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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== | ||
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</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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=== Parenthesis nesting level === | === Parenthesis nesting level === | ||
{{quote | "Ken was showing some slides — and one of his slides had something on it that I was later to learn was an APL one-liner. And he tossed this off as an example of the expressiveness of the APL notation. I believe the one-liner was one of the standard ones for indicating the nesting level of the parentheses in an algebraic expression. But the one-liner was very short — ten characters, something like that — and having been involved with programming things like that for a long time and realizing that it took a reasonable amount of code to do, I looked at it and said, “My God, there must be something in this language.”"|[[Alan Perlis]]. ''[https://www.jsoftware.com/papers/perlis78.htm Almost Perfect Artifacts Improve only in Small Ways: APL is more French than English]'' at [[APL78]].}} | |||
What was the one-liner for the nesting level of parentheses? It would take a bit of work to figure out, because at the time of the meeting Perlis described, no APL implementation existed. Two possibilities are explained here. | |||
==== Method A ==== | |||
For this more complex computation, we can expand on the previous example's use of <source lang=apl inline>∘.=</source>. First we compare all characters to the opening and closing characters; | |||
<source lang=apl> | <source lang=apl> | ||
'()'∘.='plus(square(a),plus(square(b),times(2,plus(a,b)))' | '()'∘.='plus(square(a),plus(square(b),times(2,plus(a,b)))' | ||
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<source lang=apl> | <source lang=apl> | ||
+\-⌿'()'∘.='plus(square(a),plus(square(b),times(2,plus(a,b)))' | +\-⌿'()'∘.='plus(square(a),plus(square(b),times(2,plus(a,b)))' | ||
0 0 0 0 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 3 2 1 | |||
</source> | |||
{{Works in|all APLs}} | |||
==== 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: | |||
<source lang=apl> | |||
'ABBA'⍳'ABC' | |||
1 2 5 | |||
'()'⍳'plus(square(a),plus(square(b),times(2,plus(a,b)))' | |||
3 3 3 3 1 3 3 3 3 3 3 1 3 2 3 3 3 3 3 1 3 3 3 3 3 3 1 3 2 3 3 3 3 3 3 1 3 3 3 3 3 3 1 3 3 3 2 2 2 | |||
</source> | |||
Whenever we have a 1 the parenthesis level increases, and when we have a 2 it decreases. If we have a 3, it remains as-is. We can do this mapping by indexing into these values: | |||
<source lang=apl> | |||
1 ¯1 0['()'⍳'plus(square(a),plus(square(b),times(2,plus(a,b)))'] | |||
0 0 0 0 1 0 0 0 0 0 0 1 0 ¯1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 ¯1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 ¯1 ¯1 ¯1 | |||
</source> | |||
The running sum is what we're looking for: | |||
<source lang=apl> | |||
+\1 ¯1 0['()'⍳'plus(square(a),plus(square(b),times(2,plus(a,b)))'] | |||
0 0 0 0 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 3 2 1 | 0 0 0 0 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 3 2 1 | ||
</source> | </source> | ||
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ILIKEAPL | ILIKEAPL | ||
</source> | </source> | ||
===References=== | |||
<references/> | <references/> | ||
{{APL development}} | {{APL development}} | ||
[[Category:Examples]] |