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module BoolExp
  ( BoolExp(..), bTrue, bFalse, bNot, bEqu, bEquVar, bindingBE, letBinding
  , forallBinding, existsBinding, assertSMT, allSymbolsOfBE, simpBE
  , showBoolExp, smtBE, asLisp, prettyBE, withBracket ) where

import qualified SetFunctions
import qualified Char
import qualified List

data BoolExp = BVar Int
             | BTerm String [BoolExp]
             | Conj [BoolExp]
             | Disj [BoolExp]
             | Not BoolExp
             | Binding String [(Int,BoolExp)] BoolExp

bTrue :: BoolExp
bTrue = BTerm "true" []

bFalse :: BoolExp
bFalse = BTerm "false" []

bNot :: BoolExp -> BoolExp
bNot = Not

bEqu :: BoolExp -> BoolExp -> BoolExp
bEqu b1 b2 = BTerm "=" [b1,b2]

bEquVar :: Int -> BoolExp -> BoolExp
bEquVar v bexp = BTerm "=" [BVar v,bexp]

bindingBE :: String -> [(Int,BoolExp)] -> BoolExp -> BoolExp
bindingBE bkind bs exp
  | null bs = exp
  | otherwise = Binding bkind bs exp

letBinding :: [(Int,BoolExp)] -> BoolExp -> BoolExp
letBinding = bindingBE "let"

forallBinding :: [(Int,BoolExp)] -> BoolExp -> BoolExp
forallBinding = bindingBE "forall"

existsBinding :: [(Int,BoolExp)] -> BoolExp -> BoolExp
existsBinding = bindingBE "exists"

assertSMT :: BoolExp -> BoolExp
assertSMT be = BTerm "assert" [be]

allSymbolsOfBE :: BoolExp -> [String]
allSymbolsOfBE (BVar _) = []
allSymbolsOfBE (BTerm s args) = foldr List.union [s] (map allSymbolsOfBE args)
allSymbolsOfBE (Conj args) = foldr List.union [] (map allSymbolsOfBE args)
allSymbolsOfBE (Disj args) = foldr List.union [] (map allSymbolsOfBE args)
allSymbolsOfBE (Not arg) = allSymbolsOfBE arg
allSymbolsOfBE (Binding _ bs e) =
  foldr List.union [] (map allSymbolsOfBE (e : map snd bs))

simpBE :: BoolExp -> BoolExp
simpBE x1 = SetFunctions.selectValue (SetFunctions.set1 simpBE_ORGNDFUN x1)

simpBE_ORGNDFUN_ORGRULES :: BoolExp -> BoolExp
simpBE_ORGNDFUN_ORGRULES (Conj (bs1 ++ ([BTerm "true" []] ++ bs2))) =
  simpBE (Conj (bs1 ++ bs2))
simpBE_ORGNDFUN_ORGRULES (Conj (_ ++ ([BTerm "false" []] ++ _))) = bFalse
simpBE_ORGNDFUN_ORGRULES (Conj (bs1 ++ ([Conj bs2] ++ bs3))) =
  simpBE (Conj (bs1 ++ (bs2 ++ bs3)))
simpBE_ORGNDFUN_ORGRULES (Conj bs) =
  if null bs then bTrue else Conj (map simpBE bs)
simpBE_ORGNDFUN_ORGRULES (Disj (bs1 ++ ([BTerm "false" []] ++ bs2))) =
  simpBE (Disj (bs1 ++ bs2))
simpBE_ORGNDFUN_ORGRULES (Disj (_ ++ ([BTerm "true" []] ++ _))) = bTrue
simpBE_ORGNDFUN_ORGRULES (Disj (bs1 ++ ([Disj bs2] ++ bs3))) =
  simpBE (Disj (bs1 ++ (bs2 ++ bs3)))
simpBE_ORGNDFUN_ORGRULES (Disj bs) =
  if null bs then bFalse else Disj (map simpBE bs)
simpBE_ORGNDFUN_ORGRULES (Not (Not b)) = b
simpBE_ORGNDFUN_ORGRULES (Binding _ [] e) = e
simpBE_ORGNDFUN_ORGRULES (BTerm f args) = BTerm f (map simpBE args)

