    ----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.SBV.SMT.SMTLib2
    -- Copyright   :  (c) Levent Erkok
    -- License     :  BSD3
    -- Maintainer  :  erkokl@gmail.com
    -- Stability   :  experimental
    --
    -- Conversion of symbolic programs to SMTLib format, Using v2 of the standard
    -----------------------------------------------------------------------------
    {-# LANGUAGE PatternGuards #-}

    module Data.SBV.SMT.SMTLib2(cvt, addNonEqConstraints) where

    import Data.Bits     (bit)
    import Data.Function (on)
    import Data.Ord      (comparing)
    import Data.List     (intercalate, partition, groupBy, sortBy)

    import qualified Data.Foldable as F (toList)
    import qualified Data.Map      as M
    import qualified Data.IntMap   as IM
    import qualified Data.Set      as Set

    import Data.SBV.BitVectors.Data
    import Data.SBV.BitVectors.PrettyNum (smtRoundingMode, cwToSMTLib)

    -- | Add constraints to generate /new/ models. This function is used to query the SMT-solver, while
    -- disallowing a previous model.
    addNonEqConstraints :: RoundingMode -> [(Quantifier, NamedSymVar)] -> [[(String, CW)]] -> SMTLibPgm -> Maybe String
    addNonEqConstraints rm qinps allNonEqConstraints (SMTLibPgm _ (aliasTable, pre, post))
      | null allNonEqConstraints
      = Just $ intercalate "\n" $ pre ++ post
      | null refutedModel
      = Nothing
      | True
      = Just $ intercalate "\n" $ pre
        ++ [ "; --- refuted-models ---" ]
        ++ refutedModel
        ++ post
     where refutedModel = concatMap (nonEqs rm . map intName) nonEqConstraints
           intName (s, c)
              | Just sw <- s `lookup` aliasTable = (show sw, c)
              | True                             = (s, c)
           -- with existentials, we only add top-level existentials to the refuted-models list
           nonEqConstraints = filter (not . null) $ map (filter (\(s, _) -> s `elem` topUnivs)) allNonEqConstraints
           topUnivs = [s | (_, (_, s)) <- takeWhile (\p -> fst p == EX) qinps]

    nonEqs :: RoundingMode -> [(String, CW)] -> [String]
    nonEqs rm scs = format $ interp ps ++ disallow (map eqClass uninterpClasses)
      where isFree (KUserSort _ (Left _)) = True
            isFree _                      = False
            (ups, ps) = partition (isFree . kindOf . snd) scs
            format []     =  []
            format [m]    =  ["(assert " ++ m ++ ")"]
            format (m:ms) =  ["(assert (or " ++ m]
                          ++ map ("            " ++) ms
                          ++ ["        ))"]
            -- Regular (or interpreted) sorts simply get a constraint that we disallow the current assignment
            interp = map $ nonEq rm
            -- Determine the equivalence classes of uninterpreted sorts:
            uninterpClasses = filter (\l -> length l > 1) -- Only need this class if it has at least two members
                            . map (map fst)               -- throw away sorts, we only need the names
                            . groupBy ((==) `on` snd)     -- make sure they belong to the same sort and have the same value
                            . sortBy (comparing snd)      -- sort them according to their sorts first
                            $ ups                         -- take the uninterpreted sorts
            -- Uninterpreted sorts get a constraint that says the equivalence classes as determined by the solver are disallowed:
            eqClass :: [String] -> String
            eqClass [] = error "SBV.allSat.nonEqs: Impossible happened, disallow received an empty list"
            eqClass cs = "(= " ++ unwords cs ++ ")"
            -- Now, take the conjunction of equivalence classes and assert it's negation:
            disallow = map $ \ec -> "(not " ++ ec ++ ")"

    nonEq :: RoundingMode -> (String, CW) -> String
    nonEq rm (s, c) = "(not (= " ++ s ++ " " ++ cvtCW rm c ++ "))"

