content: {-
  (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
  
  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 AllowAmbiguousTypes #-}
  {-# LANGUAGE DeriveFunctor #-}
  {-# LANGUAGE LambdaCase #-}
  {-# LANGUAGE MultiWayIf #-}
  {-# LANGUAGE PatternSynonyms #-}
  {-# LANGUAGE RankNTypes #-}
  {-# LANGUAGE ScopedTypeVariables #-}
  {-# LANGUAGE TypeApplications #-}
  {-# LANGUAGE ViewPatterns #-}
  
  {-# OPTIONS_GHC -optc-DNON_POSIX_SOURCE #-}
  
  -- | Constant Folder
  module GHC.Core.Opt.ConstantFold
     ( primOpRules
     , builtinRules
     , caseRules
     , caseRules2
     )
  where
  
  import GHC.Prelude
  
  import GHC.Platform
  import GHC.Float
  
  import GHC.Types.Id.Make ( unboxedUnitExpr )
  import GHC.Types.Id
  import GHC.Types.Literal
  import GHC.Types.Name.Occurrence ( occNameFS )
  import GHC.Types.Tickish
  import GHC.Types.Name ( Name, nameOccName )
  import GHC.Types.Basic
  
  import GHC.Core
  import GHC.Core.Make
  import GHC.Core.SimpleOpt (  exprIsConApp_maybe, exprIsLiteral_maybe )
  import GHC.Core.DataCon ( DataCon,dataConTagZ, dataConTyCon, dataConWrapId, dataConWorkId )
  import GHC.Core.Utils  ( cheapEqExpr, exprIsHNF
                         , stripTicksTop, stripTicksTopT, mkTicks )
  import GHC.Core.Multiplicity
  import GHC.Core.Rules.Config
  import GHC.Core.Type
  import GHC.Core.TyCo.Compare( eqType )
  import GHC.Core.TyCon
     ( TyCon, tyConDataCons_maybe, tyConDataCons, tyConSingleDataCon, tyConFamilySize
     , isEnumerationTyCon, isValidDTT2TyCon, isNewTyCon )
  import GHC.Core.Map.Expr ( eqCoreExpr )
  
  import GHC.Builtin.PrimOps ( PrimOp(..), tagToEnumKey )
  import GHC.Builtin.PrimOps.Ids (primOpId)
  import GHC.Builtin.Types
  import GHC.Builtin.Types.Prim
  import GHC.Builtin.Names
  
  import GHC.Cmm.MachOp ( FMASign(..) )
  import GHC.Cmm.Type ( Width(..) )
  
  import GHC.Data.FastString
  
  import GHC.Utils.Outputable
  import GHC.Utils.Misc
  import GHC.Utils.Panic
  
  import Control.Applicative ( Alternative(..) )
  import Control.Monad
  import Data.Functor (($>))
  import qualified Data.ByteString as BS
  import Data.Ratio
  import Data.Word
  import Data.Maybe (fromMaybe, fromJust)
  
  {-
  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
  primOpRules nm = \case
     TagToEnumOp -> mkPrimOpRule nm 2 [ tagToEnumRule ]
     DataToTagSmallOp -> mkPrimOpRule nm 3 [ dataToTagRule ]
     DataToTagLargeOp -> mkPrimOpRule nm 3 [ dataToTagRule ]
  
     -- Int8 operations
     Int8AddOp   -> mkPrimOpRule nm 2 [ binaryLit (int8Op2 (+))
                                      , identity zeroI8
                                      , addFoldingRules Int8AddOp int8Ops
                                      ]
     Int8SubOp   -> mkPrimOpRule nm 2 [ binaryLit (int8Op2 (-))
                                      , rightIdentity zeroI8
                                      , equalArgs $> Lit zeroI8
                                      , subFoldingRules Int8SubOp int8Ops
                                      ]
     Int8MulOp   -> mkPrimOpRule nm 2 [ binaryLit (int8Op2 (*))
                                      , zeroElem
                                      , identity oneI8
                                      , mulFoldingRules Int8MulOp int8Ops
                                      ]
     Int8QuotOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int8Op2 quot)
                                      , leftZero
                                      , rightIdentity oneI8
                                      , equalArgs $> Lit oneI8
                                      , quotFoldingRules int8Ops
                                      ]
     Int8RemOp   -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int8Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroI8
                                      , equalArgs $> Lit zeroI8 ]
     Int8NegOp   -> mkPrimOpRule nm 1 [ unaryLit negOp
                                      , semiInversePrimOp Int8NegOp ]
     Int8SllOp   -> mkPrimOpRule nm 2 [ shiftRule LitNumInt8 (const shiftL)
                                      , rightIdentity zeroI8 ]
     Int8SraOp   -> mkPrimOpRule nm 2 [ shiftRule LitNumInt8 (const shiftR)
                                      , rightIdentity zeroI8 ]
     Int8SrlOp   -> mkPrimOpRule nm 2 [ shiftRule LitNumInt8 $ const $ shiftRightLogical @Word8
                                      , rightIdentity zeroI8 ]
  
     -- Word8 operations
     Word8AddOp  -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 (+))
                                      , identity zeroW8
                                      , addFoldingRules Word8AddOp word8Ops
                                      ]
     Word8SubOp  -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 (-))
                                      , rightIdentity zeroW8
                                      , equalArgs $> Lit zeroW8
                                      , subFoldingRules Word8SubOp word8Ops
                                      ]
     Word8MulOp  -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 (*))
                                      , identity oneW8
                                      , mulFoldingRules Word8MulOp word8Ops
                                      ]
     Word8QuotOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word8Op2 quot)
                                      , rightIdentity oneW8
                                      , quotFoldingRules word8Ops
                                      ]
     Word8RemOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word8Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroW8
                                      , equalArgs $> Lit zeroW8 ]
     Word8AndOp  -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identity (mkLitWord8 0xFF)
                                      , sameArgIdempotentCommut Word8AndOp
                                      , andFoldingRules word8Ops
                                      ]
     Word8OrOp   -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 (.|.))
                                      , idempotent
                                      , identity zeroW8
                                      , sameArgIdempotentCommut Word8OrOp
                                      , orFoldingRules word8Ops
                                      ]
     Word8XorOp  -> mkPrimOpRule nm 2 [ binaryLit (word8Op2 xor)
                                      , identity zeroW8
                                      , equalArgs $> Lit zeroW8 ]
     Word8NotOp  -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp Word8NotOp ]
     Word8SllOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumWord8 (const shiftL) ]
     Word8SrlOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumWord8 $ const $ shiftRightLogical @Word8 ]
  
  
     -- Int16 operations
     Int16AddOp  -> mkPrimOpRule nm 2 [ binaryLit (int16Op2 (+))
                                      , identity zeroI16
                                      , addFoldingRules Int16AddOp int16Ops
                                      ]
     Int16SubOp  -> mkPrimOpRule nm 2 [ binaryLit (int16Op2 (-))
                                      , rightIdentity zeroI16
                                      , equalArgs $> Lit zeroI16
                                      , subFoldingRules Int16SubOp int16Ops
                                      ]
     Int16MulOp  -> mkPrimOpRule nm 2 [ binaryLit (int16Op2 (*))
                                      , zeroElem
                                      , identity oneI16
                                      , mulFoldingRules Int16MulOp int16Ops
                                      ]
     Int16QuotOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int16Op2 quot)
                                      , leftZero
                                      , rightIdentity oneI16
                                      , equalArgs $> Lit oneI16
                                      , quotFoldingRules int16Ops
                                      ]
     Int16RemOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int16Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroI16
                                      , equalArgs $> Lit zeroI16 ]
     Int16NegOp  -> mkPrimOpRule nm 1 [ unaryLit negOp
                                      , semiInversePrimOp Int16NegOp ]
     Int16SllOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt16 (const shiftL)
                                      , rightIdentity zeroI16 ]
     Int16SraOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt16 (const shiftR)
                                      , rightIdentity zeroI16 ]
     Int16SrlOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt16 $ const $ shiftRightLogical @Word16
                                      , rightIdentity zeroI16 ]
  
     -- Word16 operations
     Word16AddOp -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 (+))
                                      , identity zeroW16
                                      , addFoldingRules Word16AddOp word16Ops
                                      ]
     Word16SubOp -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 (-))
                                      , rightIdentity zeroW16
                                      , equalArgs $> Lit zeroW16
                                      , subFoldingRules Word16SubOp word16Ops
                                      ]
     Word16MulOp -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 (*))
                                      , identity oneW16
                                      , mulFoldingRules Word16MulOp word16Ops
                                      ]
     Word16QuotOp-> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word16Op2 quot)
                                      , rightIdentity oneW16
                                      , quotFoldingRules word16Ops
                                      ]
     Word16RemOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word16Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroW16
                                      , equalArgs $> Lit zeroW16 ]
     Word16AndOp -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identity (mkLitWord16 0xFFFF)
                                      , sameArgIdempotentCommut Word16AndOp
                                      , andFoldingRules word16Ops
                                      ]
     Word16OrOp  -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 (.|.))
                                      , idempotent
                                      , identity zeroW16
                                      , sameArgIdempotentCommut Word16OrOp
                                      , orFoldingRules word16Ops
                                      ]
     Word16XorOp -> mkPrimOpRule nm 2 [ binaryLit (word16Op2 xor)
                                      , identity zeroW16
                                      , equalArgs $> Lit zeroW16 ]
     Word16NotOp -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp Word16NotOp ]
     Word16SllOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord16 (const shiftL) ]
     Word16SrlOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord16 $ const $ shiftRightLogical @Word16 ]
  
