Uiua
Uiua is a stack-based array language emphasizing tacit programming, designed by Kai Schmidt. Initially influenced strongly by BQN, Uiua has added original stack-based features and glyphs and moved to the boxed array model of SHARP APL and J. It also makes functions second-class rather than first-class to facilitate features that depend on the number of arguments functions take.
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, Uiua supports only flat arrays with a homogeneous type, and has a dedicated box type for array nesting. However, arithmetic is pervasive as in the nested array model. Arithmetic also follows leading axis agreement, extended so that a length-1 axis is matched with an axis of any length by replicating along it (like the broadcasting system of Julia and NumPy). It supports character arithmetic as in BQN, as well as other primitives characteristic of BQN such as structural Under, Classify, and a Transpose that rotates the axes of its argument by one.
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 based on Uiua version 0.8.0.
Stack
Work with the stack
| 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
| 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
| 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)
| 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 from imaginary and real parts | com |
Monadic Array
Operate on a single array
| 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 (documentation) |
Dyadic Array
Operate on two arrays
| 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 |
⊡ |
Pick | Index a row or elements from an array |
↯ |
Reshape | Change the shape of an array |
☇ |
Rerank | Change the rank of an array's rows |
↙ |
Take | Take the first n elements of an array |
↘ |
Drop | Drop the first n elements of an array |
↻ |
Rotate | Rotate the elements of an array by n |
◫ |
Windows | The n-wise windows of an array |
▽ |
Keep | Discard or copy some rows of an array |
⌕ |
Find | Find the occurrence's of one array in another |
∊ |
Member | Check if each row of one array exists in another |
⊗ |
Indexof | Find the first index of each row of one array in another |
External links
- Uiua on the concatenative language wiki
- Uiua, a Stack based Array language on the Array Cast
- Doc for the Documentation
- Interpreter for the interpreter
- Basic to start learning Uiua
| APL dialects [edit] | |
|---|---|
| Maintained | APL+Win ∙ APL2 ∙ APL64 ∙ APL\iv ∙ Aplette ∙ April ∙ Co-dfns ∙ Dyalog APL ∙ Dyalog APL Vision ∙ dzaima/APL ∙ GNU APL ∙ Kap ∙ NARS2000 ∙ Pometo ∙ TinyAPL |
| Historical | A Programming Language ∙ A+ (A) ∙ APL# ∙ APL2C ∙ APL\360 ∙ APL/700 ∙ APL\1130 ∙ APL\3000 ∙ APL.68000 ∙ APL*PLUS ∙ APL.jl ∙ APL.SV ∙ APLX ∙ Extended Dyalog APL ∙ Iverson notation ∙ IVSYS/7090 ∙ NARS ∙ ngn/apl ∙ openAPL ∙ Operators and Functions ∙ PAT ∙ Rowan ∙ SAX ∙ SHARP APL ∙ Rationalized APL ∙ VisualAPL (APLNext) ∙ VS APL ∙ York APL |
| Derivatives | AHPL ∙ BQN ∙ CoSy ∙ ELI ∙ Glee ∙ I ∙ Ivy ∙ J ∙ Jelly ∙ K (Goal, Klong, Q) ∙ KamilaLisp ∙ Lang5 ∙ Lil ∙ Nial ∙ RAD ∙ Uiua |
| Overviews | Comparison of APL dialects ∙ Timeline of array languages ∙ Timeline of influential array languages ∙ Family tree of array languages |