    tbd :: String -> a
    tbd e = error $ "SBV.SMTLib2: Not-yet-supported: " ++ e

    -- | Translate a problem into an SMTLib2 script
    cvt :: RoundingMode                 -- ^ User selected rounding mode to be used for floating point arithmetic
        -> Maybe Logic                  -- ^ SMT-Lib logic, if requested by the user
        -> SolverCapabilities           -- ^ capabilities of the current solver
        -> Set.Set Kind                 -- ^ kinds used
        -> Bool                         -- ^ is this a sat problem?
        -> [String]                     -- ^ extra comments to place on top
        -> [(Quantifier, NamedSymVar)]  -- ^ inputs
        -> [Either SW (SW, [SW])]       -- ^ skolemized version inputs
        -> [(SW, CW)]                   -- ^ constants
        -> [((Int, Kind, Kind), [SW])]  -- ^ auto-generated tables
        -> [(Int, ArrayInfo)]           -- ^ user specified arrays
        -> [(String, SBVType)]          -- ^ uninterpreted functions/constants
        -> [(String, [String])]         -- ^ user given axioms
        -> SBVPgm                       -- ^ assignments
        -> [SW]                         -- ^ extra constraints
        -> SW                           -- ^ output variable
        -> ([String], [String])
    cvt rm smtLogic solverCaps kindInfo isSat comments inputs skolemInps consts tbls arrs uis axs (SBVPgm asgnsSeq) cstrs out = (pre, [])
      where -- the logic is an over-approaximation
            hasInteger     = KUnbounded `Set.member` kindInfo
            hasReal        = KReal      `Set.member` kindInfo
            hasFloat       = KFloat     `Set.member` kindInfo
            hasDouble      = KDouble    `Set.member` kindInfo
            hasBVs         = not $ null [() | KBounded{} <- Set.toList kindInfo]
            usorts         = [(s, dt) | KUserSort s dt <- Set.toList kindInfo]
            hasNonBVArrays = (not . null) [() | (_, (_, (k1, k2), _)) <- arrs, not (isBounded k1 && isBounded k2)]
            logic
               | Just l <- smtLogic
               = ["(set-logic " ++ show l ++ ") ; NB. User specified."]
               | hasDouble || hasFloat    -- NB. We don't check for quantifiers here, we probably should..
               = if hasBVs
                 then ["(set-logic QF_FPBV)"]
                 else ["(set-logic QF_FP)"]
               | hasInteger || hasReal || not (null usorts) || hasNonBVArrays
               = let why | hasInteger        = "has unbounded values"
                         | hasReal           = "has algebraic reals"
                         | not (null usorts) = "has user-defined sorts"
                         | hasNonBVArrays    = "has non-bitvector arrays"
                         | True              = "cannot determine the SMTLib-logic to use"
                 in case mbDefaultLogic solverCaps hasReal of
                      Nothing -> ["; " ++ why ++ ", no logic specified."]
                      Just l  -> ["(set-logic " ++ l ++ "); " ++ why ++ ", using solver-default logic."]
               | True
               = ["(set-logic " ++ qs ++ as ++ ufs ++ "BV)"]
              where qs  | null foralls && null axs = "QF_"  -- axioms are likely to contain quantifiers
                        | True                     = ""
                    as  | null arrs                = ""
                        | True                     = "A"
                    ufs | null uis && null tbls    = ""     -- we represent tables as UFs
                        | True                     = "UF"
            getModels
              | supportsProduceModels solverCaps = ["(set-option :produce-models true)"]
              | True                             = []
            pre  =  ["; Automatically generated by SBV. Do not edit."]
                 ++ map ("; " ++) comments
                 ++ getModels
                 ++ logic
                 ++ [ "; --- uninterpreted sorts ---" ]
                 ++ concatMap declSort usorts
                 ++ [ "; --- literal constants ---" ]
                 ++ concatMap (declConst (supportsMacros solverCaps)) consts
                 ++ [ "; --- skolem constants ---" ]
                 ++ [ "(declare-fun " ++ show s ++ " " ++ swFunType ss s ++ ")" ++ userName s | Right (s, ss) <- skolemInps]
                 ++ [ "; --- constant tables ---" ]
                 ++ concatMap constTable constTables
                 ++ [ "; --- skolemized tables ---" ]
                 ++ map (skolemTable (unwords (map swType foralls))) skolemTables
                 ++ [ "; --- arrays ---" ]
                 ++ concat arrayConstants
                 ++ [ "; --- uninterpreted constants ---" ]
                 ++ concatMap declUI uis
                 ++ [ "; --- user given axioms ---" ]
                 ++ map declAx axs
                 ++ [ "; --- formula ---" ]
                 ++ [if null foralls
                     then "(assert ; no quantifiers"
                     else "(assert (forall (" ++ intercalate "\n                 "
                                                 ["(" ++ show s ++ " " ++ swType s ++ ")" | s <- foralls] ++ ")"]
                 ++ map (letAlign . mkLet) asgns
                 ++ map letAlign (if null delayedEqualities then [] else ("(and " ++ deH) : map (align 5) deTs)
                 ++ [ impAlign (letAlign assertOut) ++ replicate noOfCloseParens ')' ]
            noOfCloseParens = length asgns + (if null foralls then 1 else 2) + (if null delayedEqualities then 0 else 1)
            (constTables, skolemTables) = ([(t, d) | (t, Left d) <- allTables], [(t, d) | (t, Right d) <- allTables])
            allTables = [(t, genTableData rm skolemMap (not (null foralls), forallArgs) (map fst consts) t) | t <- tbls]
            (arrayConstants, allArrayDelayeds) = unzip $ map (declArray (not (null foralls)) (map fst consts) skolemMap) arrs
            delayedEqualities@(~(deH:deTs)) = concatMap snd skolemTables ++ concat allArrayDelayeds
            foralls = [s | Left s <- skolemInps]
            forallArgs = concatMap ((" " ++) . show) foralls
            letAlign s
              | null foralls = "   " ++ s
              | True         = "            " ++ s
            impAlign s
              | null delayedEqualities = s
              | True                   = "     " ++ s
            align n s = replicate n ' ' ++ s
            -- if sat,   we assert cstrs /\ out
            -- if prove, we assert ~(cstrs => out) = cstrs /\ not out
            assertOut
               | null cstrs = o
               | True       = "(and " ++ unwords (map mkConj cstrs ++ [o]) ++ ")"
               where mkConj = cvtSW skolemMap
                     o | isSat =            mkConj out
                       | True  = "(not " ++ mkConj out ++ ")"
            skolemMap = M.fromList [(s, ss) | Right (s, ss) <- skolemInps, not (null ss)]
            tableMap  = IM.fromList $ map mkConstTable constTables ++ map mkSkTable skolemTables
              where mkConstTable (((t, _, _), _), _) = (t, "table" ++ show t)
                    mkSkTable    (((t, _, _), _), _) = (t, "table" ++ show t ++ forallArgs)
            asgns = F.toList asgnsSeq
            mkLet (s, SBVApp (Label m) [e]) = "(let ((" ++ show s ++ " " ++ cvtSW     skolemMap          e ++ ")) ; " ++ m
            mkLet (s, e)                    = "(let ((" ++ show s ++ " " ++ cvtExp rm skolemMap tableMap e ++ "))"
            declConst useDefFun (s, c)
              | useDefFun = ["(define-fun "   ++ varT ++ " " ++ cvtCW rm c ++ ")"]
              | True      = [ "(declare-fun " ++ varT ++ ")"
                            , "(assert (= "   ++ show s ++ " " ++ cvtCW rm c ++ "))"
                            ]
              where varT = show s ++ " " ++ swFunType [] s
            userName s = case s `lookup` map snd inputs of
                            Just u  | show s /= u -> " ; tracks user variable " ++ show u
                            _ -> ""
            -- following sorts are built-in; do not translate them:
            builtInSort = (`elem` ["RoundingMode"])
            declSort (s, _)
              | builtInSort s           = []
            declSort (s, Left  r ) = ["(declare-sort " ++ s ++ " 0)  ; N.B. Uninterpreted: " ++ r]
            declSort (s, Right fs) = [ "(declare-datatypes () ((" ++ s ++ " " ++ unwords (map (\c -> "(" ++ c ++ ")") fs) ++ ")))"
                                     , "(define-fun " ++ s ++ "_constrIndex ((x " ++ s ++ ")) Int"
                                     ] ++ ["   " ++ body fs (0::Int)] ++ [")"]
                    where body []     _ = ""
                          body [_]    i = show i
                          body (c:cs) i = "(ite (= x " ++ c ++ ") " ++ show i ++ " " ++ body cs (i+1) ++ ")"

