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


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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 0 0 1
0 0 0 1
</source>
</syntaxhighlight>


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


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


== See also ==
== See also ==
Line 43: Line 43:
* [http://microapl.com/apl_help/ch_020_020_430.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_430.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#dyadic NuVoc]
* J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#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 22:08, 10 September 2022

∧

And (∧) is a dyadic scalar boolean function which tests if both arguments are true: it returns 1 if both are 1 and 0 if one or both are 0. It represents the logical conjunction in Boolean logic. In many APLs, And is a special case of the LCM function.

∧ 0 1
0 0 0
1 0 1

Examples

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

      0 0 1 1 ∧ 0 1 0 1
0 0 0 1

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

      ∧/ 1 1 1 1 1
1
      ∧/ 1 0 0 1 1
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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