# Rank PolymoRphic Text editor (RPRT)

A compositional, point-free language for text manipulation.

# 1. Core Concepts

## 1.1 Two Fundamental Types

All functions work with two core types:

1. **Selection** — addresses and regions in buffers

   Every selection exists within one or more buffers. Selections have a rank:

   - **Rank 0**: Position — a natural number offset within a single buffer
   - **Rank 1**: Range — a pair of positions `[start, end)` with capture groups, within a single buffer
   - **Rank 2**: Ranges — a list of ranges with capture groups, within a single buffer
   - **Rank 3**: Multi-buffer selection — a mapping from buffer identifiers to rank 2 selections

   Ranks 0-2 operate within a single buffer (typically the current buffer). Rank 3 is distinguished by spanning multiple buffers simultaneously.

2. **Text** — string data

### Function Types

A **Selection function** is something of signature `Selection × Selection → Selection`.

A **Text function** is something of signature `Selection × Text → Selection`.

Following APL conventions, functions may have nullary, monadic, and dyadic forms. In these cases the number of arguments that they take varies (though not their types).

### Type Coercion

When a Text argument is required, a Selection is implicitly coerced to Text by extracting its contents. This coercion has no side effects.

| Input rank | Coerced Text                                      |
|------------|---------------------------------------------------|
| 0          | Empty string (position has no extent)             |
| 1          | Contents of the range                             |
| 2          | Contents of each range (multiple text values)     |
| 3          | Contents per buffer per range (multiple values)   |

For ranks 2 and 3, the selection provides multiple text values. Text functions pair these values with selection ranges following the broadcasting rules in §1.2.

**Text constants as functions:** A Text constant (string literal) `"text"` can be used as a constant nullary or monadic Text function that always returns `"text"`, ignoring its argument. This allows Text constants to be composed with other functions using combinators like hooks and trains.

## 1.2 Notation, [Leading axis theory](https://aplwiki.com/wiki/Leading_axis_theory), and broadcasting

**Notation:** In dyadic function application `α F ω`, `α` (alpha) is the left argument, `F` is the function, and `ω` (omega) is the right argument. For Selection functions `ω` may be omitted to obtain the monadic form `α F` of `F`. For Text functions `α` may be omitted to obtain the monadic form `F ω` of `F`.

Selections have a hierarchical structure with two axes, ordered from outermost (leading) to innermost:

1. **Buffer axis**: Distinct buffer identifiers (rank 3 only)
2. **Range axis**: Range index within list of ranges (ranks 2-3)

Selection functions define distinct **rank 0** and **rank 1** semantics. Higher rank selections are processed by **vectorisation**: the rank 1 semantics are applied to each range.

**Monadic rank polymorphism** for `α F`:

| `α` rank | Semantics                                                                                     |
|----------|-----------------------------------------------------------------------------------------------|
| 0        | Apply rank 0 semantics of `F`                                                                 |
| 1        | Apply rank 1 semantics of `F`                                                                 |
| 2        | Vectorise: collect `α' F` into ranges, where `α'` varies over each range in `α`               |
| 3        | Vectorise: collect `α' F` per buffer, where `α'` varies over the ranges in each buffer of `α` |

**Dyadic selection functions:** The span function `-` (§2.1) is the only dyadic selection function. It broadcasts its rank 0 and rank 1 semantics across higher ranks following the table above. See §2.1 for the complete broadcasting table.

**Text functions:** Text functions `α F τ` (§3) broadcast along the selection's axes when `α` has rank 2+. If the text argument `τ` is itself a Selection that coerces (§1.1) to multiple text values (rank 2+), the text values are paired with the ranges in `α`.

The buffer axis (rank 3) is the **leading axis**: operations on rank 3 selections distribute per-buffer first, then per-range within each buffer.

### Trains

A **train** is a sequence of functions that compose according to specific rules, following [APL train syntax](https://aplwiki.com/wiki/Train).

