%ignore /[ \t\n\r]+/

%ignore "\\," | "\\thinspace" | "\\:" | "\\medspace" | "\\;" | "\\thickspace"
%ignore "\\quad" | "\\qquad"
%ignore "\\!" | "\\negthinspace" | "\\negmedspace" | "\\negthickspace"
%ignore "\\vrule" | "\\vcenter" | "\\vbox" | "\\vskip" | "\\vspace" | "\\hfill"
%ignore "\\*" | "\\-" | "\\." | "\\/" | "\\\\" | "\\(" | "\\="

%ignore "\\left" | "\\right"
%ignore "\\limits" | "\\nolimits"
%ignore "\\displaystyle"

///////////////////// tokens ///////////////////////

// basic binary operators
ADD: "+"
SUB: "-"
MUL: "*"
DIV: "/"

// tokens with distinct left and right symbols
L_BRACE: "{"
R_BRACE: "}"
L_BRACE_LITERAL: "\\{"
R_BRACE_LITERAL: "\\}"
L_BRACKET: "["
R_BRACKET: "]"
L_CEIL: "\\lceil"
R_CEIL: "\\rceil"
L_FLOOR: "\\lfloor"
R_FLOOR: "\\rfloor"
L_PAREN: "("
R_PAREN: ")"

// limit, integral, sum, and product symbols
FUNC_LIM:  "\\lim"
LIM_APPROACH_SYM: "\\to" | "\\rightarrow" | "\\Rightarrow" | "\\longrightarrow" | "\\Longrightarrow"
FUNC_INT:  "\\int" | "\\intop"
FUNC_SUM:  "\\sum"
FUNC_PROD: "\\prod"

// common functions
FUNC_EXP:  "\\exp"
FUNC_LOG:  "\\log"
FUNC_LN:   "\\ln"
FUNC_LG:   "\\lg"
FUNC_MIN: "\\min"
FUNC_MAX: "\\max"

// trigonometric functions
FUNC_SIN:  "\\sin"
FUNC_COS:  "\\cos"
FUNC_TAN:  "\\tan"
FUNC_CSC:  "\\csc"
FUNC_SEC:  "\\sec"
FUNC_COT:  "\\cot"

// inverse trigonometric functions
FUNC_ARCSIN: "\\arcsin"
FUNC_ARCCOS: "\\arccos"
FUNC_ARCTAN: "\\arctan"
FUNC_ARCCSC: "\\arccsc"
FUNC_ARCSEC: "\\arcsec"
FUNC_ARCCOT: "\\arccot"

// hyperbolic trigonometric functions
FUNC_SINH: "\\sinh"
FUNC_COSH: "\\cosh"
FUNC_TANH: "\\tanh"
FUNC_ARSINH: "\\arsinh"
FUNC_ARCOSH: "\\arcosh"
FUNC_ARTANH: "\\artanh"

FUNC_SQRT: "\\sqrt"

// miscellaneous symbols
CMD_TIMES: "\\times"
CMD_CDOT:  "\\cdot"
CMD_DIV:   "\\div"
CMD_FRAC:  "\\frac" | "\\dfrac" | "\\tfrac" | "\\nicefrac"
CMD_BINOM: "\\binom" | "\\dbinom" | "\\tbinom"
CMD_OVERLINE: "\\overline"
CMD_LANGLE: "\\langle"
CMD_RANGLE: "\\rangle"

CMD_MATHIT: "\\mathit"

CMD_INFTY: "\\infty"

BANG: "!"
BAR: "|"
CARET: "^"
COLON: ":"
UNDERSCORE: "_"

// relational symbols
EQUAL: "="
NOT_EQUAL: "\\neq" | "\\ne"
LT: "<"
LTE: "\\leq" | "\\le" | "\\leqslant"
GT: ">"
GTE: "\\geq" | "\\ge" | "\\geqslant"

