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This page contains examples that show APL's strengths. The examples require minimal background and have no special dependencies. | This page contains examples that show APL's strengths. The examples require minimal background and have no special dependencies. If these examples are too simple for you, have a look at our [[advanced examples]]. | ||
== Arithmetic mean == | == Arithmetic mean == | ||
| Line 11: | Line 5: | ||
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: | ||
<source lang=apl> | <source lang=apl> | ||
{⍺,', ',⍵}⌿'cow' 'sheep' 'cat' 'dog' | |||
┌────────────────────┐ | ┌────────────────────┐ | ||
│cow, sheep, cat, dog│ | │cow, sheep, cat, dog│ | ||
└────────────────────┘ | └────────────────────┘ | ||
</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> | ||
=== Tacit programming === | === Tacit programming === | ||
{{Main|Tacit}} | |||
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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(+⌿÷≢) 3 4.5 7 21 | (+⌿÷≢) 3 4.5 7 21 | ||
8.875 | 8.875 | ||
</source> | </source> | ||
| Line 116: | Line 97: | ||
</source> | </source> | ||
{{Works in|[[Dyalog APL]], [[NARS2000]], [[dzaima/APL]]}} | {{Works in|[[Dyalog APL]], [[NARS2000]], [[dzaima/APL]]}} | ||
=== Frequency of characters in a string === | |||
The [[Outer Product]] allows for an intuitive way to compute the occurrence of characters at a given location in a string: | |||
<source lang=apl> | |||
'abcd' ∘.= 'cabbage' | |||
0 1 0 0 1 0 0 | |||
0 0 1 1 0 0 0 | |||
1 0 0 0 0 0 0 | |||
0 0 0 0 0 0 0 | |||
</source> | |||
Then it is simply a matter of performing a sum-reduce <source lang=apl inline>+/</source> to calculate the total frequency of each character:<ref name="Marshall LambaConf 2019">[[Marshall Lochbaum]] used this example as part of his talk on [[Outer Product]] at LambdaConf 2019.</ref> | |||
<source lang=apl> | |||
+/ 'abcd' ∘.= 'cabbage' | |||
2 2 1 0 | |||
</source> | |||
=== Parenthesis nesting level === | === Parenthesis nesting level === | ||
First we compare all characters to the opening and closing characters; | {{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> | </source> | ||
{{Works in|all APLs}} | {{Works in|all APLs}} | ||
{{APL | ==== 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 | |||
</source> | |||
{{Works in|all APLs}} | |||
=== Grille cypher === | |||
A [[wikipedia:grille (cryptography)|grille]] is a 500 year old method for encrypting messages. | |||
[[File:Grille.png|none|500px|frameless|The application of a grille cypher]] | |||
<p> | |||
Represent both the grid of letters and the grille as character matrices. | |||
<source lang=apl> | |||
⎕←(grid grille)←5 5∘⍴¨'VRYIALCLQIFKNEVPLARKMPLFF' '⌺⌺⌺ ⌺ ⌺⌺⌺ ⌺ ⌺ ⌺⌺⌺ ⌺⌺⌺ ⌺⌺' | |||
┌─────┬─────┐ | |||
│VRYIA│⌺⌺⌺ ⌺│ | |||
│LCLQI│ ⌺⌺⌺ │ | |||
│FKNEV│⌺ ⌺ ⌺│ | |||
│PLARK│⌺⌺ ⌺⌺│ | |||
│MPLFF│⌺ ⌺⌺│ | |||
└─────┴─────┘ | |||
</source> | |||
</p> | |||
Retrieve elements of the grid where there are spaces in the grille. | |||
<source lang=apl> | |||
grid[⍸grille=' '] | |||
ILIKEAPL | |||
</source> | |||
An alternative method using [[ravel]]. | |||
<source lang=apl> | |||
(' '=,grille)/,grid | |||
ILIKEAPL | |||
</source> | |||
===References=== | |||
<references/> | |||
{{APL development}} | |||
[[Category:Examples]] | |||