
Type[Cardinal][streamObject]
...returns the number of bytes in the
current element of StreamObject,
streamObject.
Similarly, if dataType is a DataType,
Type[Cardinal][dataType]
...returns the number of bytes in the StreamObject,
dataType.
All of the `Logic` Keywords, (except Xor), progress from left to right through their arguments until a boolean value ends their reckoning. These are called the Cardinal[`Logic`word][arg1, arg2,...] elicitations.
Here is the "CardinalAnd" elicitation:
(7) Cardinal[And][arg1, arg2,...]
The above returns the position of the first False
element.
There is also the "CardinalNotAnd":
(8)
Cardinal[Not[And]][arg1, arg2,...]
The above returns the position of the first True
element.
Here is the "CardinalOr" elicitation:
(9)
Cardinal[Or][arg1,
arg2,...]
The above returns the position of the first True
element.
There is also the "CardinalNotOr":
(10)
Cardinal[Not[Or]][arg1,
arg2,...]
...returns the position where Not[Or]
first encounters a False
element.
If body is Loop's body, then...
(11) Cardinal[Loop][body]
...evaluates body in the same way that
Loop
would, but returns the Cardinal number of loops
executed.
The result of the last Loop iteration of body
is not returned.
If Noop[Loop] is encountered, it terminates the Loop and (11) returns Noop rather then a Cardinal.
If expr is any unevaluated Expression,
then...
(12)
Cardinal[Expression][expr]
...evaluates expr to its result
returning the form...
(13)
result[machinInstr1, machinInstr2, ...,
machinInstrN]
...where each machinInstr is a Cardinal
number which designates a
machine instruction.
Immediately after result, in the square
brackets, is the cardinal-coded sequence of machine instructions
(13) required to evaluate expr.
A reference for this algorithm is CONSTRUCTING INSTRUCTION TRACES from CACHE-FILTERED
ADDRESS TRACES (CITCAT).
Expression[Cardinal][expr]
is the number of bytes in expr, whereas
Cardinal[Expression][
expr]
...evaluates expr and returns the
result followed by the bracketed sequence of cardinal
machine instructions...
result[machinInstr1, machinInstr2,
..., machinInstrN]
cardinal number Math.
a A primary number used in simple counting, etc.; one answering the question, how many.. as, one, two, three, etc. A cardinal number is the symbol of abstraction of everything but mere repetition in any assemblage, that is, the elements of the assemblage for a process of counting. This consideration involves double disregard (or abstraction); first, of the character of the elements (either as like or unlike) and, second, of their order.
b The power of an aggregate of two equivalent aggregates. Cf. POWER OF AN AGGREGATE
Cardinal adj.
1. Of basic importance; underlying; hence, pre-eminent in importance; superior; chief; principal; as, cardinal principles, virtues, etc.
2. Zool. a Of or pertaining to the hinge of a bivalve shell.
b Of or pertaining to the cardo of an insect.
3. Of or pertaining to a cardinal or the cardinals.
Syn -- See RADICAL.
Cardinal n.
1. R. C. Ch. On of the ecclesiastical princes who constitute the Pope's council, or the college of cardinals, and who are appointed by the Pope. Since the time of Sixtus V, their number can never exceed 70 (6 of episcopal rank, 50 priests, 14 deacons), and the number of cardinal priests and deacons is seldom full. When the papal cair is vacant a pope is elected by the college of cardinals. See POPE. The cardinals take precedence of all dignitaries except the Pope. The principal parts of a cardinal's costume are a red cassock, a rocet, a short purple mantle, and a red hat with a small crown and broad brim, with cord ...
[From Websters1949Unabridged.]
(c) 2004-2007 by
John Van Wie Bergamini.
All rights reserved.