# Arithmetic-grammar

#######################################################################
#
#  EBNF-Directives
#
#######################################################################

@ whitespace  = vertical           # implicit whitespace, includes any number of line feeds
@ literalws   = right              # literals have implicit whitespace on the right hand side
@ comment     = /#.*/              # comments range from a '#'-character to the end of the line
@ ignorecase  = False              # literals and regular expressions are case-sensitive
@ drop        = whitespace, token  # drop anonymous whitespace

#######################################################################
#
#: Structure and Components
#
#######################################################################

expression = term  { (PLUS|MINUS) term}
term       = factor { (DIV|MUL) factor}
factor     = [sign] ( NUMBER | VARIABLE | group )
sign       = POSITIVE | NEGATIVE
group      = "(" expression ")"

#######################################################################
#
#: "Leaf"-Expressions
#
#######################################################################

PLUS       = "+"
MINUS      = "-"
MUL        = "*" | &factor  # TODO: higher precedence of &factor
DIV        = "/"

POSITIVE   = /[+]/      # no implicit whitespace after signs
NEGATIVE   = /[-]/

NUMBER     = /(?:0|(?:[1-9]\d*))(?:\.\d+)?/~
VARIABLE   = /[A-Za-z]/~