    declUI :: (String, SBVType) -> [String]
    declUI (i, t) = ["(declare-fun " ++ i ++ " " ++ cvtType t ++ ")"]

    -- NB. We perform no check to as to whether the axiom is meaningful in any way.
    declAx :: (String, [String]) -> String
    declAx (nm, ls) = (";; -- user given axiom: " ++ nm ++ "\n") ++ intercalate "\n" ls

    constTable :: (((Int, Kind, Kind), [SW]), [String]) -> [String]
    constTable (((i, ak, rk), _elts), is) = decl : map wrap is
      where t       = "table" ++ show i
            decl    = "(declare-fun " ++ t ++ " (" ++ smtType ak ++ ") " ++ smtType rk ++ ")"
            wrap  s = "(assert " ++ s ++ ")"

    skolemTable :: String -> (((Int, Kind, Kind), [SW]), [String]) -> String
    skolemTable qsIn (((i, ak, rk), _elts), _) = decl
      where qs   = if null qsIn then "" else qsIn ++ " "
            t    = "table" ++ show i
            decl = "(declare-fun " ++ t ++ " (" ++ qs ++ smtType ak ++ ") " ++ smtType rk ++ ")"

    -- Left if all constants, Right if otherwise
    genTableData :: RoundingMode -> SkolemMap -> (Bool, String) -> [SW] -> ((Int, Kind, Kind), [SW]) -> Either [String] [String]
    genTableData rm skolemMap (_quantified, args) consts ((i, aknd, _), elts)
      | null post = Left  (map (topLevel . snd) pre)
      | True      = Right (map (nested   . snd) (pre ++ post))
      where ssw = cvtSW skolemMap
            (pre, post) = partition fst (zipWith mkElt elts [(0::Int)..])
            t           = "table" ++ show i
            mkElt x k   = (isReady, (idx, ssw x))
              where idx = cvtCW rm (mkConstCW aknd k)
                    isReady = x `elem` consts
            topLevel (idx, v) = "(= (" ++ t ++ " " ++ idx ++ ") " ++ v ++ ")"
            nested   (idx, v) = "(= (" ++ t ++ args ++ " " ++ idx ++ ") " ++ v ++ ")"