  
     -- Int32 operations
     Int32AddOp  -> mkPrimOpRule nm 2 [ binaryLit (int32Op2 (+))
                                      , identity zeroI32
                                      , addFoldingRules Int32AddOp int32Ops
                                      ]
     Int32SubOp  -> mkPrimOpRule nm 2 [ binaryLit (int32Op2 (-))
                                      , rightIdentity zeroI32
                                      , equalArgs $> Lit zeroI32
                                      , subFoldingRules Int32SubOp int32Ops
                                      ]
     Int32MulOp  -> mkPrimOpRule nm 2 [ binaryLit (int32Op2 (*))
                                      , zeroElem
                                      , identity oneI32
                                      , mulFoldingRules Int32MulOp int32Ops
                                      ]
     Int32QuotOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int32Op2 quot)
                                      , leftZero
                                      , rightIdentity oneI32
                                      , equalArgs $> Lit oneI32
                                      , quotFoldingRules int32Ops
                                      ]
     Int32RemOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int32Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroI32
                                      , equalArgs $> Lit zeroI32 ]
     Int32NegOp  -> mkPrimOpRule nm 1 [ unaryLit negOp
                                      , semiInversePrimOp Int32NegOp ]
     Int32SllOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt32 (const shiftL)
                                      , rightIdentity zeroI32 ]
     Int32SraOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt32 (const shiftR)
                                      , rightIdentity zeroI32 ]
     Int32SrlOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt32 $ const $ shiftRightLogical @Word32
                                      , rightIdentity zeroI32 ]
  
     -- Word32 operations
     Word32AddOp -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 (+))
                                      , identity zeroW32
                                      , addFoldingRules Word32AddOp word32Ops
                                      ]
     Word32SubOp -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 (-))
                                      , rightIdentity zeroW32
                                      , equalArgs $> Lit zeroW32
                                      , subFoldingRules Word32SubOp word32Ops
                                      ]
     Word32MulOp -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 (*))
                                      , identity oneW32
                                      , mulFoldingRules Word32MulOp word32Ops
                                      ]
     Word32QuotOp-> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word32Op2 quot)
                                      , rightIdentity oneW32
                                      , quotFoldingRules word32Ops
                                      ]
     Word32RemOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word32Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroW32
                                      , equalArgs $> Lit zeroW32 ]
     Word32AndOp -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identity (mkLitWord32 0xFFFFFFFF)
                                      , sameArgIdempotentCommut Word32AndOp
                                      , andFoldingRules word32Ops
                                      ]
     Word32OrOp  -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 (.|.))
                                      , idempotent
                                      , identity zeroW32
                                      , sameArgIdempotentCommut Word32OrOp
                                      , orFoldingRules word32Ops
                                      ]
     Word32XorOp -> mkPrimOpRule nm 2 [ binaryLit (word32Op2 xor)
                                      , identity zeroW32
                                      , equalArgs $> Lit zeroW32 ]
     Word32NotOp -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp Word32NotOp ]
     Word32SllOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord32 (const shiftL) ]
     Word32SrlOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord32 $ const $ shiftRightLogical @Word32 ]
  
     -- Int64 operations
     Int64AddOp  -> mkPrimOpRule nm 2 [ binaryLit (int64Op2 (+))
                                      , identity zeroI64
                                      , addFoldingRules Int64AddOp int64Ops
                                      ]
     Int64SubOp  -> mkPrimOpRule nm 2 [ binaryLit (int64Op2 (-))
                                      , rightIdentity zeroI64
                                      , equalArgs $> Lit zeroI64
                                      , subFoldingRules Int64SubOp int64Ops
                                      ]
     Int64MulOp  -> mkPrimOpRule nm 2 [ binaryLit (int64Op2 (*))
                                      , zeroElem
                                      , identity oneI64
                                      , mulFoldingRules Int64MulOp int64Ops
                                      ]
     Int64QuotOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int64Op2 quot)
                                      , leftZero
                                      , rightIdentity oneI64
                                      , equalArgs $> Lit oneI64
                                      , quotFoldingRules int64Ops
                                      ]
     Int64RemOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (int64Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroI64
                                      , equalArgs $> Lit zeroI64 ]
     Int64NegOp  -> mkPrimOpRule nm 1 [ unaryLit negOp
                                      , semiInversePrimOp Int64NegOp ]
     Int64SllOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt64 (const shiftL)
                                      , rightIdentity zeroI64 ]
     Int64SraOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt64 (const shiftR)
                                      , rightIdentity zeroI64 ]
     Int64SrlOp  -> mkPrimOpRule nm 2 [ shiftRule LitNumInt64 $ const $ shiftRightLogical @Word64
                                      , rightIdentity zeroI64 ]
  
     -- Word64 operations
     Word64AddOp -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 (+))
                                      , identity zeroW64
                                      , addFoldingRules Word64AddOp word64Ops
                                      ]
     Word64SubOp -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 (-))
                                      , rightIdentity zeroW64
                                      , equalArgs $> Lit zeroW64
                                      , subFoldingRules Word64SubOp word64Ops
                                      ]
     Word64MulOp -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 (*))
                                      , identity oneW64
                                      , mulFoldingRules Word64MulOp word64Ops
                                      ]
     Word64QuotOp-> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word64Op2 quot)
                                      , rightIdentity oneW64
                                      , quotFoldingRules word64Ops
                                      ]
     Word64RemOp -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (word64Op2 rem)
                                      , leftZero
                                      , oneLit 1 $> Lit zeroW64
                                      , equalArgs $> Lit zeroW64 ]
     Word64AndOp -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identity (mkLitWord64 0xFFFFFFFFFFFFFFFF)
                                      , sameArgIdempotentCommut Word64AndOp
                                      , andFoldingRules word64Ops
                                      ]
     Word64OrOp  -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 (.|.))
                                      , idempotent
                                      , identity zeroW64
                                      , sameArgIdempotentCommut Word64OrOp
                                      , orFoldingRules word64Ops
                                      ]
     Word64XorOp -> mkPrimOpRule nm 2 [ binaryLit (word64Op2 xor)
                                      , identity zeroW64
                                      , equalArgs $> Lit zeroW64 ]
     Word64NotOp -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp Word64NotOp ]
     Word64SllOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord64 (const shiftL) ]
     Word64SrlOp -> mkPrimOpRule nm 2 [ shiftRule LitNumWord64 $ const $ shiftRightLogical @Word64 ]
  
     -- Int operations
     IntAddOp    -> mkPrimOpRule nm 2 [ binaryLit (intOp2 (+))
                                      , identityPlatform zeroi
                                      , addFoldingRules IntAddOp intOps
                                      ]
     IntSubOp    -> mkPrimOpRule nm 2 [ binaryLit (intOp2 (-))
                                      , rightIdentityPlatform zeroi
                                      , equalArgs >> retLit zeroi
                                      , subFoldingRules IntSubOp intOps
                                      ]
     IntAddCOp   -> mkPrimOpRule nm 2 [ binaryLit (intOpC2 (+))
                                      , identityCPlatform zeroi ]
     IntSubCOp   -> mkPrimOpRule nm 2 [ binaryLit (intOpC2 (-))
                                      , rightIdentityCPlatform zeroi
                                      , equalArgs >> retLitNoC zeroi ]
     IntMulOp    -> mkPrimOpRule nm 2 [ binaryLit (intOp2 (*))
                                      , zeroElem
                                      , identityPlatform onei
                                      , mulFoldingRules IntMulOp intOps
                                      ]
     IntMul2Op   -> mkPrimOpRule nm 2 [ do
                                          [Lit (LitNumber _ l1), Lit (LitNumber _ l2)] <- getArgs
                                          platform <- getPlatform
                                          let r = l1 * l2
                                          pure $ mkCoreUnboxedTuple
                                            [ Lit (if platformInIntRange platform r then zeroi platform else onei platform)
                                            , mkIntLitWrap platform (r `shiftR` platformWordSizeInBits platform)
                                            , mkIntLitWrap platform r
                                            ]
  
                                      , zeroElem >>= \z ->
                                          pure (mkCoreUnboxedTuple [z,z,z])
  
