# Pattern for blank space, includes
# spaces, newlines, and comments 
# that begin with a hash.
skipper = \b([ \t\n\r]+|\#.*)*

# An integer
int = -?[0-9]+
end = ([ \t]+|\#.*)*\r*\n
keywords = to|default|if|then|else|end|begin|and|or
bare_name = \b(?!D{keywords}\b)[A-Za-z][A-Za-z0-9]*

# A name that isn't a keyword or operator
name = \b(?![DO]|{keywords}\b)[A-Za-z][A-Za-z0-9]*
bracket = \[ {expr} (, {expr} (, {expr} |)|)\]

# C-identifier
lower_index = ({index_symbol}|\({index_expr}(,{index_expr})*\))
upper_index = ({index_symbol}|\({index_expr}(,{index_expr})*\))
indices = (\_{lower_index}+|\^{upper_index}+)*

# Indexes can be single letters with primes, or digits
index_symbol = [a-zA-Z]'*|[0-9]
index_op = [+-]
index_expr = {index_symbol}({index_op}{int}|)
tensor = {name}{indices}( {bracket}|)

# Tensor name
tname = {tensor}|{name}
dname = [DO][a-z0-9]*
dtensor = {dname}{indices}? {tensor}

# Parse a floating point number
number = -?[0-9]+(\.[0-9]*|)([eEdD][+-]?[0-9]+|)

# Supported function names
fname = (a?sinh?|a?cosh?|a?tanh?|pow|exp|log|min|max|copysign|abs)

# A function call
func = {fname} \( ({expr}( , {expr})*|) \)

neg = -

# A value
value = {neg}?({func}|{dtensor}|{tensor}|{number}|{ifexpr}|\( {expr} \))

# Powers
pow = {neg}?{value}( \*\* {value}|)

# multiplication / division expression
mulop = [*/%]
mulimp = [ \t]*(?!-)
mul = {pow}( {mulop} {pow}|{mulimp}{pow})*

# addition / subtraction expression
addop = [+-]
expr = {mul}( {addop} {mul})*

# Compare expression
cmpop = (<=?|>=?|==|!=)
coexpr = {expr} {cmpop} {expr}|\( {cexpr} \)

# Logical operation
logop = and|or

# Conditional expression
cexpr = {coexpr}( {logop} {coexpr})*

# For step functions, etc.
ifexpr = if {cexpr} then {expr} else {expr} 

# Differential name plus indices
doper = {dname}{indices}

# Differential equations
deqn = {doper} {bare_name} \= {expr}{-end}
deqns = {deqn}( {deqn})*

# One or more equations
eqn = ({dtensor}|{tensor}) \= {expr}{-end}

# The last group in the file is the default
# rule to use first in parsing.
eqns = {eqn}( {eqn})*