prelude/PrelRules.hs

    {-
    (c) The GRASP/AQUA Project, Glasgow University, 1992-1998

    \section[ConFold]{Constant Folder}

    Conceptually, constant folding should be parameterized with the kind
    of target machine to get identical behaviour during compilation time
    and runtime. We cheat a little bit here...

    ToDo:
       check boundaries before folding, e.g. we can fold the Float addition
       (i1 + i2) only if it results in a valid Float.
    -}

    {-# LANGUAGE CPP, RankNTypes #-}
    {-# OPTIONS_GHC -optc-DNON_POSIX_SOURCE #-}

    module PrelRules
       ( primOpRules
       , builtinRules
       , caseRules
       )
    where

    #include "HsVersions.h"
    #include "../includes/MachDeps.h"

    import {-# SOURCE #-} MkId ( mkPrimOpId, magicDictId )

    import CoreSyn
    import MkCore
    import Id
    import Literal
    import CoreOpt     ( exprIsLiteral_maybe )
    import PrimOp      ( PrimOp(..), tagToEnumKey )
    import TysWiredIn
    import TysPrim
    import TyCon       ( tyConDataCons_maybe, isEnumerationTyCon, isNewTyCon, unwrapNewTyCon_maybe )
    import DataCon     ( dataConTag, dataConTyCon, dataConWorkId )
    import CoreUtils   ( cheapEqExpr, exprIsHNF )
    import CoreUnfold  ( exprIsConApp_maybe )
    import Type
    import OccName     ( occNameFS )
    import PrelNames
    import Maybes      ( orElse )
    import Name        ( Name, nameOccName )
    import Outputable
    import FastString
    import BasicTypes
    import DynFlags
    import Platform
    import Util
    import Coercion     (mkUnbranchedAxInstCo,mkSymCo,Role(..))

    import Control.Applicative ( Alternative(..) )

    import Control.Monad
    #if __GLASGOW_HASKELL__ > 710
    import qualified Control.Monad.Fail as MonadFail
    #endif
    import Data.Bits as Bits
    import qualified Data.ByteString as BS
    import Data.Int
    import Data.Ratio
    import Data.Word

    {-
    Note [Constant folding]
    ~~~~~~~~~~~~~~~~~~~~~~~
    primOpRules generates a rewrite rule for each primop
    These rules do what is often called "constant folding"
    E.g. the rules for +# might say
            4 +# 5 = 9
    Well, of course you'd need a lot of rules if you did it
    like that, so we use a BuiltinRule instead, so that we
    can match in any two literal values.  So the rule is really
    more like
            (Lit x) +# (Lit y) = Lit (x+#y)
    where the (+#) on the rhs is done at compile time

    That is why these rules are built in here.
    -}

    primOpRules :: Name -> PrimOp -> Maybe CoreRule
        -- ToDo: something for integer-shift ops?
        --       NotOp
    primOpRules nm TagToEnumOp = mkPrimOpRule nm 2 [ tagToEnumRule ]
    primOpRules nm DataToTagOp = mkPrimOpRule nm 2 [ dataToTagRule ]

    -- Int operations
    primOpRules nm IntAddOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (+))
                                                   , identityDynFlags zeroi ]
    primOpRules nm IntSubOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (-))
                                                   , rightIdentityDynFlags zeroi
                                                   , equalArgs >> retLit zeroi ]
    primOpRules nm IntMulOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (*))
                                                   , zeroElem zeroi
                                                   , identityDynFlags onei ]
    primOpRules nm IntQuotOp   = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 quot)
                                                   , leftZero zeroi
                                                   , rightIdentityDynFlags onei
                                                   , equalArgs >> retLit onei ]
    primOpRules nm IntRemOp    = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 rem)
                                                   , leftZero zeroi
                                                   , do l <- getLiteral 1
                                                        dflags <- getDynFlags
                                                        guard (l == onei dflags)
                                                        retLit zeroi
                                                   , equalArgs >> retLit zeroi
                                                   , equalArgs >> retLit zeroi ]
    primOpRules nm AndIOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 (.&.))
                                                   , idempotent
                                                   , zeroElem zeroi ]
    primOpRules nm OrIOp       = mkPrimOpRule nm 2 [ binaryLit (intOp2 (.|.))
                                                   , idempotent
                                                   , identityDynFlags zeroi ]
    primOpRules nm XorIOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 xor)
                                                   , identityDynFlags zeroi
                                                   , equalArgs >> retLit zeroi ]
    primOpRules nm NotIOp      = mkPrimOpRule nm 1 [ unaryLit complementOp
                                                   , inversePrimOp NotIOp ]
    primOpRules nm IntNegOp    = mkPrimOpRule nm 1 [ unaryLit negOp
                                                   , inversePrimOp IntNegOp ]
    primOpRules nm ISllOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 Bits.shiftL)
                                                   , rightIdentityDynFlags zeroi ]
    primOpRules nm ISraOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 Bits.shiftR)
                                                   , rightIdentityDynFlags zeroi ]
    primOpRules nm ISrlOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2' shiftRightLogical)
                                                   , rightIdentityDynFlags zeroi ]

    -- Word operations
    primOpRules nm WordAddOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (+))
                                                   , identityDynFlags zerow ]
    primOpRules nm WordSubOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (-))
                                                   , rightIdentityDynFlags zerow
                                                   , equalArgs >> retLit zerow ]
    primOpRules nm WordMulOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (*))
                                                   , identityDynFlags onew ]
    primOpRules nm WordQuotOp  = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 quot)
                                                   , rightIdentityDynFlags onew ]
    primOpRules nm WordRemOp   = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 rem)
                                                   , leftZero zerow
                                                   , do l <- getLiteral 1
                                                        dflags <- getDynFlags
                                                        guard (l == onew dflags)
                                                        retLit zerow
                                                   , equalArgs >> retLit zerow ]
    primOpRules nm AndOp       = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.&.))
                                                   , idempotent
                                                   , zeroElem zerow ]
    primOpRules nm OrOp        = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.|.))
                                                   , idempotent
                                                   , identityDynFlags zerow ]
    primOpRules nm XorOp       = mkPrimOpRule nm 2 [ binaryLit (wordOp2 xor)
                                                   , identityDynFlags zerow
                                                   , equalArgs >> retLit zerow ]
    primOpRules nm NotOp       = mkPrimOpRule nm 1 [ unaryLit complementOp
                                                   , inversePrimOp NotOp ]
    primOpRules nm SllOp       = mkPrimOpRule nm 2 [ wordShiftRule (const Bits.shiftL) ]
    primOpRules nm SrlOp       = mkPrimOpRule nm 2 [ wordShiftRule shiftRightLogical ]