    -- TODO: We currently do not support non-constant arrays when quantifiers are present, as
    -- we might have to skolemize those. Implement this properly.
    -- The difficulty is with the ArrayReset/Mutate/Merge: We have to postpone an init if
    -- the components are themselves postponed, so this cannot be implemented as a simple map.
    declArray :: Bool -> [SW] -> SkolemMap -> (Int, ArrayInfo) -> ([String], [String])
    declArray quantified consts skolemMap (i, (_, (aKnd, bKnd), ctx)) = (adecl : map wrap pre, map snd post)
      where topLevel = not quantified || case ctx of
                                           ArrayFree Nothing -> True
                                           ArrayFree (Just sw) -> sw `elem` consts
                                           ArrayReset _ sw     -> sw `elem` consts
                                           ArrayMutate _ a b   -> all (`elem` consts) [a, b]
                                           ArrayMerge c _ _    -> c `elem` consts
            (pre, post) = partition fst ctxInfo
            nm = "array_" ++ show i
            ssw sw
             | topLevel || sw `elem` consts
             = cvtSW skolemMap sw
             | True
             = tbd "Non-constant array initializer in a quantified context"
            adecl = "(declare-fun " ++ nm ++ " () (Array " ++ smtType aKnd ++ " " ++ smtType bKnd ++ "))"
            ctxInfo = case ctx of
                        ArrayFree Nothing   -> []
                        ArrayFree (Just sw) -> declA sw
                        ArrayReset _ sw     -> declA sw
                        ArrayMutate j a b -> [(all (`elem` consts) [a, b], "(= " ++ nm ++ " (store array_" ++ show j ++ " " ++ ssw a ++ " " ++ ssw b ++ "))")]
                        ArrayMerge  t j k -> [(t `elem` consts,            "(= " ++ nm ++ " (ite " ++ ssw t ++ " array_" ++ show j ++ " array_" ++ show k ++ "))")]
            declA sw = let iv = nm ++ "_freeInitializer"
                       in [ (True,             "(declare-fun " ++ iv ++ " () " ++ smtType aKnd ++ ")")
                          , (sw `elem` consts, "(= (select " ++ nm ++ " " ++ iv ++ ") " ++ ssw sw ++ ")")
                          ]
            wrap (False, s) = s
            wrap (True, s)  = "(assert " ++ s ++ ")"

    swType :: SW -> String
    swType s = smtType (kindOf s)

    swFunType :: [SW] -> SW -> String
    swFunType ss s = "(" ++ unwords (map swType ss) ++ ") " ++ swType s

    smtType :: Kind -> String
    smtType KBool           = "Bool"
    smtType (KBounded _ sz) = "(_ BitVec " ++ show sz ++ ")"
    smtType KUnbounded      = "Int"
    smtType KReal           = "Real"
    smtType KFloat          = "(_ FloatingPoint  8 24)"
    smtType KDouble         = "(_ FloatingPoint 11 53)"
    smtType (KUserSort s _) = s

    cvtType :: SBVType -> String
    cvtType (SBVType []) = error "SBV.SMT.SMTLib2.cvtType: internal: received an empty type!"
    cvtType (SBVType xs) = "(" ++ unwords (map smtType body) ++ ") " ++ smtType ret
      where (body, ret) = (init xs, last xs)

    type SkolemMap = M.Map  SW [SW]
    type TableMap  = IM.IntMap String

    cvtSW :: SkolemMap -> SW -> String
    cvtSW skolemMap s
      | Just ss <- s `M.lookup` skolemMap
      = "(" ++ show s ++ concatMap ((" " ++) . show) ss ++ ")"
      | True
      = show s

    cvtCW :: RoundingMode -> CW -> String
    cvtCW = cwToSMTLib

    getTable :: TableMap -> Int -> String
    getTable m i
      | Just tn <- i `IM.lookup` m = tn
      | True                       = error $ "SBV.SMTLib2: Cannot locate table " ++ show i