**2-train (Atop)** `F G`:
- Niladic: `F G` = (F) G`; `F` is evaluated niladically and `G` is evaluated monadically on the result
- Monadic: `ω (F G) = (ω F) G`
- Dyadic: `ω (F G) α = (ω F α) G`

**3-train (Fork)** `F G H`:
- Niladic: `F G H` = `(F) G (H)`; `F`, `H` are evaluated niladically and `G` is evaluated dyadically on the result
- Monadic: `ω (F G H) = (ω F) G (ω H)`
- Dyadic: `ω (F G H) α = (ω F α) G (ω H α)`

**Longer trains**: Parsed left-associatively. A train of n functions is parsed by taking the leftmost 3 functions as a fork (if n is odd and ≥3) or the leftmost 2 functions as atop (if n is even), then recursively parsing the remaining functions as the right part. For example:
- 4 functions `F G H I` → `(F G H) I` (I atop a fork)
- 5 functions `F G H I J` → `(F G H) (I J)` (atop, atop a fork)

### Hooks

RPRT provides two explicit hook combinators from BQN for flexible function composition:

**Before (Left Hook)** `F>G`:
- Niladic: `F>G = (F) G`; `F` is evaluated niladically and `G` is evaluated monadically on the result
- Monadic: `ω (F>G) = (ω F) G ω`
- Dyadic: `ω (F>G) α = (ω F) G α`

**After (Right Hook)** `F<G`:
- Niladic: `F<G = ???` TODO: undefined?
- Monadic: `ω (F<G) = ω F (G ω)`
- Dyadic: `ω (F<G) α = ω F (G α)`

These combinators bind more tightly than trains and enable partial application patterns. Hooks are **right-associative**, the _opposite_ of BQN's modifier associativity: `F<G<H` parses as `F<(G<H)`.

## 1.3 The Editor State Monad

All RPRT expressions evaluate within an implicit `EditorState` monad containing:
- Buffer contents (for all open buffers)
- Current buffer
- Current selection
- File/buffer mappings

Selection and Text functions have signatures `EditorState Selection` and `EditorState Text` respectively.

## 1.5 Evaluation Contexts

**Top-level Selection:** At the top level, all expressions are evaluated niladically (with no arguments). The result is used to set the editor's current selection.
```
F           # Applies selection function F niladically and sets the selection to the result
```

**All text operations:** Modify editor content. Note that `F` returns a selection, so at the top level this also changes the current selection.
```
α F τ       # F modifies contents, sets selection to changed region.
α F (β G τ) # Inner G modifies contents but doesn't set selection. F modifies contents and sets the new selection.
```

**Buffer switching statement:** The `b` statement changes the current buffer in the EditorState.
```
b "name"    # Switch current buffer to "name"
/pattern/   # Searches in "name"
```

The `b` statement is not a function and cannot be composed. It only appears as a top-level statement.

## 1.6 The Grouping Operator `{}`

The grouping operator `{}` provides transactional semantics: all operations within see the same input editor state, and their modifications are merged with position tracking where possible. Any error aborts the entire evaluation.

**Syntax:** `{ op₁ , op₂ , ... , opₙ }`

**Semantics:**
- All operations compute addresses in the original, unmodified editor state
- Changes are validated before application: they must be "in sequence" (non-overlapping and monotonically ordered on position)
- Successive insertions at the same position are concatenated in order
- Changes are applied atomically after all operations complete
- Returns the union of all resulting Selections
- Any validation failure aborts the entire group

# 1.7 Composition and Parsing

**Precedence and Associativity:**:
- Hooks bind tighter than trains
- Hooks are right-associative: `F<G<H` = `F<(G<H)`
- Trains are left-associative: `F G H I` = `(F G) H I`
- Functions and operators apply left-to-right
- Dyadic functions are infix

Note that the associativity of operations here is _reversed_ compared to BQN. Our reasoning for breaking with this convention is purely for convenience of the user: the monadic semantics for search functions is given on a _left_ argument, which matches the usual order in which expressions are made, "first select this, then using that selection do that, then ...".


# 2. Selection Functions

Selection functions produce Selection outputs and take zero (nullary functions), one (monadic functions), or two (dyadic functions) inputs of type Selection.