    -- coercions
    primOpRules nm Word2IntOp     = mkPrimOpRule nm 1 [ liftLitDynFlags word2IntLit
                                                      , inversePrimOp Int2WordOp ]
    primOpRules nm Int2WordOp     = mkPrimOpRule nm 1 [ liftLitDynFlags int2WordLit
                                                      , inversePrimOp Word2IntOp ]
    primOpRules nm Narrow8IntOp   = mkPrimOpRule nm 1 [ liftLit narrow8IntLit
                                                      , subsumedByPrimOp Narrow8IntOp
                                                      , Narrow8IntOp `subsumesPrimOp` Narrow16IntOp
                                                      , Narrow8IntOp `subsumesPrimOp` Narrow32IntOp ]
    primOpRules nm Narrow16IntOp  = mkPrimOpRule nm 1 [ liftLit narrow16IntLit
                                                      , subsumedByPrimOp Narrow8IntOp
                                                      , subsumedByPrimOp Narrow16IntOp
                                                      , Narrow16IntOp `subsumesPrimOp` Narrow32IntOp ]
    primOpRules nm Narrow32IntOp  = mkPrimOpRule nm 1 [ liftLit narrow32IntLit
                                                      , subsumedByPrimOp Narrow8IntOp
                                                      , subsumedByPrimOp Narrow16IntOp
                                                      , subsumedByPrimOp Narrow32IntOp
                                                      , removeOp32 ]
    primOpRules nm Narrow8WordOp  = mkPrimOpRule nm 1 [ liftLit narrow8WordLit
                                                      , subsumedByPrimOp Narrow8WordOp
                                                      , Narrow8WordOp `subsumesPrimOp` Narrow16WordOp
                                                      , Narrow8WordOp `subsumesPrimOp` Narrow32WordOp ]
    primOpRules nm Narrow16WordOp = mkPrimOpRule nm 1 [ liftLit narrow16WordLit
                                                      , subsumedByPrimOp Narrow8WordOp
                                                      , subsumedByPrimOp Narrow16WordOp
                                                      , Narrow16WordOp `subsumesPrimOp` Narrow32WordOp ]
    primOpRules nm Narrow32WordOp = mkPrimOpRule nm 1 [ liftLit narrow32WordLit
                                                      , subsumedByPrimOp Narrow8WordOp
                                                      , subsumedByPrimOp Narrow16WordOp
                                                      , subsumedByPrimOp Narrow32WordOp
                                                      , removeOp32 ]
    primOpRules nm OrdOp          = mkPrimOpRule nm 1 [ liftLit char2IntLit
                                                      , inversePrimOp ChrOp ]
    primOpRules nm ChrOp          = mkPrimOpRule nm 1 [ do [Lit lit] <- getArgs
                                                           guard (litFitsInChar lit)
                                                           liftLit int2CharLit
                                                      , inversePrimOp OrdOp ]
    primOpRules nm Float2IntOp    = mkPrimOpRule nm 1 [ liftLit float2IntLit ]
    primOpRules nm Int2FloatOp    = mkPrimOpRule nm 1 [ liftLit int2FloatLit ]
    primOpRules nm Double2IntOp   = mkPrimOpRule nm 1 [ liftLit double2IntLit ]
    primOpRules nm Int2DoubleOp   = mkPrimOpRule nm 1 [ liftLit int2DoubleLit ]
    -- SUP: Not sure what the standard says about precision in the following 2 cases
    primOpRules nm Float2DoubleOp = mkPrimOpRule nm 1 [ liftLit float2DoubleLit ]
    primOpRules nm Double2FloatOp = mkPrimOpRule nm 1 [ liftLit double2FloatLit ]

    -- Float
    primOpRules nm FloatAddOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (+))
                                                    , identity zerof ]
    primOpRules nm FloatSubOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (-))
                                                    , rightIdentity zerof ]
    primOpRules nm FloatMulOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (*))
                                                    , identity onef
                                                    , strengthReduction twof FloatAddOp  ]
                             -- zeroElem zerof doesn't hold because of NaN
    primOpRules nm FloatDivOp   = mkPrimOpRule nm 2 [ guardFloatDiv >> binaryLit (floatOp2 (/))
                                                    , rightIdentity onef ]
    primOpRules nm FloatNegOp   = mkPrimOpRule nm 1 [ unaryLit negOp
                                                    , inversePrimOp FloatNegOp ]

    -- Double
    primOpRules nm DoubleAddOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (+))
                                                     , identity zerod ]
    primOpRules nm DoubleSubOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (-))
                                                     , rightIdentity zerod ]
    primOpRules nm DoubleMulOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (*))
                                                     , identity oned
                                                     , strengthReduction twod DoubleAddOp  ]
                              -- zeroElem zerod doesn't hold because of NaN
    primOpRules nm DoubleDivOp   = mkPrimOpRule nm 2 [ guardDoubleDiv >> binaryLit (doubleOp2 (/))
                                                     , rightIdentity oned ]
    primOpRules nm DoubleNegOp   = mkPrimOpRule nm 1 [ unaryLit negOp
                                                     , inversePrimOp DoubleNegOp ]

    -- Relational operators

    primOpRules nm IntEqOp    = mkRelOpRule nm (==) [ litEq True ]
    primOpRules nm IntNeOp    = mkRelOpRule nm (/=) [ litEq False ]
    primOpRules nm CharEqOp   = mkRelOpRule nm (==) [ litEq True ]
    primOpRules nm CharNeOp   = mkRelOpRule nm (/=) [ litEq False ]

    primOpRules nm IntGtOp    = mkRelOpRule nm (>)  [ boundsCmp Gt ]
    primOpRules nm IntGeOp    = mkRelOpRule nm (>=) [ boundsCmp Ge ]
    primOpRules nm IntLeOp    = mkRelOpRule nm (<=) [ boundsCmp Le ]
    primOpRules nm IntLtOp    = mkRelOpRule nm (<)  [ boundsCmp Lt ]

    primOpRules nm CharGtOp   = mkRelOpRule nm (>)  [ boundsCmp Gt ]
    primOpRules nm CharGeOp   = mkRelOpRule nm (>=) [ boundsCmp Ge ]
    primOpRules nm CharLeOp   = mkRelOpRule nm (<=) [ boundsCmp Le ]
    primOpRules nm CharLtOp   = mkRelOpRule nm (<)  [ boundsCmp Lt ]

    primOpRules nm FloatGtOp  = mkFloatingRelOpRule nm (>)
    primOpRules nm FloatGeOp  = mkFloatingRelOpRule nm (>=)
    primOpRules nm FloatLeOp  = mkFloatingRelOpRule nm (<=)
    primOpRules nm FloatLtOp  = mkFloatingRelOpRule nm (<)
    primOpRules nm FloatEqOp  = mkFloatingRelOpRule nm (==)
    primOpRules nm FloatNeOp  = mkFloatingRelOpRule nm (/=)

    primOpRules nm DoubleGtOp = mkFloatingRelOpRule nm (>)
    primOpRules nm DoubleGeOp = mkFloatingRelOpRule nm (>=)
    primOpRules nm DoubleLeOp = mkFloatingRelOpRule nm (<=)
    primOpRules nm DoubleLtOp = mkFloatingRelOpRule nm (<)
    primOpRules nm DoubleEqOp = mkFloatingRelOpRule nm (==)
    primOpRules nm DoubleNeOp = mkFloatingRelOpRule nm (/=)

    primOpRules nm WordGtOp   = mkRelOpRule nm (>)  [ boundsCmp Gt ]
    primOpRules nm WordGeOp   = mkRelOpRule nm (>=) [ boundsCmp Ge ]
    primOpRules nm WordLeOp   = mkRelOpRule nm (<=) [ boundsCmp Le ]
    primOpRules nm WordLtOp   = mkRelOpRule nm (<)  [ boundsCmp Lt ]
    primOpRules nm WordEqOp   = mkRelOpRule nm (==) [ litEq True ]
    primOpRules nm WordNeOp   = mkRelOpRule nm (/=) [ litEq False ]

    primOpRules nm AddrAddOp  = mkPrimOpRule nm 2 [ rightIdentityDynFlags zeroi ]

    primOpRules nm SeqOp      = mkPrimOpRule nm 4 [ seqRule ]
    primOpRules nm SparkOp    = mkPrimOpRule nm 4 [ sparkRule ]

    primOpRules _  _          = Nothing

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Doing the business}
    *                                                                      *
    ************************************************************************
    -}

    -- useful shorthands
    mkPrimOpRule :: Name -> Int -> [RuleM CoreExpr] -> Maybe CoreRule
    mkPrimOpRule nm arity rules = Just $ mkBasicRule nm arity (msum rules)

    mkRelOpRule :: Name -> (forall a . Ord a => a -> a -> Bool)
                -> [RuleM CoreExpr] -> Maybe CoreRule
    mkRelOpRule nm cmp extra
      = mkPrimOpRule nm 2 $
        binaryCmpLit cmp : equal_rule : extra
      where
            -- x `cmp` x does not depend on x, so
            -- compute it for the arbitrary value 'True'
            -- and use that result
        equal_rule = do { equalArgs
                        ; dflags <- getDynFlags
                        ; return (if cmp True True
                                  then trueValInt  dflags
                                  else falseValInt dflags) }

    {- Note [Rules for floating-point comparisons]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    We need different rules for floating-point values because for floats
    it is not true that x = x (for NaNs); so we do not want the equal_rule
    rule that mkRelOpRule uses.

    Note also that, in the case of equality/inequality, we do /not/
    want to switch to a case-expression.  For example, we do not want
    to convert
       case (eqFloat# x 3.8#) of
         True -> this
         False -> that
    to
      case x of
        3.8#::Float# -> this
        _            -> that
    See Trac #9238.  Reason: comparing floating-point values for equality
    delicate, and we don't want to implement that delicacy in the code for
    case expressions.  So we make it an invariant of Core that a case
    expression never scrutinises a Float# or Double#.

