### LaTeX Math with Integrals and Functions

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/latex_math/strip.rs.html

Examples of LaTeX math expressions involving integrals with limits, and function notations with subscripts and superscripts.

```Rust
            "\\int_0^1 f(x) dx",
```

```Rust
            "\\xrightarrow[g]{f}",
```

```Rust
            "\\xrightleftharpoons[g]{f}",
```

```Rust
            "\\xrightleftharpoons[a[b]c]{label}"
```

--------------------------------

### Example BrailleRule Implementation

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/traits.rs.html

Illustrates how to implement the BrailleRule trait for a specific rule, including metadata, phase, matching, and application logic.

```rust
struct Rule11VowelYe;

implement BrailleRule for Rule11VowelYe {
    fn meta(&self) -> &'static RuleMeta { &META }
    fn phase(&self) -> Phase { Phase::InterCharacter }
    fn matches(&self, ctx: &RuleContext) -> bool { /* check conditions */ }
    fn apply(&self, ctx: &mut RuleContext) -> Result<RuleResult, String> {
        ctx.emit(36); // ⠤ separator
        Ok(RuleResult::Continue)
    }
}
```

--------------------------------

### RuleEngine Usage Example

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Demonstrates how to create a new RuleEngine, register rules, disable a specific rule by its section ID, and apply the engine to a character context.

```rust
let mut engine = RuleEngine::new();
engine.register(Box::new(Rule11VowelYe));
engine.register(Box::new(Rule12VowelAe));

// Disable a specific rule:
engine.disable("12");

// Apply to a character context:
engine.apply(&mut ctx)?;
```

--------------------------------

### RuleEngine Usage Example

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/mod.rs.html

Demonstrates how to initialize a RuleEngine, register braille rules, disable specific rules, and apply enabled rules to a context. This is useful for setting up the braille conversion process.

```rust
let mut engine = RuleEngine::new();
engine.register(Box::new(korean::rule_11::Rule11));
engine.register(Box::new(korean::rule_12::Rule12));
engine.disable("12"); // disable a specific rule
engine.apply(&mut ctx)?;
```

--------------------------------

### Encode Digital Notations

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/digital_notation.rs.html

Examples of encoding different digital notations including sharps, flats, slashes, underscores, and colons.

```rust
let _ = crate::encode("c#d");
let _ = crate::encode("e//f");
let _ = crate::encode("g_h.i");
let _ = crate::encode("x_y:z");
```

--------------------------------

### Initialize Encoder with Rules

Source: https://docs.rs/braillify/2.0.1/src/braillify/encoder.rs.html

Constructs a new `Encoder` instance and registers a comprehensive set of Korean-specific encoding rules with its `RuleEngine`. This setup is crucial for correct Braille conversion.

```rust
impl Encoder {
    pub fn new(english_indicator: bool) -> Self {
        let mut rule_engine = rules::engine::RuleEngine::new();

        // ── Preprocessing ────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_53::Rule53));

        // ── WordShortcut ─────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_18::Rule18));

        // ── ModeManagement ───────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_29::Rule29));

        // ── CoreEncoding ─────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_44::Rule44));
        rule_engine.register(Box::new(rules::korean::rule_66::Rule66));
        rule_engine.register(Box::new(rules::korean::rule_67::Rule67));
        rule_engine.register(Box::new(rules::korean::rule_27::Rule27));
        rule_engine.register(Box::new(rules::korean::rule_19::Rule19));
        rule_engine.register(Box::new(rules::korean::rule_20::Rule20));
        rule_engine.register(Box::new(rules::korean::rule_21::Rule21));
        rule_engine.register(Box::new(rules::korean::rule_22::Rule22));
        rule_engine.register(Box::new(rules::korean::rule_23::Rule23));
        rule_engine.register(Box::new(rules::korean::rule_24::Rule24));
        rule_engine.register(Box::new(rules::korean::rule_25::Rule25));
        rule_engine.register(Box::new(rules::korean::rule_26::Rule26));
        rule_engine.register(Box::new(rules::korean::rule_16::Rule16));
        rule_engine.register(Box::new(rules::korean::rule_14::Rule14));
        rule_engine.register(Box::new(rules::korean::rule_13::Rule13));
        rule_engine.register(Box::new(rules::korean::rule_korean::RuleKorean));
        rule_engine.register(Box::new(rules::korean::rule_28::Rule28));
        rule_engine.register(Box::new(rules::korean::rule_40::Rule40));
        rule_engine.register(Box::new(rules::korean::rule_31::Rule31));
        rule_engine.register(Box::new(rules::korean::rule_8::Rule8));
        rule_engine.register(Box::new(rules::korean::rule_2::Rule2));
        rule_engine.register(Box::new(rules::korean::rule_1::Rule1));
        rule_engine.register(Box::new(rules::korean::rule_3::Rule3));
        rule_engine.register(Box::new(
            rules::korean::rule_english_symbol::RuleEnglishSymbol,
        ));
        rule_engine.register(Box::new(rules::korean::rule_68::Rule68));
        rule_engine.register(Box::new(rules::korean::rule_69::Rule69));
        rule_engine.register(Box::new(rules::korean::rule_70::Rule70));
        rule_engine.register(Box::new(rules::korean::rule_71::Rule71));
        rule_engine.register(Box::new(rules::korean::rule_72::Rule72));
        rule_engine.register(Box::new(rules::korean::rule_73::Rule73));
        rule_engine.register(Box::new(rules::korean::rule_74::Rule74));
        rule_engine.register(Box::new(rules::korean::rule_61::Rule61));
        rule_engine.register(Box::new(rules::korean::rule_41::Rule41));
        rule_engine.register(Box::new(rules::korean::rule_56::Rule56));
        rule_engine.register(Box::new(rules::korean::rule_57::Rule57));
        rule_engine.register(Box::new(rules::korean::rule_58::Rule58));
        rule_engine.register(Box::new(rules::korean::rule_60::Rule60));
        rule_engine.register(Box::new(rules::korean::rule_64::Rule64));
        rule_engine.register(Box::new(rules::korean::rule_64::Rule64Square));
        rule_engine.register(Box::new(rules::korean::rule_65::Rule65));
        rule_engine.register(Box::new(rules::korean::rule_49::Rule49));
        rule_engine.register(Box::new(rules::korean::rule_space::RuleSpace));

        // ... other fields initialization ...
        Encoder {
            is_english: false, // Default or determined elsewhere
            triple_big_english: false,
            english_indicator,
            has_processed_word: false,
            needs_english_continuation: false,
            parenthesis_stack: Vec::new(),
            default_mode: None,
            matrix_context_active: false,
            math_mode_active: false,
            rule_engine,
            token_engine: rules::token_engine::TokenRuleEngine::new(),
        }
    }
}

