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== Overview == | == Overview == | ||
Uiua uses concatenative evaluation (a [[wikipedia:context-free grammar|context-free grammar]]) with a right-to-left ordering as in [[Wikipedia: Polish notation Polish notation]]. The language supports [[tacit programming]] using stack manipulation [[primitive]]s, and all complex functions must be defined this way as there is no explicit function form that allows local variables. [[Function]]s have a fixed number of input and output values, meaning the overloading of [[ambivalent function]]s 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 [[ | Uiua uses concatenative evaluation (a [[wikipedia:context-free grammar|context-free grammar]]) with a right-to-left ordering as in [[Wikipedia: Polish notation|Polish notation]]. The language supports [[tacit programming]] using stack manipulation [[primitive]]s, and all complex functions must be defined this way as there is no explicit function form that allows local variables. [[Function]]s have a fixed number of input and output values, meaning the overloading of [[ambivalent function]]s 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 [[typing glyphs]] necessitating 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 [[Array_model#Flat_array_theory|flat arrays]] with a homogeneous [[type]], and has a dedicated [[box]] type for [[Nested array|array nesting]]. However, arithmetic is [[pervasion|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 [[wikipedia:Julia (programming language)|Julia]] and [[wikipedia:NumPy|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. | Like the [[SHARP APL]] family, Uiua supports only [[Array_model#Flat_array_theory|flat arrays]] with a homogeneous [[type]], and has a dedicated [[box]] type for [[Nested array|array nesting]]. However, arithmetic is [[pervasion|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 [[wikipedia:Julia (programming language)|Julia]] and [[wikipedia:NumPy|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 == | == Primitives == | ||
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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. | 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. | ||
Tables below are based on Uiua version 0.8.0, with since-removed primitives taken out. | |||
==== Stack ==== | ==== Stack ==== | ||
Work with the stack | Work with the stack | ||
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| <code>♭</code> || [[Deshape]] || Make an array 1-dimensional | | <code>♭</code> || [[Deshape]] || Make an array 1-dimensional | ||
|- | |- | ||
| <code>¤</code> || [[Fix]] || Add a length-1 axis to an array | | <code>¤</code> || [[Promote|Fix]] || Add a length-1 axis to an array | ||
|- | |- | ||
| <code>⋯</code> || [[Encode|Bits]] || Encode an array as bits (LSB-first) | | <code>⋯</code> || [[Encode|Bits]] || Encode an array as bits (LSB-first) | ||
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This is the element-wise version of <code>≡ rows.</code> | This is the element-wise version of <code>≡ rows.</code> | ||
|- | |- | ||
| <code>≡</code> || | | <code>≡</code> || Rows || Monadic modifier ||Apply a function to each row of an array or arrays. | ||
This is the row-wise version of <code>∵ each.</code> | This is the row-wise version of <code>∵ each.</code> | ||
|- | |- | ||
| <code>⊞</code> || | | <code>⊞</code> || Table || Monadic 2-argument modifier || Apply a function to each combination of rows of two arrays. | ||
This is often what you want instead of <code>∵ each.</code> | This is often what you want instead of <code>∵ each.</code> | ||
|- | |- | ||
| <code>⍥</code> || [[Repeat]] || Monadic modifier || Repeat a function a number of times | | <code>⍥</code> || [[Repeat]] || Monadic modifier || Repeat a function a number of times | ||
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For reducing with an initial value, see <code>∧ fold</code> | For reducing with an initial value, see <code>∧ fold</code> | ||
|- | |- | ||
| <code>∧</code> || | | <code>∧</code> || Fold || Apply a function to aggregate arrays. | ||
|- | |- | ||
| <code>\</code> || [[Scan]] || Reduce, but keep intermediate values | | <code>\</code> || [[Scan]] || Reduce, but keep intermediate values | ||
|- | |- | ||
| <code>⊕</code> || [[Group]] || Group elements of an array into buckets by index | | <code>⊕</code> || [[Group (BQN)|Group]] || Group elements of an array into buckets by index | ||
Takes a function and two arrays. | Takes a function and two arrays. | ||
The arrays must be the same <code>⧻ length.</code> | The arrays must be the same <code>⧻ length.</code> | ||
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Keys <code>≤0</code> will be omitted. | Keys <code>≤0</code> will be omitted. | ||
The function then processes each group in order. The result depends on what the function is. | The function then processes each group in order. The result depends on what the function is. | ||
If the function takes 0 or 1 arguments, then <code>⊜ partition</code> behaves like ≡ rows. This is called iterating <code>⊜ partition.</code> | If the function takes 0 or 1 arguments, then <code>⊜ partition</code> behaves like <code>≡ rows</code>. This is called iterating <code>⊜ partition.</code> | ||
|} | |} | ||
==== Inversion Modifiers ==== | ==== Inversion Modifiers ==== | ||
Work with the inverses of functions | Work with the inverses of functions | ||
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| <code>°</code> || [[Un]] || Monadic modifier || Invert the behavior of a function | | <code>°</code> || [[Un]] || Monadic modifier || Invert the behavior of a function | ||
Most functions are not invertible. | Most functions are not invertible. | ||
|- | |- | ||
| <code>⍜</code> || [[Under]] || Dyadic modifier || Apply a function under another | | <code>⍜</code> || [[Under]] || Dyadic modifier || Apply a function under another | ||
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Any function that can be <code>° un</code>ed can be used with <code>⍜ under</code>. | Any function that can be <code>° un</code>ed can be used with <code>⍜ under</code>. | ||
Some functions that can't be <code>° un</code>ed can still be used with <code>⍜ under</code>. | Some functions that can't be <code>° un</code>ed can still be used with <code>⍜ under</code>. | ||
You can go to ([https://www.uiua.org/docs/under To See more information about the <code>⍜ under</code> function]) | |||
|} | |} | ||
==== 🌎 Planet 🪐 ==== | |||
Advanced stack manipulation | |||
{| class="wikitable" | |||
|+ Table of Iterating Modifiers in Uiua | |||
! Glyph !! Name !! Type !! Definition | |||
|- | |||
| <code>∘</code> || [[Identity]] || Monadic function || Do nothing with one value | |||
|- | |||
| <code>⋅</code> || Gap || Monadic modifier || Discard the top stack value then call a function | |||
|- | |||
| <code>⊙</code> || Dip || Monadic modifier || Temporarily pop the top value off the stack and call a function | |||
|- | |||
| <code>∩</code> || Both || Monadic 2-argument modifier || Call a function on two sets of values | |||
For monadic functions, <code>∩ both</code> calls its function on each of the top 2 values on the stack. | |||
|- | |||
| <code>⊃</code> || [[Fork]] || Dyadic modifier || Call two functions on the same values | |||
<code>⊃ fork</code> is one of the most important functions for working with the stack. | |||
|- | |||
| <code>⊓</code> || Bracket || Dyadic modifier || Call two functions on two distinct sets of values | |||
|} | |||
== External links == | == External links == | ||
* [https://concatenative.org/wiki/view/Uiua Uiua] on the concatenative language wiki | * [https://concatenative.org/wiki/view/Uiua Uiua] on the concatenative language wiki | ||