    cvtExp :: RoundingMode -> SkolemMap -> TableMap -> SBVExpr -> String
    cvtExp rm skolemMap tableMap expr@(SBVApp _ arguments) = sh expr
      where ssw = cvtSW skolemMap
            bvOp     = all isBounded       arguments
            intOp    = any isInteger       arguments
            realOp   = any isReal          arguments
            doubleOp = any isDouble        arguments
            floatOp  = any isFloat         arguments
            boolOp   = all isBoolean       arguments
            bad | intOp = error $ "SBV.SMTLib2: Unsupported operation on unbounded integers: " ++ show expr
                | True  = error $ "SBV.SMTLib2: Unsupported operation on real values: " ++ show expr
            ensureBVOrBool = bvOp || boolOp || bad
            ensureBV       = bvOp || bad
            addRM s = s ++ " " ++ smtRoundingMode rm
            lift2  o _ [x, y] = "(" ++ o ++ " " ++ x ++ " " ++ y ++ ")"
            lift2  o _ sbvs   = error $ "SBV.SMTLib2.sh.lift2: Unexpected arguments: "   ++ show (o, sbvs)
            -- lift a binary operation with rounding-mode added; used for floating-point arithmetic
            lift2WM o fo | doubleOp || floatOp = lift2 (addRM fo)
                         | True                = lift2 o
            lift1FP o fo | doubleOp || floatOp = lift1 fo
                         | True                = lift1 o
            liftAbs sgned args | doubleOp || floatOp = lift1 "fp.abs" sgned args
                               | intOp               = lift1 "abs"    sgned args
                               | bvOp, sgned         = mkAbs (head args) "bvslt" "bvneg"
                               | bvOp                = head args
                               | True                = mkAbs (head args) "<"     "-"
              where mkAbs x cmp neg = "(ite " ++ ltz ++ " " ++ nx ++ " " ++ x ++ ")"
                      where ltz = "(" ++ cmp ++ " " ++ x ++ " " ++ z ++ ")"
                            nx  = "(" ++ neg ++ " " ++ x ++ ")"
                            z   = cvtCW rm (mkConstCW (kindOf (head arguments)) (0::Integer))
            lift2B bOp vOp
              | boolOp = lift2 bOp
              | True   = lift2 vOp
            lift1B bOp vOp
              | boolOp = lift1 bOp
              | True   = lift1 vOp
            eqBV  = lift2 "="
            neqBV = lift2 "distinct"
            equal sgn sbvs
              | doubleOp = lift2 "fp.eq" sgn sbvs
              | floatOp  = lift2 "fp.eq" sgn sbvs
              | True     = lift2 "=" sgn sbvs
            notEqual sgn sbvs
              | doubleOp = "(not " ++ equal sgn sbvs ++ ")"
              | floatOp  = "(not " ++ equal sgn sbvs ++ ")"
              | True     = lift2 "distinct" sgn sbvs
            lift2S oU oS sgn = lift2 (if sgn then oS else oU) sgn
            lift2Cmp o fo | doubleOp || floatOp = lift2 fo
                          | True                = lift2 o
            unintComp o [a, b]
              | KUserSort s (Right _) <- kindOf (head arguments)
              = let idx v = "(" ++ s ++ "_constrIndex " ++ " " ++ v ++ ")" in "(" ++ o ++ " " ++ idx a ++ " " ++ idx b ++ ")"
            unintComp o sbvs = error $ "SBV.SMT.SMTLib2.sh.unintComp: Unexpected arguments: "   ++ show (o, sbvs)
            lift1  o _ [x]    = "(" ++ o ++ " " ++ x ++ ")"
            lift1  o _ sbvs   = error $ "SBV.SMT.SMTLib2.sh.lift1: Unexpected arguments: "   ++ show (o, sbvs)
            sh (SBVApp Ite [a, b, c]) = "(ite " ++ ssw a ++ " " ++ ssw b ++ " " ++ ssw c ++ ")"
            sh (SBVApp (LkUp (t, aKnd, _, l) i e) [])
              | needsCheck = "(ite " ++ cond ++ ssw e ++ " " ++ lkUp ++ ")"
              | True       = lkUp
              where needsCheck = case aKnd of
                                  KBool         -> (2::Integer) > fromIntegral l
                                  KBounded _ n  -> (2::Integer)^n > fromIntegral l
                                  KUnbounded    -> True
                                  KReal         -> error "SBV.SMT.SMTLib2.cvtExp: unexpected real valued index"
                                  KFloat        -> error "SBV.SMT.SMTLib2.cvtExp: unexpected float valued index"
                                  KDouble       -> error "SBV.SMT.SMTLib2.cvtExp: unexpected double valued index"
                                  KUserSort s _ -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected uninterpreted valued index: " ++ s
                    lkUp = "(" ++ getTable tableMap t ++ " " ++ ssw i ++ ")"
                    cond
                     | hasSign i = "(or " ++ le0 ++ " " ++ gtl ++ ") "
                     | True      = gtl ++ " "
                    (less, leq) = case aKnd of
                                    KBool         -> error "SBV.SMT.SMTLib2.cvtExp: unexpected boolean valued index"
                                    KBounded{}    -> if hasSign i then ("bvslt", "bvsle") else ("bvult", "bvule")
                                    KUnbounded    -> ("<", "<=")
                                    KReal         -> ("<", "<=")
                                    KFloat        -> ("fp.lt", "fp.leq")
                                    KDouble       -> ("fp.lt", "fp.geq")
                                    KUserSort s _ -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected uninterpreted valued index: " ++ s
                    mkCnst = cvtCW rm . mkConstCW (kindOf i)
                    le0  = "(" ++ less ++ " " ++ ssw i ++ " " ++ mkCnst 0 ++ ")"
                    gtl  = "(" ++ leq  ++ " " ++ mkCnst l ++ " " ++ ssw i ++ ")"
            sh (SBVApp (IntCast f t) [a]) = handleIntCast f t (ssw a)
            sh (SBVApp (ArrEq i j) [])  = "(= array_" ++ show i ++ " array_" ++ show j ++")"
            sh (SBVApp (ArrRead i) [a]) = "(select array_" ++ show i ++ " " ++ ssw a ++ ")"
            sh (SBVApp (Uninterpreted nm) [])   = nm
            sh (SBVApp (Uninterpreted nm) args) = "(" ++ nm ++ " " ++ unwords (map ssw args) ++ ")"
            sh (SBVApp (Extract i j) [a]) | ensureBV = "((_ extract " ++ show i ++ " " ++ show j ++ ") " ++ ssw a ++ ")"
            sh (SBVApp (Rol i) [a])
               | bvOp  = rot  ssw "rotate_left"  i a
               | intOp = sh (SBVApp (Shl i) [a])       -- Haskell treats rotateL as shiftL for unbounded values
               | True  = bad
            sh (SBVApp (Ror i) [a])
               | bvOp  = rot  ssw "rotate_right" i a
               | intOp = sh (SBVApp (Shr i) [a])     -- Haskell treats rotateR as shiftR for unbounded values
               | True  = bad
            sh (SBVApp (Shl i) [a])
               | bvOp   = shft rm ssw "bvshl"  "bvshl"  i a
