%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]'*/
GREEK_SYMBOL_WITH_PRIMES: GREEK_SYMBOL "'"*
LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT: /([a-zA-Z]'*)_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+'*)\})/
LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT: /([a-zA-Z]'*)_/ GREEK_SYMBOL | /([a-zA-Z]'*)_/ L_BRACE GREEK_SYMBOL_WITH_PRIMES 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_SYMBOL_WITH_LATIN_SUBSCRIPT: GREEK_SYMBOL_WITH_PRIMES /_(([A-Za-z0-9]|[a-zA-Z]+)|\{([A-Za-z0-9]|[a-zA-Z]+'*)\})/
GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT: GREEK_SYMBOL_WITH_PRIMES /_/ (GREEK_SYMBOL | L_BRACE GREEK_SYMBOL_WITH_PRIMES R_BRACE)
MULTI_LETTER_SYMBOL: /[a-zA-Z]+(\s+[a-zA-Z]+)*'*/

%import common.DIGIT -> DIGIT

CMD_PRIME: "\\prime"
CMD_ASTERISK: "\\ast"

PRIMES: "'"+
STARS: "*"+
PRIMES_VIA_CMD: CMD_PRIME+
STARS_VIA_CMD: CMD_ASTERISK+

CMD_IMAGINARY_UNIT: "\\imaginaryunit"

CMD_BEGIN: "\\begin"
CMD_END: "\\end"

// matrices
IGNORE_L: /[ \t\n\r]*/ L_BRACE* /[ \t\n\r]*/
IGNORE_R: /[ \t\n\r]*/ R_BRACE* /[ \t\n\r]*/
ARRAY_MATRIX_BEGIN: L_BRACE "array" R_BRACE L_BRACE /[^}]*/ R_BRACE
ARRAY_MATRIX_END: L_BRACE "array" R_BRACE
AMSMATH_MATRIX: L_BRACE "matrix" R_BRACE
AMSMATH_PMATRIX: L_BRACE "pmatrix" R_BRACE
AMSMATH_BMATRIX: L_BRACE "bmatrix" R_BRACE
// Without the (L|R)_PARENs and (L|R)_BRACKETs, a matrix defined using
// \begin{array}...\end{array} or \begin{matrix}...\end{matrix} must
// not qualify as a complete matrix expression; this is done so that
// if we have \begin{array}...\end{array} or \begin{matrix}...\end{matrix}
// between BAR pairs, then they should be interpreted as determinants as
// opposed to sympy.Abs (absolute value) applied to a matrix.
CMD_BEGIN_AMSPMATRIX_AMSBMATRIX: CMD_BEGIN (AMSMATH_PMATRIX | AMSMATH_BMATRIX)
CMD_BEGIN_ARRAY_AMSMATRIX: (L_PAREN | L_BRACKET) IGNORE_L CMD_BEGIN (ARRAY_MATRIX_BEGIN | AMSMATH_MATRIX)
CMD_MATRIX_BEGIN: CMD_BEGIN_AMSPMATRIX_AMSBMATRIX | CMD_BEGIN_ARRAY_AMSMATRIX
CMD_END_AMSPMATRIX_AMSBMATRIX: CMD_END (AMSMATH_PMATRIX | AMSMATH_BMATRIX)
CMD_END_ARRAY_AMSMATRIX: CMD_END (ARRAY_MATRIX_END | AMSMATH_MATRIX) IGNORE_R "\\right"? (R_PAREN | R_BRACKET)
CMD_MATRIX_END: CMD_END_AMSPMATRIX_AMSBMATRIX | CMD_END_ARRAY_AMSMATRIX
MATRIX_COL_DELIM: "&"
MATRIX_ROW_DELIM: "\\\\"
FUNC_MATRIX_TRACE: "\\trace"
FUNC_MATRIX_ADJUGATE: "\\adjugate"

// determinants
AMSMATH_VMATRIX: L_BRACE "vmatrix" R_BRACE
CMD_DETERMINANT_BEGIN_SIMPLE: CMD_BEGIN AMSMATH_VMATRIX
CMD_DETERMINANT_BEGIN_VARIANT: BAR IGNORE_L CMD_BEGIN (ARRAY_MATRIX_BEGIN | AMSMATH_MATRIX)
CMD_DETERMINANT_BEGIN: CMD_DETERMINANT_BEGIN_SIMPLE | CMD_DETERMINANT_BEGIN_VARIANT
CMD_DETERMINANT_END_SIMPLE: CMD_END AMSMATH_VMATRIX
CMD_DETERMINANT_END_VARIANT: CMD_END (ARRAY_MATRIX_END | AMSMATH_MATRIX) IGNORE_R "\\right"? BAR
CMD_DETERMINANT_END: CMD_DETERMINANT_END_SIMPLE | CMD_DETERMINANT_END_VARIANT
FUNC_DETERMINANT: "\\det"

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

latex_string: _relation | _expression

_one_letter_symbol: SYMBOL
    | LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT
    | LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT
    | GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT
    | GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT
    | GREEK_SYMBOL_WITH_PRIMES
// LuaTeX-generated outputs of \mathit{foo'} and \mathit{foo}'
// seem to be the same on the surface. We allow both styles.
multi_letter_symbol: CMD_MATHIT L_BRACE MULTI_LETTER_SYMBOL R_BRACE
    | CMD_MATHIT L_BRACE MULTI_LETTER_SYMBOL R_BRACE /'+/
number: /\d+(\.\d*)?/ | CMD_IMAGINARY_UNIT

_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
    | 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_mul

_expression_func: _expression_core
    | group_round_parentheses
    | fraction
    | binomial
    | _function
    | _integral// | derivative
    | limit
    | matrix

_expression_power: _expression_func | superscript | matrix_prime | symbol_prime

_expression_mul: _expression_power
    | mul | div | adjacent_expressions
    | summation | product

_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 | CMD_PRIME | CMD_ASTERISK)
    | _expression_func CARET L_BRACE (PRIMES | STARS | PRIMES_VIA_CMD | STARS_VIA_CMD) R_BRACE

matrix_prime: (matrix | group_round_parentheses) PRIMES

symbol_prime: (LATIN_SYMBOL_WITH_LATIN_SUBSCRIPT
    | LATIN_SYMBOL_WITH_GREEK_SUBSCRIPT
    | GREEK_SYMBOL_WITH_LATIN_SUBSCRIPT
    | GREEK_SYMBOL_WITH_GREEK_SUBSCRIPT) PRIMES

fraction: _basic_fraction
    | _simple_fraction
    | _general_fraction

_basic_fraction: CMD_FRAC DIGIT (DIGIT | SYMBOL | GREEK_SYMBOL_WITH_PRIMES)

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

_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_WITH_PRIMES)

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

_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
    | determinant
    | trace
    | adjugate

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_func 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

matrix: CMD_MATRIX_BEGIN matrix_body CMD_MATRIX_END
matrix_body: matrix_row (MATRIX_ROW_DELIM matrix_row)* (MATRIX_ROW_DELIM)?
matrix_row: _expression (MATRIX_COL_DELIM _expression)*
determinant: (CMD_DETERMINANT_BEGIN matrix_body CMD_DETERMINANT_END)
    | FUNC_DETERMINANT _expression
trace: FUNC_MATRIX_TRACE _expression
adjugate: FUNC_MATRIX_ADJUGATE _expression
