latexgrambot/internal/rich/latex.go

package rich

import (
	"strings"
	"unicode"
)

// textCommands marks a document as text-mode LaTeX (as opposed to a bare
// math expression) when any of these is present.
var textCommands = map[string]bool{
	"textbf": true, "textit": true, "emph": true, "underline": true,
	"uline": true, "texttt": true, "textsuperscript": true,
	"textsubscript": true, "textrm": true, "textsf": true, "textnormal": true,
	"textup": true, "textmd": true, "textcolor": true,
	"href": true, "url": true, "hyperlink": true, "hypertarget": true,
	"section": true, "subsection": true,
	"subsubsection": true, "item": true, "maketitle": true, "title": true,
	"author": true, "documentclass": true, "par": true,
}

// wrapperEnvironments are environments whose markers are dropped from text
// mode; their content is rendered inline.
var wrapperEnvironments = map[string]bool{
	"itemize": true, "enumerate": true, "center": true, "flushleft": true,
	"flushright": true, "quote": true, "quotation": true, "description": true,
	"small": true, "footnotesize": true, "large": true, "Large": true,
	"document": true,
}

// documentClassEnvironments are math environments that keep a \begin{...}
// source in math mode.
var mathEnvironments = map[string]bool{
	"equation": true, "equation*": true, "align": true, "align*": true,
	"aligned": true, "gather": true, "gather*": true, "multline": true,
	"multline*": true, "eqnarray": true, "eqnarray*": true, "array": true,
	"matrix": true, "pmatrix": true, "bmatrix": true, "vmatrix": true,
	"Vmatrix": true, "Bmatrix": true, "cases": true, "split": true,
	"displaymath": true, "math": true,
}

// symbolCommands maps exotic symbol commands that client math engines
// commonly lack to Unicode. Standard LaTeX/AMS math commands (\int, \sum,
// Greek letters, arrows, relations, ...) are deliberately NOT translated:
// the client engine renders them natively, while Unicode replacements are
// not drawn by every math font.
var symbolCommands = map[string]string{
	"heartsuit": "♡", "diamondsuit": "♢", "spadesuit": "♠", "clubsuit": "♣",
	"checkmark": "✓", "textbullet": "•", "degree": "°", "celsius": "°C",
	"copyright": "©", "registered": "®", "circledR": "®", "pounds": "£",
	"euro": "€", "yen": "¥", "male": "♂", "female": "♀",
	"flat": "♭", "natural": "♮", "sharp": "♯",
	"Box": "□", "square": "□", "blacksquare": "■",
	"triangle": "△", "blacktriangle": "▲", "blacktriangledown": "▼",
	"bigstar": "★", "lozenge": "◊", "blacklozenge": "⧫",
	"measuredangle": "∡", "sphericalangle": "∢",
	"therefore": "∴", "because": "∵", "maltese": "✠",
	"diagup": "╱", "diagdown": "╲", "complement": "∁", "eth": "ð",
	"Finv": "Ⅎ", "Game": "⅁", "circledS": "Ⓢ", "mho": "℧",
}

// translateSymbols replaces known symbol commands with Unicode. Font
// commands such as \mathbb are left untouched: client math engines render
// them themselves and their Unicode math-alphanumeric fallbacks are not
// supported everywhere.
func translateSymbols(source string) string {
	if !strings.Contains(source, `\`) {
		return source
	}
	var out strings.Builder
	for index := 0; index < len(source); {
		if source[index] != '\\' {
			out.WriteByte(source[index])
			index++
			continue
		}
		name, next := readCommand(source, index)
		if name == "" {
			out.WriteString(source[index:next])
			index = next
			continue
		}
		if replacement, ok := symbolCommands[name]; ok {
			out.WriteString(replacement)
			index = skipEmptyGroup(source, next)
			continue
		}
		out.WriteString(source[index:next])
		index = next
	}
	return out.String()
}