```

--------------------------------

### Encoder Initialization with Korean Rules

Source: https://docs.rs/braillify/latest/src/braillify/encoder.rs.html

Initializes a new `Encoder` instance and registers a comprehensive set of Korean-specific rules with the `RuleEngine`. This setup is crucial for accurate Korean Braille conversion.

```rust
impl Encoder {
    pub fn new(english_indicator: bool) -> Self {
        let mut rule_engine = rules::engine::RuleEngine::new();

        // ── Preprocessing ────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_53::Rule53));

        // ── WordShortcut ─────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_18::Rule18));

        // ── ModeManagement ───────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_29::Rule29));

        // ── CoreEncoding ─────────────────────────────────
        rule_engine.register(Box::new(rules::korean::rule_44::Rule44));
        rule_engine.register(Box::new(rules::korean::rule_66::Rule66));
        rule_engine.register(Box::new(rules::korean::rule_67::Rule67));
        rule_engine.register(Box::new(rules::korean::rule_27::Rule27));
        rule_engine.register(Box::new(rules::korean::rule_19::Rule19));
        rule_engine.register(Box::new(rules::korean::rule_20::Rule20));
        rule_engine.register(Box::new(rules::korean::rule_21::Rule21));
        rule_engine.register(Box::new(rules::korean::rule_22::Rule22));
        rule_engine.register(Box::new(rules::korean::rule_23::Rule23));
        rule_engine.register(Box::new(rules::korean::rule_24::Rule24));
        rule_engine.register(Box::new(rules::korean::rule_25::Rule25));
        rule_engine.register(Box::new(rules::korean::rule_26::Rule26));
        rule_engine.register(Box::new(rules::korean::rule_16::Rule16));
        rule_engine.register(Box::new(rules::korean::rule_14::Rule14));
        rule_engine.register(Box::new(rules::korean::rule_13::Rule13));
        rule_engine.register(Box::new(rules::korean::rule_korean::RuleKorean));
        rule_engine.register(Box::new(rules::korean::rule_28::Rule28));
        rule_engine.register(Box::new(rules::korean::rule_40::Rule40));
        rule_engine.register(Box::new(rules::korean::rule_31::Rule31));
        rule_engine.register(Box::new(rules::korean::rule_8::Rule8));
        rule_engine.register(Box::new(rules::korean::rule_2::Rule2));
        rule_engine.register(Box::new(rules::korean::rule_1::Rule1));
        rule_engine.register(Box::new(rules::korean::rule_3::Rule3));
        rule_engine.register(Box::new(
            rules::korean::rule_english_symbol::RuleEnglishSymbol,
        ));
        rule_engine.register(Box::new(rules::korean::rule_68::Rule68));
        rule_engine.register(Box::new(rules::korean::rule_69::Rule69));
        rule_engine.register(Box::new(rules::korean::rule_70::Rule70));
        rule_engine.register(Box::new(rules::korean::rule_71::Rule71));
        rule_engine.register(Box::new(rules::korean::rule_72::Rule72));
        rule_engine.register(Box::new(rules::korean::rule_73::Rule73));
        rule_engine.register(Box::new(rules::korean::rule_74::Rule74));
        rule_engine.register(Box::new(rules::korean::rule_61::Rule61));
        rule_engine.register(Box::new(rules::korean::rule_41::Rule41));
        rule_engine.register(Box::new(rules::korean::rule_56::Rule56));
        rule_engine.register(Box::new(rules::korean::rule_57::Rule57));
        rule_engine.register(Box::new(rules::korean::rule_58::Rule58));
        rule_engine.register(Box::new(rules::korean::rule_60::Rule60));
        rule_engine.register(Box::new(rules::korean::rule_64::Rule64));
        rule_engine.register(Box::new(rules::korean::rule_64::Rule64Square));
        rule_engine.register(Box::new(rules::korean::rule_65::Rule65));
        rule_engine.register(Box::new(rules::korean::rule_49::Rule49));
        rule_engine.register(Box::new(rules::korean::rule_space::RuleSpace));

        // ... other fields initialization ...

        Encoder {
            is_english: false, // Default or based on logic
            triple_big_english: false,
            english_indicator,
            has_processed_word: false,
            needs_english_continuation: false,
            parenthesis_stack: Vec::new(),
            default_mode: None,
            matrix_context_active: false,
            math_mode_active: false,
            rule_engine,
            token_engine: rules::token_engine::TokenRuleEngine::new(),
        }
    }
}
```