    This transformation is what the litEq rule does;
    see Note [The litEq rule: converting equality to case].
    So we /refrain/ from using litEq for mkFloatingRelOpRule.
    -}

    mkFloatingRelOpRule :: Name -> (forall a . Ord a => a -> a -> Bool)
                        -> Maybe CoreRule
    -- See Note [Rules for floating-point comparisons]
    mkFloatingRelOpRule nm cmp
      = mkPrimOpRule nm 2 [binaryCmpLit cmp]

    -- common constants
    zeroi, onei, zerow, onew :: DynFlags -> Literal
    zeroi dflags = mkMachInt  dflags 0
    onei  dflags = mkMachInt  dflags 1
    zerow dflags = mkMachWord dflags 0
    onew  dflags = mkMachWord dflags 1

    zerof, onef, twof, zerod, oned, twod :: Literal
    zerof = mkMachFloat 0.0
    onef  = mkMachFloat 1.0
    twof  = mkMachFloat 2.0
    zerod = mkMachDouble 0.0
    oned  = mkMachDouble 1.0
    twod  = mkMachDouble 2.0

    cmpOp :: DynFlags -> (forall a . Ord a => a -> a -> Bool)
          -> Literal -> Literal -> Maybe CoreExpr
    cmpOp dflags cmp = go
      where
        done True  = Just $ trueValInt  dflags
        done False = Just $ falseValInt dflags

        -- These compares are at different types
        go (MachChar i1)   (MachChar i2)   = done (i1 `cmp` i2)
        go (MachInt i1)    (MachInt i2)    = done (i1 `cmp` i2)
        go (MachInt64 i1)  (MachInt64 i2)  = done (i1 `cmp` i2)
        go (MachWord i1)   (MachWord i2)   = done (i1 `cmp` i2)
        go (MachWord64 i1) (MachWord64 i2) = done (i1 `cmp` i2)
        go (MachFloat i1)  (MachFloat i2)  = done (i1 `cmp` i2)
        go (MachDouble i1) (MachDouble i2) = done (i1 `cmp` i2)
        go _               _               = Nothing

    --------------------------

    negOp :: DynFlags -> Literal -> Maybe CoreExpr  -- Negate
    negOp _      (MachFloat 0.0)  = Nothing  -- can't represent -0.0 as a Rational
    negOp dflags (MachFloat f)    = Just (mkFloatVal dflags (-f))
    negOp _      (MachDouble 0.0) = Nothing
    negOp dflags (MachDouble d)   = Just (mkDoubleVal dflags (-d))
    negOp dflags (MachInt i)      = intResult dflags (-i)
    negOp _      _                = Nothing

    complementOp :: DynFlags -> Literal -> Maybe CoreExpr  -- Binary complement
    complementOp dflags (MachWord i) = wordResult dflags (complement i)
    complementOp dflags (MachInt i)  = intResult  dflags (complement i)
    complementOp _      _            = Nothing

    --------------------------
    intOp2 :: (Integral a, Integral b)
           => (a -> b -> Integer)
           -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
    intOp2 = intOp2' . const

    intOp2' :: (Integral a, Integral b)
            => (DynFlags -> a -> b -> Integer)
            -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
    intOp2' op dflags (MachInt i1) (MachInt i2) =
      let o = op dflags
      in  intResult dflags (fromInteger i1 `o` fromInteger i2)
    intOp2' _  _      _            _            = Nothing  -- Could find LitLit

    shiftRightLogical :: DynFlags -> Integer -> Int -> Integer
    -- Shift right, putting zeros in rather than sign-propagating as Bits.shiftR would do
    -- Do this by converting to Word and back.  Obviously this won't work for big
    -- values, but its ok as we use it here
    shiftRightLogical dflags x n
      | wordSizeInBits dflags == 32 = fromIntegral (fromInteger x `shiftR` n :: Word32)
      | wordSizeInBits dflags == 64 = fromIntegral (fromInteger x `shiftR` n :: Word64)
      | otherwise = panic "shiftRightLogical: unsupported word size"

    --------------------------
    retLit :: (DynFlags -> Literal) -> RuleM CoreExpr
    retLit l = do dflags <- getDynFlags
                  return $ Lit $ l dflags

    wordOp2 :: (Integral a, Integral b)
            => (a -> b -> Integer)
            -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
    wordOp2 op dflags (MachWord w1) (MachWord w2)
        = wordResult dflags (fromInteger w1 `op` fromInteger w2)
    wordOp2 _ _ _ _ = Nothing  -- Could find LitLit

    wordShiftRule :: (DynFlags -> Integer -> Int -> Integer) -> RuleM CoreExpr
                     -- Shifts take an Int; hence third arg of op is Int
    -- See Note [Guarding against silly shifts]
    wordShiftRule shift_op
      = do { dflags <- getDynFlags
           ; [e1, Lit (MachInt shift_len)] <- getArgs
           ; case e1 of
               _ | shift_len == 0
                 -> return e1
                 | shift_len < 0 || wordSizeInBits dflags < shift_len
                 -> return (mkRuntimeErrorApp rUNTIME_ERROR_ID wordPrimTy
                                            ("Bad shift length" ++ show shift_len))
               Lit (MachWord x)
                 -> let op = shift_op dflags
                    in  liftMaybe $ wordResult dflags (x `op` fromInteger shift_len)
                        -- Do the shift at type Integer, but shift length is Int
               _ -> mzero }

    wordSizeInBits :: DynFlags -> Integer
    wordSizeInBits dflags = toInteger (platformWordSize (targetPlatform dflags) `shiftL` 3)

    --------------------------
    floatOp2 :: (Rational -> Rational -> Rational)
             -> DynFlags -> Literal -> Literal
             -> Maybe (Expr CoreBndr)
    floatOp2 op dflags (MachFloat f1) (MachFloat f2)
      = Just (mkFloatVal dflags (f1 `op` f2))
    floatOp2 _ _ _ _ = Nothing

    --------------------------
    doubleOp2 :: (Rational -> Rational -> Rational)
              -> DynFlags -> Literal -> Literal
              -> Maybe (Expr CoreBndr)
    doubleOp2 op dflags (MachDouble f1) (MachDouble f2)
      = Just (mkDoubleVal dflags (f1 `op` f2))
    doubleOp2 _ _ _ _ = Nothing

    --------------------------
    {- Note [The litEq rule: converting equality to case]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    This stuff turns
         n ==# 3#
    into
         case n of
           3# -> True
           m  -> False

    This is a Good Thing, because it allows case-of case things
    to happen, and case-default absorption to happen.  For
    example:

         if (n ==# 3#) || (n ==# 4#) then e1 else e2
    will transform to
         case n of
           3# -> e1
           4# -> e1
           m  -> e2
    (modulo the usual precautions to avoid duplicating e1)
    -}

    litEq :: Bool  -- True <=> equality, False <=> inequality
          -> RuleM CoreExpr
    litEq is_eq = msum
      [ do [Lit lit, expr] <- getArgs
           dflags <- getDynFlags
           do_lit_eq dflags lit expr
      , do [expr, Lit lit] <- getArgs
           dflags <- getDynFlags
           do_lit_eq dflags lit expr ]
      where
        do_lit_eq dflags lit expr = do
          guard (not (litIsLifted lit))
          return (mkWildCase expr (literalType lit) intPrimTy
                        [(DEFAULT,    [], val_if_neq),
                         (LitAlt lit, [], val_if_eq)])
          where
            val_if_eq  | is_eq     = trueValInt  dflags
                       | otherwise = falseValInt dflags
            val_if_neq | is_eq     = falseValInt dflags
                       | otherwise = trueValInt  dflags