                                        -- timesInt2# 1# other
                                        -- ~~~>
                                        -- (# 0#, 0# -# (other >># (WORD_SIZE_IN_BITS-1)), other #)
                                        -- The second element is the sign bit
                                        -- repeated to fill a word.
                                      , identityPlatform onei >>= \other -> do
                                          platform <- getPlatform
                                          pure $ mkCoreUnboxedTuple
                                            [ Lit (zeroi platform)
                                            , mkCoreApps (Var (primOpId IntSubOp))
                                                [ Lit (zeroi platform)
                                                , mkCoreApps (Var (primOpId IntSrlOp))
                                                  [ other
                                                  , mkIntLit platform (fromIntegral (platformWordSizeInBits platform - 1))
                                                  ]
                                                ]
                                            , other
                                            ]
                                      ]
     IntQuotOp   -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 quot)
                                      , leftZero
                                      , rightIdentityPlatform onei
                                      , equalArgs >> retLit onei
                                      , quotFoldingRules intOps
                                      ]
     IntRemOp    -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 rem)
                                      , leftZero
                                      , oneLit 1 >> retLit zeroi
                                      , equalArgs >> retLit zeroi ]
     IntAndOp    -> mkPrimOpRule nm 2 [ binaryLit (intOp2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identityPlatform (\p -> mkLitInt p (-1))
                                      , sameArgIdempotentCommut IntAndOp
                                      , andFoldingRules intOps
                                      ]
     IntOrOp     -> mkPrimOpRule nm 2 [ binaryLit (intOp2 (.|.))
                                      , idempotent
                                      , identityPlatform zeroi
                                      , sameArgIdempotentCommut IntOrOp
                                      , orFoldingRules intOps
                                      ]
     IntXorOp    -> mkPrimOpRule nm 2 [ binaryLit (intOp2 xor)
                                      , identityPlatform zeroi
                                      , equalArgs >> retLit zeroi ]
     IntNotOp    -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp IntNotOp ]
     IntNegOp    -> mkPrimOpRule nm 1 [ unaryLit negOp
                                      , semiInversePrimOp IntNegOp ]
     IntSllOp    -> mkPrimOpRule nm 2 [ shiftRule LitNumInt (const shiftL)
                                      , rightIdentityPlatform zeroi ]
     IntSraOp    -> mkPrimOpRule nm 2 [ shiftRule LitNumInt (const shiftR)
                                      , rightIdentityPlatform zeroi ]
     IntSrlOp    -> mkPrimOpRule nm 2 [ shiftRule LitNumInt shiftRightLogicalNative
                                      , rightIdentityPlatform zeroi ]
  
     -- Word operations
     WordAddOp   -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 (+))
                                      , identityPlatform zerow
                                      , addFoldingRules WordAddOp wordOps
                                      ]
     WordSubOp   -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 (-))
                                      , rightIdentityPlatform zerow
                                      , equalArgs >> retLit zerow
                                      , subFoldingRules WordSubOp wordOps
                                      ]
     WordAddCOp  -> mkPrimOpRule nm 2 [ binaryLit (wordOpC2 (+))
                                      , identityCPlatform zerow ]
     WordSubCOp  -> mkPrimOpRule nm 2 [ binaryLit (wordOpC2 (-))
                                      , rightIdentityCPlatform zerow
                                      , equalArgs >> retLitNoC zerow ]
     WordMulOp   -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 (*))
                                      , identityPlatform onew
                                      , mulFoldingRules WordMulOp wordOps
                                      ]
     WordQuotOp  -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 quot)
                                      , rightIdentityPlatform onew
                                      , quotFoldingRules wordOps
                                      ]
     WordRemOp   -> mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 rem)
                                      , leftZero
                                      , oneLit 1 >> retLit zerow
                                      , equalArgs >> retLit zerow ]
     WordAndOp   -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.&.))
                                      , idempotent
                                      , zeroElem
                                      , identityPlatform (\p -> mkLitWord p (platformMaxWord p))
                                      , sameArgIdempotentCommut WordAndOp
                                      , andFoldingRules wordOps
                                      ]
     WordOrOp    -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.|.))
                                      , idempotent
                                      , identityPlatform zerow
                                      , sameArgIdempotentCommut WordOrOp
                                      , orFoldingRules wordOps
                                      ]
     WordXorOp   -> mkPrimOpRule nm 2 [ binaryLit (wordOp2 xor)
                                      , identityPlatform zerow
                                      , equalArgs >> retLit zerow ]
     WordNotOp   -> mkPrimOpRule nm 1 [ unaryLit complementOp
                                      , semiInversePrimOp WordNotOp ]
     WordSllOp   -> mkPrimOpRule nm 2 [ shiftRule LitNumWord (const shiftL) ]
     WordSrlOp   -> mkPrimOpRule nm 2 [ shiftRule LitNumWord shiftRightLogicalNative ]
  
     PopCnt8Op   -> mkPrimOpRule nm 1 [ pop_count @Word8  ]
     PopCnt16Op  -> mkPrimOpRule nm 1 [ pop_count @Word16 ]
     PopCnt32Op  -> mkPrimOpRule nm 1 [ pop_count @Word32 ]
     PopCnt64Op  -> mkPrimOpRule nm 1 [ pop_count @Word64 ]
     PopCntOp    -> mkPrimOpRule nm 1 [ getWordSize >>= \case
                                          PW4 -> pop_count @Word32
                                          PW8 -> pop_count @Word64
                                      ]
  
     Ctz8Op      -> mkPrimOpRule nm 1 [ ctz @Word8  ]
     Ctz16Op     -> mkPrimOpRule nm 1 [ ctz @Word16 ]
     Ctz32Op     -> mkPrimOpRule nm 1 [ ctz @Word32 ]
     Ctz64Op     -> mkPrimOpRule nm 1 [ ctz @Word64 ]
     CtzOp       -> mkPrimOpRule nm 1 [ getWordSize >>= \case
                                          PW4 -> ctz @Word32
                                          PW8 -> ctz @Word64
                                      ]
  
     Clz8Op      -> mkPrimOpRule nm 1 [ clz @Word8  ]
     Clz16Op     -> mkPrimOpRule nm 1 [ clz @Word16 ]
     Clz32Op     -> mkPrimOpRule nm 1 [ clz @Word32 ]
     Clz64Op     -> mkPrimOpRule nm 1 [ clz @Word64 ]
     ClzOp       -> mkPrimOpRule nm 1 [ getWordSize >>= \case
                                          PW4 -> clz @Word32
                                          PW8 -> clz @Word64
                                      ]
  
     -- coercions
  
     Int8ToIntOp    -> mkPrimOpRule nm 1 [ liftLitPlatform convertToIntLit ]
     Int16ToIntOp   -> mkPrimOpRule nm 1 [ liftLitPlatform convertToIntLit ]
     Int32ToIntOp   -> mkPrimOpRule nm 1 [ liftLitPlatform convertToIntLit ]
     Int64ToIntOp   -> mkPrimOpRule nm 1 [ liftLitPlatform convertToIntLit ]
     IntToInt8Op    -> mkPrimOpRule nm 1 [ liftLit narrowInt8Lit
                                         , narrowSubsumesAnd IntAndOp IntToInt8Op 8 ]
     IntToInt16Op   -> mkPrimOpRule nm 1 [ liftLit narrowInt16Lit
                                         , narrowSubsumesAnd IntAndOp IntToInt16Op 16 ]
     IntToInt32Op   -> mkPrimOpRule nm 1 [ liftLit narrowInt32Lit
                                         , narrowSubsumesAnd IntAndOp IntToInt32Op 32 ]
     IntToInt64Op   -> mkPrimOpRule nm 1 [ liftLit narrowInt64Lit ]
  
     Word8ToWordOp  -> mkPrimOpRule nm 1 [ liftLitPlatform convertToWordLit
                                         , extendNarrowPassthrough WordToWord8Op 0xFF
                                         ]
     Word16ToWordOp -> mkPrimOpRule nm 1 [ liftLitPlatform convertToWordLit
                                         , extendNarrowPassthrough WordToWord16Op 0xFFFF
                                         ]
     Word32ToWordOp -> mkPrimOpRule nm 1 [ liftLitPlatform convertToWordLit
                                         , extendNarrowPassthrough WordToWord32Op 0xFFFFFFFF
                                         ]
     Word64ToWordOp -> mkPrimOpRule nm 1 [ liftLitPlatform convertToWordLit ]
  
     WordToWord8Op  -> mkPrimOpRule nm 1 [ liftLit narrowWord8Lit
                                         , narrowSubsumesAnd WordAndOp WordToWord8Op 8 ]
     WordToWord16Op -> mkPrimOpRule nm 1 [ liftLit narrowWord16Lit
                                         , narrowSubsumesAnd WordAndOp WordToWord16Op 16 ]
     WordToWord32Op -> mkPrimOpRule nm 1 [ liftLit narrowWord32Lit
                                         , narrowSubsumesAnd WordAndOp WordToWord32Op 32 ]
     WordToWord64Op -> mkPrimOpRule nm 1 [ liftLit narrowWord64Lit ]
  
     Word8ToInt8Op  -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumInt8) ]
     Int8ToWord8Op  -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumWord8) ]
     Word16ToInt16Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumInt16) ]
     Int16ToWord16Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumWord16) ]
     Word32ToInt32Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumInt32) ]
     Int32ToWord32Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumWord32) ]
     Word64ToInt64Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumInt64) ]
     Int64ToWord64Op-> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumWord64) ]
  
     WordToIntOp    -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumInt) ]
     IntToWordOp    -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumCoerce LitNumWord) ]
  