--------------------------------

### LaTeX Geometric and Perpendicularity Symbols

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/latex_math/strip.rs.html

Examples of LaTeX commands for geometric shapes like angles and triangles, and symbols indicating perpendicularity and parallelism.

```Rust
            "\\angle ABC",
```

```Rust
            "\\triangle ABC",
```

```Rust
            "\\perp",
```

```Rust
            "\\parallel"
```

--------------------------------

### DefiniteIntegralRule Application Example

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/math/rule_57.rs.html

Demonstrates the application of the DefiniteIntegralRule with a specific set of math tokens, including an opening parenthesis but no closing parenthesis. It asserts that the rule should result in a Skip outcome.

```rust
use crate::rules::math::parser::{BracketKind, MathToken};
        let r = super::DefiniteIntegralRule;
        let toks = vec![
            MathToken::MathSymbol('\u{222B}'),
            MathToken::OpenParen(BracketKind::MathParen),
            MathToken::Variable('a'),
            // No CloseParen
        ];
        let mut state = MathEncodeState::with_context(false, MathContext::default());
        let mut result = Vec::new();
        let engine = crate::rules::math::math_token_rule::MathTokenEngine::with_context(
            MathContext::default(),
        );
        let res = r.apply(&toks, 0, &mut result, &mut state, &engine);
        assert!(matches!(
            res,
            Ok(crate::rules::math::math_token_rule::MathTokenResult::Skip)
        ));
```

--------------------------------

### Registering and Applying a Rule

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Demonstrates how to create a `RuleEngine`, register a custom rule (`TestRule`), and then apply it to a `RuleContext`. Asserts that the rule is applied and produces the expected output.

```rust
let mut engine = RuleEngine::new();
engine.register(Box::new(TestRule));
assert_eq!(engine.rule_count(), 1);

let word_chars = vec!['가'];
let char_type = crate::char_struct::CharType::new('가').unwrap();
let mut state = EncoderState::new(false);
let mut result = Vec::new();
let mut skip = 0usize;
let empty: Vec<&str> = vec![];
let mut ctx = RuleContext {
    word_chars: &word_chars,
    index: 0,
    char_type: &char_type,
    prev_word: "",
    remaining_words: &empty,
    has_korean_char: true,
    is_all_uppercase: false,
    ascii_starts_at_beginning: false,
    skip_count: &mut skip,
    state: &mut state,
    result: &mut result,
};

let outcome = engine.apply(&mut ctx).unwrap();
assert_eq!(outcome, RuleResult::Consumed);
assert_eq!(result, vec![99]);
```

--------------------------------

### Test: Decimal Starting with Dot is Math Expression

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/math_expression.rs.html

Verifies that decimal numbers starting with a dot are identified as math expressions.

```rust
#[test]
fn test_decimal_starting_with_dot_is_math() {
    // ".47"처럼 점으로 시작하는 형태는 math expression.
    let chars: Vec<char> = ".47".chars().collect();
    assert!(is_math_expression(&chars, ".47"));
}
```

--------------------------------

### Detect Starts with Math Symbol and Digits as Math

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/math_expression/detect.rs.html

Identifies tokens starting with a math symbol followed by digits as mathematical expressions.

```Rust
if starts_with_math_symbol && has_digits {
        return true;
    }
```

--------------------------------

### Check for Hangul Wrap Start Bytes

Source: https://docs.rs/braillify/latest/src/braillify/rules/emit.rs.html

Checks if a token's byte slice matches the Hangul wrap start braille pattern (⠸⠷).

```rust
fn is_hangul_wrap_start(token: &Token<'_>) -> bool {
    matches!(token, Token::PreEncoded(bytes) if bytes.as_slice() == HANGUL_WRAP_START_BYTES)
}
```

--------------------------------

### RuleContext Initialization and Phase Application

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Demonstrates the initialization of a `RuleContext` and the application of a specific phase using the `engine.apply_phase` method. This snippet is useful for understanding the state management and rule execution flow within the Braillify engine.

```rust
let mut state = EncoderState::new(false);
let mut result = Vec::new();
let mut ctx = RuleContext {
    word_chars: &word_chars,
    index: 0,
    char_type: &char_type,
    prev_word: "",
    remaining_words: &empty,
    has_korean_char: false,
    is_all_uppercase: false,
    ascii_starts_at_beginning: false,
    skip_count: &mut skip,
    state: &mut state,
    result: &mut result,
};
let outcome = engine.apply_phase(Phase::CoreEncoding, &mut ctx).unwrap();
assert_eq!(outcome, RuleResult::Skip);
```