// Document converts a LaTeX source into a rich message. Math segments
// ($...$, $$...$$, \(...\), \[...\]) become math nodes; text paragraphs keep
// their line structure and map the common text-mode formatting commands to
// rich text nodes. With defaultMath, a source with no math delimiters and
// no known text-mode command is treated as a single math expression;
// otherwise such a source is parsed as text and formulas need delimiters.
func Document(source string, defaultMath bool) *Message {
	source = documentBody(source)
	source = translateSymbols(source)
	trimmed := strings.TrimSpace(source)
	if trimmed == "" {
		return &Message{Blocks: []Block{{Type: "paragraph", Text: " "}}}
	}
	if defaultMath && isPureMath(trimmed) {
		if isSymbolsOnly(trimmed) {
			// Client math fonts often lack exotic symbols; the regular
			// text font renders them everywhere.
			return &Message{Blocks: []Block{{Type: "paragraph", Text: trimmed}}}
		}
		return &Message{Blocks: []Block{{Type: "mathematical_expression", Expression: trimmed}}}
	}
	parser := &parser{src: source}
	blocks := parser.parseBlocks()
	if len(blocks) == 0 {
		blocks = []Block{{Type: "paragraph", Text: " "}}
	}
	return &Message{Blocks: blocks}
}

// IsMathExpression reports whether the source is a math expression: bare
// math commands with no text-mode command, a delimited math segment, or a
// math environment. Used to decide whether a failed compile may be retried
// with the expression forced into math mode.
func IsMathExpression(source string) bool {
	trimmed := strings.TrimSpace(source)
	if trimmed == "" {
		return false
	}
	if stripOuterMathDelimiters(trimmed) != trimmed {
		return true
	}
	// Delimiters somewhere inside mean mixed text and math: not entirely
	// math, so no retry.
	if strings.Contains(trimmed, "$") || strings.Contains(trimmed, `\(`) || strings.Contains(trimmed, `\[`) {
		return false
	}
	for _, command := range commandsIn(trimmed) {
		if textCommands[command] {
			return false
		}
	}
	for _, environment := range environmentsIn(trimmed) {
		if !mathEnvironments[environment] {
			return false
		}
	}
	return true
}

// ContainsMathEnvironment reports whether the source contains a math
// environment such as align or matrix; those compile standalone and must
// not be wrapped again.
func ContainsMathEnvironment(source string) bool {
	for _, environment := range environmentsIn(source) {
		if mathEnvironments[environment] {
			return true
		}
	}
	return false
}

// stripOuterMathDelimiters removes matching outer math delimiters.
func stripOuterMathDelimiters(expr string) string {
	for _, pair := range [][2]string{{`$$`, `$$`}, {`$`, `$`}, {`\[`, `\]`}, {`\(`, `\)`}} {
		if len(expr) >= len(pair[0])+len(pair[1]) &&
			strings.HasPrefix(expr, pair[0]) && strings.HasSuffix(expr, pair[1]) {
			return strings.TrimSpace(expr[len(pair[0]) : len(expr)-len(pair[1])])
		}
	}
	return expr
}

// isSymbolsOnly reports whether the source consists only of symbols and
// punctuation: no letters, digits or LaTeX math structure.
func isSymbolsOnly(source string) bool {
	for _, r := range source {
		switch r {
		case '\\', '_', '{', '}', '$', '&', '#', '^':
			return false
		}
		if r < 128 && !unicode.IsPunct(r) && !unicode.IsSpace(r) {
			return false
		}
	}
	return true
}

// InlineDocument is Document prepared for inline answers: a leading math
// expression renders inline one space after the bot mention instead of as a
// display block, and a leading paragraph starts with one space.
func InlineDocument(source string, defaultMath bool) *Message {
	message := Document(source, defaultMath)
	if len(message.Blocks) == 0 {
		return message
	}
	first := &message.Blocks[0]
	switch first.Type {
	case "mathematical_expression":
		*first = Block{Type: "paragraph", Text: []any{
			" ",
			Inline{Type: "mathematical_expression", Expression: first.Expression},
		}}
	case "paragraph":
		first.Text = prependSpace(first.Text)
	}
	return message
}

func prependSpace(text any) any {
	switch value := text.(type) {
	case string:
		return " " + value
	case []any:
		return append([]any{" "}, value...)
	default:
		return text
	}
}

// documentBody reduces a full document to the content of its document
// environment.
func documentBody(source string) string {
	const begin = `\begin{document}`
	const end = `\end{document}`
	index := strings.Index(source, begin)
	if index < 0 {
		return source
	}
	source = source[index+len(begin):]
	if index = strings.Index(source, end); index >= 0 {
		source = source[:index]
	}
	return source
}

