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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.
* [[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
</source>{{Works in|[[Dyalog APL]]}}
 
While the mathematical definition of GCD does not cover non-integers, some implementations accept them as arguments. In this case, the return value of <source lang=apl inline>R←X∨Y</source> is chosen so that both <source lang=apl inline>X÷R</source> and <source lang=apl inline>Y÷R</source> are integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers).
 
<source lang=apl>
      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 65: 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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