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{{Built-in|Membership|∊}}, also called '''Member Of''' or '''Member In''', is a [[dyadic]] [[primitive function]] which tests if each of the elements of the left [[argument]] appears as an element of the right argument. Membership uses the [[glyph]] Epsilon, which resembles the mathematical notation <math>\in</math>.
{{Built-in|Membership|∊}}, also called '''Member In''', '''Member Of''', or '''Element Of''', is a [[dyadic]] [[primitive function]] which tests if each of the elements of the left [[argument]] appears as an element of the right argument. Membership derives from the traditional mathematical notation <math>\in</math> (''Element of'') and therefore uses that [[glyph]] (lunate epsilon).


== Examples ==
== Examples ==
Line 5: Line 5:
Both arguments can be arrays of any [[shape]]. Each element of the left argument is tested against elements of the right argument, and the result is a [[boolean]] array having the same shape as the left argument.
Both arguments can be arrays of any [[shape]]. Each element of the left argument is tested against elements of the right argument, and the result is a [[boolean]] array having the same shape as the left argument.


<source lang=apl>
<syntaxhighlight lang=apl>
       'THIS NOUN'∊'THAT WORD'
       'THIS NOUN'∊'THAT WORD'
1 1 0 0 1 0 1 0 0
1 1 0 0 1 0 1 0 0
Line 14: Line 14:
0 0 1
0 0 1
0 0 1
0 0 1
</source>
</syntaxhighlight>


For [[nested array|nested arrays]], Membership tests for exact [[match]] between the elements.
For [[nested array|nested arrays]], Membership tests for exact [[match]] between the elements.


<source lang=apl>
<syntaxhighlight lang=apl>
       'CAT' 'DOG' 'MOUSE' ∊ 'CAT' 'FOX' 'DOG' 'LLAMA'
       'CAT' 'DOG' 'MOUSE' ∊ 'CAT' 'FOX' 'DOG' 'LLAMA'
1 1 0
1 1 0
</source>
</syntaxhighlight>


=== Leading axis model ===
=== Leading axis model ===


The behavior of Membership was changed to follow [[leading axis model]] in some implementations such as [[J]]. In this case, if the right argument is a higher-[[rank]] array, the [[cell|cells]] of the left argument with appropriate rank are compared against the [[major cell|major cells]] of the right argument.
The behavior of Membership was changed to follow [[leading axis model]] in some implementations such as [[J]] (spelled <syntaxhighlight lang=j inline>e.</syntaxhighlight>). In this case, if the right argument is a higher-[[rank]] array, the [[cell|cells]] of the left argument with appropriate rank are compared against the [[major cell|major cells]] of the right argument.


<source lang=j>
<syntaxhighlight lang=j>
       ]mat=.>'able';'acre';'idle'
       ]mat=.>'able';'acre';'idle'
able
able
Line 42: Line 42:
1 1 1
1 1 1
1 1 1
1 1 1
</source>
</syntaxhighlight>
In other dialects, a leading axis membership function can be defined as:
<syntaxhighlight lang=apl>
      Membership←{(≢⍵)≥⍵⍳⍺}
      ⎕←mat←3 4⍴'ableacreidle'
able
acre
idle
      'able' Membership mat
1
</syntaxhighlight>{{Works in|[[Dyalog APL]], [[NARS2000]], [[dzaima/APL]], [[Extended Dyalog APL]], [[GNU APL]]}}


== See also ==
* [[Equal to]]
* [[Match]]
* [[Find]]
* [[Index of]]
== External links ==
== External links ==


Line 51: Line 66:
* [http://microapl.com/apl_help/ch_020_020_380.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_380.htm APLX]
* J [https://www.jsoftware.com/help/dictionary/dedot.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/edot#dyadic NuVoc]
* J [https://www.jsoftware.com/help/dictionary/dedot.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/edot#dyadic NuVoc]
* [https://mlochbaum.github.io/BQN/doc/search.html#member-of BQN]


{{APL built-ins}}[[Category:Primitive functions]]
{{APL built-ins}}[[Category:Primitive functions]]

Latest revision as of 15:33, 11 January 2024

∊

Membership (∊), also called Member In, Member Of, or Element Of, is a dyadic primitive function which tests if each of the elements of the left argument appears as an element of the right argument. Membership derives from the traditional mathematical notation (Element of) and therefore uses that glyph (lunate epsilon).

Examples

Both arguments can be arrays of any shape. Each element of the left argument is tested against elements of the right argument, and the result is a boolean array having the same shape as the left argument. 

      'THIS NOUN'∊'THAT WORD'
1 1 0 0 1 0 1 0 0
      3 6 9∊3 3⍴⍳9
1 1 1
      (3 3⍴⍳9)∊3 6 9
0 0 1
0 0 1
0 0 1

For nested arrays, Membership tests for exact match between the elements. 

      'CAT' 'DOG' 'MOUSE' ∊ 'CAT' 'FOX' 'DOG' 'LLAMA'
1 1 0

Leading axis model

The behavior of Membership was changed to follow leading axis model in some implementations such as J (spelled e.). In this case, if the right argument is a higher-rank array, the cells of the left argument with appropriate rank are compared against the major cells of the right argument. 

      ]mat=.>'able';'acre';'idle'
able
acre
idle
      'able' e. mat
1
      (<'able') e. mat
0
      'ab' e. mat
0
      (3 3 4$'able') e. mat  NB. the resulting shape is trailing axes (corresponding to the major cells of mat) removed
1 1 1
1 1 1
1 1 1

In other dialects, a leading axis membership function can be defined as: 

      Membership←{(≢⍵)≥⍵⍳⍺}
      ⎕←mat←3 4⍴'ableacreidle'
able
acre
idle
      'able' Membership mat
1
Works in: Dyalog APL, NARS2000, dzaima/APL, Extended Dyalog APL, GNU APL

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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