DIV_SYMBOL: CMD_DIV | DIV
MUL_SYMBOL: MUL | CMD_TIMES | CMD_CDOT

%import .greek_symbols.GREEK_SYMBOL

UPRIGHT_DIFFERENTIAL_SYMBOL: "\\text{d}" | "\\mathrm{d}"
DIFFERENTIAL_SYMBOL: "d" | UPRIGHT_DIFFERENTIAL_SYMBOL

// disallow "d" as a variable name because we want to parse "d" as a differential symbol.
SYMBOL: /[a-zA-Z]/
BASIC_SUBSCRIPTED_SYMBOL: /([a-zA-Z])_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+)\})/
SYMBOL_WITH_GREEK_SUBSCRIPT: /([a-zA-Z])_/ GREEK_SYMBOL | /([a-zA-Z])_/ L_BRACE GREEK_SYMBOL R_BRACE
// best to define the variant with braces like that instead of shoving it all into one case like in
// /([a-zA-Z])_/ L_BRACE? GREEK_SYMBOL R_BRACE? because then we can easily error out on input like
// r"h_{\theta"
GREEK_SUBSCRIPTED_SYMBOL: GREEK_SYMBOL /_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+)\})/

%import common.DIGIT -> DIGIT

//////////////////// grammar //////////////////////

latex_string: _relation | _expression

_one_letter_symbol: SYMBOL
    | BASIC_SUBSCRIPTED_SYMBOL
    | SYMBOL_WITH_GREEK_SUBSCRIPT
    | GREEK_SUBSCRIPTED_SYMBOL
    | GREEK_SYMBOL
multi_letter_symbol: CMD_MATHIT L_BRACE /[a-zA-Z]+(\s+[a-zA-Z]+)*/ R_BRACE
number: /\d+(\.\d*)?/

_atomic_expr: _one_letter_symbol
    | multi_letter_symbol
    | number
    | CMD_INFTY

group_round_parentheses: L_PAREN _expression R_PAREN
group_square_brackets: L_BRACKET _expression R_BRACKET
group_curly_parentheses: L_BRACE _expression R_BRACE

_relation: eq | ne | lt | lte | gt | gte

eq: _expression EQUAL _expression
ne: _expression NOT_EQUAL _expression
lt: _expression LT _expression
lte: _expression LTE _expression
gt: _expression GT _expression
gte: _expression GTE _expression

_expression_core: _atomic_expr | group_curly_parentheses

add: _expression ADD _expression_mul
sub: _expression SUB _expression_mul
    | SUB _expression_mul
mul: _expression_mul MUL_SYMBOL _expression_power
div: _expression_mul DIV_SYMBOL _expression_power

adjacent_expressions: (_one_letter_symbol | number) _expression_mul
    | group_round_parentheses (group_round_parentheses | _one_letter_symbol)
    | _function _function
    | fraction _expression

_expression_func: _expression_core
    | group_round_parentheses
    | fraction
    | binomial
    | _function

_expression_power: _expression_func | superscript

_expression_mul: _expression_power
    | mul | div | adjacent_expressions
    | _integral// | derivative
    | summation | product
    | limit

_expression: _expression_mul | add | sub

_limit_dir: "+" | "-" | L_BRACE ("+" | "-") R_BRACE

limit_dir_expr: _expression CARET _limit_dir

group_curly_parentheses_lim: L_BRACE _expression LIM_APPROACH_SYM (limit_dir_expr | _expression) R_BRACE

limit: FUNC_LIM UNDERSCORE group_curly_parentheses_lim _expression

differential: DIFFERENTIAL_SYMBOL _one_letter_symbol

//_derivative_operator: CMD_FRAC L_BRACE DIFFERENTIAL_SYMBOL R_BRACE L_BRACE differential R_BRACE

//derivative: _derivative_operator _expression

_integral: normal_integral | integral_with_special_fraction

normal_integral: FUNC_INT _expression DIFFERENTIAL_SYMBOL _one_letter_symbol
    | FUNC_INT (CARET _expression_core UNDERSCORE _expression_core)? _expression? DIFFERENTIAL_SYMBOL _one_letter_symbol
    | FUNC_INT (UNDERSCORE _expression_core CARET _expression_core)? _expression? DIFFERENTIAL_SYMBOL _one_letter_symbol

group_curly_parentheses_int: L_BRACE _expression? differential R_BRACE

special_fraction: CMD_FRAC group_curly_parentheses_int group_curly_parentheses

integral_with_special_fraction: FUNC_INT special_fraction
    | FUNC_INT (CARET _expression_core UNDERSCORE _expression_core)? special_fraction
    | FUNC_INT (UNDERSCORE _expression_core CARET _expression_core)? special_fraction

group_curly_parentheses_special: UNDERSCORE L_BRACE _atomic_expr EQUAL _atomic_expr R_BRACE CARET _expression_core
    | CARET _expression_core UNDERSCORE L_BRACE _atomic_expr EQUAL _atomic_expr R_BRACE

summation: FUNC_SUM group_curly_parentheses_special _expression
    | FUNC_SUM group_curly_parentheses_special _expression

product: FUNC_PROD group_curly_parentheses_special _expression
    | FUNC_PROD group_curly_parentheses_special _expression

superscript: _expression_func CARET _expression_power

fraction: _basic_fraction
    | _simple_fraction
    | _general_fraction

_basic_fraction: CMD_FRAC DIGIT (DIGIT | SYMBOL | GREEK_SYMBOL)

