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Here is an APL program to calculate the average (arithmetic mean) of a list of numbers, written as a [[dfn]]: | Here is an APL program to calculate the average (arithmetic mean) of a list of numbers, written as a [[dfn]]: | ||
<source lang=apl> | <source lang=apl> | ||
{(+ | {(+⌿⍵)÷≢⍵} | ||
</source> | </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. | 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> | The <source lang=apl inline>⍵</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>⍵</source>. The divide symbol <source lang=apl inline>÷</source> has its usual meaning. | ||
The parenthesised <source lang=apl inline>+ | The parenthesised <source lang=apl inline>+⌿⍵</source> denotes the sum of all the elements of <source lang=apl inline>⍵</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>⍵</source>, so that | ||
<source lang=apl> | <source lang=apl> | ||
+⌿ 1 2 3 4 5 6 | +⌿ 1 2 3 4 5 6 | ||
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[[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 | [[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> | <source lang=apl> | ||
{ | {⍺,', ',⍵}⌿ | ||
</source> | </source> | ||
will transform a list of strings representing words into a comma-separated list: | will transform a list of strings representing words into a comma-separated list: | ||
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└────────────────────┘ | └────────────────────┘ | ||
</source> | </source> | ||
So back to our mean example. <source lang=apl inline>(+ | So back to our mean example. <source lang=apl inline>(+⌿⍵)</source> gives the sum of the list, which is then divided by <source lang=apl inline>≢⍵</source>, the number elements in it. | ||
<source lang=apl> | <source lang=apl> | ||
{(+ | {(+⌿⍵)÷≢⍵} 3 4.5 7 21 | ||
8.875 | 8.875 | ||
</source> | </source> | ||
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=== Tacit programming === | === Tacit programming === | ||
{{Main|Tacit}} | {{Main|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: | 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: | ||
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</source> | </source> | ||
This is a so called 3-train, also known as a ''fork''. It is evaluated like this: | |||
<source lang=apl> | {| | ||
|<source lang=apl>(+⌿ ÷ ≢) 3 4.5 7 21</source>|| {{←→}} ||<source lang=apl>(+⌿ 3 4.5 7 21) ÷ (≢ 3 4.5 7 21)</source> | |||
3. | |} | ||
</source> | |||
Note that <source lang=apl inline>+⌿</source> is evaluated as a single derived function. | |||
<source lang=apl> | The general scheme for monadic 3-trains is the following: | ||
{| | |||
|<source lang=apl>(f g h) ⍵</source>|| {{←→}} ||<source lang=apl>(f ⍵) g (h ⍵)</source> | |||
|} | |||
But other types of [[Tacit programming#Trains|trains]] are also possible. | |||
</source> | |||
==Text processing== | ==Text processing== | ||
| Line 94: | Line 92: | ||
</source> | </source> | ||
{{Works in|[[Dyalog APL]]}} | {{Works in|[[Dyalog APL]]}} | ||
Notice | Notice that you can read the [[tacit]] function <source lang=apl inline>≠⊆⊢</source> like an English sentence: ''The inequality partitions the right argument''. | ||
=== Indices of multiple elements === | === Indices of multiple elements === | ||
<source lang=apl inline>∊</source> gives us a mask for elements (characters) in the left argument that are members of the right argument: | <source lang=apl inline>∊</source> gives us a mask for elements (characters) in the left argument that are members of the right argument: | ||
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{{Works in|all APLs}} | {{Works in|all APLs}} | ||
==== Method B ==== | ==== Method B ==== | ||
Alternatively, we can utilise that if the [Index Of]] function <source lang=apl inline>⍳</source> doesn't find what it is looking for, it returns the next index after the last element in the the lookup array: | Alternatively, we can utilise that if the [[Index Of]] function <source lang=apl inline>⍳</source> doesn't find what it is looking for, it returns the next index after the last element in the the lookup array: | ||
<source lang=apl> | <source lang=apl> | ||
'ABBA'⍳'ABC' | 'ABBA'⍳'ABC' | ||
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<references/> | <references/> | ||
{{APL development}} | {{APL development}} | ||
[[Category:Examples]] | |||