## 2.1 Core Selection Functions

There are ten core selection functions in RPRT. All ten have nullary and monadic forms, while the function `-` additionally has dyadic semantics---it is the only selection function that may take two arguments.

| Function   | Nullary semantics                                          | Output rank |
|------------|------------------------------------------------------------|-------------|
| `e`        | Empty selection                                            | 3           |
| `$`        | End of buffer                                              | 0           |
| `#n` (n∈ℕ) | Character n in buffer                                      | 0           |
| `n`  (n∈ℕ) | Line n in buffer                                           | 1           |
| `/re/`     | First match forward in buffer from start                   | 1           |
| `x/re/`    | All matches within buffer                                  | 2           |
| `+n`       | Line n in buffer                                           | 1           |
| `B/re/`    | All buffers whose name match re, mapping to their contents | 3           |
| `-`        | Entire buffer (0-$)                                        | 2           |

In the monadic case, functions have distinct rank 0 and rank 1 semantics. For ranks 2-3, the rank 1 semantics vectorise across ranges (see §1.2 for broadcasting and vectorisation).

| Function  | Semantics for rank 0 `α`         | Semantics for rank 1 `α`                 |
|-----------|----------------------------------|------------------------------------------|
| `α e`     | Empty selection (rank 3)         | Empty selection (rank 3)                 |
| `α $`     | `α`                              | End position of `α`                      |
| `α #n`    | `α`                              | Char n within `α`                        |
| `α n`     | `α`                              | Line n within `α`                        |
| `α /re/`  | `α`                              | First re within `α`                      |
| `α x/re/` | `α`                              | All re within `α`                        |
| `α +n`    | `α`                              | Line n within `α`                        |
| `α B/re/` | Buffer matches `re`? `α` : empty | buffer matches `re`? `α` : empty         |
| `α -`     | Range from `α` to end of buffer  | Range from start of `α` to end of buffer |

The span function `-` is the only selection function with dyadic semantics. It creates ranges by spanning from one selection to another.

| Rank of `α` | Rank of `ω` | Rank of `α-ω` | Semantics                                             |
|-------------|-------------|---------------|-------------------------------------------------------|
| 0           | 0           | 1             | Range from `α` to `ω`                                 |
| 0           | 1           | 1             | Range from `α` to end of `ω`                          |
| 1           | 0           | 1             | Range from start of `α` to `ω`                        |
| 1           | 1           | 1             | Range from start of `α` to end of `ω`                 |
| 0/1         | 2           | 2             | `α` to each range in `ω` (broadcast)                  |
| 2           | 0/1         | 2             | Each range in `α` to `ω` (broadcast)                  |
| 2           | 2           | 2             | Pairwise ranges (zip shortest)                        |
| 0           | 3           | 3             | `α` to each range in `ω` (broadcast)                  |
| 3           | 0           | 3             | Each range in `α` to `ω` (broadcast)                  |
| 3           | 1/2         | -             | Erroneous (TODO: maybe makes sense if indices align?) |
| 1/2         | 3           | -             | Erroneous (TODO: maybe makes sense if indices align?) |

### 2.1.1 Examples: Searching Within Buffer vs Current Selection

Because top-level expressions are evaluated niladically (§1.5), searching requires explicit composition to operate on the current selection (see §3.1, Text function `.`):

**Search from buffer start:** `/re/`
Niladic application searches from beginning of buffer

**Search within current selection:** `.>/re/`
In the niladic form this is `(.) /re/` (left hook semantics, §1.2), and `.` niladically is the current selection (§3.1). Thus `.>/re/` applies `/re/` to the current selection.

The After hook `F<G` has niladic semantics `F (G)`, making `.< /re/` evaluate to `/re/ (.)`—applying the search function to the current selection.

## 2.2 Selection Function Operators

Operators take functions as arguments and return new functions. Selection function operators fall into two categories which compose in a restricted manner:

**Search Modifiers** (at most one allowed):
- _(none)_ — Unmodified search semantics (see §2.1)
- `'` — Reverse (§2.2.2)
- `;` — Sequential (§2.2.3)
- `';` — Reverse-Sequential
- `;'` — Sequential-Reverse

**Result Transformations** (at most one allowed):
- _(none)_ — Unmodified result
- `~` — Complement (§2.2.4)
- `?` — Conditional (§2.2.5)
- `~?` — Complement-Conditional
- `?~` — Conditional-Complement

A fully-specified selection function has the form:

```
[result transformation] [search modifier] [base function]
```

where both operators are optional. Order matters: `';F` is not `;'F` and `~?F` is not `?~F`.