--------------------------------

### Test: Invalid Start >= End Span

Source: https://docs.rs/braillify/2.0.1/src/braillify/encoder.rs.html

Tests the error condition where a formatting span's start index is greater than or equal to its end index.

```rust
/// `inject_formatting_tokens` Err arm for span start >= end (line 297).
#[test]
fn inject_formatting_invalid_start_ge_end() {
    let text = "abc";
    let spans = vec![FormattingSpan {
        kind: FormattingKind::Emphasis,
        range: 2..2,
    }];
    let mut tokens: Vec<Token<'_>> = vec![];
    let result = inject_formatting_tokens(text, &spans, &mut tokens);
    assert!(result.is_err());
}

```

--------------------------------

### LaTeX Matrix Environments

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/latex_math.rs.html

Tests various LaTeX matrix environments including \begin{matrix}, \begin{pmatrix}, \begin{bmatrix}, \begin{Bmatrix}, \begin{vmatrix}, \begin{Vmatrix}, and \begin{array}.

```rust
fn latex_matrix_environments() {
        let inputs: &[&str] = &[
            // matrix family
            "$\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}$",
            "$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$",
            "$\begin{bmatrix} 1 \\ 2 \end{bmatrix}$",
            "$\begin{Bmatrix} x & y \end{Bmatrix}$",
            "$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$",
            "$\begin{Vmatrix} 1 & 0 \\ 0 & 1 \end{Vmatrix}$",
            // arrays
            "$\begin{array}{cc} x & y \\ z & w \end{array}$",
            "$\begin{array}{ll} a & b \\ c & d \end{array}$",
            // determinant
            "$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$",
        ];
        for input in inputs {
            let _ = enc(input);
        }
    }
```

--------------------------------

### Count English and Korean Words in Tokens

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/english_dominant_korean_wrap.rs.html

Counts the number of words that start with an ASCII alphabetic character (English) and those that start with a Korean character from a given slice of tokens.

```rust
fn count_script_words(tokens: &[Token<'_>]) -> (usize, usize) {
    let mut english_words = 0usize;
    let mut korean_words = 0usize;

    for token in tokens.iter() {
        let Token::Word(word) = token else { continue };
        let Some(c) = first_script_char(word) else {
            continue;
        };
        if c.is_ascii_alphabetic() {
            english_words += 1;
        } else if is_korean_char(c) {
            korean_words += 1;
        }
    }

    (english_words, korean_words)
}
```

--------------------------------

### Test Rule 18 Matches at Word Start Only

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_18.rs.html

Ensures that Rule 18's matching logic only triggers when the shortcut is at the beginning of a word. It tests both a matching case at the start and a non-matching case in the middle of the word.

```rust
#[test]
    fn rule18_matches_at_word_start_only() {
        use crate::char_struct::CharType;
        use crate::rules::context::EncoderState;
        let word_chars: Vec<char> = "그래서".chars().collect();
        let ct0 = CharType::new(word_chars[0]).unwrap();
        let mut skip = 0usize;
        let mut state = EncoderState::new(false);
        let mut result = Vec::new();
        let ctx_start = make_ctx(&word_chars, 0, &ct0, &mut skip, &mut state, &mut result);
        assert!(Rule18.matches(&ctx_start));

        let ct1 = CharType::new(word_chars[1]).unwrap();
        let mut skip2 = 0usize;
        let mut state2 = EncoderState::new(false);
        let mut result2 = Vec::new();
        let ctx_mid = make_ctx(&word_chars, 1, &ct1, &mut skip2, &mut state2, &mut result2);
        assert!(!Rule18.matches(&ctx_mid));
    }
```

--------------------------------

### Check if Next Non-Space Token is Hangul Wrap Start

Source: https://docs.rs/braillify/latest/src/braillify/rules/emit.rs.html

Determines if the first non-space token after a given index is a Hangul wrap start. This is used to skip emitting the end-of-word wrap symbol when a Hangul wrap is intended to maintain English mode.

```rust
fn next_non_space_is_hangul_wrap_start<'a>(tokens: &'a [Token<'a>], after_index: usize) -> bool {
    for token in tokens.iter().skip(after_index + 1) {
        match token {
            Token::Space(_) => continue,
            t => return is_hangul_wrap_start(t),
        }
    }
    false
}
```

--------------------------------

### MathTokenEngine::with_context Constructor

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/math/math_token_rule.rs.html

Creates a new MathTokenEngine with a specified MathContext.

```rust
impl MathTokenEngine {
    pub fn with_context(context: MathContext) -> Self {
        Self {
            rules: Vec::new(),
            context,
        }
    }

```

--------------------------------

### Get Word Length in RuleContext

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Returns the total number of characters in the current word.

```rust
pub fn word_len(&self) -> usize {
        self.word_chars.len()
    }
```

--------------------------------

### Apply Rule 69: Percent-per Shortcut

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_69.rs.html

Handles the specific sequence '%p' followed by a non-alphabetic character or end of word. It encodes it as '⠴⠏⠏' and conditionally emits a zero-width space if followed by a Korean character.

```Rust
if ctx.current_char() == '%'
            && ctx.word_chars.get(ctx.index + 1) == Some(&'p')
            && ctx
                .word_chars
                .get(ctx.index + 2)
                .is_none_or(|ch| !ch.is_ascii_alphabetic())
        {
            ctx.emit_slice(&encode_unicode_cells("⠴⠏⠏"));
            *ctx.skip_count = 1;
            if ctx
                .word_chars
                .get(ctx.index + 2)
                .is_some_and(|ch| crate::utils::is_korean_char(*ch))
            {
                ctx.emit(0);
            }
            return Ok(RuleResult::Consumed);
        }
```

