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*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/doc/fromDyalog.html).*
# BQN–Dyalog APL dictionary
A few tables to help users of Dyalog APL (or similar) get started quickly on BQN. For a higher-level comparison, check [Why BQN?](../commentary/why.md#versus-apl-and-j). Here we assume `⎕ML` is 1 for Dyalog.
## Terminology
### Array model
BQN uses the [based array model](based.md), so that a Dyalog simple scalar corresponds to many BQN values: an atom, its enclose, and so on.
| Dyalog | BQN |
|---------------|-------|
| Simple scalar | Atom |
| Scalar | Unit |
| Vector | List |
| Matrix | Table |
BQN shares the terms "cell" and "major cell" with Dyalog, and uses
"element" (which may mean different things to different Dyalog users) *not* for a 0-cell but for the value it contains.
### Roles
Dyalog uses value types (array, function, and so on) to determine syntax while BQN uses a separate concept called syntactic roles. See [context-free grammar](context.md).
| Dyalog type | BQN role |
|------------------|------------|
| Array | Subject |
| Function | Function |
| Monadic operator | 1-modifier |
| Dyadic operator | 2-modifier |
| Niladic function | *go away* |
## Syntax
BQN comments are written with `#`, not `⍝`. BQN strings use double quotes `""` while single quotes `''` enclose a character.
BQN's functions use `{}`, like Dyalog's dfns. The names for inputs and self-reference are different:
| Dyalog | BQN |
|--------|-----|
| `⍺` | `𝕨` |
| `⍵` | `𝕩` |
| `∇` | `𝕊` |
| `⍺⍺` | `𝔽` |
| `⍵⍵` | `𝔾` |
| `∇∇` | `𝕣` |
BQN doesn't have guards: it uses modifiers or [control structures](control.md) instead. However, BQN function and modifier blocks have headers that allow pattern matching. See the [block](block.md) documentation.
The assignment arrow `←` defines a new variable in a block, while `↩` modifies an existing one.
BQN uses the ligature character `‿` for stranding, instead of plain juxtaposition. It also has a [list notation](arrayrepr.md#brackets) using `⟨⟩`.
## For reading
Here are some closest equivalents in Dyalog APL for the BQN functions that don't use the same glyphs as APL. Correspondence can be approximate, and `⌽` is just used as a decorator to mean "reverse some things".
| BQN | `⋆` | `√` | `∧` | `∨` | `¬` | `=` | `≠` | `<` | `>` | `≢` | `⥊` |
|:-----:|:---:|:--------:|:-----:|:-----:|:-----:|:-----:|:---:|:---:|:---:|:---:|:---:|
| Monad | `*` | `*∘(÷2)` | `[⍋]` | `[⍒]` | `~` | `≢⍤⍴` | `≢` | `⊂` | `↑` | `⍴` | `,` |
| Dyad | `*` | `*∘÷⍨` | `∧` | `∨` | `1+-` | `=` | `≠` | `<` | `>` | `≢` | `⍴` |
| BQN | `∾` | `≍` | `⋈` | `↑` | `↓` | `↕` | `»` | `«` |
|:-----:|:-----:|:------:|:-----:|:----:|:-------:|:----:|:------------:|:-------------:|
| Monad | `⊃,⌿` | `↑,⍥⊂` | `,⍥⊂` | `,⍀` | `⌽,⌽⍀⌽` | `⍳` | `≢↑(¯1-≢)↑⊢` | `-⍤≢↑(1+≢)↑⊢` |
| Dyad | `⍪` | `↑,⍥⊂` | `,⍥⊂` | `↑` | `↓` | `,⌿` | `≢⍤⊢↑⍪` | `-⍤≢⍤⊢↑⍪⍨` |
| BQN | `/` | `⍋` | `⍒` | `⊏` | `⊑` | `⊐` | `⊒` | `∊` | `⍷` | `⊔` |
|:-----:|:---:|:---:|:-----:|:----:|:---:|:-----:|:---:|:---:|:---:|:----------:|
| Monad | `⍸` | `⍋` | `⍒` | `⊣⌿` | `⊃` | `∪⍳⊢` | `…` | `≠` | `∪` | `⌸` |
| Dyad | `⌿` | `⍸` | `⌽⍸⌽` | `⌷` | `⊃` | `⍳` | `…` | `∊` | `⍷` | `⌸` or `⊆` |
Modifiers are a little harder. Many have equivalents in some cases, but Dyalog sometimes chooses different functionality based on whether the operand is an array. In BQN an array is always treated as a constant function.
