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In a [[Nested array model|nested]] APL, Equal to is pervasive, and compares all [[simple scalar]]s found in a [[nested array]]. | In a [[Nested array model|nested]] APL, Equal to is pervasive, and compares all [[simple scalar]]s found in a [[nested array]]. | ||
<source lang=apl> | <source lang=apl> | ||
⎕←n ← ((2 1)0)(1 0 3)(2 2⍴4 0) | |||
┌───────┬─────┬───┐ | ┌───────┬─────┬───┐ | ||
│┌───┬─┐│1 0 3│4 0│ | │┌───┬─┐│1 0 3│4 0│ | ||
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== Boolean function == | == Boolean function == | ||
{{Main|Boolean function}} | |||
When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments). This function is also known as xnor or the Kronecker delta. | When the arguments to Equal to are [[Boolean]], it is the [[wikipedia:Logical biconditional|Logical biconditional]] function, or the [[Not|negation]] of the [[xor]] function (which is [[Not Equal to]] restricted to Boolean arguments): | ||
{|class=wikitable | |||
!<source lang=apl inline>=</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>0</source> | |||
|<source lang=apl inline>1</source>||<source lang=apl inline>0</source> | |||
|- | |||
!<source lang=apl inline>1</source> | |||
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source> | |||
|} | |||
In the context of logic, it can be read as ''if and only if''. This function is also known as xnor or the Kronecker delta. | |||
[[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | [[Reduction]] with <source lang=apl inline>=</source> is the same as reduction with xor (<source lang=apl inline>≠</source>), but [[Not|inverted]] if the number of reduced elements is even. The left and right [[identity element]] for Boolean <source lang=apl inline>=</source> is 1. | ||
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=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Equal.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_310.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_310.htm APLX] | ||
* J [https://www.jsoftware.com/help/dictionary/d000.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/eq#dyadic NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d000.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/eq#dyadic NuVoc] | ||
{{APL built-ins}} | * [https://mlochbaum.github.io/BQN/doc/arithmetic.html#comparisons BQN] | ||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Comparison functions]] | |||