     Narrow8IntOp   -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumInt8)
                                         , subsumedByPrimOp Narrow8IntOp
                                         , Narrow8IntOp `subsumesPrimOp` Narrow16IntOp
                                         , Narrow8IntOp `subsumesPrimOp` Narrow32IntOp
                                         , narrowSubsumesAnd IntAndOp Narrow8IntOp 8 ]
     Narrow16IntOp  -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumInt16)
                                         , subsumedByPrimOp Narrow8IntOp
                                         , subsumedByPrimOp Narrow16IntOp
                                         , Narrow16IntOp `subsumesPrimOp` Narrow32IntOp
                                         , narrowSubsumesAnd IntAndOp Narrow16IntOp 16 ]
     Narrow32IntOp  -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumInt32)
                                         , subsumedByPrimOp Narrow8IntOp
                                         , subsumedByPrimOp Narrow16IntOp
                                         , subsumedByPrimOp Narrow32IntOp
                                         , removeOp32
                                         , narrowSubsumesAnd IntAndOp Narrow32IntOp 32 ]
     Narrow8WordOp  -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumWord8)
                                         , subsumedByPrimOp Narrow8WordOp
                                         , Narrow8WordOp `subsumesPrimOp` Narrow16WordOp
                                         , Narrow8WordOp `subsumesPrimOp` Narrow32WordOp
                                         , narrowSubsumesAnd WordAndOp Narrow8WordOp 8 ]
     Narrow16WordOp -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumWord16)
                                         , subsumedByPrimOp Narrow8WordOp
                                         , subsumedByPrimOp Narrow16WordOp
                                         , Narrow16WordOp `subsumesPrimOp` Narrow32WordOp
                                         , narrowSubsumesAnd WordAndOp Narrow16WordOp 16 ]
     Narrow32WordOp -> mkPrimOpRule nm 1 [ liftLitPlatform (litNumNarrow LitNumWord32)
                                         , subsumedByPrimOp Narrow8WordOp
                                         , subsumedByPrimOp Narrow16WordOp
                                         , subsumedByPrimOp Narrow32WordOp
                                         , removeOp32
                                         , narrowSubsumesAnd WordAndOp Narrow32WordOp 32 ]
  
     CastWord64ToDoubleOp -> mkPrimOpRule nm 1
        [ unaryLit $ \_env -> \case
           LitNumber _ n
               | v <- castWord64ToDouble (fromInteger n)
               -- we can't represent those float literals in Core until #18897 is fixed
               , not (isNaN v || isInfinite v || isNegativeZero v)
               -> Just (mkDoubleLitDouble v)
           _   -> Nothing
        ]
  
     CastWord32ToFloatOp -> mkPrimOpRule nm 1
        [ unaryLit $ \_env -> \case
            LitNumber _ n
                | v <- castWord32ToFloat (fromInteger n)
                -- we can't represent those float literals in Core until #18897 is fixed
                , not (isNaN v || isInfinite v || isNegativeZero v)
                -> Just (mkFloatLitFloat v)
            _   -> Nothing
        ]
  
     CastDoubleToWord64Op -> mkPrimOpRule nm 1
        [ unaryLit $ \_env -> \case
           LitDouble n -> Just (mkWord64LitWord64 (castDoubleToWord64 (fromRational n)))
           _           -> Nothing
        ]
  
     CastFloatToWord32Op -> mkPrimOpRule nm 1
        [ unaryLit $ \_env -> \case
            LitFloat n -> Just (mkWord32LitWord32 (castFloatToWord32 (fromRational n)))
            _          -> Nothing
        ]
  
     OrdOp          -> mkPrimOpRule nm 1 [ liftLit charToIntLit
                                         , semiInversePrimOp ChrOp ]
     ChrOp          -> mkPrimOpRule nm 1 [ do [Lit lit] <- getArgs
                                              guard (litFitsInChar lit)
                                              liftLit intToCharLit
                                         , semiInversePrimOp OrdOp ]
     FloatToIntOp    -> mkPrimOpRule nm 1 [ liftLit floatToIntLit ]
     IntToFloatOp    -> mkPrimOpRule nm 1 [ liftLit intToFloatLit ]
     DoubleToIntOp   -> mkPrimOpRule nm 1 [ liftLit doubleToIntLit ]
     IntToDoubleOp   -> mkPrimOpRule nm 1 [ liftLit intToDoubleLit ]
     -- SUP: Not sure what the standard says about precision in the following 2 cases
     FloatToDoubleOp -> mkPrimOpRule nm 1 [ liftLit floatToDoubleLit ]
     DoubleToFloatOp -> mkPrimOpRule nm 1 [ liftLit doubleToFloatLit ]
  
     -- Float
     FloatAddOp        -> mkPrimOpRule nm 2 [ binaryLit (floatOp2 (+))
                                            , identity zerof ]
     FloatSubOp        -> mkPrimOpRule nm 2 [ binaryLit (floatOp2 (-))
                                            , rightIdentity zerof ]
     FloatMulOp        -> mkPrimOpRule nm 2 [ binaryLit (floatOp2 (*))
                                            , identity onef
                                            , strengthReduction twof FloatAddOp  ]
     FloatFMAdd        -> mkPrimOpRule nm 3 (fmaRules FMAdd  W32)
     FloatFMSub        -> mkPrimOpRule nm 3 (fmaRules FMSub  W32)
     FloatFNMAdd       -> mkPrimOpRule nm 3 (fmaRules FNMAdd W32)
     FloatFNMSub       -> mkPrimOpRule nm 3 (fmaRules FNMSub W32)
  
               -- zeroElem zerof doesn't hold because of NaN
     FloatDivOp        -> mkPrimOpRule nm 2 [ guardFloatDiv >> binaryLit (floatOp2 (/))
                                            , rightIdentity onef ]
     FloatNegOp        -> mkPrimOpRule nm 1 [ unaryLit negOp
                                            , semiInversePrimOp FloatNegOp ]
     FloatDecode_IntOp -> mkPrimOpRule nm 1 [ unaryLit floatDecodeOp ]
  
     -- Double
     DoubleAddOp          -> mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (+))
                                               , identity zerod ]
     DoubleSubOp          -> mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (-))
                                               , rightIdentity zerod ]
     DoubleMulOp          -> mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (*))
                                               , identity oned
                                               , strengthReduction twod DoubleAddOp  ]
     DoubleFMAdd          -> mkPrimOpRule nm 3 (fmaRules FMAdd  W64)
     DoubleFMSub          -> mkPrimOpRule nm 3 (fmaRules FMSub  W64)
     DoubleFNMAdd         -> mkPrimOpRule nm 3 (fmaRules FNMAdd W64)
     DoubleFNMSub         -> mkPrimOpRule nm 3 (fmaRules FNMSub W64)
                -- zeroElem zerod doesn't hold because of NaN
     DoubleDivOp          -> mkPrimOpRule nm 2 [ guardDoubleDiv >> binaryLit (doubleOp2 (/))
                                               , rightIdentity oned ]
     DoubleNegOp          -> mkPrimOpRule nm 1 [ unaryLit negOp
                                               , semiInversePrimOp DoubleNegOp ]
     DoubleDecode_Int64Op -> mkPrimOpRule nm 1 [ unaryLit doubleDecodeOp ]
  
     -- Relational operators, equality
  
     Int8EqOp   -> mkRelOpRule nm (==) [ litEq True ]
     Int8NeOp   -> mkRelOpRule nm (/=) [ litEq False ]
  
     Int16EqOp  -> mkRelOpRule nm (==) [ litEq True ]
     Int16NeOp  -> mkRelOpRule nm (/=) [ litEq False ]
  
     Int32EqOp  -> mkRelOpRule nm (==) [ litEq True ]
     Int32NeOp  -> mkRelOpRule nm (/=) [ litEq False ]
  
     Int64EqOp  -> mkRelOpRule nm (==) [ litEq True ]
     Int64NeOp  -> mkRelOpRule nm (/=) [ litEq False ]
  
     IntEqOp    -> mkRelOpRule nm (==) [ litEq True ]
     IntNeOp    -> mkRelOpRule nm (/=) [ litEq False ]
  
     Word8EqOp  -> mkRelOpRule nm (==) [ litEq True ]
     Word8NeOp  -> mkRelOpRule nm (/=) [ litEq False ]
  
     Word16EqOp -> mkRelOpRule nm (==) [ litEq True ]
     Word16NeOp -> mkRelOpRule nm (/=) [ litEq False ]
  
     Word32EqOp -> mkRelOpRule nm (==) [ litEq True ]
     Word32NeOp -> mkRelOpRule nm (/=) [ litEq False ]
  
     Word64EqOp -> mkRelOpRule nm (==) [ litEq True ]
     Word64NeOp -> mkRelOpRule nm (/=) [ litEq False ]
  
     WordEqOp   -> mkRelOpRule nm (==) [ litEq True ]
     WordNeOp   -> mkRelOpRule nm (/=) [ litEq False ]
  
     CharEqOp   -> mkRelOpRule nm (==) [ litEq True ]
     CharNeOp   -> mkRelOpRule nm (/=) [ litEq False ]
  
     FloatEqOp  -> mkFloatingRelOpRule nm (==)
     FloatNeOp  -> mkFloatingRelOpRule nm (/=)
  
     DoubleEqOp -> mkFloatingRelOpRule nm (==)
     DoubleNeOp -> mkFloatingRelOpRule nm (/=)
  