               | i < 0  = sh (SBVApp (Shr (-i)) [a])  -- flip sign/direction
               | intOp  = "(* " ++ ssw a ++ " " ++ show (bit i :: Integer) ++ ")"  -- Implement shiftL by multiplication by 2^i
               | True   = bad
            sh (SBVApp (Shr i) [a])
               | bvOp  = shft rm ssw "bvlshr" "bvashr" i a
               | i < 0 = sh (SBVApp (Shl (-i)) [a])  -- flip sign/direction
               | intOp = "(div " ++ ssw a ++ " " ++ show (bit i :: Integer) ++ ")"  -- Implement shiftR by division by 2^i
               | True  = bad
            sh (SBVApp op args)
              | Just f <- lookup op smtBVOpTable, ensureBVOrBool
              = f (any hasSign args) (map ssw args)
              where -- The first 4 operators below do make sense for Integer's in Haskell, but there's
                    -- no obvious counterpart for them in the SMTLib translation.
                    -- TODO: provide support for these.
                    smtBVOpTable = [ (And,  lift2B "and" "bvand")
                                   , (Or,   lift2B "or"  "bvor")
                                   , (XOr,  lift2B "xor" "bvxor")
                                   , (Not,  lift1B "not" "bvnot")
                                   , (Join, lift2 "concat")
                                   ]
            sh (SBVApp (Label _)                       [a]) = cvtSW skolemMap a  -- This won't be reached; but just in case!
            sh (SBVApp (IEEEFP (FP_Cast kFrom kTo m)) args) = handleFPCast kFrom kTo (ssw m) (unwords (map ssw args))
            sh (SBVApp (IEEEFP w                    ) args) = "(" ++ show w ++ " " ++ unwords (map ssw args) ++ ")"
            sh inp@(SBVApp op args)
              | intOp, Just f <- lookup op smtOpIntTable
              = f True (map ssw args)
              | boolOp, Just f <- lookup op boolComps
              = f (map ssw args)
              | bvOp, Just f <- lookup op smtOpBVTable
              = f (any hasSign args) (map ssw args)
              | realOp, Just f <- lookup op smtOpRealTable
              = f (any hasSign args) (map ssw args)
              | floatOp || doubleOp, Just f <- lookup op smtOpFloatDoubleTable
              = f (any hasSign args) (map ssw args)
              | Just f <- lookup op uninterpretedTable
              = f (map ssw args)
              | True
              = error $ "SBV.SMT.SMTLib2.cvtExp.sh: impossible happened; can't translate: " ++ show inp
              where smtOpBVTable  = [ (Plus,          lift2   "bvadd")
                                    , (Minus,         lift2   "bvsub")
                                    , (Times,         lift2   "bvmul")
                                    , (UNeg,          lift1B  "not"    "bvneg")
                                    , (Abs,           liftAbs)
                                    , (Quot,          lift2S  "bvudiv" "bvsdiv")
                                    , (Rem,           lift2S  "bvurem" "bvsrem")
                                    , (Equal,         eqBV)
                                    , (NotEqual,      neqBV)
                                    , (LessThan,      lift2S  "bvult" "bvslt")
                                    , (GreaterThan,   lift2S  "bvugt" "bvsgt")
                                    , (LessEq,        lift2S  "bvule" "bvsle")
                                    , (GreaterEq,     lift2S  "bvuge" "bvsge")
                                    ]
                    -- Boolean comparisons.. SMTLib's bool type doesn't do comparisons, but Haskell does.. Sigh
                    boolComps      = [ (LessThan,      blt)
                                     , (GreaterThan,   blt . swp)
                                     , (LessEq,        blq)
                                     , (GreaterEq,     blq . swp)
                                     ]
                                   where blt [x, y] = "(and (not " ++ x ++ ") " ++ y ++ ")"
                                         blt xs     = error $ "SBV.SMT.SMTLib2.boolComps.blt: Impossible happened, incorrect arity (expected 2): " ++ show xs
                                         blq [x, y] = "(or (not " ++ x ++ ") " ++ y ++ ")"
                                         blq xs     = error $ "SBV.SMT.SMTLib2.boolComps.blq: Impossible happened, incorrect arity (expected 2): " ++ show xs
                                         swp [x, y] = [y, x]
                                         swp xs     = error $ "SBV.SMT.SMTLib2.boolComps.swp: Impossible happened, incorrect arity (expected 2): " ++ show xs
                    smtOpRealTable =  smtIntRealShared
                                   ++ [ (Quot,        lift2WM "/" "fp.div")
                                      ]
                    smtOpIntTable  = smtIntRealShared
                                   ++ [ (Quot,        lift2   "div")
                                      , (Rem,         lift2   "mod")
                                      ]
                    smtOpFloatDoubleTable = smtIntRealShared
                                      ++ [(Quot, lift2WM "/" "fp.div")]
                    smtIntRealShared  = [ (Plus,          lift2WM "+" "fp.add")
                                        , (Minus,         lift2WM "-" "fp.sub")
                                        , (Times,         lift2WM "*" "fp.mul")
                                        , (UNeg,          lift1FP "-" "fp.neg")
                                        , (Abs,           liftAbs)
                                        , (Equal,         equal)
                                        , (NotEqual,      notEqual)
                                        , (LessThan,      lift2Cmp  "<"  "fp.lt")
                                        , (GreaterThan,   lift2Cmp  ">"  "fp.gt")
                                        , (LessEq,        lift2Cmp  "<=" "fp.leq")
                                        , (GreaterEq,     lift2Cmp  ">=" "fp.geq")
                                        ]
                    -- equality and comparisons are the only thing that works on uninterpreted sorts
                    uninterpretedTable = [ (Equal,       lift2S "="        "="        True)
                                         , (NotEqual,    lift2S "distinct" "distinct" True)
                                         , (LessThan,    unintComp "<")
                                         , (GreaterThan, unintComp ">")
                                         , (LessEq,      unintComp "<=")
                                         , (GreaterEq,   unintComp ">=")
                                         ]

