What ⍵ means
It stands for the value given to a function on its right.
APL is a programming language that grew out of a mathematical notation Kenneth Iverson designed around 1960. It works on whole lists and tables at once and writes most operations as single symbols, which is why its code is full of characters you won't find on an ordinary keyboard.
In a direct function (often called a dfn), the code sits between braces and ⍵ names the argument written to its right, the one to its left. In 3 {⍵} 4 the result is 7. A function with only one argument uses just ⍵: {⍵2} doubles whatever it is given.
The pair is a small joke with a logic to it: alpha and omega are the first and last letters of the Greek alphabet, so takes the left side and ⍵ the right.
How do I type ⍵ without an APL keyboard?
Use an APL input method or the Unicode code 2375.
Most APL editors and online APL sites let you press a prefix key, usually the backtick , then w. Outside them, enter the code point with your system's Unicode method (see How to type). If you see an empty box, your font lacks APL symbols; the character is still there, and an APL font such as APL385 or a broad font like DejaVu Sans Mono will show it.
Pure programming notation: precise and compact inside APL code, puzzling anywhere else.
Greek ω looks the same but is a different character; APL code using it will not run.
Part of the collection
Don't confuse it with
2
Related characters
1
Combination ideas
2Worth knowing
- Direct functions with and ⍵ came from John Scholes at Dyalog in the 1990s, decades after APL itself; the omega symbol had been in the APL character set earlier.
Questions people ask
2Can I use ⍵ instead of ω in Greek or maths?
No. Use ω . ⍵ is an APL symbol, so spellcheck, search and screen readers won't treat it as the Greek letter.
Does ⍵ mean anything outside APL?
Not as a standard symbol. Outside APL code it is usually a decorative omega or a mix-up for the Greek ω.
More like this
12
How to type or find ⍵
- Search it as
- ⍵ · right argument · dfn · alpha omega · APL symbol · U+2375 · lowercase omega · greek omega · curly w
- Shows up in
- Anything that takes text · its shape is whatever your font draws
⍵\2375 then w (⍺ is then a).Why is ⍵ a box on my screen?
fsymbols draws rare signs with its own fonts, so they show here even where your device has none. An app or website without such a font shows an empty box (□) or a question mark instead. Turn our fonts off to see each sign as your device draws it by itself: a box here means a box in your chats and documents too.
Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.