     -- Relational operators, ordering
  
     Int8GtOp   -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Int8GeOp   -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Int8LeOp   -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Int8LtOp   -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Int16GtOp  -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Int16GeOp  -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Int16LeOp  -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Int16LtOp  -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Int32GtOp  -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Int32GeOp  -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Int32LeOp  -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Int32LtOp  -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Int64GtOp  -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Int64GeOp  -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Int64LeOp  -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Int64LtOp  -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     IntGtOp    -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     IntGeOp    -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     IntLeOp    -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     IntLtOp    -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Word8GtOp  -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Word8GeOp  -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Word8LeOp  -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Word8LtOp  -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Word16GtOp -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Word16GeOp -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Word16LeOp -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Word16LtOp -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Word32GtOp -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Word32GeOp -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Word32LeOp -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Word32LtOp -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     Word64GtOp -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     Word64GeOp -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     Word64LeOp -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     Word64LtOp -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     WordGtOp   -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     WordGeOp   -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     WordLeOp   -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     WordLtOp   -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     CharGtOp   -> mkRelOpRule nm (>)  [ boundsCmp Gt ]
     CharGeOp   -> mkRelOpRule nm (>=) [ boundsCmp Ge ]
     CharLeOp   -> mkRelOpRule nm (<=) [ boundsCmp Le ]
     CharLtOp   -> mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
     FloatGtOp  -> mkFloatingRelOpRule nm (>)
     FloatGeOp  -> mkFloatingRelOpRule nm (>=)
     FloatLeOp  -> mkFloatingRelOpRule nm (<=)
     FloatLtOp  -> mkFloatingRelOpRule nm (<)
  
     DoubleGtOp -> mkFloatingRelOpRule nm (>)
     DoubleGeOp -> mkFloatingRelOpRule nm (>=)
     DoubleLeOp -> mkFloatingRelOpRule nm (<=)
     DoubleLtOp -> mkFloatingRelOpRule nm (<)
  
     -- Misc
  
     AddrAddOp  -> mkPrimOpRule nm 2 [ rightIdentityPlatform zeroi ]
  
     SparkOp    -> mkPrimOpRule nm 4 [ sparkRule ]
  
     _          -> 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
                      ; platform <- getPlatform
                      ; return (if cmp True True
                                then trueValInt  platform
                                else falseValInt platform) }
  
  {- 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 #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 :: Platform -> Literal
  zeroi platform = mkLitInt  platform 0
  onei  platform = mkLitInt  platform 1
  zerow platform = mkLitWord platform 0
  onew  platform = mkLitWord platform 1
  
  zeroI8, oneI8, zeroW8, oneW8 :: Literal
  zeroI8 = mkLitInt8  0
  oneI8  = mkLitInt8  1
  zeroW8 = mkLitWord8 0
  oneW8  = mkLitWord8 1
  
  zeroI16, oneI16, zeroW16, oneW16 :: Literal
  zeroI16 = mkLitInt16  0
  oneI16  = mkLitInt16  1
  zeroW16 = mkLitWord16 0
  oneW16  = mkLitWord16 1
  
  zeroI32, oneI32, zeroW32, oneW32 :: Literal
  zeroI32 = mkLitInt32  0
  oneI32  = mkLitInt32  1
  zeroW32 = mkLitWord32 0
  oneW32  = mkLitWord32 1
  
  zeroI64, oneI64, zeroW64, oneW64 :: Literal
  zeroI64 = mkLitInt64  0
  oneI64  = mkLitInt64  1
  zeroW64 = mkLitWord64 0
  oneW64  = mkLitWord64 1
  
  zerof, onef, twof, zerod, oned, twod :: Literal
  zerof = mkLitFloat 0.0
  onef  = mkLitFloat 1.0
  twof  = mkLitFloat 2.0
  zerod = mkLitDouble 0.0
  oned  = mkLitDouble 1.0
  twod  = mkLitDouble 2.0
  
  cmpOp :: Platform -> (forall a . Ord a => a -> a -> Bool)
        -> Literal -> Literal -> Maybe CoreExpr
  cmpOp platform cmp = go
    where
      done True  = Just $ trueValInt  platform
      done False = Just $ falseValInt platform
  
      -- These compares are at different types
      go (LitChar i1)   (LitChar i2)   = done (i1 `cmp` i2)
      go (LitFloat i1)  (LitFloat i2)  = done (i1 `cmp` i2)
      go (LitDouble i1) (LitDouble i2) = done (i1 `cmp` i2)
      go (LitNumber nt1 i1) (LitNumber nt2 i2)
        | nt1 /= nt2 = Nothing
        | otherwise  = done (i1 `cmp` i2)
      go _               _               = Nothing
  
  --------------------------
  
  negOp :: RuleOpts -> Literal -> Maybe CoreExpr  -- Negate
  negOp env = \case
     (LitFloat 0.0)  -> Nothing  -- can't represent -0.0 as a Rational
     (LitFloat f)    -> Just (mkFloatVal env (-f))
     (LitDouble 0.0) -> Nothing
     (LitDouble d)   -> Just (mkDoubleVal env (-d))
     (LitNumber nt i)
        | litNumIsSigned nt -> Just (Lit (mkLitNumberWrap (roPlatform env) nt (-i)))
     _ -> Nothing
  
  complementOp :: RuleOpts -> Literal -> Maybe CoreExpr  -- Binary complement
  complementOp env (LitNumber nt i) =
     Just (Lit (mkLitNumberWrap (roPlatform env) nt (complement i)))
  complementOp _      _            = Nothing
  
  int8Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  int8Op2 op _ (LitNumber LitNumInt8 i1) (LitNumber LitNumInt8 i2) =
    int8Result (fromInteger i1 `op` fromInteger i2)
  int8Op2 _ _ _ _ = Nothing
  
  int16Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  int16Op2 op _ (LitNumber LitNumInt16 i1) (LitNumber LitNumInt16 i2) =
    int16Result (fromInteger i1 `op` fromInteger i2)
  int16Op2 _ _ _ _ = Nothing
  
  int32Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  int32Op2 op _ (LitNumber LitNumInt32 i1) (LitNumber LitNumInt32 i2) =
    int32Result (fromInteger i1 `op` fromInteger i2)
  int32Op2 _ _ _ _ = Nothing
  
  int64Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  int64Op2 op _ (LitNumber LitNumInt64 i1) (LitNumber LitNumInt64 i2) =
    int64Result (fromInteger i1 `op` fromInteger i2)
  int64Op2 _ _ _ _ = Nothing
  
  intOp2 :: (Integral a, Integral b)
         => (a -> b -> Integer)
         -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  intOp2 = intOp2' . const
  
  intOp2' :: (Integral a, Integral b)
          => (RuleOpts -> a -> b -> Integer)
          -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  intOp2' op env (LitNumber LitNumInt i1) (LitNumber LitNumInt i2) =
    let o = op env
    in  intResult (roPlatform env) (fromInteger i1 `o` fromInteger i2)
  intOp2' _ _ _ _ = Nothing
  
  intOpC2 :: (Integral a, Integral b)
          => (a -> b -> Integer)
          -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  intOpC2 op env (LitNumber LitNumInt i1) (LitNumber LitNumInt i2) =
    intCResult (roPlatform env) (fromInteger i1 `op` fromInteger i2)
  intOpC2 _ _ _ _ = Nothing
  
  shiftRightLogical :: forall t. (Integral t, Bits t) => Integer -> Int -> Integer
  shiftRightLogical x n = fromIntegral (fromInteger x `shiftR` n :: t)
  
  -- | Shift right, putting zeros in rather than sign-propagating as
  -- 'Bits.shiftR' would do. Do this by converting to the appropriate Word
  -- and back. Obviously this won't work for too-big values, but its ok as
  -- we use it here.
  shiftRightLogicalNative :: Platform -> Integer -> Int -> Integer
  shiftRightLogicalNative platform =
      case platformWordSize platform of
        PW4 -> shiftRightLogical @Word32
        PW8 -> shiftRightLogical @Word64
  
  --------------------------
  retLit :: (Platform -> Literal) -> RuleM CoreExpr
  retLit l = do platform <- getPlatform
                return $ Lit $ l platform
  
  retLitNoC :: (Platform -> Literal) -> RuleM CoreExpr
  retLitNoC l = do platform <- getPlatform
                   let lit = l platform
                   return $ mkCoreUnboxedTuple [Lit lit, Lit (zeroi platform)]
  
  word8Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  word8Op2 op _ (LitNumber LitNumWord8 i1) (LitNumber LitNumWord8 i2) =
    word8Result (fromInteger i1 `op` fromInteger i2)
  word8Op2 _ _ _ _ = Nothing
  
  word16Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  word16Op2 op _ (LitNumber LitNumWord16 i1) (LitNumber LitNumWord16 i2) =
    word16Result (fromInteger i1 `op` fromInteger i2)
  word16Op2 _ _ _ _ = Nothing
  
  word32Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  word32Op2 op _ (LitNumber LitNumWord32 i1) (LitNumber LitNumWord32 i2) =
    word32Result (fromInteger i1 `op` fromInteger i2)
  word32Op2 _ _ _ _ = Nothing
  
  word64Op2
    :: (Integral a, Integral b)
    => (a -> b -> Integer)
    -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  word64Op2 op _ (LitNumber LitNumWord64 i1) (LitNumber LitNumWord64 i2) =
    word64Result (fromInteger i1 `op` fromInteger i2)
  word64Op2 _ _ _ _ = Nothing
  
  wordOp2 :: (Integral a, Integral b)
          => (a -> b -> Integer)
          -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  wordOp2 op env (LitNumber LitNumWord w1) (LitNumber LitNumWord w2)
      = wordResult (roPlatform env) (fromInteger w1 `op` fromInteger w2)
  wordOp2 _ _ _ _ = Nothing
  