--------------------------------

### Get Current Character in RuleContext

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Accesses the character at the current index within the word being processed.

```rust
pub fn current_char(&self) -> char {
        self.word_chars[self.index]
    }
```

--------------------------------

### Test encode_compact_ascii_notation for Out of Bounds Index

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_68.rs.html

Checks that `encode_compact_ascii_notation` returns `None` for both invalid suffixes and out-of-bounds starting indices.

```rust
    #[test]
    fn encode_compact_ascii_notation_out_of_bounds() {
        let word: Vec<char> = "A".chars().collect();
        // Returns None because no suffix after A
        let result = encode_compact_ascii_notation(&word, 0, false).unwrap();
        assert!(result.is_none());
        // Out of range index
        let result = encode_compact_ascii_notation(&word, 99, false).unwrap();
        assert!(result.is_none());
    }
```

--------------------------------

### build_math_engine

Source: https://docs.rs/braillify/latest/src/braillify/rules/math/encoder.rs.html

Constructs and configures a `MathTokenEngine` with a specific set of rules based on the provided `MathContext`.

```APIDOC
## build_math_engine

### Description
This function initializes a new `MathTokenEngine` and registers a series of rules with it. The rules are registered in a specific order based on their priority, ensuring correct parsing and encoding of mathematical expressions. The engine is then finalized before being returned.

### Parameters
- `context` (MathContext): The context for which the engine is being built. This influences which rules might be relevant or how they behave, although the current implementation registers a fixed set of rules regardless of context.

### Returns
- `MathTokenEngine`: A fully configured `MathTokenEngine` instance.

### Registered Rules (by priority):
- **Priority 10 (Lookahead Rules):**
  - `ConditionalProbFractionRule`
  - `GroupedFractionReversalRule`
  - `FractionReversalRule`
  - `VariableFractionInListRule`
  - `CombinatoricsRule`
  - `PartialDerivativeFractionRule`
  - `DefiniteIntegralRule`
- **Priority 50 (Core Token Rules):**
  - `NumberRule`
  - `VariableRule`
  - `UpperVariableRule`
  - `KoreanWordRule`
  - `OperatorRule`
  - `FunctionNameRule`
  - `BracketRule`
  - `SuperscriptRule`
  - `SubscriptRule`
  - `DecimalPointRule`
  - `DigitSeparatorRule`
  - `SpaceRule`
  - `PrimeRule`
- **Priority 100 (Math Symbol Dispatch):**
  - `MathSymbolRule`
  - `RawTokenRule`
```

--------------------------------

### RuleEngine Initialization

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Creates a new, empty RuleEngine instance with no rules registered and the sorted flag set to false.

```rust
pub fn new() -> Self {
    Self {
        rules: Vec::new(),
        disabled: HashSet::new(),
        sorted: false,
    }
}
```

--------------------------------

### Get KoreanChar Type

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Checks if the current character is Korean and returns it as a `KoreanChar` if true. Otherwise, returns None.

```rust
pub fn as_korean(&self) -> Option<&KoreanChar> {
        if let CharType::Korean(k) = self.char_type {
            Some(k)
        } else {
            None
        }
    }
```

--------------------------------

### Building a Math Token Engine

Source: https://docs.rs/braillify/latest/src/braillify/rules/math/encoder.rs.html

Constructs and configures a `MathTokenEngine` by registering various rules for different priorities, including lookahead rules, core token rules, and math symbol dispatch rules.

```rust
fn build_math_engine(context: MathContext) -> MathTokenEngine {
    let mut engine = MathTokenEngine::with_context(context);

    // Priority 10 — lookahead rules
    engine.register(Box::new(rule_7::ConditionalProbFractionRule));
    engine.register(Box::new(rule_7::GroupedFractionReversalRule));
    engine.register(Box::new(rule_7::FractionReversalRule));
    engine.register(Box::new(rule_7::VariableFractionInListRule));
    engine.register(Box::new(rule_12::CombinatoricsRule));
    engine.register(Box::new(rule_54::PartialDerivativeFractionRule));
    engine.register(Box::new(rule_57::DefiniteIntegralRule));

    // Priority 50 — core token rules
    engine.register(Box::new(rule_1::NumberRule));
    engine.register(Box::new(rule_12::VariableRule));
    engine.register(Box::new(rule_12::UpperVariableRule));
    engine.register(Box::new(KoreanWordRule));
    engine.register(Box::new(rule_2::OperatorRule));
    engine.register(Box::new(rule_47::FunctionNameRule));
    engine.register(Box::new(rule_6::BracketRule));
    engine.register(Box::new(rule_18::SuperscriptRule));
    engine.register(Box::new(rule_19::SubscriptRule));
    engine.register(Box::new(rule_8::DecimalPointRule));
    engine.register(Box::new(DigitSeparatorRule));
    engine.register(Box::new(SpaceRule));
    engine.register(Box::new(rule_53::PrimeRule));

    // Priority 100 — math symbol dispatch
    engine.register(Box::new(MathSymbolRule));
    engine.register(Box::new(RawTokenRule));

    engine.finalize();
    engine
}
```

--------------------------------

### Get Previous Character in RuleContext

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Safely retrieves the previous character in the word, returning None if at the beginning of the word.

```rust
pub fn prev_char(&self) -> Option<char> {
        if self.index > 0 {
            Some(self.word_chars[self.index - 1])
        } else {
            None
        }
    }
```