// isPureMath reports whether the source should be rendered as one math
// expression: no math delimiters, no known text-mode command and no
// non-math environment.
func isPureMath(source string) bool {
	if strings.Contains(source, "$") || strings.Contains(source, `\(`) || strings.Contains(source, `\[`) {
		return false
	}
	for _, command := range commandsIn(source) {
		if textCommands[command] {
			return false
		}
	}
	for _, env := range environmentsIn(source) {
		if !mathEnvironments[env] {
			return false
		}
	}
	return true
}

func commandsIn(source string) []string {
	var commands []string
	for i := 0; i < len(source); i++ {
		if source[i] != '\\' || i+1 >= len(source) {
			continue
		}
		if source[i+1] == '\\' {
			commands = append(commands, `\\`)
			i++
			continue
		}
		name := ""
		next := i + 1
		for next < len(source) && isCommandLetter(source[next]) {
			name += string(source[next])
			next++
		}
		if name != "" {
			commands = append(commands, name)
			i = next - 1
		}
	}
	return commands
}

func environmentsIn(source string) []string {
	var envs []string
	for index := 0; index < len(source); {
		position := strings.Index(source[index:], `\begin{`)
		if position < 0 {
			break
		}
		position += index
		start := position + len(`\begin{`)
		end := strings.IndexByte(source[start:], '}')
		if end < 0 {
			break
		}
		envs = append(envs, source[start:start+end])
		index = start
	}
	return envs
}

// readEnvironment reads \begin{name} or \end{name} at index and returns the
// environment name and the position after the closing brace.
func readEnvironment(source string, index int) (string, int, bool) {
	prefix := `\begin{`
	if strings.HasPrefix(source[index:], `\end{`) {
		prefix = `\end{`
	} else if !strings.HasPrefix(source[index:], prefix) {
		return "", index, false
	}
	start := index + len(prefix)
	end := strings.IndexByte(source[start:], '}')
	if end < 0 {
		return "", index, false
	}
	return source[start : start+end], start + end + 1, true
}

func isCommandLetter(c byte) bool {
	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z')
}

type parser struct {
	src string
	pos int
}

func (p *parser) eof() bool { return p.pos >= len(p.src) }

func (p *parser) startsWith(prefix string) bool {
	return strings.HasPrefix(p.src[p.pos:], prefix)
}

func (p *parser) parseBlocks() []Block {
	var blocks []Block
	var text strings.Builder
	flush := func() {
		trimmed := strings.TrimSpace(text.String())
		text.Reset()
		if trimmed == "" {
			return
		}
		blocks = append(blocks, Block{Type: "paragraph", Text: parseInline(trimmed)})
	}

	for !p.eof() {
		switch {
		case p.startsWith(`\[`):
			flush()
			p.pos += 2
			expression := strings.TrimSpace(p.readUntil(`\]`))
			if isSymbolsOnly(expression) {
				blocks = append(blocks, Block{Type: "paragraph", Text: strings.TrimSpace(expression)})
			} else {
				blocks = append(blocks, Block{Type: "mathematical_expression", Expression: expression})
			}
		case p.startsWith("$$"):
			flush()
			p.pos += 2
			expression := strings.TrimSpace(p.readUntil("$$"))
			if isSymbolsOnly(expression) {
				blocks = append(blocks, Block{Type: "paragraph", Text: strings.TrimSpace(expression)})
			} else {
				blocks = append(blocks, Block{Type: "mathematical_expression", Expression: expression})
			}
		case p.startsWith(`\section`):
			flush()
			p.pos += len(`\section`)
			if title, ok := p.readOptionalStarAndGroup(); ok {
				blocks = append(blocks, Block{Type: "heading", Text: parseInline(title), Size: 2})
			}
		case p.startsWith(`\subsection`):
			flush()
			p.pos += len(`\subsection`)
			if title, ok := p.readOptionalStarAndGroup(); ok {
				blocks = append(blocks, Block{Type: "heading", Text: parseInline(title), Size: 3})
			}
		case p.startsWith(`\subsubsection`):
			flush()
			p.pos += len(`\subsubsection`)
			if title, ok := p.readOptionalStarAndGroup(); ok {
				blocks = append(blocks, Block{Type: "heading", Text: parseInline(title), Size: 4})
			}
		case p.startsWith(`\item`):
			flush()
			text.WriteString("• ")
			p.pos += len(`\item`)
			for p.pos < len(p.src) && (p.src[p.pos] == ' ' || p.src[p.pos] == '\t') {
				p.pos++
			}
		case p.startsWith(`\begin{`), p.startsWith(`\end{`):
			environment, after, ok := readEnvironment(p.src, p.pos)
			if ok && wrapperEnvironments[environment] {
				flush()
				p.pos = after
			} else {
				text.WriteByte(p.src[p.pos])
				p.pos++
			}
		case p.startsWith(`\par`), p.startsWith(`\\`):
			flush()
			if p.startsWith(`\par`) {
				p.pos += len(`\par`)
			} else {
				p.pos += 2
			}
		case p.src[p.pos] == '\n' && p.blankLineAhead():
			flush()
			for !p.eof() && (p.src[p.pos] == '\n' || p.src[p.pos] == ' ' || p.src[p.pos] == '\t' || p.src[p.pos] == '\r') {
				p.pos++
			}
		default:
			text.WriteByte(p.src[p.pos])
			p.pos++
		}
	}
	flush()
	return blocks
}

