Hello Cafe,
 I am trying to write a parser for propositional logic[1]. It's working fine for every input except equivalence ( <=> ).


*Main> calculator "a=>b"
Imp (Lit 'a') (Lit 'b')
*Main> calculator "a<=b"
Red (Lit 'a') (Lit 'b')
*Main> calculator "a<=>b"
*** Exception: failed to parse

*Main> calculator "a<=>b"
Eqi (Lit 'a') (Lit 'b')

Could some please tell me how to solve this problem.  I also tried fixity declaration but got this error
LogicPraser.hs:12:10:
    The fixity signature for `<=>' lacks an accompanying binding

-Mukesh Tiwari

[1] http://logic.stanford.edu/classes/cs157/2010/notes/chap02.html


{-# LANGUAGE NoMonomorphismRestriction #-}
import Text.Parsec.Token
import Text.Parsec.Prim
import Text.Parsec.Char
import Text.Parsec.Expr
import Text.Parsec.Combinator
import Text.Parsec.Language
import Control.Applicative hiding ( ( <|> ) , many )
import Data.Maybe ( fromJust )


--infixl 9 <=>

data LExpr = Lit Char
           | Not LExpr
           | And LExpr LExpr
           | Or LExpr LExpr
           | Imp LExpr LExpr  -- (=>)
           | Red LExpr LExpr  -- ( <= )
           | Eqi LExpr LExpr  -- ( <=> )
           deriving Show

exprCal = buildExpressionParser table atom

table = [  [ Prefix ( Not <$ string  "~"  ) ]
         , [ Infix  ( And <$ string  "&"  ) AssocLeft ]
         , [ Infix  ( Or  <$ string "|"   ) AssocLeft ]
         , [  Infix  ( Imp <$ string "=>"  ) AssocLeft 
            , Infix  (  Red <$ string "<=" ) AssocLeft
            , Infix  ( Eqi <$ string "<=>" ) AssocLeft
           ]
        ]


atom =  char '(' *>  exprCal   <* char ')'
     <|> ( Lit <$> letter )

calculator :: String -> LExpr
calculator expr = case parse  exprCal ""  expr of
                       Left msg -> error "failed to parse"
                       Right ( val ) -> val
~