--------------------------------

### Get Next Character in RuleContext

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Safely retrieves the next character in the word, returning None if at the end of the word.

```rust
pub fn next_char(&self) -> Option<char> {
        self.word_chars.get(self.index + 1).copied()
    }
```

--------------------------------

### Rule Sorting by Phase and Priority

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Implements two rules, `PostRule` and `CoreRule`, with different phases. Demonstrates registering them and ensuring they are sorted correctly by the engine, verifying that `CoreEncoding` rules are processed before `PostProcessing` rules.

```rust
static META_A: RuleMeta = RuleMeta {
    section: "a",
    subsection: None,
    name: "post",
    standard_ref: "",
    description: "",
};
static META_B: RuleMeta = RuleMeta {
    section: "b",
    subsection: None,
    name: "core",
    standard_ref: "",
    description: "",
};

struct PostRule;
impl BrailleRule for PostRule {
    fn meta(&self) -> &'static RuleMeta {
        &META_A
    }
    fn phase(&self) -> Phase {
        Phase::PostProcessing
    }
    fn matches(&self, _: &RuleContext) -> bool {
        false
    }
    fn apply(&self, _: &mut RuleContext) -> Result<RuleResult, String> {
        Ok(RuleResult::Skip)
    }
}
struct CoreRule;
impl BrailleRule for CoreRule {
    fn meta(&self) -> &'static RuleMeta {
        &META_B
    }
    fn phase(&self) -> Phase {
        Phase::CoreEncoding
    }
    fn matches(&self, _: &RuleContext) -> bool {
        false
    }
    fn apply(&self, _: &mut RuleContext) -> Result<RuleResult, String> {
        Ok(RuleResult::Skip)
    }
}

let mut engine = RuleEngine::new();
engine.register(Box::new(PostRule));
engine.register(Box::new(CoreRule));
engine.ensure_sorted();

let metas = engine.list_rules();
assert_eq!(metas[0].name, "core"); // CoreEncoding before PostProcessing
assert_eq!(metas[1].name, "post");
```

--------------------------------

### LaTeX Delimiters and Floor/Ceiling Functions

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/latex_math/strip.rs.html

Shows the use of LaTeX commands for adjustable-size delimiters like parentheses, brackets, and braces, as well as floor and ceiling functions.

```Rust
            "\\left(x\right)",
```

```Rust
            "\\left[x\right]",
```

```Rust
            "\\left\{x\right\}",
```

```Rust
            "\\lfloor x \rfloor",
```

```Rust
            "\\lceil x \rceil"
```

--------------------------------

### Getting Rule Count

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Returns the total number of rules currently registered in the engine. This function is only available in test configurations.

```rust
pub fn rule_count(&self) -> usize {
    self.rules.len()
}
```

--------------------------------

### Generic CloneToUninit Implementation

Source: https://docs.rs/braillify/2.0.1/braillify/struct.EncodeOptions.html

An experimental nightly-only API for copying data to uninitialized memory.

```rust
unsafe fn clone_to_uninit(&self, dest: *mut u8)
```

--------------------------------

### Encode Because Symbol at Start of Expression

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/math/encoder/symbol_rule.rs.html

Tests the encoding of the because symbol '∵' when it appears at the very beginning of an expression, ensuring no leading spaces are added.

```rust
fn because_at_start_of_expression() {
        let result = enc("\u{2235}x");
        assert!(!result.is_empty(), "∵x must encode");
    }
```

--------------------------------

### RuleEngine::new

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/engine.rs.html

Creates a new, empty RuleEngine instance with no rules registered and no rules disabled.

```APIDOC
## RuleEngine::new

### Description
Creates a new, empty `RuleEngine` instance.

### Returns
A new `RuleEngine` with an empty list of rules and an empty set of disabled rules.
```

--------------------------------

### Apply Rule 69: Percent-ile Shortcut

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_69.rs.html

Handles the specific sequence '%ile' by encoding it as '⠴⠏⠞' and consuming three characters.

```Rust
if ctx.current_char() == '%'
            && ctx.word_chars.get(ctx.index + 1) == Some(&'i')
            && ctx.word_chars.get(ctx.index + 2) == Some(&'l')
            && ctx.word_chars.get(ctx.index + 3) == Some(&'e')
        {
            let encoded = encode_unicode_cells("⠴⠏⠞");
            ctx.emit_slice(&encoded);
            *ctx.skip_count = 3;
            return Ok(RuleResult::Consumed);
        }
```

--------------------------------

### Check for ASCII Alphabet Start

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/roman_numeral.rs.html

Determines if a string begins with an ASCII alphabetic character. Useful for distinguishing between different token types.

```Rust
    #[rstest::rstest]
    #[case::lowercase_alpha("abc", true)]
    #[case::uppercase_alpha("Z", true)]
    #[case::digit_prefix("123", false)]
    #[case::empty("", false)]
    #[case::symbol_prefix("-", false)]
    fn starts_with_ascii_alpha_branches(#[case] input: &str, #[case] expected: bool) {
        assert_eq!(starts_with_ascii_alpha(input), expected);
    }
```

--------------------------------

### Initialize Matrix Math Mode Engine

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/math/encoder.rs.html

Tests the initialization of the `MATRIX_MATH_MODE_ENGINE` lazy block by calling `math_engine_for_context` with active matrix and math modes.

```rust
let _ = math_engine_for_context(MathContext {
            matrix_context_active: true,
            math_mode_active: true,
        });
```

