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diff --git a/doc/fromJ.md b/doc/fromJ.md new file mode 100644 index 00000000..53565405 --- /dev/null +++ b/doc/fromJ.md @@ -0,0 +1,143 @@ +*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/doc/fromJ.html).* + +# BQN–J dictionary + +<!--GEN +"style" Enc ".Comment { color: inherit; }" +--> + +A guide to help users of J get up to speed with BQN quickly. + +## Terminology + +### Array model + +BQN uses the [based array model](based.md), which is fundamentally different from J's flat array model. BQN uses non-array values such as characters and numbers, called "atoms", while in J every noun is an array. A BQN array can contain any values in any mixture, while a J array must be uniformly numbers, characters, or boxes (BQN doesn't use boxes). + +The J terms "atom" and "element" are used to mean different things by different authors. In BQN, an atom or rank-0 array is called a "unit", and the values contained in an array—which may or may not be arrays—are called "elements". Each element is contained in a 0-cell, or rank-0 subarray. BQN uses the term "major cell" for what J calls an "item" of an array: a cell with rank one less than that array. BQN shares the terms "list" and "table" for rank-1 and rank-2 arrays with J. + +BQN uses "[depth](depth.md)" rather than "boxing level". BQN gives atoms depth 0, so that the depth of a BQN array is one higher than the boxing level of the corresponding J array. + +### Roles + +In J, the part of speech is an inherent property of a value, while in BQN it is determined by how the value is used in a particular expression, and can be different from the value's type. See [context-free grammar](context.md). + +| J part of speech | BQN role | +|---------------------|------------| +| Noun | Subject | +| Verb | Function | +| Adverb | 1-modifier | +| Conjunction | 2-modifier | + +## Syntax + +| J | BQN | Remarks +|-------------------|-------------|--------- +| `NB.` | `#` | +| `'` | `"` | `'` creates characters +| `=.` and `=:` | `←` and `↩` | `←` to define; `↩` to modify +| `3 :…` or `{{…}}` | `;` | To separate function cases +| `:` | `{…}` | +| `x` `y` | `𝕨` `𝕩` | `𝕊` for block function self-reference +| `u` `v` | `𝔽` `𝔾` | `𝕣` for block modifier self-reference +| `_` | `¯` or `∞` | +| `2 3 4` | `2‿3‿4` | +| `[:` | `·` | Cap +| `assert.` | `!` | + +BQN's explicit functions and modifiers are called "blocks", and have a more sophisticated syntax than J; see [the documentation](block.md). BQN uses lexical scope, and has no global variables. BQN also has a [list notation](syntax.md#list-notation) using `⟨⟩`. + +## For reading + +J analogues of BQN primitive functions are given below. They are not always the same; usually this is because BQN has extra functionality relative to J, although in some cases it has less or different functionality. + +Functions `+` `-` `|` `<` `>` are the same in both languages. + +| BQN | `×` | `÷` | `⋆` | `√` | `⌊` | `⌈` | `≤` | `≥` | `⊣` | `⊢` | `⌽` | `⍉` | +|:---:|:---:|:---:|:---:|:----:|:----:|:----:|:----:|:----:|:---:|:---:|:-----:|:-----:| +| J | `*` | `%` | `^` | `%:` | `<.` | `>.` | `<:` | `>:` | `[` | `]` | `\|.` | `\|:` | + +| BQN | `∧` | `∨` | `¬` | `=` | `≠` | `≡` | `≢` | `⥊` | `∾` | `≍` | +|:-----:|:-----:|:-----:|:-----:|:-----:|:----:|:----:|:-------:|:---:|:---:|:----:| +| Monad | `/:~` | `\:~` | `-.` | `#@$` | `#` | `L.