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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 == | |||
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>≢ω</source>, the number elements in it. | |||
<source lang=apl> | |||
{(+⌿)÷≢ω} 3 4.5 7 21 | |||
8.875 | |||
</source> | |||
=== 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: | |||
<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> | |||
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== | ||
APL represents text as character lists (vectors), making many text operations trivial. | APL represents text as character lists (vectors), making many text operations trivial. | ||
=== Split text by delimiter === | |||
<source lang=apl inline>≠</source> gives 1 for true and 0 for false. It [[scalar function|pairs up]] a single element argument with all the elements of the other arguments: | |||
<source lang=apl> | |||
','≠'comma,delimited,text' | |||
1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 | |||
</source> | |||
<source lang=apl inline>⊢</source> returns its right argument: | |||
<source lang=apl> | |||
','⊢'comma,delimited,text' | |||
comma,delimited,text | |||
</source> | |||
<source lang=apl inline>⊆</source> returns a list of runs as indicated by runs of 1s, leaving out elements indicated by 0s: | |||
<source lang=apl> | |||
1 1 0 1 1 1⊆'Hello!' | |||
┌──┬───┐ | |||
│He│lo!│ | |||
└──┴───┘ | |||
</source> | |||
We use the comparison [[vector]] to [[partition]] the right argument: | |||
[https://tryapl.org/?a=%27%2C%27%28%u2260%u2286%u22A2%29%27comma%2Cdelimited%2Ctext%27&run Try it now!] | |||
<source lang=apl> | |||
','(≠⊆⊢)'comma,delimited,text' | |||
┌─────┬─────────┬────┐ | |||
│comma│delimited│text│ | |||
└─────┴─────────┴────┘ | |||
</source> | |||
{{Works in|[[Dyalog APL]]}} | |||
Notice of 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> | <source lang=apl> | ||
'mississippi'∊'sp' | 'mississippi'∊'sp' | ||
0 0 1 1 0 1 1 0 1 1 0 | 0 0 1 1 0 1 1 0 1 1 0 | ||
</source> | </source> | ||
< | <source lang=apl inline>⍸</source> gives us the indices where true (1): | ||
<source lang=apl> | <source lang=apl> | ||
⍸'mississippi'∊'sp' | ⍸'mississippi'∊'sp' | ||
Line 38: | Line 131: | ||
</source> | </source> | ||
{{Works in|all APLs}} | {{Works in|all APLs}} | ||
{{APL | |||
=== 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> | |||
{{APL development}} |