    -- | Check if there is comparison with minBound or maxBound, that is
    -- always true or false. For instance, an Int cannot be smaller than its
    -- minBound, so we can replace such comparison with False.
    boundsCmp :: Comparison -> RuleM CoreExpr
    boundsCmp op = do
      dflags <- getDynFlags
      [a, b] <- getArgs
      liftMaybe $ mkRuleFn dflags op a b

    data Comparison = Gt | Ge | Lt | Le

    mkRuleFn :: DynFlags -> Comparison -> CoreExpr -> CoreExpr -> Maybe CoreExpr
    mkRuleFn dflags Gt (Lit lit) _ | isMinBound dflags lit = Just $ falseValInt dflags
    mkRuleFn dflags Le (Lit lit) _ | isMinBound dflags lit = Just $ trueValInt  dflags
    mkRuleFn dflags Ge _ (Lit lit) | isMinBound dflags lit = Just $ trueValInt  dflags
    mkRuleFn dflags Lt _ (Lit lit) | isMinBound dflags lit = Just $ falseValInt dflags
    mkRuleFn dflags Ge (Lit lit) _ | isMaxBound dflags lit = Just $ trueValInt  dflags
    mkRuleFn dflags Lt (Lit lit) _ | isMaxBound dflags lit = Just $ falseValInt dflags
    mkRuleFn dflags Gt _ (Lit lit) | isMaxBound dflags lit = Just $ falseValInt dflags
    mkRuleFn dflags Le _ (Lit lit) | isMaxBound dflags lit = Just $ trueValInt  dflags
    mkRuleFn _ _ _ _                                       = Nothing

    isMinBound :: DynFlags -> Literal -> Bool
    isMinBound _      (MachChar c)   = c == minBound
    isMinBound dflags (MachInt i)    = i == tARGET_MIN_INT dflags
    isMinBound _      (MachInt64 i)  = i == toInteger (minBound :: Int64)
    isMinBound _      (MachWord i)   = i == 0
    isMinBound _      (MachWord64 i) = i == 0
    isMinBound _      _              = False

    isMaxBound :: DynFlags -> Literal -> Bool
    isMaxBound _      (MachChar c)   = c == maxBound
    isMaxBound dflags (MachInt i)    = i == tARGET_MAX_INT dflags
    isMaxBound _      (MachInt64 i)  = i == toInteger (maxBound :: Int64)
    isMaxBound dflags (MachWord i)   = i == tARGET_MAX_WORD dflags
    isMaxBound _      (MachWord64 i) = i == toInteger (maxBound :: Word64)
    isMaxBound _      _              = False

    -- Note [Word/Int underflow/overflow]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    --
    -- According to the Haskell Report 2010 (Sections 18.1 and 23.1 about signed and
    -- unsigned integral types): "All arithmetic is performed modulo 2^n, where n is
    -- the number of bits in the type."
    --
    -- GHC stores Word# and Int# constant values as Integer. Core optimizations such
    -- as constant folding must ensure that the Integer value remains in the valid
    -- target Word/Int range (see #13172). The following functions are used to
    -- ensure this.
    --
    -- Note that we *don't* warn the user about overflow. It's not done at runtime
    -- either, and compilation of completely harmless things like
    --    ((124076834 :: Word32) + (2147483647 :: Word32))
    -- doesn't yield a warning. Instead we simply squash the value into the *target*
    -- Int/Word range.

    -- | Ensure the given Integer is in the target Int range
    intResult' :: DynFlags -> Integer -> Integer
    intResult' dflags result = case platformWordSize (targetPlatform dflags) of
       4 -> toInteger (fromInteger result :: Int32)
       8 -> toInteger (fromInteger result :: Int64)
       w -> panic ("intResult: Unknown platformWordSize: " ++ show w)

    -- | Ensure the given Integer is in the target Word range
    wordResult' :: DynFlags -> Integer -> Integer
    wordResult' dflags result = case platformWordSize (targetPlatform dflags) of
       4 -> toInteger (fromInteger result :: Word32)
       8 -> toInteger (fromInteger result :: Word64)
       w -> panic ("wordResult: Unknown platformWordSize: " ++ show w)

    -- | Create an Int literal expression while ensuring the given Integer is in the
    -- target Int range
    intResult :: DynFlags -> Integer -> Maybe CoreExpr
    intResult dflags result = Just (mkIntVal dflags (intResult' dflags result))

    -- | Create a Word literal expression while ensuring the given Integer is in the
    -- target Word range
    wordResult :: DynFlags -> Integer -> Maybe CoreExpr
    wordResult dflags result = Just (mkWordVal dflags (wordResult' dflags result))

    inversePrimOp :: PrimOp -> RuleM CoreExpr
    inversePrimOp primop = do
      [Var primop_id `App` e] <- getArgs
      matchPrimOpId primop primop_id
      return e

    subsumesPrimOp :: PrimOp -> PrimOp -> RuleM CoreExpr
    this `subsumesPrimOp` that = do
      [Var primop_id `App` e] <- getArgs
      matchPrimOpId that primop_id
      return (Var (mkPrimOpId this) `App` e)

    subsumedByPrimOp :: PrimOp -> RuleM CoreExpr
    subsumedByPrimOp primop = do
      [e@(Var primop_id `App` _)] <- getArgs
      matchPrimOpId primop primop_id
      return e

    idempotent :: RuleM CoreExpr
    idempotent = do [e1, e2] <- getArgs
                    guard $ cheapEqExpr e1 e2
                    return e1

    {-
    Note [Guarding against silly shifts]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    Consider this code:

      import Data.Bits( (.|.), shiftL )
      chunkToBitmap :: [Bool] -> Word32
      chunkToBitmap chunk = foldr (.|.) 0 [ 1 `shiftL` n | (True,n) <- zip chunk [0..] ]

    This optimises to:
    Shift.$wgo = \ (w_sCS :: GHC.Prim.Int#) (w1_sCT :: [GHC.Types.Bool]) ->
        case w1_sCT of _ {
          [] -> 0##;
          : x_aAW xs_aAX ->
            case x_aAW of _ {
              GHC.Types.False ->
                case w_sCS of wild2_Xh {
                  __DEFAULT -> Shift.$wgo (GHC.Prim.+# wild2_Xh 1) xs_aAX;
                  9223372036854775807 -> 0## };
              GHC.Types.True ->
                case GHC.Prim.>=# w_sCS 64 of _ {
                  GHC.Types.False ->
                    case w_sCS of wild3_Xh {
                      __DEFAULT ->
                        case Shift.$wgo (GHC.Prim.+# wild3_Xh 1) xs_aAX of ww_sCW { __DEFAULT ->
                          GHC.Prim.or# (GHC.Prim.narrow32Word#
                                          (GHC.Prim.uncheckedShiftL# 1## wild3_Xh))
                                       ww_sCW
                         };
                      9223372036854775807 ->
                        GHC.Prim.narrow32Word#
    !!!!-->                  (GHC.Prim.uncheckedShiftL# 1## 9223372036854775807)
                    };
                  GHC.Types.True ->
                    case w_sCS of wild3_Xh {
                      __DEFAULT -> Shift.$wgo (GHC.Prim.+# wild3_Xh 1) xs_aAX;
                      9223372036854775807 -> 0##
                    } } } }

    Note the massive shift on line "!!!!".  It can't happen, because we've checked
    that w < 64, but the optimiser didn't spot that. We DO NO want to constant-fold this!
    Moreover, if the programmer writes (n `uncheckedShiftL` 9223372036854775807), we
    can't constant fold it, but if it gets to the assember we get
         Error: operand type mismatch for `shl'

    So the best thing to do is to rewrite the shift with a call to error,
    when the second arg is stupid.

    ************************************************************************
    *                                                                      *
    \subsection{Vaguely generic functions}
    *                                                                      *
    ************************************************************************
    -}

    mkBasicRule :: Name -> Int -> RuleM CoreExpr -> CoreRule
    -- Gives the Rule the same name as the primop itself
    mkBasicRule op_name n_args rm
      = BuiltinRule { ru_name = occNameFS (nameOccName op_name),
                      ru_fn = op_name,
                      ru_nargs = n_args,
                      ru_try = \ dflags in_scope _ -> runRuleM rm dflags in_scope }

    newtype RuleM r = RuleM
      { runRuleM :: DynFlags -> InScopeEnv -> [CoreExpr] -> Maybe r }

    instance Functor RuleM where
        fmap = liftM

    instance Applicative RuleM where
        pure x = RuleM $ \_ _ _ -> Just x
        (<*>) = ap

    instance Monad RuleM where
      RuleM f >>= g = RuleM $ \dflags iu e -> case f dflags iu e of
        Nothing -> Nothing
        Just r -> runRuleM (g r) dflags iu e
      fail _ = mzero