    -----------------------------------------------------------------------------------------------
    -- Casts supported by SMTLib. (From: http://smtlib.cs.uiowa.edu/theories/FloatingPoint.smt2)
    --   ; from another floating point sort
    --   ((_ to_fp eb sb) RoundingMode (_ FloatingPoint mb nb) (_ FloatingPoint eb sb))
    --
    --   ; from real
    --   ((_ to_fp eb sb) RoundingMode Real (_ FloatingPoint eb sb))
    --
    --   ; from signed machine integer, represented as a 2's complement bit vector
    --   ((_ to_fp eb sb) RoundingMode (_ BitVec m) (_ FloatingPoint eb sb))
    --
    --   ; from unsigned machine integer, represented as bit vector
    --   ((_ to_fp_unsigned eb sb) RoundingMode (_ BitVec m) (_ FloatingPoint eb sb))
    --
    --   ; to unsigned machine integer, represented as a bit vector
    --   ((_ fp.to_ubv m) RoundingMode (_ FloatingPoint eb sb) (_ BitVec m))
    --
    --   ; to signed machine integer, represented as a 2's complement bit vector
    --   ((_ fp.to_sbv m) RoundingMode (_ FloatingPoint eb sb) (_ BitVec m))
    --
    --   ; to real
    --   (fp.to_real (_ FloatingPoint eb sb) Real)
    -----------------------------------------------------------------------------------------------