### 2.2.1 Search modifiers

#### The Reverse Operator `'`

The reverse operator `'` takes a selection function and reverses its direction.

**Note:** `'F` is not defined when `F` is one of the functions `B-` .

| Function | Nullary                        | Rank |
|----------|--------------------------------|------|
| `'e`     | synonymous with `e`            | 2    |
| `'$`     | Start of buffer (position 0)   | 0    |
| `'#n`    | Character n from end of buffer | 0    |
| `'n`     | Line n from end of buffer      | 1    |
| `'/re/`  | First match backward from end  | 1    |
| `'x/re/` | All matches, right-to-left     | 2    |
| `'+n`    | Line -n in buffer              | 1    |

In the monadic case, all functions are rank preserving, and all of the above functions are the identity on rank 0 inputs. For ranks 2-3, the rank 1 semantics vectorise (see §1.2).

| Function   | Semantics for rank 0 `α` | Semantics for rank 1 `α`         |
|------------|--------------------------|----------------------------------|
| `α 'e`     | Empty selection (rank 2) | Empty selection (rank 2)         |
| `α '$`     | `α`                      | Start position of `α`            |
| `α '#n`    | `α`                      | Char n from end of `α`           |
| `α 'n`     | `α`                      | Line n from end of `α`           |
| `α '/re/`  | `α`                      | First match backward within `α`  |
| `α 'x/re/` | `α`                      | All matches right-to-left in `α` |
| `α '+n`    | `α`                      | Line -n within `α`               |


#### The Sequential Operator `;`

The sequential operator `;` transforms a selection function from operating "within" a selection to operating "starting from the end" of that selection.

**Note:** It is erroneous to use `;F` in the nullary case. TODO: or are there interesting semantics?

**Note:** `;F` is not defined when `F` is one of `B-` .

| Function   | Semantics for rank 0 `α`     | Semantics for rank 1 `α`            |
|------------|------------------------------|-------------------------------------|
| `α ;e`     | Empty selection (rank 2)     | Empty selection (rank 2)            |
| `α ;$`     | End of buffer                | End of buffer (ignores `α`)         |
| `α ;#n`    | Character n after `α`        | Character n after end of `α`        |
| `α ;n`     | Line n after `α`             | Line n after end of `α`             |
| `α ;/re/`  | First match forward from `α` | First match forward from end of `α` |
| `α ;x/re/` | All matches forward from `α` | All matches forward from end of `α` |
| `α ;+n`    | Line n after `α`             | Line n after end of `α`             |

#### Combined Search Modifiers

The reverse and sequential operators may be composed in either order, producing distinct semantics:

**`;'F` (Sequential-Reverse):**
- Start from the end boundary of the selection
- Search backward (in reverse direction)

**`';F` (Reverse-Sequential):**
- Start from the start boundary of the selection
- Search backward (in reverse direction)

The key distinction is the starting position: `;'F` begins at the end and searches backward, while `';F` begins at the start and searches backward.

### 2.2.2 Result transformations

#### The Complement Operator `~`

The complement operator `~` takes a selection function and produces a new selection function which returns the complement. Naturally this changes rank somewhat, as explained in the below table.

| Rank of output of `F` | Rank of output of `~F` | Semantics                                                        |
|-----------------------|------------------------|------------------------------------------------------------------|
| 0                     | 2                      | The complement of the position its buffer as a selection         |
| 1                     | 2                      | The complement of the range in its buffer as a selection         |
| 2                     | 2                      | The selection corresponding to the ranges between the selections |
| 3                     | 3                      | The broadcast of `~` to each buffer                              |

#### The Conditional Operator `?`

The conditional operator `?` takes a selection function and produces a new selection function with the following semantics.

| Expression      | Semantics                                        |
|-----------------|--------------------------------------------------|
| Nullary `?F`    | exactly as `F`                                   |
| Monadic `α ?F`  | if `α F` is non-empty then `α` otherwise empty   |
| Dyadic `α ?F β` | if `α F β` is non-empty then `α` otherwise empty |

#### Combined Result Transformations

The complement and conditional operators may be composed in either order, producing distinct semantics:

**`~?F` (Complement-Conditional):**
1. Evaluate function `F` to obtain result `α`
2. Apply conditional: if `α` is non-empty, return input selection; otherwise return empty
3. Apply complement to the conditional result

**`?~F` (Conditional-Complement):**
1. Evaluate function `F` to obtain result `α`
2. Apply complement to `α` to obtain `β`
3. Apply conditional to `β`

The key distinction is when the complement is applied: `~?F` complements the conditional result, while `?~F` applies conditional to the complemented result of `F`.