--------------------------------

### Get Current Encoding Mode

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/context.rs.html

Retrieves the current encoding mode from the top of the mode stack. Defaults to Korean if the stack is empty.

```rust
pub fn current_mode(&self) -> EncodingMode {
        self.mode_stack
            .last()
            .copied()
            .unwrap_or(EncodingMode::Korean)
    }
```

--------------------------------

### Parse Underline-Notation Fraction Paths

Source: https://docs.rs/braillify/latest/src/braillify/rules/math/parser.rs.html

Tests various underline-notation fraction parsing scenarios, including suffixes on digit prefixes and generic underline-fractions.

```rust
    /// Underline-notation fraction normalization paths (lines around 300-330).
    #[test]
    fn underline_notation_fraction_paths() {
        // U+0332 suffix on digit prefix → digits/1
        let _ = parse_math_expression("123\u{0332}");
        // "1?/(...)" pattern
        let _ = parse_math_expression("1\u{0332}/(x+y)");
        // "X?/Y" generic underline-fraction
        let _ = parse_math_expression("A\u{0332}/B");
    }
```

--------------------------------

### Pass-through Logic for English Mode

Source: https://docs.rs/braillify/latest/src/braillify/english_logic.rs.html

Demonstrates that `should_keep_english_mode_for_symbol` passes through the result of `should_render_symbol_as_english` when both pre-conditions are met, using an email-like string as an example.

```rust
let chars: Vec<char> = "user@host.com".chars().collect();
        // '@' at index 4
        let _ = super::should_keep_english_mode_for_symbol('@', &chars, 4, &[]);
```

--------------------------------

### Create Token Rule Engine

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/emit.rs.html

Initializes and populates a `TokenRuleEngine` with various token-level rules. This engine handles transformations on tokens before final Braille output.

```rust
fn make_token_engine() -> crate::rules::token_engine::TokenRuleEngine {
        let mut engine = crate::rules::token_engine::TokenRuleEngine::new();
        engine.register(Box::new(
            crate::rules::token_rules::normalize::NormalizeEllipsis,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::emphasis_ring::EmphasisRingRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::latex_fraction::LatexFractionRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::inline_fraction::InlineFractionRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::word_shortcut::WordShortcutRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::uppercase_passage::UppercasePassageRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::middle_dot_spacing::MiddleDotSpacingRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::quote_attachment::QuoteAttachmentRule,
        ));
        engine.register(Box::new(
            crate::rules::token_rules::spacing::AsteriskSpacingRule,
        ));
        engine
    }
```

--------------------------------

### Braillify CLI Main Function

Source: https://docs.rs/braillify/2.0.1/src/braillify/cli.rs.html

The main entry point for the Braillify CLI. It handles argument parsing, including reading from stdin if not a terminal, and dispatches to either one-shot conversion or REPL mode.

```rust
use std::io::{self, IsTerminal, Read, Write};

use anyhow::{Result, bail};
use clap::Parser;
use rustyline::{DefaultEditor, error::ReadlineError};

use crate::encode_to_unicode;

#[derive(Parser, Debug)]
#[command(name = "braillify", about = "한국어 점자 변환 CLI", version)]
struct Cli {
    /// 입력 문자열. 없으면 REPL 모드로 진입합니다
    input: Option<String>,
}

pub fn run_cli(mut args: Vec<String>) -> Result<()> {
    if args.len() == 1 && !std::io::stdin().is_terminal() {
        let mut buffer = vec![];
        io::stdin().read_to_end(&mut buffer)?;
        if !buffer.is_empty() {
            args.push(String::from_utf8(buffer)?);
        }
    }
    match Cli::parse_from(args).input {
        Some(text) => run_one_shot(&text),
        None => run_repl(),
    }
}

fn run_one_shot(text: &str) -> Result<()> {
    let out = encode_to_unicode(text).map_err(|e| anyhow::anyhow!("점자 변환 실패: {}", e))?;
    let mut stdout = io::stdout();
    stdout.write_all(out.as_bytes())?;
    stdout.flush()?;
    Ok(())
}

/// Format a single REPL input line for printing.
///
/// Pure function so unit tests can exercise the encode-success vs encode-error
/// branches without spinning up rustyline. The outer `run_repl` loop is just
/// `read line → format → write` glue; all logic lives here.
pub(crate) fn process_repl_line(line: &str) -> String {
    match encode_to_unicode(line) {
        Ok(out) => out,
        Err(e) => format!("오류: {}", e),
    }
}

// Interactive rustyline loop is unreachable in cargo-tarpaulin runs (stdin is
// never a terminal in CI/test harness). The pure encoding logic was extracted
// to `process_repl_line` which is unit-tested directly above.
#[cfg(not(tarpaulin_include))]
fn run_repl() -> Result<()> {
    let mut rl = DefaultEditor::new()?;
    let mut stdout = io::stdout();
    writeln!(
        stdout,
        "braillify REPL - 입력을 점자로 변환합니다. 종료: Ctrl+C or Ctrl+D"
    )?;
    stdout.flush()?;

    loop {
        match rl.readline("> ") {
            Ok(line) => {
                rl.add_history_entry(&line).ok();
                writeln!(stdout, "{}", process_repl_line(&line))?;
                stdout.flush()?;
            }
            Err(ReadlineError::Interrupted) | Err(ReadlineError::Eof) => {
                writeln!(stdout, "종료합니다.")?;
                stdout.flush()?;
                break;
            }
            Err(err) => bail!("입력 오류: {}", err),
        }
    }
    Ok(())
}