    #if __GLASGOW_HASKELL__ > 710
    instance MonadFail.MonadFail RuleM where
        fail _ = mzero
    #endif

    instance Alternative RuleM where
      empty = RuleM $ \_ _ _ -> Nothing
      RuleM f1 <|> RuleM f2 = RuleM $ \dflags iu args ->
        f1 dflags iu args <|> f2 dflags iu args

    instance MonadPlus RuleM

    instance HasDynFlags RuleM where
        getDynFlags = RuleM $ \dflags _ _ -> Just dflags

    liftMaybe :: Maybe a -> RuleM a
    liftMaybe Nothing = mzero
    liftMaybe (Just x) = return x

    liftLit :: (Literal -> Literal) -> RuleM CoreExpr
    liftLit f = liftLitDynFlags (const f)

    liftLitDynFlags :: (DynFlags -> Literal -> Literal) -> RuleM CoreExpr
    liftLitDynFlags f = do
      dflags <- getDynFlags
      [Lit lit] <- getArgs
      return $ Lit (f dflags lit)

    removeOp32 :: RuleM CoreExpr
    removeOp32 = do
      dflags <- getDynFlags
      if wordSizeInBits dflags == 32
      then do
        [e] <- getArgs
        return e
      else mzero

    getArgs :: RuleM [CoreExpr]
    getArgs = RuleM $ \_ _ args -> Just args

    getInScopeEnv :: RuleM InScopeEnv
    getInScopeEnv = RuleM $ \_ iu _ -> Just iu

    -- return the n-th argument of this rule, if it is a literal
    -- argument indices start from 0
    getLiteral :: Int -> RuleM Literal
    getLiteral n = RuleM $ \_ _ exprs -> case drop n exprs of
      (Lit l:_) -> Just l
      _ -> Nothing

    unaryLit :: (DynFlags -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
    unaryLit op = do
      dflags <- getDynFlags
      [Lit l] <- getArgs
      liftMaybe $ op dflags (convFloating dflags l)

    binaryLit :: (DynFlags -> Literal -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
    binaryLit op = do
      dflags <- getDynFlags
      [Lit l1, Lit l2] <- getArgs
      liftMaybe $ op dflags (convFloating dflags l1) (convFloating dflags l2)

    binaryCmpLit :: (forall a . Ord a => a -> a -> Bool) -> RuleM CoreExpr
    binaryCmpLit op = do
      dflags <- getDynFlags
      binaryLit (\_ -> cmpOp dflags op)

    leftIdentity :: Literal -> RuleM CoreExpr
    leftIdentity id_lit = leftIdentityDynFlags (const id_lit)

    rightIdentity :: Literal -> RuleM CoreExpr
    rightIdentity id_lit = rightIdentityDynFlags (const id_lit)

    identity :: Literal -> RuleM CoreExpr
    identity lit = leftIdentity lit `mplus` rightIdentity lit

    leftIdentityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
    leftIdentityDynFlags id_lit = do
      dflags <- getDynFlags
      [Lit l1, e2] <- getArgs
      guard $ l1 == id_lit dflags
      return e2

    rightIdentityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
    rightIdentityDynFlags id_lit = do
      dflags <- getDynFlags
      [e1, Lit l2] <- getArgs
      guard $ l2 == id_lit dflags
      return e1

    identityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
    identityDynFlags lit = leftIdentityDynFlags lit `mplus` rightIdentityDynFlags lit

    leftZero :: (DynFlags -> Literal) -> RuleM CoreExpr
    leftZero zero = do
      dflags <- getDynFlags
      [Lit l1, _] <- getArgs
      guard $ l1 == zero dflags
      return $ Lit l1

    rightZero :: (DynFlags -> Literal) -> RuleM CoreExpr
    rightZero zero = do
      dflags <- getDynFlags
      [_, Lit l2] <- getArgs
      guard $ l2 == zero dflags
      return $ Lit l2

    zeroElem :: (DynFlags -> Literal) -> RuleM CoreExpr
    zeroElem lit = leftZero lit `mplus` rightZero lit

    equalArgs :: RuleM ()
    equalArgs = do
      [e1, e2] <- getArgs
      guard $ e1 `cheapEqExpr` e2

    nonZeroLit :: Int -> RuleM ()
    nonZeroLit n = getLiteral n >>= guard . not . isZeroLit

    -- When excess precision is not requested, cut down the precision of the
    -- Rational value to that of Float/Double. We confuse host architecture
    -- and target architecture here, but it's convenient (and wrong :-).
    convFloating :: DynFlags -> Literal -> Literal
    convFloating dflags (MachFloat  f) | not (gopt Opt_ExcessPrecision dflags) =
       MachFloat  (toRational (fromRational f :: Float ))
    convFloating dflags (MachDouble d) | not (gopt Opt_ExcessPrecision dflags) =
       MachDouble (toRational (fromRational d :: Double))
    convFloating _ l = l

    guardFloatDiv :: RuleM ()
    guardFloatDiv = do
      [Lit (MachFloat f1), Lit (MachFloat f2)] <- getArgs
      guard $ (f1 /=0 || f2 > 0) -- see Note [negative zero]
           && f2 /= 0            -- avoid NaN and Infinity/-Infinity

    guardDoubleDiv :: RuleM ()
    guardDoubleDiv = do
      [Lit (MachDouble d1), Lit (MachDouble d2)] <- getArgs
      guard $ (d1 /=0 || d2 > 0) -- see Note [negative zero]
           && d2 /= 0            -- avoid NaN and Infinity/-Infinity
    -- Note [negative zero] Avoid (0 / -d), otherwise 0/(-1) reduces to
    -- zero, but we might want to preserve the negative zero here which
    -- is representable in Float/Double but not in (normalised)
    -- Rational. (#3676) Perhaps we should generate (0 :% (-1)) instead?

    strengthReduction :: Literal -> PrimOp -> RuleM CoreExpr
    strengthReduction two_lit add_op = do -- Note [Strength reduction]
      arg <- msum [ do [arg, Lit mult_lit] <- getArgs
                       guard (mult_lit == two_lit)
                       return arg
                  , do [Lit mult_lit, arg] <- getArgs
                       guard (mult_lit == two_lit)
                       return arg ]
      return $ Var (mkPrimOpId add_op) `App` arg `App` arg

    -- Note [Strength reduction]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~
    --
    -- This rule turns floating point multiplications of the form 2.0 * x and
    -- x * 2.0 into x + x addition, because addition costs less than multiplication.
    -- See #7116

    -- Note [What's true and false]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    --
    -- trueValInt and falseValInt represent true and false values returned by
    -- comparison primops for Char, Int, Word, Integer, Double, Float and Addr.
    -- True is represented as an unboxed 1# literal, while false is represented
    -- as 0# literal.
    -- We still need Bool data constructors (True and False) to use in a rule
    -- for constant folding of equal Strings

    trueValInt, falseValInt :: DynFlags -> Expr CoreBndr
    trueValInt  dflags = Lit $ onei  dflags -- see Note [What's true and false]
    falseValInt dflags = Lit $ zeroi dflags

    trueValBool, falseValBool :: Expr CoreBndr
    trueValBool   = Var trueDataConId -- see Note [What's true and false]
    falseValBool  = Var falseDataConId

    ltVal, eqVal, gtVal :: Expr CoreBndr
    ltVal = Var ltDataConId
    eqVal = Var eqDataConId
    gtVal = Var gtDataConId

    mkIntVal :: DynFlags -> Integer -> Expr CoreBndr
    mkIntVal dflags i = Lit (mkMachInt dflags i)
    mkWordVal :: DynFlags -> Integer -> Expr CoreBndr
    mkWordVal dflags w = Lit (mkMachWord dflags w)
    mkFloatVal :: DynFlags -> Rational -> Expr CoreBndr
    mkFloatVal dflags f = Lit (convFloating dflags (MachFloat  f))
    mkDoubleVal :: DynFlags -> Rational -> Expr CoreBndr
    mkDoubleVal dflags d = Lit (convFloating dflags (MachDouble d))

    matchPrimOpId :: PrimOp -> Id -> RuleM ()
    matchPrimOpId op id = do
      op' <- liftMaybe $ isPrimOpId_maybe id
      guard $ op == op'

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Special rules for seq, tagToEnum, dataToTag}
    *                                                                      *
    ************************************************************************

    Note [tagToEnum#]
    ~~~~~~~~~~~~~~~~~
    Nasty check to ensure that tagToEnum# is applied to a type that is an
    enumeration TyCon.  Unification may refine the type later, but this
    check won't see that, alas.  It's crude but it works.

