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Miraheze>Adám Brudzewsky No edit summary |
Miraheze>Adám Brudzewsky |
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* [[APL Wiki logo]] | * [[APL Wiki logo]] | ||
== Arithmetic mean == | |||
Here is an APL program to calculate the average (arithmetic mean) of a list of numbers, written as a [[dfn]]: | |||
<source lang=apl> | |||
{(+⌿ω)÷≢ω} | |||
</source> | |||
It is unnamed: the enclosing braces mark it as a function definition. It can be assigned a name for use later, or used anonymously in a more complex expression. | |||
The <source lang=apl inline>ω</source> refers to the argument of the function, a list (or 1-dimensional array) of numbers. The <source lang=apl inline>≢</source> denotes the [[tally]] function, which returns here the length of (number of elements in) the argument <source lang=apl inline>ω</source>. The divide symbol <source lang=apl inline>÷</source> has its usual meaning. | |||
The parenthesised <source lang=apl inline>+⌿ω</source> denotes the sum of all the elements of <source lang=apl inline>ω</source>. The <source lang=apl inline>⌿</source> operator combines with the <source lang=apl inline>+</source> function: the <source lang=apl inline>⌿</source> fixes the <source lang=apl inline>+</source> function between each element of <source lang=apl inline>ω</source>, so that | |||
<source lang=apl> | |||
+⌿ 1 2 3 4 5 6 | |||
21 | |||
</source> | |||
is the same as | |||
<source lang=apl> | |||
1+2+3+4+5+6 | |||
21 | |||
</source> | |||
=== Operators === | |||
[[Operator]]s like <source lang=apl inline>⌿</source> can be used to derive new functions not only from [[primitive function]]s like <source lang=apl inline>+</source>, but also from defined functions. For example | |||
<source lang=apl> | |||
{α,', ',ω}⌿ | |||
</source> | |||
will transform a list of strings representing words into a comma-separated list: | |||
<source lang=apl> | |||
{⍺,', ',⍵}⌿'cow' 'sheep' 'cat' 'dog' | |||
┌────────────────────┐ | |||
│cow, sheep, cat, dog│ | |||
└────────────────────┘ | |||
</source> | |||
So back to our mean example. <source lang=apl inline>(+/ω)</source> gives the sum of the list, which is then divided by <source lang=apl inline>ρω</source>, the number of its elements. | |||
<source lang=apl> | |||
{(+/ω)÷ρω} 3 4.5 7 21 | |||
8.875 | |||
</source> | |||
=== Tacit programming === | |||
In APL’s tacit definition, no braces are needed to mark the definition of a function: primitive functions just combine in a way that enables us to omit any reference to the function arguments — hence ''tacit''. Here is the same calculation written tacitly: | |||
<source lang=apl> | |||
(+⌿÷≢) 3 4.5 7 21 | |||
8.875 | |||
</source> | |||
The operator <source lang=apl inline>/</source> can also be used to modify the <source lang=apl inline>(+⌿÷≢)</source> function to produce a moving average. | |||
<source lang=apl> | |||
2 (+⌿÷≢)/ 3 4.5 7 21 | |||
3.75 5.75 14 | |||
</source> | |||
or, more verbosely | |||
<source lang=apl inline> | |||
ave ← +⌿÷≢ | |||
ave 3 4.5 7 21 | |||
8.875 | |||
mave ← ave/ | |||
2 mave 3 4.5 7 21 | |||
3.75 5.75 14 | |||
</source> | |||
==Text processing== | ==Text processing== | ||