simpBE_ORGNDFUN_APPLICABLE :: BoolExp -> ()
simpBE_ORGNDFUN_APPLICABLE (Conj (_ ++ ([BTerm "true" []] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Conj (_ ++ ([BTerm "false" []] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Conj (_ ++ ([Conj _] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Conj _) = ()
simpBE_ORGNDFUN_APPLICABLE (Disj (_ ++ ([BTerm "false" []] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Disj (_ ++ ([BTerm "true" []] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Disj (_ ++ ([Disj _] ++ _))) = ()
simpBE_ORGNDFUN_APPLICABLE (Disj _) = ()
simpBE_ORGNDFUN_APPLICABLE (Not (Not _)) = ()
simpBE_ORGNDFUN_APPLICABLE (Binding _ [] _) = ()
simpBE_ORGNDFUN_APPLICABLE (BTerm _ _) = ()

simpBE_ORGNDFUN_DEFAULT :: BoolExp -> BoolExp
simpBE_ORGNDFUN_DEFAULT be
  | SetFunctions.isEmpty (SetFunctions.set1 simpBE_ORGNDFUN_APPLICABLE be)
  = be

simpBE_ORGNDFUN :: BoolExp -> BoolExp
simpBE_ORGNDFUN x1 = simpBE_ORGNDFUN_ORGRULES x1 ? simpBE_ORGNDFUN_DEFAULT x1

showBoolExp :: BoolExp -> String
showBoolExp = smtBE . simpBE

smtBE :: BoolExp -> String
smtBE (BVar i) = 'x' : show i
smtBE (BTerm f args)
  | f == "=" = asLisp ["=",smtBE (head args),smtBE (args !! 1)]
  | f == "/=" = smtBE (Not (BTerm "=" args))
  | f == "let"
  = asLisp
     ["let"
     ,asLisp (map (\(BTerm _ [v,e]) -> asLisp [smtBE v,smtBE e]) (tail args))
     ,smtBE (head args)]
  | otherwise = if null args then f else asLisp $ (f : map smtBE args)
smtBE (Conj bs) =
  case bs of
    [] -> "true"
    [b] -> smtBE b
    _ -> asLisp $ ("and" : map smtBE bs)
smtBE (Disj bs) =
  case bs of
    [] -> "false"
    [b] -> smtBE b
    _ -> asLisp $ ("or" : map smtBE bs)
smtBE (Not b) = asLisp ["not",smtBE b]
smtBE (Binding s bs e) =
  asLisp
   [s,asLisp (map (\(v,b) -> asLisp [smtBE (BVar v),smtBE b]) bs),smtBE e]

asLisp :: [String] -> String
asLisp = withBracket . unwords

prettyBE :: BoolExp -> String
prettyBE (BVar i) = 'x' : show i
prettyBE (BTerm f args)
  | f == "=" = prettyBE (head args) ++ (" = " ++ prettyBE (args !! 1))
  | f == "/=" = prettyBE (Not (BTerm "=" args))
  | null args = f
  | not (Char.isAlpha (head f)) && (length args == 2)
  = prettyBE (args !! 0) ++ (f ++ prettyBE (args !! 1))
  | otherwise = f ++ withBracket (List.intercalate "," (map prettyBE args))
prettyBE (Conj bs) =
  case bs of
    [] -> "true"
    [b] -> prettyBE b
    _ -> withBracket (List.intercalate " && " (map prettyBE bs))
prettyBE (Disj bs) =
  case bs of
    [] -> "false"
    [b] -> prettyBE b
    _ -> withBracket (List.intercalate " || " (map prettyBE bs))
prettyBE (Not b) = withBracket ("not " ++ prettyBE b)
prettyBE (Binding s bs e) =
  withBracket
   $ (unwords
       $ [s
         ,"{"
         ,List.intercalate ";"
           (map (\(v,b) -> unwords [prettyBE (BVar v),"=",prettyBE b]) bs)
         ,"}"
         ,prettyBE e])

withBracket :: String -> String
withBracket s = '(' : (s ++ ")")