  wordOpC2 :: (Integral a, Integral b)
          => (a -> b -> Integer)
          -> RuleOpts -> Literal -> Literal -> Maybe CoreExpr
  wordOpC2 op env (LitNumber LitNumWord w1) (LitNumber LitNumWord w2) =
    wordCResult (roPlatform env) (fromInteger w1 `op` fromInteger w2)
  wordOpC2 _ _ _ _ = Nothing
  
  shiftRule :: LitNumType
            -> (Platform -> Integer -> Int -> Integer)
            -> RuleM CoreExpr
  -- Shifts take an Int; hence third arg of op is Int
  -- Used for shift primops
  --    IntSllOp, IntSraOp, IntSrlOp :: Int# -> Int# -> Int#
  --    SllOp, SrlOp                 :: Word# -> Int# -> Word#
  shiftRule lit_num_ty shift_op = do
    platform <- getPlatform
    [e1, Lit (LitNumber LitNumInt shift_len)] <- getArgs
  
    bit_size <- case litNumBitSize platform lit_num_ty of
     Nothing -> mzero
     Just bs -> pure (toInteger bs)
  
    case e1 of
      _ | shift_len == 0 -> pure e1
  
        -- See Note [Guarding against silly shifts]
      _ | shift_len < 0 || shift_len >= bit_size
        -> pure $ Lit $ mkLitNumberWrap platform lit_num_ty 0
             -- Be sure to use lit_num_ty here, so we get a correctly typed zero.
             -- See #18589
  
      Lit (LitNumber nt x)
         | 0 < shift_len && shift_len <= bit_size
         -> assert (nt == lit_num_ty) $
            let op = shift_op platform
                -- Do the shift at type Integer, but shift length is Int.
                -- Using host's Int is ok even if target's Int has a different size
                -- because we test that shift_len <= bit_size (which is at most 64)
                y  = x `op` fromInteger shift_len
            in pure $ Lit $ mkLitNumberWrap platform nt y
  
      _ -> mzero
  
  --------------------------
  floatOp2 :: (Rational -> Rational -> Rational)
           -> RuleOpts -> Literal -> Literal
           -> Maybe (Expr CoreBndr)
  floatOp2 op env (LitFloat f1) (LitFloat f2)
    = Just (mkFloatVal env (f1 `op` f2))
  floatOp2 _ _ _ _ = Nothing
  
  --------------------------
  floatDecodeOp :: RuleOpts -> Literal -> Maybe CoreExpr
  floatDecodeOp env (LitFloat ((decodeFloat . fromRational @Float) -> (m, e)))
    = Just $ mkCoreUnboxedTuple [ mkIntVal (roPlatform env) (toInteger m)
                                , mkIntVal (roPlatform env) (toInteger e) ]
  floatDecodeOp _   _
    = Nothing
  
  --------------------------
  doubleOp2 :: (Rational -> Rational -> Rational)
            -> RuleOpts -> Literal -> Literal
            -> Maybe (Expr CoreBndr)
  doubleOp2 op env (LitDouble f1) (LitDouble f2)
    = Just (mkDoubleVal env (f1 `op` f2))
  doubleOp2 _ _ _ _ = Nothing
  
  --------------------------
  doubleDecodeOp :: RuleOpts -> Literal -> Maybe CoreExpr
  doubleDecodeOp env (LitDouble ((decodeFloat . fromRational @Double) -> (m, e)))
    = Just $ mkCoreUnboxedTuple [ Lit (mkLitInt64Wrap (toInteger m))
                                , mkIntVal platform (toInteger e) ]
    where
      platform = roPlatform env
  doubleDecodeOp _   _
    = Nothing
  
  --------------------------
  
  -- | Constant folding rules for fused multiply-add operations.
  fmaRules :: FMASign -> Width -> [RuleM CoreExpr]
  fmaRules signs width =
       [ fmaLit signs width
       , fmaZero_z signs width
       , fmaOne signs width ]
  
  -- | Compute @a * b + c@ when @a@, @b@, @c@ are all literals.
  fmaLit :: FMASign -> Width -> RuleM CoreExpr
  fmaLit signs width = do
    env <- getRuleOpts
    [Lit l1, Lit l2, Lit l3] <- getArgs
    liftMaybe $
      op env
        (convFloating env l1)
        (convFloating env l2)
        (convFloating env l3)
  
    where
      op env l1 l2 l3 =
        case width of
          W32
            | LitFloat x <- l1
            , LitFloat y <- l2
            , LitFloat z <- l3
            -> Just $ mkFloatVal env $
              case signs of
                FMAdd  -> x * y + z
                FMSub  -> x * y - z
                FNMAdd -> negate ( x * y ) + z
                FNMSub -> negate ( x * y ) - z
          W64
            | LitDouble x <- l1
            , LitDouble y <- l2
            , LitDouble z <- l3
            -> Just $ mkDoubleVal env $
              case signs of
                FMAdd  -> x * y + z
                FMSub  -> x * y - z
                FNMAdd -> negate ( x * y ) + z
                FNMSub -> negate ( x * y ) - z
          _ -> Nothing
  
  -- | @x * y + 0 = x * y@.
  fmaZero_z :: FMASign -> Width -> RuleM CoreExpr
  fmaZero_z signs width = do
    [x, y, Lit z] <- getArgs
    let
      -- TODO: we should additionally check the sign of z.
      -- FMAdd, FNMAdd: should be -0.0.
      -- FMSub, FNMSub: should be +0.0.
      ok =
        case width of
          W32
            | LitFloat 0 <- z
            -> True
          W64
            | LitDouble 0 <- z
            -> True
          _ -> False
      neg = case width of
        W32 ->  FloatNegOp
        W64 -> DoubleNegOp
        _   -> panic "fmaZero_xy: not Float# or Double#"
      mul = case width of
        W32 ->  FloatMulOp
        W64 -> DoubleMulOp
        _   -> panic "fmaZero_z: not Float# or Double#"
    if ok
    then return $ case signs of
      FMAdd  -> Var (primOpId mul) `App` x `App` y
      FMSub  -> Var (primOpId mul) `App` x `App` y
      FNMAdd -> Var (primOpId neg) `App` (Var (primOpId mul) `App` x `App` y)
      FNMSub -> Var (primOpId neg) `App` (Var (primOpId mul) `App` x `App` y)
    else mzero
  
  -- | @±1 * y + z ==> z ± y@ and @x * ±1 + z ==> z ± x@.
  fmaOne :: FMASign -> Width -> RuleM CoreExpr
  fmaOne signs width = do
    [x, y, z] <- getArgs
    let
      posNegOne_maybe :: Rational -> Maybe Bool
      posNegOne_maybe i
        | i == 1
        = Just False
        | i == -1
        = Just True
        | otherwise
        = Nothing
      ok =
        case width of
          W32
            | Lit (LitFloat i) <- x
            , Just sgn <- posNegOne_maybe i
            -> Just (sgn, y)
            | Lit (LitFloat i) <- y
            , Just sgn <- posNegOne_maybe i
            -> Just (sgn, x)
          W64
            | Lit (LitDouble i) <- x
            , Just sgn <- posNegOne_maybe i
            -> Just (sgn, y)
            | Lit (LitDouble i) <- y
            , Just sgn <- posNegOne_maybe i
            -> Just (sgn, x)
          _ -> Nothing
      neg = case width of
        W32 ->  FloatNegOp
        W64 -> DoubleNegOp
        _   -> panic "fmaOne: not Float# or Double#"
      add = case width of
        W32 ->  FloatAddOp
        W64 -> DoubleAddOp
        _   -> panic "fmaOne: not Float# or Double#"
      sub = case width of
        W32 ->  FloatSubOp
        W64 -> DoubleSubOp
        _   -> panic "fmaOne: not Float# or Double#"
    case ok of
      Nothing  -> mzero
      Just (sgn, t) -> return $
        if -- t + z
           |  ( signs ==  FMAdd && sgn == False )
           || ( signs == FNMAdd && sgn == True  )
           -> Var (primOpId add) `App` t `App` z
           -- - t + z
           |  signs ==  FMAdd
           || signs == FNMAdd
           -> Var (primOpId sub) `App` z `App` t
           -- t - z
           |  ( signs ==  FMSub && sgn == False )
           || ( signs == FNMSub && sgn == True  )
           -> Var (primOpId sub) `App` t `App` z
           -- - t - z
           |  signs ==  FMSub
           || signs == FNMSub
           -> Var (primOpId neg) `App` (Var (primOpId add) `App` t `App` z)
           | otherwise
           -> pprPanic "fmaOne: non-exhaustive pattern match" $
                vcat [ text "signs:" <+> text (show signs)
                     , text "sign:" <+> ppr sgn ]
  
  --------------------------
  {- 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
         platform <- getPlatform
         do_lit_eq platform lit expr
    , do [expr, Lit lit] <- getArgs
         platform <- getPlatform
         do_lit_eq platform lit expr ]
    where
      do_lit_eq platform lit expr = do
        guard (not (litIsLifted lit))
        return (mkWildCase expr (unrestricted $ literalType lit) intPrimTy
                      [ Alt DEFAULT      [] val_if_neq
                      , Alt (LitAlt lit) [] val_if_eq])
        where
          val_if_eq  | is_eq     = trueValInt  platform
                     | otherwise = falseValInt platform
          val_if_neq | is_eq     = falseValInt platform
                     | otherwise = trueValInt  platform
  