` | `$` | `,` | `;` | `,:` | +| Dyad | `*.` | `+.` | `+-.` | `=` | `~:` | `-:` | `-.@-:` | `$` | `,` | `,:` | + +| BQN | `↑` | `↓` | `↕` | `»` | `«` | `/` | +|:-----:|:----:|:-----:|:----:|:--------------:|:---------------:|:----:| +| Monad | `<\` | `<\.` | `i.` | `#{.(_1-#){.]` | `-@#{.(1+#){.]` | `I.` | +| Dyad | `{.` | `}.` | `<\` | `#@]{.,` | `-@#@]{.,~` | `#` | + +| BQN | `⍋` | `⍒` | `⊏` | `⊑` | `⊐` | `⊒` | `∊` | `⍷` | `⊔` | +|:-----:|:----:|:-------:|:----:|:-------:|:-------:|:---:|:----:|:----:|:---------:| +| Monad | `/:` | `/:` | `{.` | `0{::,` | `i.~~.` | `…` | `~:` | `~.` | `</.i.@#` | +| Dyad | `I.` | `I.&:-` | `{` | `{::` | `i.` | `…` | `e.` | `E.` | `</.` | + +Most of BQN's combinators have J equivalents. The J equivalent `"_` for `˙` assumes a noun operand, but `˙` makes a constant function for any operand. `◶` has arguments reversed relative to `@.`, and uses an actual array of functions rather than gerunds. Besides these, BQN's `⟜` is like a J hook, that is, `F⟜G` is `(F G)`, and `⊸` applies in the opposite direction. + +| BQN | `˙` | `˜` | `∘` | `○` | `⌾` | `⊘` | `◶` | +|:---:|:----:|:---:|:----:|:----:|:-----:|:---:|:----:| +| J | `"_` | `~` | `@:` | `&:` | `&.:` | `:` | `@.` | + +For other modifiers the correspondence is looser. Here `⌜` shows the dyadic case and `´` the monadic case only. + +| BQN | `¨` | `⌜` | `´` | `˝` | `` ` `` | `˘` | `⎉` | `⚇` | `⍟` | `⁼` | +|:---:|:-----:|:------:|:------:|:---:|:-------:|:-----:|:---:|:----:|:----:|:------:| +| J | `&.>` | `&.>/` | `&.>/` | `/` | `/\` | `"_1` | `"` | `L:` | `^:` | `^:_1` | + +## For writing + +J's primitive nouns are easily defined in BQN. + +| J | BQN | +|------|----------| +| `a.` | `@+↕256` | +| `a:` | `<↕0` | + +Functions `+` `-` `|` `<` `>` are the same in both languages. + +Some other primitives are essentially the same in J and BQN, but with different spellings (but [transpose](transpose.md) behaves differently; J's dyadic `|:` is more like `⍉⁼`): + +| J | `*` | `%` | `^` | `^.` | `%:` | `<.` | `>.` | `[` | `]` | `\|.` | `\|:` | +|:---:|:---:|:---:|:---:|:----:|:----:|:----:|:----:|:---:|:---:|:-----:|:-----:| +| BQN | `×` | `÷` | `⋆` | `⋆⁼` | `√` | `⌊` | `⌈` | `⊣` | `⊢` | `⌽` | `⍉` | + +Additionally, `|.!.f` is `⥊⟜f⊸«` with a natural number left argument. Change `«` to `»` to rotate right instead of left. + +The tables below give approximate implementations of J primitives. J has a whole lot of complicated primitives that no one uses (some of which are officially deprecated), so not everything is translated here. + +| J | Monad | Dyad +|------|-------------------------|----- +| `=` | `⍷⊸(≡⌜)` | `=` +| `<:` | `-⟜1` | `≤` +| `>:` | `1⊸+` | `≥` +| `+.` | | `∨` +| `+:` | `2⊸×` | `¬∨` +| `*:` | `ט` | `¬∧` +| `-.` | `¬` | `¬∘∊/⊣` +| `-:` | `÷⟜2` | `≡` +| `%.` | | `+˝∘×⎉1‿∞⁼` +| `$` | `≢` | `⥊` +| `~.` | `⍷` | +| `~:` | `∊` | `≠` +| `,` | `⥊` | `∾` +| `,.` | `⥊˘` | `∾˘` +| `,:` | `≍` | +| `;` | `∾` | `∾⟜(<⍟(1≥≡))` +| `#` | `≠` | `/` +| `#.` | `+˜⊸+˜´∘⌽` | +| `#:` | `⌽2\|⌊∘÷⟜2⍟(↕1+·⌊2⋆⁼⊢)` | ``{𝕨\|1↓⌊∘÷`⌾⌽𝕨∾<𝕩}`` +| `!` | `×´1+↕` | `-˜(+÷○(×´)⊢)1+↕∘⊣` +| `/:` | `⍋` | `⍋⊸⊏` +| `\:` | `⍒` | `⍒⊸⊏` +| `{` | `(<⟨⟩)<⊸∾⌜´⊢` | `⊏` +| `{.` | `⊏` | `↑` +| `{:` | `⊢˝` | +| `{::`| | `⊑` +| `}.` | `1⊸↓` | `↓` +| `}:` | `¯1⊸↓` | +| `e.` | `><∘∾∊¨⊢` | `∊` +| `E.` | | `⍷` +| `i.` | `↕` | `⊐` +| `i:` | `{𝕩-˜↕1+2×𝕩}` | `≠∘⊣-1+⌽⊸⊐` +| `I.` | `/` | `⍋` +| `L.` | `≡` | |