    Here's are two cases that should fail
            f :: forall a. a
            f = tagToEnum# 0        -- Can't do tagToEnum# at a type variable

            g :: Int
            g = tagToEnum# 0        -- Int is not an enumeration

    We used to make this check in the type inference engine, but it's quite
    ugly to do so, because the delayed constraint solving means that we don't
    really know what's going on until the end. It's very much a corner case
    because we don't expect the user to call tagToEnum# at all; we merely
    generate calls in derived instances of Enum.  So we compromise: a
    rewrite rule rewrites a bad instance of tagToEnum# to an error call,
    and emits a warning.
    -}

    tagToEnumRule :: RuleM CoreExpr
    -- If     data T a = A | B | C
    -- then   tag2Enum# (T ty) 2# -->  B ty
    tagToEnumRule = do
      [Type ty, Lit (MachInt i)] <- getArgs
      case splitTyConApp_maybe ty of
        Just (tycon, tc_args) | isEnumerationTyCon tycon -> do
          let tag = fromInteger i
              correct_tag dc = (dataConTag dc - fIRST_TAG) == tag
          (dc:rest) <- return $ filter correct_tag (tyConDataCons_maybe tycon `orElse` [])
          ASSERT(null rest) return ()
          return $ mkTyApps (Var (dataConWorkId dc)) tc_args

        -- See Note [tagToEnum#]
        _ -> WARN( True, text "tagToEnum# on non-enumeration type" <+> ppr ty )
             return $ mkRuntimeErrorApp rUNTIME_ERROR_ID ty "tagToEnum# on non-enumeration type"

    {-
    For dataToTag#, we can reduce if either

            (a) the argument is a constructor
            (b) the argument is a variable whose unfolding is a known constructor
    -}

    dataToTagRule :: RuleM CoreExpr
    dataToTagRule = a `mplus` b
      where
        a = do
          [Type ty1, Var tag_to_enum `App` Type ty2 `App` tag] <- getArgs
          guard $ tag_to_enum `hasKey` tagToEnumKey
          guard $ ty1 `eqType` ty2
          return tag -- dataToTag (tagToEnum x)   ==>   x
        b = do
          dflags <- getDynFlags
          [_, val_arg] <- getArgs
          in_scope <- getInScopeEnv
          (dc,_,_) <- liftMaybe $ exprIsConApp_maybe in_scope val_arg
          ASSERT( not (isNewTyCon (dataConTyCon dc)) ) return ()
          return $ mkIntVal dflags (toInteger (dataConTag dc - fIRST_TAG))

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Rules for seq# and spark#}
    *                                                                      *
    ************************************************************************
    -}

    -- seq# :: forall a s . a -> State# s -> (# State# s, a #)
    seqRule :: RuleM CoreExpr
    seqRule = do
      [Type ty_a, Type ty_s, a, s] <- getArgs
      guard $ exprIsHNF a
      return $ mkCoreUbxTup [mkStatePrimTy ty_s, ty_a] [s, a]

    -- spark# :: forall a s . a -> State# s -> (# State# s, a #)
    sparkRule :: RuleM CoreExpr
    sparkRule = seqRule -- reduce on HNF, just the same
      -- XXX perhaps we shouldn't do this, because a spark eliminated by
      -- this rule won't be counted as a dud at runtime?

    {-
    ************************************************************************
    *                                                                      *
    \subsection{Built in rules}
    *                                                                      *
    ************************************************************************

    Note [Scoping for Builtin rules]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    When compiling a (base-package) module that defines one of the
    functions mentioned in the RHS of a built-in rule, there's a danger
    that we'll see

            f = ...(eq String x)....

            ....and lower down...

            eqString = ...

    Then a rewrite would give

            f = ...(eqString x)...
            ....and lower down...
            eqString = ...

    and lo, eqString is not in scope.  This only really matters when we get to code
    generation.  With -O we do a GlomBinds step that does a new SCC analysis on the whole
    set of bindings, which sorts out the dependency.  Without -O we don't do any rule
    rewriting so again we are fine.

    (This whole thing doesn't show up for non-built-in rules because their dependencies
    are explicit.)
    -}

    builtinRules :: [CoreRule]
    -- Rules for non-primops that can't be expressed using a RULE pragma
    builtinRules
      = [BuiltinRule { ru_name = fsLit "AppendLitString",
                       ru_fn = unpackCStringFoldrName,
                       ru_nargs = 4, ru_try = match_append_lit },
         BuiltinRule { ru_name = fsLit "EqString", ru_fn = eqStringName,
                       ru_nargs = 2, ru_try = match_eq_string },
         BuiltinRule { ru_name = fsLit "Inline", ru_fn = inlineIdName,
                       ru_nargs = 2, ru_try = \_ _ _ -> match_inline },
         BuiltinRule { ru_name = fsLit "MagicDict", ru_fn = idName magicDictId,
                       ru_nargs = 4, ru_try = \_ _ _ -> match_magicDict },
         mkBasicRule divIntName 2 $ msum
            [ nonZeroLit 1 >> binaryLit (intOp2 div)
            , leftZero zeroi
            , do
              [arg, Lit (MachInt d)] <- getArgs
              Just n <- return $ exactLog2 d
              dflags <- getDynFlags
              return $ Var (mkPrimOpId ISraOp) `App` arg `App` mkIntVal dflags n
            ],
         mkBasicRule modIntName 2 $ msum
            [ nonZeroLit 1 >> binaryLit (intOp2 mod)
            , leftZero zeroi
            , do
              [arg, Lit (MachInt d)] <- getArgs
              Just _ <- return $ exactLog2 d
              dflags <- getDynFlags
              return $ Var (mkPrimOpId AndIOp)
                `App` arg `App` mkIntVal dflags (d - 1)
            ]
         ]
     ++ builtinIntegerRules

    builtinIntegerRules :: [CoreRule]
    builtinIntegerRules =
     [rule_IntToInteger   "smallInteger"        smallIntegerName,
      rule_WordToInteger  "wordToInteger"       wordToIntegerName,
      rule_Int64ToInteger  "int64ToInteger"     int64ToIntegerName,
      rule_Word64ToInteger "word64ToInteger"    word64ToIntegerName,
      rule_convert        "integerToWord"       integerToWordName       mkWordLitWord,
      rule_convert        "integerToInt"        integerToIntName        mkIntLitInt,
      rule_convert        "integerToWord64"     integerToWord64Name     (\_ -> mkWord64LitWord64),
      rule_convert        "integerToInt64"      integerToInt64Name      (\_ -> mkInt64LitInt64),
      rule_binop          "plusInteger"         plusIntegerName         (+),
      rule_binop          "minusInteger"        minusIntegerName        (-),
      rule_binop          "timesInteger"        timesIntegerName        (*),
      rule_unop           "negateInteger"       negateIntegerName       negate,
      rule_binop_Prim     "eqInteger#"          eqIntegerPrimName       (==),
      rule_binop_Prim     "neqInteger#"         neqIntegerPrimName      (/=),
      rule_unop           "absInteger"          absIntegerName          abs,
      rule_unop           "signumInteger"       signumIntegerName       signum,
      rule_binop_Prim     "leInteger#"          leIntegerPrimName       (<=),
      rule_binop_Prim     "gtInteger#"          gtIntegerPrimName       (>),
      rule_binop_Prim     "ltInteger#"          ltIntegerPrimName       (<),
      rule_binop_Prim     "geInteger#"          geIntegerPrimName       (>=),
      rule_binop_Ordering "compareInteger"      compareIntegerName      compare,
      rule_encodeFloat    "encodeFloatInteger"  encodeFloatIntegerName  mkFloatLitFloat,
      rule_convert        "floatFromInteger"    floatFromIntegerName    (\_ -> mkFloatLitFloat),
      rule_encodeFloat    "encodeDoubleInteger" encodeDoubleIntegerName mkDoubleLitDouble,
      rule_decodeDouble   "decodeDoubleInteger" decodeDoubleIntegerName,
      rule_convert        "doubleFromInteger"   doubleFromIntegerName   (\_ -> mkDoubleLitDouble),
      rule_rationalTo     "rationalToFloat"     rationalToFloatName     mkFloatExpr,
      rule_rationalTo     "rationalToDouble"    rationalToDoubleName    mkDoubleExpr,
      rule_binop          "gcdInteger"          gcdIntegerName          gcd,
      rule_binop          "lcmInteger"          lcmIntegerName          lcm,
      rule_binop          "andInteger"          andIntegerName          (.&.),
      rule_binop          "orInteger"           orIntegerName           (.|.),
      rule_binop          "xorInteger"          xorIntegerName          xor,
      rule_unop           "complementInteger"   complementIntegerName   complement,
      rule_Int_binop      "shiftLInteger"       shiftLIntegerName       shiftL,
      rule_Int_binop      "shiftRInteger"       shiftRIntegerName       shiftR,
      rule_bitInteger     "bitInteger"          bitIntegerName,
      -- See Note [Integer division constant folding] in libraries/base/GHC/Real.hs
      rule_divop_one      "quotInteger"         quotIntegerName         quot,
      rule_divop_one      "remInteger"          remIntegerName          rem,
      rule_divop_one      "divInteger"          divIntegerName          div,
      rule_divop_one      "modInteger"          modIntegerName          mod,
      rule_divop_both     "divModInteger"       divModIntegerName       divMod,
      rule_divop_both     "quotRemInteger"      quotRemIntegerName      quotRem,
      -- These rules below don't actually have to be built in, but if we
      -- put them in the Haskell source then we'd have to duplicate them
      -- between all Integer implementations
      rule_XToIntegerToX "smallIntegerToInt"       integerToIntName    smallIntegerName,
      rule_XToIntegerToX "wordToIntegerToWord"     integerToWordName   wordToIntegerName,
      rule_XToIntegerToX "int64ToIntegerToInt64"   integerToInt64Name  int64ToIntegerName,
      rule_XToIntegerToX "word64ToIntegerToWord64" integerToWord64Name word64ToIntegerName,
      rule_smallIntegerTo "smallIntegerToWord"   integerToWordName     Int2WordOp,
      rule_smallIntegerTo "smallIntegerToFloat"  floatFromIntegerName  Int2FloatOp,
      rule_smallIntegerTo "smallIntegerToDouble" doubleFromIntegerName Int2DoubleOp
      ]
        where rule_convert str name convert
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_Integer_convert convert }
              rule_IntToInteger str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_IntToInteger }
              rule_WordToInteger str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_WordToInteger }
              rule_Int64ToInteger str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_Int64ToInteger }
              rule_Word64ToInteger str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_Word64ToInteger }
              rule_unop str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_Integer_unop op }
              rule_bitInteger str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_IntToInteger_unop (bit . fromIntegral) }
              rule_binop str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_binop op }
              rule_divop_both str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_divop_both op }
              rule_divop_one str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_divop_one op }
              rule_Int_binop str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_Int_binop op }
              rule_binop_Prim str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_binop_Prim op }
              rule_binop_Ordering str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_binop_Ordering op }
              rule_encodeFloat str name op
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_Integer_Int_encodeFloat op }
              rule_decodeDouble str name
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_decodeDouble }
              rule_XToIntegerToX str name toIntegerName
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_XToIntegerToX toIntegerName }
              rule_smallIntegerTo str name primOp
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                               ru_try = match_smallIntegerTo primOp }
              rule_rationalTo str name mkLit
               = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                               ru_try = match_rationalTo mkLit }

