Uiua

Uiua
Developer	Kai Schmidt
Released	2023
Latest release	2024 (unversioned)
Array model	flat with box-like niladic functions
Index origin	0
Function styles	stack-based tacit
Numeric types	64-bit float
Unicode support	full
File extensions	.ua
Implementation languages	Rust
Source code	GitHub
Platforms	native, in-browser
License	MIT
Website	uiua.org
Documentation	Documentation
Run online	Pad
Influenced by	Forth, BQN

Uiua is a stack-based array language designed by Kai Schmidt using glyphs inspired mainly by BQN.

Overview

Uiua uses concatenative evaluation (a context-free grammar) with a right-to-left ordering as in Polish notation. The language supports tacit programming using stack manipulation primitives, and all complex functions must be defined this way as there is no explicit function form that allows local variables. Functions have a fixed number of input and output values, meaning the overloading of ambivalent functions is removed. Because of this, Uiua often splits APL primitives into two functions. Its primitives use Unicode glyphs including many not found in other languages. To avoid the need for a keyboard layout containing these, each primitive can also be spelled using a name that consists of lowercase letters (user-defined names must have at least one uppercase letter). By default, the language formats source files when run to convert these names into the corresponding glyphs.

Like the SHARP APL family, arrays are flat with a homogeneous type; however, functions in Uiua are first-class values, and instead of boxes, niladic constant-valued functions are used to provide array nesting.

Uiua was featured on Array Cast in 2023.

Primitives

Function

In the web version of Uiua, we can type in the name of the function or a part of it and when run, the interpreter will format the name to Unicode Symbol, so that we don't need use of non-ASCII keyboards. All table below are base on the Uiua 0.8.0 Version.

Stack

Work with the stack

Table of Stack function in Uiua

Glyph	Name	Type	Definition
.	Duplicate	Monadic 2-output function	Duplicate the top value on the stack
,	Over	Dyadic 3-output function	Duplicate the second-to-top value to the top of the stack
:	Flip	Dyadic 2-output function	Swap the top two values on the stack
◌(;)	Pop	Monadic 0-output function	Discard the top stack value
?	Stack	Noadic 0-output function	Debug print all stack values without popping them
⸮	Trace	Monadic function	Debug print the top value on the stack without popping it

Constants

Push a constant value onto the stack

Table of Constants in Uiua

Glyph	Name	Definition
η	Eta	The number of radians in a quarter circle
π	Pi	The ratio of a circle's circumference to its diameter
τ	Tau	The ratio of a circle's circumference to its radius
∞	Infinity	The biggest number

Monadic Pervasive

Operate on every element in an array

Table of Monadic Pervasive in Uiua

Glyph	Name	Definition
¬	Not	Logical not
±	Sign	Numerical sign (1, ¯1, or 0)
¯	Negate	Negate a number
⌵	Absolute value	Get the absolute value of a number
√	Sqrt	Take the square root of a number
○	Sine	Get the sine of a number
⌊	Floor	Round to the nearest integer towards ¯∞
⌈	Ceiling	Round to the nearest integer towards ∞
⁅	Round	Round to the nearest integer

Dyadic Pervasive

Operate on every pair of elements in two arrays (Note that True is 1 and False is 0)

Table of Monadic Pervasive in Uiua

Glyph	Name	Definition	Formats from:
=	Equals	Compare for equality	=
≠	Not equals	Compare for inequality	!=
<	Less than	Compare for less than	<
>	Greater than	Compare for greater than	>
≤	Less or equal	Compare for less than or equal	<=
≥	Greater or equal	Compare for greater than or equal	>=
+	Add	Add values	+
-	Subtract	Subtract values	-
×	Multiply	Multiply values	*
÷	Divide	Divide values	%
◿	Modulus	Modulo values	mod
ⁿ	Power	Raise a value to a power	pow
ₙ	Logarithm	Get the based logarithm of a number	log
↧	Minimum/Logical And	Take the minimum of two arrays (Can use for logical AND.)	min
↥	Maximum/Logical Or	Take the maximum of two arrays (Can use for logical OR.)	max
∠	Atangent	Take the arctangent of two numbers	atan
ℂ	Complex	Make a complex number.The first argument is the imaginary part, and the second argument is the real part	com

Monadic Array

Operate on a single array

Table of Monadic Array in Uiua

Glyph	Name	Definition
⧻	Length	Get the number of rows in an array
△	Shape	Get the dimensions of an array
⇡	Range	Make an array of all natural numbers less than a number
⊢	First	Get the first row of an array
⇌	Reverse	Reverse the rows of an array
♭	Deshape	Make an array 1-dimensional
¤	Fix	Add a length-1 axis to an array
⋯	Bits	Encode an array as bits (LSB-first)
⍉	Transpose	Rotate the shape of an array
⍏	Rise	Get the indices into an array if it were sorted ascending
⍖	Fall	Get the indices into an array if it were sorted descending
⊚	Where	Get indices where array values are not equal to zero
⊛	Classify	Assign a unique index to each unique element in an array
◴	Deduplicate	Remove duplicate elements from an array
◰	Unique	Get a mask of first occurrences of items in an array
□	Box	Turn an array into a box. The box function is complicated, so you can look at [1] for more information

Dyadic Array

Operate on two arrays

Table of Monadic Array in Uiua

Glyph	Name	Definition
≍	Match	Check if two arrays are exactly the same
⊟	Couple	Combine two arrays as rows of a new array
⊂	Join	Append two arrays end-to-end
⊏	Select	Select multiple rows from an array

External links

• Uiua on the concatenative language wiki
• Doc for the Documentation
• Interpreter for the interpreter
• Basic to start learning Uiua