_simple_fraction: CMD_FRAC DIGIT group_curly_parentheses
    | CMD_FRAC group_curly_parentheses (DIGIT | SYMBOL | GREEK_SYMBOL)

_general_fraction: CMD_FRAC group_curly_parentheses group_curly_parentheses

binomial: _basic_binomial
    | _simple_binomial
    | _general_binomial

_basic_binomial: CMD_BINOM DIGIT (DIGIT | SYMBOL | GREEK_SYMBOL)

_simple_binomial: CMD_BINOM DIGIT group_curly_parentheses
    | CMD_BINOM group_curly_parentheses (DIGIT | SYMBOL | GREEK_SYMBOL)

_general_binomial: CMD_BINOM group_curly_parentheses group_curly_parentheses

list_of_expressions: _expression ("," _expression)*

function_applied: _one_letter_symbol L_PAREN list_of_expressions R_PAREN

min: FUNC_MIN L_PAREN list_of_expressions R_PAREN

max: FUNC_MAX L_PAREN list_of_expressions R_PAREN

bra: CMD_LANGLE _expression BAR

ket: BAR _expression CMD_RANGLE

inner_product: CMD_LANGLE _expression BAR _expression CMD_RANGLE

_function: function_applied
    | abs | floor | ceil
    | _trigonometric_function | _inverse_trigonometric_function
    | _trigonometric_function_power
    | _hyperbolic_trigonometric_function | _inverse_hyperbolic_trigonometric_function
    | exponential
    | log
    | square_root
    | factorial
    | conjugate
    | max | min
    | bra | ket | inner_product

exponential: FUNC_EXP _expression

log: FUNC_LOG _expression
    | FUNC_LN _expression
    | FUNC_LG _expression
    | FUNC_LOG UNDERSCORE (DIGIT | _one_letter_symbol) _expression
    | FUNC_LOG UNDERSCORE group_curly_parentheses _expression

square_root: FUNC_SQRT group_curly_parentheses
    | FUNC_SQRT group_square_brackets group_curly_parentheses

factorial: _expression BANG

conjugate: CMD_OVERLINE group_curly_parentheses
    | CMD_OVERLINE DIGIT

_trigonometric_function: sin | cos | tan | csc | sec | cot

sin: FUNC_SIN _expression
cos: FUNC_COS _expression
tan: FUNC_TAN _expression
csc: FUNC_CSC _expression
sec: FUNC_SEC _expression
cot: FUNC_COT _expression

_trigonometric_function_power: sin_power | cos_power | tan_power | csc_power | sec_power | cot_power

sin_power: FUNC_SIN CARET _expression_core _expression
cos_power: FUNC_COS CARET _expression_core _expression
tan_power: FUNC_TAN CARET _expression_core _expression
csc_power: FUNC_CSC CARET _expression_core _expression
sec_power: FUNC_SEC CARET _expression_core _expression
cot_power: FUNC_COT CARET _expression_core _expression

_hyperbolic_trigonometric_function: sinh | cosh | tanh

sinh: FUNC_SINH _expression
cosh: FUNC_COSH _expression
tanh: FUNC_TANH _expression

_inverse_trigonometric_function: arcsin | arccos | arctan | arccsc | arcsec | arccot

arcsin: FUNC_ARCSIN _expression
arccos: FUNC_ARCCOS _expression
arctan: FUNC_ARCTAN _expression
arccsc: FUNC_ARCCSC _expression
arcsec: FUNC_ARCSEC _expression
arccot: FUNC_ARCCOT _expression

_inverse_hyperbolic_trigonometric_function: asinh | acosh | atanh

asinh: FUNC_ARSINH _expression
acosh: FUNC_ARCOSH _expression
atanh: FUNC_ARTANH _expression

abs: BAR _expression BAR
floor: L_FLOOR _expression R_FLOOR
ceil: L_CEIL _expression R_CEIL