This data type specifies operators that work on values of type a.
An operator is either binary infix or unary prefix or postfix. A
binary operator has also an associated associativity.
An OperatorTable m a is a list of Operator m a
lists. The list is ordered in descending
precedence. All operators in one list have the same precedence (but
may have a different associativity).
buildExpressionParser table term builds an expression parser for
terms term with operators from table, taking the associativity
and precedence specified in table into account. Prefix and postfix
operators of the same precedence can only occur once (i.e. --2 is
not allowed if - is prefix negate). Prefix and postfix operators
of the same precedence associate to the left (i.e. if ++ is
postfix increment, than -2++ equals -1, not -3).
The buildExpressionParser takes care of all the complexity
involved in building expression parser. Here is an example of an
expression parser that handles prefix signs, postfix increment and
basic arithmetic.
import Control.Applicative ((<|>))
import Text.Parser.Combinators ((<?>))
import Text.Parser.Expression
import Text.Parser.Token (TokenParsing, natural, parens, reserve)
import Text.Parser.Token.Style (emptyOps)
expr :: (Monad m, TokenParsing m) => m Integer
expr = buildExpressionParser table term
<?> "expression"
term :: (Monad m, TokenParsing m) => m Integer
term = parens expr
<|> natural
<?> "simple expression"
table :: (Monad m, TokenParsing m) => [[Operator m Integer]]
table = [ [prefix "-" negate, prefix "+" id ]
, [postfix "++" (+1)]
, [binary "*" (*) AssocLeft, binary "/" (div) AssocLeft ]
, [binary "+" (+) AssocLeft, binary "-" (-) AssocLeft ]
]
binary name fun assoc = Infix (fun <$ reservedOp name) assoc
prefix name fun = Prefix (fun <$ reservedOp name)
postfix name fun = Postfix (fun <$ reservedOp name)
reservedOp name = reserve emptyOps name