// blankLineAhead reports whether the newline at the current position is
// followed by a blank line (two or more newlines, spaces allowed between).
func (p *parser) blankLineAhead() bool {
	index := p.pos + 1
	if index < len(p.src) && p.src[index] == '\r' {
		index++
	}
	for index < len(p.src) && (p.src[index] == ' ' || p.src[index] == '\t') {
		index++
	}
	return index < len(p.src) && p.src[index] == '\n'
}

func (p *parser) readUntil(terminator string) string {
	index := strings.Index(p.src[p.pos:], terminator)
	if index < 0 {
		result := p.src[p.pos:]
		p.pos = len(p.src)
		return result
	}
	result := p.src[p.pos : p.pos+index]
	p.pos += index + len(terminator)
	return result
}

// readOptionalStarAndGroup consumes an optional star and the following
// {group}; spaces are allowed before the brace.
func (p *parser) readOptionalStarAndGroup() (string, bool) {
	if p.pos < len(p.src) && p.src[p.pos] == '*' {
		p.pos++
	}
	return p.readGroup()
}

// readGroup reads a balanced {group} at the current position, skipping
// leading spaces.
func (p *parser) readGroup() (string, bool) {
	for p.pos < len(p.src) && (p.src[p.pos] == ' ' || p.src[p.pos] == '\t') {
		p.pos++
	}
	if p.pos >= len(p.src) || p.src[p.pos] != '{' {
		return "", false
	}
	depth := 0
	start := p.pos + 1
	for index := p.pos; index < len(p.src); index++ {
		switch p.src[index] {
		case '\\':
			index++ // skip the escaped character
		case '{':
			depth++
		case '}':
			depth--
			if depth == 0 {
				result := p.src[start:index]
				p.pos = index + 1
				return result, true
			}
		}
	}
	return "", false
}

// parseInline converts a text-mode fragment into a RichText value: a plain
// string when nothing needs formatting, or a slice of strings and inline
// nodes otherwise.
func parseInline(source string) any {
	var parts []any
	var text strings.Builder
	flush := func() {
		if text.Len() > 0 {
			parts = append(parts, text.String())
			text.Reset()
		}
	}
	appendParsed := func(value string) {
		flush()
		switch parsed := parseInline(value).(type) {
		case string:
			if parsed != "" {
				parts = append(parts, parsed)
			}
		case []any:
			parts = append(parts, parsed...)
		}
	}