# 3. Text Functions

## 3.1 Text Operations

Text operations have signature `Selection × Text → Selection`. They modify the editor state (buffer contents) and return the affected Selection.

Text operations follow the broadcasting rules described in §1.2. When the text argument `τ` is itself a Selection that coerces to Text, the text values are paired with ranges following the buffer-first, then range-within-buffer ordering (the leading axis).

| Function | Effect                                                       | Return selection     |
|----------|--------------------------------------------------------------|----------------------|
| `.`      | No-op                                                        | Current selection    |
| `c`      | No-op                                                        | Current selection    |
| `i`      | No-op                                                        | Current selection    |
| `a`      | No-op                                                        | Current selection    |
| `d`      | Delete current selection                                     | Empty selection      |
| `w`      | Write the current buffer to its associated file.             | Current selection    |
| `\|`     | Run current selection as shell commands, replace with output | Selection of outputs |

**Note:** `\|` is undefined when the rank of the current selection is 0.

| Function | Effect                                           | Return selection                            |
|----------|--------------------------------------------------|---------------------------------------------|
| `. τ`    | No-op                                            | Current selection in buffers named by `τ`   |
| `c τ`    | No-op                                            | Replace the current selection by `τ`        |
| `i τ`    | No-op                                            | Insert `τ` into the current selection       |
| `a τ`    | No-op                                            | Append `τ` to the current selection         |
| `d τ`    | Delete current selection in buffers named by `τ` | Empty selection in buffers named by `τ`     |
| `w τ`    | Write the buffers named by `τ`.                  | Current selection in buffers named by `τ`   |
| `\| τ`   | Run `τ`                                          | Return selection of ephemeral buffer output |

**Note:** The text argument `τ` may be a string literal or a Selection (which coerces to Text).
**Note:** `\|` and `d` are undefined when the rank of `τ` is 0.

| Function | Effect                                               | Semantics                                                 |
|----------|------------------------------------------------------|-----------------------------------------------------------|
| `α . τ`  | No-op                                                | Current selection in buffer(s) named by `τ` (`α` ignored) |
| `α c τ`  | No-op                                                | Change (replace) `α` with text `τ`                        |
| `α i τ`  | No-op                                                | Insert text `τ` before `α`                                |
| `α a τ`  | No-op                                                | Append text `τ` after `α`                                 |
| `α d τ`  | Delete `α` in buffers named by `τ`                   | Empty selection in buffers nameb by `τ`                   |
| `α w τ`  | Write (concatenation of) `α` in buffers named by `τ` | `α`                                                       |
| `α \| τ` | Pipe `α` through command `τ`                         | Return selection of ephemeral output buffer               |

**Examples:**

```
| "date"                # Run date with no input, returns selection to output
/pattern/ c (| "date")  # Replace pattern with date command output
α c<|<"sort"          # Pipe selection through sort, replace with result (using After hooks)
```

The third example composes two After hooks (§1.2): `|<"sort"` creates a monadic function that pipes its argument through sort, where `"sort"` is treated as a constant Text function (§1.1). Then `α c<|<"sort"` expands to `α c ((|<"sort") α)` = `α c (α | "sort")`, avoiding explicit repetition of the selection. Note that parentheses are not necessary because hooks are right-associative.

## 3.2 Text Function Operators

Text function operators modify the behavior of text functions.

### The Swap Operator

The `swap` operator reverses the arguments of a text function, converting `α F τ` into `τ F α`. For this to typecheck both arguments must be selections.

**Syntax:** `@ F`

**Semantics:** `α (@ F) τ = τ F α`

This is particularly useful for composing text operations where the natural argument order needs to be reversed.

**Idiom for moving content:**
```
α {@i , d} β
```

Using the swap operator `@`, this evaluates in parallel:
* `α @i β` which is `β i α` which means "insert at (the start of) β the content from α"
* `α d β` which means "delete α"

The net result of this is to _move_ the content of α to (the start of) the selection given by β.