```

--------------------------------

### Test FormattingKind Markers

Source: https://docs.rs/braillify/2.0.1/src/braillify/lib.rs.html

Ensures that each variant of `FormattingKind` (Emphasis, Bold, Custom1, Custom2) correctly returns its declared start and end markers.

```rust
    /// All four FormattingKind variants must produce their declared markers.
    /// Covers `FormattingKind::markers` arms for Emphasis/Bold/Custom1/Custom2.
    /// `FormattingKind::markers()` — 각 강조 종류별 시작·종료 점형 페어.
    #[rstest::rstest]
    #[case::emphasis(FormattingKind::Emphasis, [32, 36], [36, 4])]
    #[case::bold(FormattingKind::Bold, [48, 36], [36, 6])]
    #[case::custom1(FormattingKind::Custom1, [16, 36], [36, 2])]
    #[case::custom2(FormattingKind::Custom2, [8, 36], [36, 1])]
    fn formatting_kind_markers_all_variants(
        #[case] kind: FormattingKind,
        #[case] start: [u8; 2],
        #[case] end: [u8; 2],
    ) {
        assert_eq!(kind.markers(), (start, end));
    }
```

--------------------------------

### MathEncodeState::with_context Constructor

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/math/math_token_rule.rs.html

Initializes MathEncodeState with logic context and provided MathContext.

```rust
impl MathEncodeState {
    pub fn with_context(logic_context: bool, context: MathContext) -> Self {
        Self {
            prev_was_number: false,
            logic_context,
            matrix_context_active: context.matrix_context_active,
        }
    }
}

```

--------------------------------

### Test: Non-Math Letter then Digit

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/math_expression.rs.html

Ensures that strings starting with letters followed by a digit (e.g., product codes) are not identified as math expressions.

```rust
#[test]
fn test_is_not_math_letter_then_digit() {
    // "MP3" starts with letters then digit → NOT math (avoids false positive)
    let chars: Vec<char> = "MP3".chars().collect();
    assert!(!is_math_expression(&chars, "MP3"));
}
```

--------------------------------

### Parse Basic Text into Tokens

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token.rs.html

Demonstrates parsing a simple string into its constituent tokens, verifying word and space tokenization.

```Rust
let ir = DocumentIR::parse("hello world", false);
assert_eq!(ir.tokens.len(), 3);

match &ir.tokens[0] {
    Token::Word(w) => assert_eq!(w.text, "hello"),
    _ => panic!("expected first token to be word"),
}
assert!(matches!(ir.tokens[1], Token::Space(SpaceKind::Regular)));
match &ir.tokens[2] {
    Token::Word(w) => assert_eq!(w.text, "world"),
    _ => panic!("expected third token to be word"),
}
```

--------------------------------

### Test: Math Expression with Digit then Letters

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/token_rules/math_expression.rs.html

Verifies that strings starting with a digit followed by letters (implying multiplication) are identified as math expressions.

```rust
#[test]
fn test_is_math_digit_then_letter() {
    // "3ab" starts with digit then letters → math multiplication
    let chars: Vec<char> = "3ab".chars().collect();
    assert!(is_math_expression(&chars, "3ab"));
}
```

--------------------------------

### Engine Apply Phase Skips Disabled Rules Test Setup

Source: https://docs.rs/braillify/latest/src/braillify/rules/engine.rs.html

Sets up a test for the `apply_phase` method in `engine.rs`, specifically focusing on the skip arm for disabled rules. It initializes a `RuleEngine` and registers a `TestRule` which is then disabled.

```rust
use crate::char_struct::CharType;

let mut engine = RuleEngine::new();
engine.register(Box::new(TestRule));
engine.disable("test");

let word_chars = vec!['x'];
let char_type = CharType::English('x');
let empty: [&str; 0] = [];
let mut skip = 0usize;
```

--------------------------------

### Test encode_compact_ascii_notation for Lowercase Input

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_68.rs.html

Verifies that `encode_compact_ascii_notation` returns `None` when the input starts with a lowercase letter, even if followed by a valid suffix.

```rust
    #[test]
    fn encode_compact_ascii_notation_lowercase_returns_none() {
        let word: Vec<char> = "a⁺".chars().collect();
        let result = encode_compact_ascii_notation(&word, 0, false).unwrap();
        assert!(result.is_none());
    }
```

--------------------------------

### Test Rule 53 Match False When Not at Word Start

Source: https://docs.rs/braillify/2.0.1/src/braillify/rules/korean/rule_53.rs.html

Checks that Rule 53 returns false when the ellipsis pattern is not at the beginning of the word.

```rust
use crate::char_struct::CharType;
        let word_chars: Vec<char> = "......".chars().collect();
        let ct = CharType::new(word_chars[0]).unwrap();
        let mut skip = 0usize;
        let mut state = crate::rules::context::EncoderState::new(false);
        let mut out = Vec::new();
        let ctx = make_ctx(&word_chars, 1, &ct, &mut skip, &mut state, &mut out);
        assert!(!Rule53.matches(&ctx));
```