  
  -- | 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
    platform <- getPlatform
    [a, b] <- getArgs
    liftMaybe $ mkRuleFn platform op a b
  
  data Comparison = Gt | Ge | Lt | Le
  
  mkRuleFn :: Platform -> Comparison -> CoreExpr -> CoreExpr -> Maybe CoreExpr
  mkRuleFn platform Gt (Lit lit) _ | isMinBound platform lit = Just $ falseValInt platform
  mkRuleFn platform Le (Lit lit) _ | isMinBound platform lit = Just $ trueValInt  platform
  mkRuleFn platform Ge _ (Lit lit) | isMinBound platform lit = Just $ trueValInt  platform
  mkRuleFn platform Lt _ (Lit lit) | isMinBound platform lit = Just $ falseValInt platform
  mkRuleFn platform Ge (Lit lit) _ | isMaxBound platform lit = Just $ trueValInt  platform
  mkRuleFn platform Lt (Lit lit) _ | isMaxBound platform lit = Just $ falseValInt platform
  mkRuleFn platform Gt _ (Lit lit) | isMaxBound platform lit = Just $ falseValInt platform
  mkRuleFn platform Le _ (Lit lit) | isMaxBound platform lit = Just $ trueValInt  platform
  mkRuleFn _ _ _ _                                           = Nothing
  
  -- | Create an Int literal expression while ensuring the given Integer is in the
  -- target Int range
  int8Result :: Integer -> Maybe CoreExpr
  int8Result result = Just (int8Result' result)
  
  int8Result' :: Integer -> CoreExpr
  int8Result' result = Lit (mkLitInt8Wrap result)
  
  -- | Create an Int literal expression while ensuring the given Integer is in the
  -- target Int range
  int16Result :: Integer -> Maybe CoreExpr
  int16Result result = Just (int16Result' result)
  
  int16Result' :: Integer -> CoreExpr
  int16Result' result = Lit (mkLitInt16Wrap result)
  
  -- | Create an Int literal expression while ensuring the given Integer is in the
  -- target Int range
  int32Result :: Integer -> Maybe CoreExpr
  int32Result result = Just (int32Result' result)
  
  int32Result' :: Integer -> CoreExpr
  int32Result' result = Lit (mkLitInt32Wrap result)
  
  intResult :: Platform -> Integer -> Maybe CoreExpr
  intResult platform result = Just (intResult' platform result)
  
  intResult' :: Platform -> Integer -> CoreExpr
  intResult' platform result = Lit (mkLitIntWrap platform result)
  
  -- | Create an unboxed pair of an Int literal expression, ensuring the given
  -- Integer is in the target Int range and the corresponding overflow flag
  -- (@0#@/@1#@) if it wasn't.
  intCResult :: Platform -> Integer -> Maybe CoreExpr
  intCResult platform result = Just (mkCoreUnboxedTuple [Lit lit, Lit c])
    where
      (lit, b) = mkLitIntWrapC platform result
      c = if b then onei platform else zeroi platform
  
  -- | Create a Word literal expression while ensuring the given Integer is in the
  -- target Word range
  word8Result :: Integer -> Maybe CoreExpr
  word8Result result = Just (word8Result' result)
  
  word8Result' :: Integer -> CoreExpr
  word8Result' result = Lit (mkLitWord8Wrap result)
  
  -- | Create a Word literal expression while ensuring the given Integer is in the
  -- target Word range
  word16Result :: Integer -> Maybe CoreExpr
  word16Result result = Just (word16Result' result)
  
  word16Result' :: Integer -> CoreExpr
  word16Result' result = Lit (mkLitWord16Wrap result)
  
  -- | Create a Word literal expression while ensuring the given Integer is in the
  -- target Word range
  word32Result :: Integer -> Maybe CoreExpr
  word32Result result = Just (word32Result' result)
  
  word32Result' :: Integer -> CoreExpr
  word32Result' result = Lit (mkLitWord32Wrap result)
  
  -- | Create a Word literal expression while ensuring the given Integer is in the
  -- target Word range
  wordResult :: Platform -> Integer -> Maybe CoreExpr
  wordResult platform result = Just (wordResult' platform result)
  
  wordResult' :: Platform -> Integer -> CoreExpr
  wordResult' platform result = Lit (mkLitWordWrap platform result)
  
  -- | Create an unboxed pair of a Word literal expression, ensuring the given
  -- Integer is in the target Word range and the corresponding carry flag
  -- (@0#@/@1#@) if it wasn't.
  wordCResult :: Platform -> Integer -> Maybe CoreExpr
  wordCResult platform result = Just (mkCoreUnboxedTuple [Lit lit, Lit c])
    where
      (lit, b) = mkLitWordWrapC platform result
      c = if b then onei platform else zeroi platform
  
  int64Result :: Integer -> Maybe CoreExpr
  int64Result result = Just (int64Result' result)
  
  int64Result' :: Integer -> CoreExpr
  int64Result' result = Lit (mkLitInt64Wrap result)
  
  word64Result :: Integer -> Maybe CoreExpr
  word64Result result = Just (word64Result' result)
  
  word64Result' :: Integer -> CoreExpr
  word64Result' result = Lit (mkLitWord64Wrap result)
  
  
  -- | 'ambient (primop x) = x', but not necessarily 'primop (ambient x) = x'.
  semiInversePrimOp :: PrimOp -> RuleM CoreExpr
  semiInversePrimOp 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 (primOpId this) `App` e)
  
  subsumedByPrimOp :: PrimOp -> RuleM CoreExpr
  subsumedByPrimOp primop = do
    [e@(Var primop_id `App` _)] <- getArgs
    matchPrimOpId primop primop_id
    return e
  
  -- | Transform `extendWordN (narrowWordN x)` into `x .&. 0xFF..FF`
  extendNarrowPassthrough :: PrimOp -> Integer -> RuleM CoreExpr
  extendNarrowPassthrough narrow_primop n = do
    [Var primop_id `App` x] <- getArgs
    matchPrimOpId narrow_primop primop_id
    return (Var (primOpId WordAndOp) `App` x `App` Lit (LitNumber LitNumWord n))
  
  -- | narrow subsumes bitwise `and` with full mask (cf #16402):
  --
  --       narrowN (x .&. m)
  --       m .&. (2^N-1) = 2^N-1
  --       ==> narrowN x
  --
  -- e.g.  narrow16 (x .&. 0xFFFF)
  --       ==> narrow16 x
  --
  narrowSubsumesAnd :: PrimOp -> PrimOp -> Int -> RuleM CoreExpr
  narrowSubsumesAnd and_primop narrw n = do
    [Var primop_id `App` x `App` y] <- getArgs
    matchPrimOpId and_primop primop_id
    let mask = bit n -1
        g v (Lit (LitNumber _ m)) = do
           guard (m .&. mask == mask)
           return (Var (primOpId narrw) `App` v)
        g _ _ = mzero
    g x y <|> g y x
  
  idempotent :: RuleM CoreExpr
  idempotent = do [e1, e2] <- getArgs
                  guard $ cheapEqExpr e1 e2
                  return e1
  
  -- | Match
  --       (op (op v e) e)
  --    or (op e (op v e))
  --    or (op (op e v) e)
  --    or (op e (op e v))
  --  and return the innermost (op v e) or (op e v).
  sameArgIdempotentCommut :: PrimOp -> RuleM CoreExpr
  sameArgIdempotentCommut op = do
    [a,b] <- getArgs
    case (a,b) of
      (is_binop op -> Just (e1,e2), e3)
        | cheapEqExpr e2 e3 -> return a
        | cheapEqExpr e1 e3 -> return a
      (e3, is_binop op -> Just (e1,e2))
        | cheapEqExpr e2 e3 -> return b
        | cheapEqExpr e1 e3 -> return b
      _ -> mzero
  
  {-
  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 NOT 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 assembler 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 large. However, in general we cannot do this; consider
  this case
  
      let x = I# (uncheckedIShiftL# n 80)
      in ...
  
  Here x contains an invalid shift and consequently we would like to rewrite it
  as follows:
  
      let x = I# (error "invalid shift")
      in ...
  
  This was originally done in the fix to #16449 but this breaks the
  let-can-float invariant (see Note [Core let-can-float invariant] in
  GHC.Core) as noted in #16742.  For the reasons discussed under
  "NoEffect" in Note [Classifying primop effects] (in GHC.Builtin.PrimOps)
  there is no safe way to rewrite the argument of I# such that it bottoms.
  
  Consequently we instead take advantage of the fact that the result of a
  large shift is unspecified (see associated documentation in primops.txt.pp)
  and transform the invalid shift into an "obviously incorrect" value.
  
  There are two cases:
  
  - Shifting fixed-width things: the primops IntSll, Sll, etc
    These are handled by shiftRule.
  
    We are happy to shift by any amount up to wordSize but no more.
  
  - Shifting Bignums (Integer, Natural): these are handled by bignum_shift.
  
    Here we could in principle shift by any amount, but we arbitrary
    limit the shift to 4 bits; in particular we do not want shift by a
    huge amount, which can happen in code like that above.
  
