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{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic.
{{Built-in|Or|∨}} is a [[dyadic]] [[scalar function|scalar]] [[boolean function]] which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the [[wikipedia:logical disjunction|logical disjunction]] in Boolean logic. In many APLs, Or is a special case of the [[GCD]] function.


{|class=wikitable
{|class=wikitable
!<source lang=apl inline>∨</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
!<syntaxhighlight lang=apl inline>∨</syntaxhighlight>!!<syntaxhighlight lang=apl inline>0</syntaxhighlight>!!<syntaxhighlight lang=apl inline>1</syntaxhighlight>
|-
|-
!<source lang=apl inline>0</source>
!<syntaxhighlight lang=apl inline>0</syntaxhighlight>
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|<syntaxhighlight lang=apl inline>0</syntaxhighlight>||<syntaxhighlight lang=apl inline>1</syntaxhighlight>
|-
|-
!<source lang=apl inline>1</source>
!<syntaxhighlight lang=apl inline>1</syntaxhighlight>
|<source lang=apl inline>1</source>||<source lang=apl inline>1</source>
|<syntaxhighlight lang=apl inline>1</syntaxhighlight>||<syntaxhighlight lang=apl inline>1</syntaxhighlight>
|}
|}


Line 15: Line 15:
The following shows all possible combinations of inputs as a Boolean function.
The following shows all possible combinations of inputs as a Boolean function.


<source lang=apl>
<syntaxhighlight lang=apl>
       0 0 1 1 ∨ 0 1 0 1
       0 0 1 1 ∨ 0 1 0 1
0 1 1 1
0 1 1 1
</source>
</syntaxhighlight>


When combined with [[Reduce]], Or can be used to test if some value in a Boolean vector is true.
When combined with [[Reduce]], Or can be used to test if some value in a Boolean vector is true.


<source lang=apl>
<syntaxhighlight lang=apl>
       ∨/ 0 0 1 0 1
       ∨/ 0 0 1 0 1
1
1
       ∨/ 0 0 0 0 0
       ∨/ 0 0 0 0 0
0
0
</source>
</syntaxhighlight>


== Extended definition ==
== See also ==
 
* [[Add]]
Many APL implementations extend this function to non-Boolean arguments. In this case, this function behaves as '''[[wikipedia:Greatest common divisor|Greatest Common Divisor]]''' or '''GCD'''. For positive integer arguments, it is defined as the largest positive number which divides both numbers. If one of the arguments is zero, the GCD function returns the other number. While the mathematical definition of GCD does not cover non-integers, some implementations accept them as arguments, returning a value which, when dividing both arguments, gives integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when given [[complex]] numbers).
* [[Maximum]]
 
* [[Union]]
<source lang=apl>
* [[Nor]]
      ∘.∨⍨ 0,⍳10
* [[And]]
0 1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1  1
2 1 2 1 2 1 2 1 2 1  2
3 1 1 3 1 1 3 1 1 3  1
4 1 2 1 4 1 2 1 4 1  2
5 1 1 1 1 5 1 1 1 1  5
6 1 2 3 2 1 6 1 2 3  2
7 1 1 1 1 1 1 7 1 1  1
8 1 2 1 4 1 2 1 8 1  2
9 1 1 3 1 1 3 1 1 9  1
10 1 2 1 2 5 2 1 2 1 10
 
      0.6∨13÷3
0.06666666667
      0.6(13÷3)÷0.6∨13÷3
9 65
      2J2∨3J1
1J1
      2J2 3J1÷1J1
2 2J¯1
</source>{{Works in|[[Dyalog APL]]}}


== External links ==
== External links ==
Line 61: Line 40:
=== Documentation ===
=== Documentation ===


* [http://help.dyalog.com/17.1/#Language/Primitive%20Functions/Or%20Greatest%20Common%20Divisor.htm Dyalog]
* [https://help.dyalog.com/17.1/#Language/Primitive%20Functions/Or%20Greatest%20Common%20Divisor.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_420.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/d101.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plusdot#dyadic NuVoc]
* J [https://www.jsoftware.com/help/dictionary/d101.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/plusdot#dyadic NuVoc]
* [https://mlochbaum.github.io/BQN/doc/logic.html BQN]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]

Latest revision as of 22:25, 10 September 2022

∨

Or (∨) is a dyadic scalar boolean function which tests if at least one of the two arguments is true: it returns 1 if at least one side is 1 and 0 if both are 0. It represents the logical disjunction in Boolean logic. In many APLs, Or is a special case of the GCD function.

∨ 0 1
0 0 1
1 1 1

Examples

The following shows all possible combinations of inputs as a Boolean function. 

      0 0 1 1 ∨ 0 1 0 1
0 1 1 1

When combined with Reduce, Or can be used to test if some value in a Boolean vector is true. 

      ∨/ 0 0 1 0 1
1
      ∨/ 0 0 0 0 0
0

See also

External links

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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