And: Difference between revisions

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m (Text replacement - "</source>" to "</syntaxhighlight>")
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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>
!<source lang=apl inline>∧</syntaxhighlight>!!<source lang=apl inline>0</syntaxhighlight>!!<source lang=apl inline>1</syntaxhighlight>
|-
|-
!<source lang=apl inline>0</source>
!<source lang=apl inline>0</syntaxhighlight>
|<source lang=apl inline>0</source>||<source lang=apl inline>0</source>
|<source lang=apl inline>0</syntaxhighlight>||<source lang=apl inline>0</syntaxhighlight>
|-
|-
!<source lang=apl inline>1</source>
!<source lang=apl inline>1</syntaxhighlight>
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|<source lang=apl inline>0</syntaxhighlight>||<source lang=apl inline>1</syntaxhighlight>
|}
|}


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       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.
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       ∧/ 1 0 0 1 1
       ∧/ 1 0 0 1 1
0
0
</source>
</syntaxhighlight>


== See also ==
== See also ==

Revision as of 21:05, 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.

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

Examples

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

<source lang=apl> 

     0 0 1 1 ∧ 0 1 0 1

0 0 0 1 </syntaxhighlight>

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

<source lang=apl> 

     ∧/ 1 1 1 1 1

1 

     ∧/ 1 0 0 1 1

0 </syntaxhighlight>

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
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
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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