    ---------------------------------------------------
    -- The rule is this:
    --      unpackFoldrCString# "foo" c (unpackFoldrCString# "baz" c n)
    --      =  unpackFoldrCString# "foobaz" c n

    match_append_lit :: RuleFun
    match_append_lit _ id_unf _
            [ Type ty1
            , lit1
            , c1
            , Var unpk `App` Type ty2
                       `App` lit2
                       `App` c2
                       `App` n
            ]
      | unpk `hasKey` unpackCStringFoldrIdKey &&
        c1 `cheapEqExpr` c2
      , Just (MachStr s1) <- exprIsLiteral_maybe id_unf lit1
      , Just (MachStr s2) <- exprIsLiteral_maybe id_unf lit2
      = ASSERT( ty1 `eqType` ty2 )
        Just (Var unpk `App` Type ty1
                       `App` Lit (MachStr (s1 `BS.append` s2))
                       `App` c1
                       `App` n)

    match_append_lit _ _ _ _ = Nothing

    ---------------------------------------------------
    -- The rule is this:
    --      eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2) = s1==s2

    match_eq_string :: RuleFun
    match_eq_string _ id_unf _
            [Var unpk1 `App` lit1, Var unpk2 `App` lit2]
      | unpk1 `hasKey` unpackCStringIdKey
      , unpk2 `hasKey` unpackCStringIdKey
      , Just (MachStr s1) <- exprIsLiteral_maybe id_unf lit1
      , Just (MachStr s2) <- exprIsLiteral_maybe id_unf lit2
      = Just (if s1 == s2 then trueValBool else falseValBool)

    match_eq_string _ _ _ _ = Nothing

    ---------------------------------------------------
    -- The rule is this:
    --      inline f_ty (f a b c) = <f's unfolding> a b c
    -- (if f has an unfolding, EVEN if it's a loop breaker)
    --
    -- It's important to allow the argument to 'inline' to have args itself
    -- (a) because its more forgiving to allow the programmer to write
    --       inline f a b c
    --   or  inline (f a b c)
    -- (b) because a polymorphic f wll get a type argument that the
    --     programmer can't avoid
    --
    -- Also, don't forget about 'inline's type argument!
    match_inline :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
    match_inline (Type _ : e : _)
      | (Var f, args1) <- collectArgs e,
        Just unf <- maybeUnfoldingTemplate (realIdUnfolding f)
                 -- Ignore the IdUnfoldingFun here!
      = Just (mkApps unf args1)

    match_inline _ = Nothing

    -- See Note [magicDictId magic] in `basicTypes/MkId.hs`
    -- for a description of what is going on here.
    match_magicDict :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
    match_magicDict [Type _, Var wrap `App` Type a `App` Type _ `App` f, x, y ]
      | Just (fieldTy, _)   <- splitFunTy_maybe $ dropForAlls $ idType wrap
      , Just (dictTy, _)    <- splitFunTy_maybe fieldTy
      , Just dictTc         <- tyConAppTyCon_maybe dictTy
      , Just (_,_,co)       <- unwrapNewTyCon_maybe dictTc
      = Just
      $ f `App` Cast x (mkSymCo (mkUnbranchedAxInstCo Representational co [a] []))
          `App` y

    match_magicDict _ = Nothing

    -------------------------------------------------
    -- Integer rules
    --   smallInteger  (79::Int#)  = 79::Integer
    --   wordToInteger (79::Word#) = 79::Integer
    -- Similarly Int64, Word64

    match_IntToInteger :: RuleFun
    match_IntToInteger = match_IntToInteger_unop id

    match_WordToInteger :: RuleFun
    match_WordToInteger _ id_unf id [xl]
      | Just (MachWord x) <- exprIsLiteral_maybe id_unf xl
      = case splitFunTy_maybe (idType id) of
        Just (_, integerTy) ->
            Just (Lit (LitInteger x integerTy))
        _ ->
            panic "match_WordToInteger: Id has the wrong type"
    match_WordToInteger _ _ _ _ = Nothing

    match_Int64ToInteger :: RuleFun
    match_Int64ToInteger _ id_unf id [xl]
      | Just (MachInt64 x) <- exprIsLiteral_maybe id_unf xl
      = case splitFunTy_maybe (idType id) of
        Just (_, integerTy) ->
            Just (Lit (LitInteger x integerTy))
        _ ->
            panic "match_Int64ToInteger: Id has the wrong type"
    match_Int64ToInteger _ _ _ _ = Nothing

    match_Word64ToInteger :: RuleFun
    match_Word64ToInteger _ id_unf id [xl]
      | Just (MachWord64 x) <- exprIsLiteral_maybe id_unf xl
      = case splitFunTy_maybe (idType id) of
        Just (_, integerTy) ->
            Just (Lit (LitInteger x integerTy))
        _ ->
            panic "match_Word64ToInteger: Id has the wrong type"
    match_Word64ToInteger _ _ _ _ = Nothing

    -------------------------------------------------
    match_Integer_convert :: Num a
                          => (DynFlags -> a -> Expr CoreBndr)
                          -> RuleFun
    match_Integer_convert convert dflags id_unf _ [xl]
      | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
      = Just (convert dflags (fromInteger x))
    match_Integer_convert _ _ _ _ _ = Nothing

    match_Integer_unop :: (Integer -> Integer) -> RuleFun
    match_Integer_unop unop _ id_unf _ [xl]
      | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
      = Just (Lit (LitInteger (unop x) i))
    match_Integer_unop _ _ _ _ _ = Nothing

    {- Note [Rewriting bitInteger]

    For most types the bitInteger operation can be implemented in terms of shifts.
    The integer-gmp package, however, can do substantially better than this if
    allowed to provide its own implementation. However, in so doing it previously lost
    constant-folding (see Trac #8832). The bitInteger rule above provides constant folding
    specifically for this function.

