True is the affirmative Boolean value.
True[expr] returns True
if expr has no assigned
value, (and Not[True]
otherwise).
If set
is a
PatternSet, then
True[set]
...is the
subPatternSet of all
unchanging (unassigned) elements in
set.
False[set]
...is the subPatternSet whose elements have assigned values.
See English definition of "true".
True
is the affirmative Boolean
value.
False is
Not[True].
If expr is any
Expression, then...
(1)
True[expr]
...returns True if
expr has no assigned value, and Not[True] otherwise.
When the invocation of
"True[expr]" tests
expr, this may or may not change the
environment. When an
ElicitationForm invokes its
assignment, the environment changes according to the
ElicitationForm's assigned
procedure. This is usually what the programmer
expects.
On the other hand,
incorrectly invoking an
ElicitationForm can also change
the environment, and this is rarely the programmer's intent.
Whether an
ElicitationForm changes the
environment, (
Name assignments), or whether an
ElicitationForm
is written to
have no effect in its
environment, depends on how it
is written.
An ElicitationForm that changes the environment without being invoked violates the basic programmingideal that a rejected branch should leave no residue. For this reason, ElicitationForms that leave no after-effects are recommended. Where possible, ElicitationForms should have no environmental consequence. If expr is such an ElicitationForm, then True[expr] executes without changing the environment (aside from the fact of the Boolean result).
Names with the "
Pattern Attribute" have
the characteristic that elicitations have no effect on the
environment if they unsuccessfully invoke an
assignment.
Names with the "
Pattern Attribute"
enforce a
syntax on their argument(s).
In the following, set is a
PatternSet.
(2) True[set]
...is the
subPatternSet of all
unchanging (unassigned) elements in
set.
The above form (2) is the subPatternSet of set, matching unassigned Expressions.
Similarly,
Not[True][set]
(3) or
False[set]
...is the
subPatternSet of all
elements in set that have assigned
values (or which change when
Reckoned).
False[set] is the PatternSet whose elements have assigned values.
This means, if elis a member of (3), it has an assigned value, and Reckon[False[el]] returns True.
Both (2) and (3) are LogicalPatternSets.
It is possible for something to be assigned to itself. Thus an
Expression which is assigned to
its own
Name would return
False even though its evaluation
would not apparently change. For example...
Name[namedSelf, namedSelf]
...is an an
ElicitationForm such that True[namedSelf] returns
False.
This is true despite the fact that
Reckon[namedSelf]
would return namedSelf.
An
ElicitationForm, defined as
Name[expr, True] would behave as follows:
Reckon[expr] returns True.
True[expr] returns False.
trueadj.
1. Steady in adhering to friends, promises, allegiance, or the like; failthful; loyal; not false, or perfidious; as, a true friend, charge, etc.; true to his word.
2. Honest; just; upright; as, a true man. Archaic.
3. To be relied upon; certain; as, a true indication.
4. Conformable to fact; in accordance with the actual state of things; correct; not false, erroneous, inaccurate, or the like; as, a true relation or narration; a true history; a declaration is true when it states the facts; --often used elliptically for it is true, truly, doubtless.
5. Constant in telling the truth; truthful; veracious.
Dare to be true; nothing can need a lie. Herbert.
6. Sincere; unfeigning; void of deceit; as, true love.
7. Properly so called; ideally or typically such; not counterfeit or adulterated; genuine; as, true balsam; a true Christian; true justice.
True piety is cheerful as the day. Cowper.
8. Right; proper; such as it should be; as, presented in their true order and bearings.
9. Legitimate; rightful; as the true owner.
10. Placed, fitted, or formed, accurately; as, the corner of the square is not true.
11. Conformable to a standard, rule, or pattern; exact; accurate; correct; as, a true copy; a true likeness of the original; a gallop is called true when the horse gallops on the right foot when turning to the right, on the left foot in turning to the left.
Making his eye, foot, and hand keep true time. Scott.
12. Conformable to nature or reality; as, true stories.
13. Constant in direction; steady; -- of winds.
14. Biol. Genuine; real; not deviating from the essential characters of a class; as, a lizard is a true reptile; a whale is a true, but not a typical mammal. Cf. TYPICAL, adj., 2.
15. Geog. & Surveying Determined with reference to the earth s axis rather thean the Magnetic Poles; as, true north; true west; a true bearing.
[For many true phrases, see the second word.]
Syn. -Steadfast, unfaltering, devoted; authentic, pure; faithful, precise; lawful; reliable, unerring. See REAL.
Mathematica also has the following related functions:
{BitAnd, BitOr, BitXor}. These functions substitute the interpretation of True/False with 1/0.
Mathematica's
True Symbol.
(c) 2004-2007 by
John Van Wie Bergamini.
All rights reserved.