| BQN | `¨` | `⌜` | `˝` | `⎉` | `⍟` | `˜` | `∘` | `○` | `⟜` |
|:------:|:---:|:----:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| Dyalog | `¨` | `∘.` | `⌿` | `⍤` | `⍣` | `⍨` | `⍤` | `⍥` | `∘` |
In BQN `⎉` is Rank and `∘` is Atop. Dyalog's Atop (`⍤`) and Over (`⍥`) were added in version 18.0.
## For writing
The tables below give approximate implementations of Dyalog primitives for the ones that aren't the same. First- and last-axis pairs are also mostly omitted. BQN just has the first-axis form, and you can get the last-axis form with `⎉1`.
The form `F⍣G` (Power with a function right operand; Power limit) must be implemented with recursion instead of primitives because it performs unbounded iteration. The modifier `_while_ ← {𝔽⍟𝔾∘𝔽_𝕣_𝔾∘𝔽⍟𝔾𝕩}` provides similar functionality without risk of stack overflow. It's discussed [here](control.md#low-stack-version) and called as `Fn _while_ Cond arg`.
<table>
<tr><th colspan=3>Functions</th></tr>
<tr><th> Glyph </th><th> Monadic </th><th> Dyadic </th> </tr>
<tr><td> <code>*</code> </td><td colspan=2><code>⋆</code></td> </tr>
<tr><td> <code>⍟</code> </td><td colspan=2><code>⋆⁼</code></td> </tr>
<tr><td> <code>!</code> </td><td><code>×´1+↕</code> </td><td> <code>-˜(+÷○(×´)⊢)1+↕∘⊣</code></td></tr>
<tr><td> <code>○</code> </td><td> <code>π⊸×</code> </td><td> <code>•math</code></td> </tr>
<tr><td> <code>~</code> </td><td> <code>¬</code> </td><td> <code>¬∘∊/⊣</code></td> </tr>
<tr><td> <code>?</code> </td><td> <code>•rand.Range⚇0</code> </td><td> <code>•rand.Deal</code></td></tr>
<tr><td> <code>⍲</code> </td><td> </td><td> <code>¬∘∧</code></td> </tr>
<tr><td> <code>⍱</code> </td><td> </td><td> <code>¬∘∨</code></td> </tr>
<tr><td> <code>⍴</code> </td><td> <code>≢</code> </td><td> <code>⥊</code></td> </tr>
<tr><td> <code>,</code> </td><td> <code>⥊</code> </td><td> <code>∾⎉1</code></td> </tr>
<tr><td> <code>⍪</code> </td><td> <code>⥊˘</code> </td><td> <code>∾</code></td> </tr>
<tr><td> <code>⌽</code> </td><td colspan=2><code>⌽⎉0‿1</code></td> </tr>
<tr><td> <code>↑</code> </td><td> <code>></code> </td><td> <code>↑</code></td> </tr>
<tr><td> <code>↓</code> </td><td> <code><˘</code> </td><td> <code>↑</code></td> </tr>
<tr><td> <code>⊂</code> </td><td> <code><</code> </td><td> <code>+`⊸⊔</code></td> </tr>
<tr><td> <code>⊆</code> </td><td> <code><⍟(0<≡)</code> </td><td> <code>(¬-˜⊢×·+`»⊸>)⊸⊔</code></td></tr>
<tr><td> <code>∊</code> </td><td> <code>{(∾𝕊¨)⍟(0<≡𝕩)⥊𝕩}</code></td><td> <code>∊</code></td> </tr>
<tr><td> <code>⊃</code> </td><td colspan=2><code>⊑</code></td> </tr>
<tr><td> <code>⍀</code> </td><td> </td><td> <code>{𝕩⌾(𝕨⊸/)𝕨≠⊸↑0↑𝕩}</code></td></tr>
<tr><td> <code>∩</code> </td><td> </td><td> <code>∊/⊣</code></td> </tr>