    There is, however, a bit of trickiness here when it comes to ranges. While the
    AST encodes all integers (even MachInts) as Integers, `bit` expects the bit
    index to be given as an Int. Hence we coerce to an Int in the rule definition.
    This will behave a bit funny for constants larger than the word size, but the user
    should expect some funniness given that they will have at very least ignored a
    warning in this case.
    -}

    match_IntToInteger_unop :: (Integer -> Integer) -> RuleFun
    match_IntToInteger_unop unop _ id_unf fn [xl]
      | Just (MachInt x) <- exprIsLiteral_maybe id_unf xl
      = case splitFunTy_maybe (idType fn) of
        Just (_, integerTy) ->
            Just (Lit (LitInteger (unop x) integerTy))
        _ ->
            panic "match_IntToInteger_unop: Id has the wrong type"
    match_IntToInteger_unop _ _ _ _ _ = Nothing

    match_Integer_binop :: (Integer -> Integer -> Integer) -> RuleFun
    match_Integer_binop binop _ id_unf _ [xl,yl]
      | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      = Just (Lit (LitInteger (x `binop` y) i))
    match_Integer_binop _ _ _ _ _ = Nothing

    -- This helper is used for the quotRem and divMod functions
    match_Integer_divop_both
       :: (Integer -> Integer -> (Integer, Integer)) -> RuleFun
    match_Integer_divop_both divop _ id_unf _ [xl,yl]
      | Just (LitInteger x t) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      , y /= 0
      , (r,s) <- x `divop` y
      = Just $ mkCoreUbxTup [t,t] [Lit (LitInteger r t), Lit (LitInteger s t)]
    match_Integer_divop_both _ _ _ _ _ = Nothing

    -- This helper is used for the quot and rem functions
    match_Integer_divop_one :: (Integer -> Integer -> Integer) -> RuleFun
    match_Integer_divop_one divop _ id_unf _ [xl,yl]
      | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      , y /= 0
      = Just (Lit (LitInteger (x `divop` y) i))
    match_Integer_divop_one _ _ _ _ _ = Nothing

    match_Integer_Int_binop :: (Integer -> Int -> Integer) -> RuleFun
    match_Integer_Int_binop binop _ id_unf _ [xl,yl]
      | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
      , Just (MachInt y)      <- exprIsLiteral_maybe id_unf yl
      = Just (Lit (LitInteger (x `binop` fromIntegral y) i))
    match_Integer_Int_binop _ _ _ _ _ = Nothing

    match_Integer_binop_Prim :: (Integer -> Integer -> Bool) -> RuleFun
    match_Integer_binop_Prim binop dflags id_unf _ [xl, yl]
      | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      = Just (if x `binop` y then trueValInt dflags else falseValInt dflags)
    match_Integer_binop_Prim _ _ _ _ _ = Nothing

    match_Integer_binop_Ordering :: (Integer -> Integer -> Ordering) -> RuleFun
    match_Integer_binop_Ordering binop _ id_unf _ [xl, yl]
      | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      = Just $ case x `binop` y of
                 LT -> ltVal
                 EQ -> eqVal
                 GT -> gtVal
    match_Integer_binop_Ordering _ _ _ _ _ = Nothing

    match_Integer_Int_encodeFloat :: RealFloat a
                                  => (a -> Expr CoreBndr)
                                  -> RuleFun
    match_Integer_Int_encodeFloat mkLit _ id_unf _ [xl,yl]
      | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
      , Just (MachInt y)      <- exprIsLiteral_maybe id_unf yl
      = Just (mkLit $ encodeFloat x (fromInteger y))
    match_Integer_Int_encodeFloat _ _ _ _ _ = Nothing

    ---------------------------------------------------
    -- constant folding for Float/Double
    --
    -- This turns
    --      rationalToFloat n d
    -- into a literal Float, and similarly for Doubles.
    --
    -- it's important to not match d == 0, because that may represent a
    -- literal "0/0" or similar, and we can't produce a literal value for
    -- NaN or +-Inf
    match_rationalTo :: RealFloat a
                     => (a -> Expr CoreBndr)
                     -> RuleFun
    match_rationalTo mkLit _ id_unf _ [xl, yl]
      | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
      , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
      , y /= 0
      = Just (mkLit (fromRational (x % y)))
    match_rationalTo _ _ _ _ _ = Nothing

    match_decodeDouble :: RuleFun
    match_decodeDouble _ id_unf fn [xl]
      | Just (MachDouble x) <- exprIsLiteral_maybe id_unf xl
      = case splitFunTy_maybe (idType fn) of
        Just (_, res)
          | Just [_lev1, _lev2, integerTy, intHashTy] <- tyConAppArgs_maybe res
          -> case decodeFloat (fromRational x :: Double) of
               (y, z) ->
                 Just $ mkCoreUbxTup [integerTy, intHashTy]
                                     [Lit (LitInteger y integerTy),
                                      Lit (MachInt (toInteger z))]
        _ ->
            pprPanic "match_decodeDouble: Id has the wrong type"
              (ppr fn <+> dcolon <+> ppr (idType fn))
    match_decodeDouble _ _ _ _ = Nothing

    match_XToIntegerToX :: Name -> RuleFun
    match_XToIntegerToX n _ _ _ [App (Var x) y]
      | idName x == n
      = Just y
    match_XToIntegerToX _ _ _ _ _ = Nothing

    match_smallIntegerTo :: PrimOp -> RuleFun
    match_smallIntegerTo primOp _ _ _ [App (Var x) y]
      | idName x == smallIntegerName
      = Just $ App (Var (mkPrimOpId primOp)) y
    match_smallIntegerTo _ _ _ _ _ = Nothing

    --------------------------------------------------------
    -- Constant folding through case-expressions
    --
    -- cf Scrutinee Constant Folding in simplCore/SimplUtils
    --------------------------------------------------------

    -- | Match the scrutinee of a case and potentially return a new scrutinee and a
    -- function to apply to each literal alternative.
    caseRules :: DynFlags -> CoreExpr -> Maybe (CoreExpr, Integer -> Integer)
    caseRules dflags scrut = case scrut of

       -- We need to call wordResult' and intResult' to ensure that the literal
       -- alternatives remain in Word/Int target ranges (cf Note [Word/Int
       -- underflow/overflow] and #13172).

       -- v `op` x#
       App (App (Var f) v) (Lit l)
          | Just op <- isPrimOpId_maybe f
          , Just x  <- isLitValue_maybe l ->
          case op of
             WordAddOp -> Just (v, \y -> wordResult' dflags $ y-x      )
             IntAddOp  -> Just (v, \y -> intResult'  dflags $ y-x      )
             WordSubOp -> Just (v, \y -> wordResult' dflags $ y+x      )
             IntSubOp  -> Just (v, \y -> intResult'  dflags $ y+x      )
             XorOp     -> Just (v, \y -> wordResult' dflags $ y `xor` x)
             XorIOp    -> Just (v, \y -> intResult'  dflags $ y `xor` x)
             _         -> Nothing

       -- x# `op` v
       App (App (Var f) (Lit l)) v
          | Just op <- isPrimOpId_maybe f
          , Just x  <- isLitValue_maybe l ->
          case op of
             WordAddOp -> Just (v, \y -> wordResult' dflags $ y-x      )
             IntAddOp  -> Just (v, \y -> intResult'  dflags $ y-x      )
             WordSubOp -> Just (v, \y -> wordResult' dflags $ x-y      )
             IntSubOp  -> Just (v, \y -> intResult'  dflags $ x-y      )
             XorOp     -> Just (v, \y -> wordResult' dflags $ y `xor` x)
             XorIOp    -> Just (v, \y -> intResult'  dflags $ y `xor` x)
             _         -> Nothing

       -- op v
       App (Var f) v
          | Just op <- isPrimOpId_maybe f ->
          case op of
             NotOp     -> Just (v, \y -> wordResult' dflags $ complement y)
             NotIOp    -> Just (v, \y -> intResult'  dflags $ complement y)
             IntNegOp  -> Just (v, \y -> intResult'  dflags $ negate y    )
             _         -> Nothing

       _ -> Nothing