    handleFPCast :: Kind -> Kind -> String -> String -> String
    handleFPCast kFrom kTo rm  input
      | kFrom == kTo
      = input
      | True
      = "(" ++ cast kFrom kTo input ++ ")"
      where addRM a s = s ++ " " ++ rm ++ " " ++ a

            absRM a s = "ite (fp.isNegative " ++ a ++ ") (" ++ cvt1 ++ ") (" ++ cvt2 ++ ")"
              where cvt1 = "bvneg (" ++ s ++ " " ++ rm ++ " (fp.abs " ++ a ++ "))"
                    cvt2 =              s ++ " " ++ rm ++ " "         ++ a

            -- To go and back from Ints, we detour through reals
            cast KUnbounded         KFloat             a = "(_ to_fp 8 24) "  ++ rm ++ " (to_real " ++ a ++ ")"
            cast KUnbounded         KDouble            a = "(_ to_fp 11 53) " ++ rm ++ " (to_real " ++ a ++ ")"
            cast KFloat             KUnbounded         a = "to_int (fp.to_real " ++ a ++ ")"
            cast KDouble            KUnbounded         a = "to_int (fp.to_real " ++ a ++ ")"

            -- To float/double
            cast (KBounded False _) KFloat             a = addRM a "(_ to_fp_unsigned 8 24)"
            cast (KBounded False _) KDouble            a = addRM a "(_ to_fp_unsigned 11 53)"
            cast (KBounded True  _) KFloat             a = addRM a "(_ to_fp 8 24)"
            cast (KBounded True  _) KDouble            a = addRM a "(_ to_fp 11 53)"
            cast KReal              KFloat             a = addRM a "(_ to_fp 8 24)"
            cast KReal              KDouble            a = addRM a "(_ to_fp 11 53)"

            -- Between floats
            cast KFloat             KFloat             a = addRM a "(_ to_fp 8 24)"
            cast KFloat             KDouble            a = addRM a "(_ to_fp 11 53)"
            cast KDouble            KFloat             a = addRM a "(_ to_fp 8 24)"
            cast KDouble            KDouble            a = addRM a "(_ to_fp 11 53)"

            -- From float/double
            cast KFloat             (KBounded False m) a = absRM a $ "(_ fp.to_ubv " ++ show m ++ ")"
            cast KDouble            (KBounded False m) a = absRM a $ "(_ fp.to_ubv " ++ show m ++ ")"
            cast KFloat             (KBounded True  m) a = addRM a $ "(_ fp.to_sbv " ++ show m ++ ")"
            cast KDouble            (KBounded True  m) a = addRM a $ "(_ fp.to_sbv " ++ show m ++ ")"
            cast KFloat             KReal              a = "fp.to_real" ++ " " ++ a
            cast KDouble            KReal              a = "fp.to_real" ++ " " ++ a

            -- Nothing else should come up:
            cast f                  d                  _ = error $ "SBV.SMTLib2: Unexpected FPCast from: " ++ show f ++ " to " ++ show d

    rot :: (SW -> String) -> String -> Int -> SW -> String
    rot ssw o c x = "((_ " ++ o ++ " " ++ show c ++ ") " ++ ssw x ++ ")"

    shft :: RoundingMode -> (SW -> String) -> String -> String -> Int -> SW -> String
    shft rm ssw oW oS c x = "(" ++ o ++ " " ++ ssw x ++ " " ++ cvtCW rm c' ++ ")"
       where s  = hasSign x
             c' = mkConstCW (kindOf x) c
             o  = if s then oS else oW

    -- Various integer casts
    handleIntCast :: Kind -> Kind -> String -> String
    handleIntCast kFrom kTo a
      | kFrom == kTo
      = a
      | True
      = case kFrom of
          KBounded s m -> case kTo of
                            KBounded _ n -> fromBV (if s then signExtend else zeroExtend) m n
                            KUnbounded   -> b2i s m
                            _            -> noCast

          KUnbounded   -> case kTo of
                            KReal        -> "(to_real " ++ a ++ ")"
                            KBounded _ n -> i2b n
                            _            -> noCast

          _            -> noCast

      where noCast  = error $ "SBV.SMTLib2: Unexpected integer cast from: " ++ show kFrom ++ " to " ++ show kTo

            fromBV upConv m n
             | n > m  = upConv  (n - m)
             | m == n = a
             | True   = extract (n - 1)

            i2b n = "(let (" ++ reduced ++ ") (let (" ++ defs ++ ") " ++ body ++ "))"
              where b i      = show (bit i :: Integer)
                    reduced  = "(__a (mod " ++ a ++ " " ++ b n ++ "))"
                    mkBit 0  = "(__a0 (ite (= (mod __a 2) 0) #b0 #b1))"
                    mkBit i  = "(__a" ++ show i ++ " (ite (= (mod (div __a " ++ b i ++ ") 2) 0) #b0 #b1))"
                    defs     = unwords (map mkBit [0 .. n - 1])
                    body     = foldr1 (\c r -> "(concat " ++ c ++ " " ++ r ++ ")") ["__a" ++ show i | i <- [n-1, n-2 .. 0]]

            b2i s m
              | s    = "(- " ++ val ++ " " ++ valIf (2^m) sign ++ ")"
              | True = val
              where valIf v b = "(ite (= " ++ b ++ " #b1) " ++ show (v::Integer) ++ " 0)"
                    getBit i  = "((_ extract " ++ show i ++ " " ++ show i ++ ") " ++ a ++ ")"
                    bitVal i  = valIf (2^i) (getBit i)
                    val       = "(+ " ++ unwords (map bitVal [0 .. m-1]) ++ ")"
                    sign      = getBit (m-1)

            signExtend i = "((_ sign_extend " ++ show i ++  ") "  ++ a ++ ")"
            zeroExtend i = "((_ zero_extend " ++ show i ++  ") "  ++ a ++ ")"
            extract    i = "((_ extract "     ++ show i ++ " 0) " ++ a ++ ")"