<tr><td> <code>∪</code> </td><td> <code>⍷</code> </td><td> <code>⊣∾∊˜¬⊸/⊢</code></td> </tr>
<tr><td> <code>⍳</code> </td><td> <code>↕</code> </td><td> <code>⊐</code></td> </tr>
<tr><td> <code>⍸</code> </td><td> <code>/</code> </td><td> <code>⍋</code></td> </tr>
<tr><td> <code>⍋</code> </td><td> <code>⍋</code> </td><td> Give up </td> </tr>
<tr><td> <code>⍒</code> </td><td> <code>⍒</code> </td><td> Give up </td> </tr>
<tr><td> <code>≢</code> </td><td> <code>≠</code> </td><td> <code>≢</code></td> </tr>
<tr><td> <code>⍎</code> </td><td colspan=2><code>•BQN</code></td> </tr>
<tr><td> <code>⍕</code> </td><td colspan=2><code>•Fmt</code></td> </tr>
<tr><td> <code>⊥</code> </td><td> </td><td> <code>{+⟜(𝕨⊸×)´⌽𝕩}</code> </td></tr>
<tr><td> <code>⊤</code> </td><td> </td><td> <code>{>𝕨|⌊∘÷`⌾⌽𝕨«˜<𝕩}</code></td></tr>
<tr><td> <code>⌹</code> </td><td><code>Inverse</code> from <a href="https://github.com/mlochbaum/bqn-libs/blob/master/matrix.bqn">here</a></td><td><code>Solve</code></td></tr>
<tr><td> <code>⌷</code> </td><td> N/A </td><td> <code>⊏</code></td> </tr>
</table>
<table>
<tr><th colspan=3>Operators</th></tr>
<tr><th> Syntax </th><th> Monadic </th><th> Dyadic </th></tr>
<tr><td> <code>⌿</code> </td><td> <code>¨˝</code> </td><td> <code>↕</code> </td></tr>
<tr><td> <code>⍀</code> </td><td colspan=2> <code>↑</code>, or <code>`</code> if associative </td></tr>
<tr><td> <code>¨</code> </td><td colspan=2> <code>¨</code> </td></tr>
<tr><td> <code>⍨</code> </td><td colspan=2> <code>˜</code> </td></tr>
<tr><td> <code>⍣</code> </td><td colspan=2> <code>⍟</code> </td></tr>
<tr><td> <code>f.g</code> </td><td> </td><td> <code>f˝∘g⎉1‿∞</code> </td></tr>
<tr><td> <code>∘.f</code> </td><td> </td><td> <code>f⌜</code> </td></tr>
<tr><td> <code>A∘g</code> </td><td> <code>A⊸g</code> </td><td> </td></tr>
<tr><td> <code>f∘B</code> </td><td> <code>f⟜B</code> </td><td> </td></tr>
<tr><td> <code>f∘g</code> </td><td colspan=2> <code>f⟜g</code> </td></tr>
<tr><td> <code>f⍤B</code> </td><td colspan=2> <code>f⎉B</code> </td></tr>
<tr><td> <code>f⍤g</code> </td><td colspan=2> <code>f∘g</code> </td></tr>
<tr><td> <code>f⍥g</code> </td><td colspan=2> <code>f○g</code> </td></tr>
<tr><td> <code>f@v</code> </td><td colspan=2> <code>f⌾(v⊸⊏)</code> </td></tr>
<tr><td> <code>f⍠B</code> </td><td colspan=2> Uh </td></tr>
<tr><td> <code>f⌸</code> </td><td><code>⊐⊔↕∘≠</code></td><td><code>⊐⊸⊔</code> </td></tr>
<tr><td> <code>f⌺B</code> </td><td colspan=2> <code>↕</code> </td></tr>
<tr><td> <code>A⌶</code> </td><td colspan=2> <code>•Something</code> </td></tr>
<tr><td> <code>f&</code> </td><td colspan=2> Nothing yet </td></tr>
</table>
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