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== History ==
== History ==


[[A Programming Language]] negates arrays using an overbar symbol like <math>\overline{p}</math>, matching a convention sometimes used in mathematics. In [[APL\360]] the current symbol <source lang=apl inline>~</source> was chosen, also due to its use in mathematics. Mathematical usage has arguably diverged from APL in this respect, as the negation of a variable <math>p</math> is now more often written <math>\neg p</math>, using the symbol <math>¬</math>, when a prefix operator is desired.
[[A Programming Language]] negates arrays using an overbar symbol like <math>\overline{p}</math>, matching a convention sometimes used in mathematics. In [[APL\360]] the current symbol <source lang=apl inline>~</source> was chosen, also due to its use in mathematics. Mathematical usage has arguably diverged from APL in this respect, as the negation of a variable <math>p</math> is now more often written <math>\neg p</math> when a prefix operator is desired.


The arithmetic extension <source lang=apl inline>~x</source> {{←→}} <source lang=apl inline>1-x</source> was introduced to the array langauge family by [[J]]. For arguments in the interval <math>[0,1]</math> this extension may be seen as a probabilistic interpretation of negation.
The arithmetic extension <source lang=apl inline>~x</source> {{←→}} <source lang=apl inline>1-x</source> was introduced to the array langauge family by [[J]]. For arguments in the interval <math>[0,1]</math> this extension may be seen as a probabilistic interpretation of negation.

Revision as of 12:03, 21 November 2019

~

Not (~) is a primitive monadic scalar function that returns the logical negation of a Boolean argument—that is, 0 if the argument is 1 and 1 if it is 0. In some languages, such as J, it is extended so that Not x is equivalent to 1-x while in others, such as K, it is extended so that Not x is equivalent to 0=x.

Examples

      ~ 0 1 1 0 1
1 0 0 1 0

Attempting to negate a non-Boolean argument usually results in a DOMAIN ERROR. In some languages it may instead subtract the argument from one. 

      ~ 0 0.5 1
DOMAIN ERROR
      ~0 0.5 1
      ∧

Properties

Not is the only Boolean function of a single argument which depends on that argument (it is not constant) and is not trivial (the same as Identity). Not is its own Inverse.

History

A Programming Language negates arrays using an overbar symbol like , matching a convention sometimes used in mathematics. In APL\360 the current symbol ~ was chosen, also due to its use in mathematics. Mathematical usage has arguably diverged from APL in this respect, as the negation of a variable is now more often written when a prefix operator is desired.

The arithmetic extension ~x 1-x was introduced to the array langauge family by J. For arguments in the interval this extension may be seen as a probabilistic interpretation of negation.

Extensions

Extension Languages
None APL\360, APL2, APLX, SHARP APL, Dyalog APL, GNU APL, ngn/apl, dzaima/APL
1-⍵ J
0≠⍵ K

External links

Lessons

Documentation


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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