	for index := 0; index < len(source); {
		char := source[index]
		switch {
		case char == '\\':
			if index+1 >= len(source) {
				text.WriteByte(char)
				index++
				continue
			}
			switch source[index+1] {
			case '&', '%', '$', '#', '_', '{', '}':
				text.WriteByte(source[index+1])
				index += 2
				continue
			case '\\':
				text.WriteByte('\n')
				index += 2
				continue
			case '(':
				end := strings.Index(source[index+2:], `\)`)
				if end >= 0 {
					expression := source[index+2 : index+2+end]
					if isSymbolsOnly(expression) {
						text.WriteString(strings.TrimSpace(expression))
					} else {
						flush()
						parts = append(parts, Inline{Type: "mathematical_expression", Expression: expression})
					}
					index += 2 + end + 2
					continue
				}
			}
			name, next := readCommand(source, index)
			if name == "" {
				text.WriteByte(char)
				index++
				continue
			}
			arg, after, hasArg := readGroupAt(source, next)
			switch name {
			case "textbf":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "bold", Text: parseInline(arg)})
					index = after
					continue
				}
			case "textit", "emph":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "italic", Text: parseInline(arg)})
					index = after
					continue
				}
			case "underline", "uline":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "underline", Text: parseInline(arg)})
					index = after
					continue
				}
			case "texttt":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "code", Text: parseInline(arg)})
					index = after
					continue
				}
			case "textsuperscript":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "superscript", Text: parseInline(arg)})
					index = after
					continue
				}
			case "textsubscript":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "subscript", Text: parseInline(arg)})
					index = after
					continue
				}
			case "textrm", "textsf", "textnormal", "textup", "textmd", "text":
				if hasArg {
					appendParsed(arg)
					index = after
					continue
				}
			case "textcolor":
				if _, afterColor, ok := readGroupAt(source, next); ok {
					if value, afterValue, ok := readGroupAt(source, afterColor); ok {
						appendParsed(value)
						index = afterValue
						continue
					}
				}
			case "href":
				if url, afterURL, ok := readGroupAt(source, next); ok {
					if label, afterLabel, ok := readGroupAt(source, afterURL); ok {
						flush()
						parts = append(parts, Inline{Type: "url", Text: parseInline(label), URL: url})
						index = afterLabel
						continue
					}
				}
			case "hyperlink", "hypertarget":
				// Telegram rich text has no named-anchor equivalent. Keep
				// the visible label and discard the internal PDF target; the
				// PNG/PDF renderer preserves the actual hyperref command.
				if _, afterTarget, ok := readGroupAt(source, next); ok {
					if label, afterLabel, ok := readGroupAt(source, afterTarget); ok {
						appendParsed(label)
						index = afterLabel
						continue
					}
				}
			case "url":
				if hasArg {
					flush()
					parts = append(parts, Inline{Type: "url", Text: arg, URL: arg})
					index = after
					continue
				}
			case "item":
				text.WriteString("• ")
				index = skipEmptyGroup(source, next)
				continue
			case "quad", "qquad", ",", ";", ":", "!", " ":
				text.WriteByte(' ')
				index = skipEmptyGroup(source, next)
				continue
			case "ldots", "dots":
				text.WriteString("…")
				index = skipEmptyGroup(source, next)
				continue
			case "LaTeX":
				text.WriteString("LaTeX")
				index = skipEmptyGroup(source, next)
				continue
			case "TeX":
				text.WriteString("TeX")
				index = skipEmptyGroup(source, next)
				continue
			}
			text.WriteString(`\` + name)
			index = next
		case char == '$':
			end := strings.IndexByte(source[index+1:], '$')
			if end >= 0 && end > 0 {
				expression := source[index+1 : index+1+end]
				if isSymbolsOnly(expression) {
					// Client math fonts often lack exotic symbols; the
					// regular text font renders them everywhere.
					text.WriteString(strings.TrimSpace(expression))
				} else {
					flush()
					parts = append(parts, Inline{Type: "mathematical_expression", Expression: expression})
				}
				index += end + 2
				continue
			}
			text.WriteByte(char)
			index++
		case char == '~':
			text.WriteByte(' ')
			index++
		default:
			text.WriteByte(char)
			index++
		}
	}
	flush()

	if len(parts) == 1 {
		if value, ok := parts[0].(string); ok {
			return value
		}
	}
	if len(parts) == 0 {
		return ""
	}
	return parts
}

// skipEmptyGroup skips an empty {} group immediately following a control
// word, as in \LaTeX{}.
func skipEmptyGroup(source string, index int) int {
	if strings.HasPrefix(source[index:], "{}") {
		return index + 2
	}
	return index
}

// readCommand reads a backslash command name at position index.
func readCommand(source string, index int) (string, int) {
	next := index + 1
	name := ""
	for next < len(source) && isCommandLetter(source[next]) {
		name += string(source[next])
		next++
	}
	if name == "" && next < len(source) {
		// Single-character commands such as \, or \; .
		name = string(source[next])
		next++
	}
	return name, next
}

// readGroupAt reads a balanced {group} starting at position index, skipping
// spaces.
func readGroupAt(source string, index int) (string, int, bool) {
	for index < len(source) && (source[index] == ' ' || source[index] == '\t') {
		index++
	}
	if index >= len(source) || source[index] != '{' {
		return "", index, false
	}
	depth := 0
	start := index + 1
	for position := index; position < len(source); position++ {
		switch source[position] {
		case '\\':
			position++ // skip the escaped character
		case '{':
			depth++
		case '}':
			depth--
			if depth == 0 {
				return source[start:position], position + 1, true
			}
		}
	}
	return "", index, false
}