  The two cases are more different in their code paths that is comfortable,
  but that is only a historical accident.
  
  
  ************************************************************************
  *                                                                      *
  \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   = runRuleM rm }
  
  newtype RuleM r = RuleM
    { runRuleM :: RuleOpts -> InScopeEnv -> Id -> [CoreExpr] -> Maybe r }
    deriving (Functor)
  
  instance Applicative RuleM where
      pure x = RuleM $ \_ _ _ _ -> Just x
      (<*>) = ap
  
  instance Monad RuleM where
    RuleM f >>= g
      = RuleM $ \env iu fn args ->
                case f env iu fn args of
                  Nothing -> Nothing
                  Just r  -> runRuleM (g r) env iu fn args
  
  instance MonadFail RuleM where
      fail _ = mzero
  
  instance Alternative RuleM where
    empty = RuleM $ \_ _ _ _ -> Nothing
    RuleM f1 <|> RuleM f2 = RuleM $ \env iu fn args ->
      f1 env iu fn args <|> f2 env iu fn args
  
  instance MonadPlus RuleM
  
  getPlatform :: RuleM Platform
  getPlatform = roPlatform <$> getRuleOpts
  
  getWordSize :: RuleM PlatformWordSize
  getWordSize = platformWordSize <$> getPlatform
  
  getRuleOpts :: RuleM RuleOpts
  getRuleOpts = RuleM $ \rule_opts _ _ _ -> Just rule_opts
  
  liftMaybe :: Maybe a -> RuleM a
  liftMaybe Nothing = mzero
  liftMaybe (Just x) = return x
  
  liftLit :: (Literal -> Literal) -> RuleM CoreExpr
  liftLit f = liftLitPlatform (const f)
  
  liftLitPlatform :: (Platform -> Literal -> Literal) -> RuleM CoreExpr
  liftLitPlatform f = do
    platform <- getPlatform
    [Lit lit] <- getArgs
    return $ Lit (f platform lit)
  
  removeOp32 :: RuleM CoreExpr
  removeOp32 = do
    platform <- getPlatform
    case platformWordSize platform of
      PW4 -> do
        [e] <- getArgs
        return e
      PW8 ->
        mzero
  
  getArgs :: RuleM [CoreExpr]
  getArgs = RuleM $ \_ _ _ args -> Just args
  
  getInScopeEnv :: RuleM InScopeEnv
  getInScopeEnv = RuleM $ \_ iu _ _ -> Just iu
  
  getFunction :: RuleM Id
  getFunction = RuleM $ \_ _ fn _ -> Just fn
  
  isLiteral :: CoreExpr -> RuleM Literal
  isLiteral e = do
      env <- getInScopeEnv
      case exprIsLiteral_maybe env e of
          Nothing -> mzero
          Just l  -> pure l
  
  -- | Match BigNat#, Integer and Natural literals
  isBignumLiteral :: CoreExpr -> RuleM Integer
  isBignumLiteral e = isNumberLiteral e <|> isIntegerLiteral e <|> isNaturalLiteral e
  
  -- | Match numeric literals
  isNumberLiteral :: CoreExpr -> RuleM Integer
  isNumberLiteral e = isLiteral e >>= \case
    LitNumber _ x -> pure x
    _             -> mzero
  
  -- | Match the application of a DataCon to a numeric literal.
  --
  -- Can be used to match e.g.:
  --  IS 123#
  --  IP bigNatLiteral
  --  W# 123##
  isLitNumConApp :: CoreExpr -> RuleM (DataCon,Integer)
  isLitNumConApp e = do
    env <- getInScopeEnv
    case exprIsConApp_maybe env e of
      Just (_env,_fb,dc,_tys,[arg]) -> case exprIsLiteral_maybe env arg of
        Just (LitNumber _ i) -> pure (dc,i)
        _                    -> mzero
      _ -> mzero
  
  isIntegerLiteral :: CoreExpr -> RuleM Integer
  isIntegerLiteral e = do
    (dc,i) <- isLitNumConApp e
    if | dc == integerISDataCon -> pure i
       | dc == integerINDataCon -> pure (negate i)
       | dc == integerIPDataCon -> pure i
       | otherwise              -> mzero
  
  isBigIntegerLiteral :: CoreExpr -> RuleM Integer
  isBigIntegerLiteral e = do
    (dc,i) <- isLitNumConApp e
    if | dc == integerINDataCon -> pure (negate i)
       | dc == integerIPDataCon -> pure i
       | otherwise              -> mzero
  
  isNaturalLiteral :: CoreExpr -> RuleM Integer
  isNaturalLiteral e = do
    (dc,i) <- isLitNumConApp e
    if | dc == naturalNSDataCon -> pure i
       | dc == naturalNBDataCon -> pure i
       | otherwise              -> mzero
  
  -- 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 :: (RuleOpts -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
  unaryLit op = do
    env <- getRuleOpts
    [Lit l] <- getArgs
    liftMaybe $ op env (convFloating env l)
  
  binaryLit :: (RuleOpts -> Literal -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
  binaryLit op = do
    env <- getRuleOpts
    [Lit l1, Lit l2] <- getArgs
    liftMaybe $ op env (convFloating env l1) (convFloating env l2)
  
  binaryCmpLit :: (forall a . Ord a => a -> a -> Bool) -> RuleM CoreExpr
  binaryCmpLit op = do
    platform <- getPlatform
    binaryLit (\_ -> cmpOp platform op)
  
  leftIdentity :: Literal -> RuleM CoreExpr
  leftIdentity id_lit = leftIdentityPlatform (const id_lit)
  
  rightIdentity :: Literal -> RuleM CoreExpr
  rightIdentity id_lit = rightIdentityPlatform (const id_lit)
  
  identity :: Literal -> RuleM CoreExpr
  identity lit = leftIdentity lit `mplus` rightIdentity lit
  
  leftIdentityPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  leftIdentityPlatform id_lit = do
    platform <- getPlatform
    [Lit l1, e2] <- getArgs
    guard $ l1 == id_lit platform
    return e2
  
  -- | Left identity rule for PrimOps like 'IntAddC' and 'WordAddC', where, in
  -- addition to the result, we have to indicate that no carry/overflow occurred.
  leftIdentityCPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  leftIdentityCPlatform id_lit = do
    platform <- getPlatform
    [Lit l1, e2] <- getArgs
    guard $ l1 == id_lit platform
    let no_c = Lit (zeroi platform)
    return (mkCoreUnboxedTuple [e2, no_c])
  
  rightIdentityPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  rightIdentityPlatform id_lit = do
    platform <- getPlatform
    [e1, Lit l2] <- getArgs
    guard $ l2 == id_lit platform
    return e1
  
  -- | Right identity rule for PrimOps like 'IntSubC' and 'WordSubC', where, in
  -- addition to the result, we have to indicate that no carry/overflow occurred.
  rightIdentityCPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  rightIdentityCPlatform id_lit = do
    platform <- getPlatform
    [e1, Lit l2] <- getArgs
    guard $ l2 == id_lit platform
    let no_c = Lit (zeroi platform)
    return (mkCoreUnboxedTuple [e1, no_c])
  
  identityPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  identityPlatform lit =
    leftIdentityPlatform lit `mplus` rightIdentityPlatform lit
  
  -- | Identity rule for PrimOps like 'IntAddC' and 'WordAddC', where, in addition
  -- to the result, we have to indicate that no carry/overflow occurred.
  identityCPlatform :: (Platform -> Literal) -> RuleM CoreExpr
  identityCPlatform lit =
    leftIdentityCPlatform lit `mplus` rightIdentityCPlatform lit
  
  leftZero :: RuleM CoreExpr
  leftZero = do
    [Lit l1, _] <- getArgs
    guard $ isZeroLit l1
    return $ Lit l1
  
  rightZero :: RuleM CoreExpr
  rightZero = do
    [_, Lit l2] <- getArgs
    guard $ isZeroLit l2
    return $ Lit l2
  
  zeroElem :: RuleM CoreExpr
  zeroElem = leftZero `mplus` rightZero
  
  equalArgs :: RuleM ()
  equalArgs = do
    [e1, e2] <- getArgs
    guard $ e1 `cheapEqExpr` e2
  
  nonZeroLit :: Int -> RuleM ()
  nonZeroLit n = getLiteral n >>= guard . not . isZeroLit
  
  oneLit :: Int -> RuleM ()
  oneLit n = getLiteral n >>= guard . isOneLit
  
  lift_bits_op :: forall a. (Num a, FiniteBits a) => (a -> Integer) -> RuleM CoreExpr
  lift_bits_op op = do
    platform <- getPlatform
    [Lit (LitNumber _ l)] <- getArgs
    pure $ mkWordLit platform $ op (fromInteger l :: a)
  
  pop_count :: forall a. (Num a, FiniteBits a) => RuleM CoreExpr
  pop_count = lift_bits_op @a (fromIntegral . popCount)
  
  ctz :: forall a. (Num a, FiniteBits a) => RuleM CoreExpr
  ctz = lift_bits_op @a (fromIntegral . countTrailingZeros)
  
  clz :: forall a. (Num a, FiniteBits a) => RuleM CoreExpr
  clz = lift_bits_op @a (fromIntegral . countLeadingZeros)
  
  -- 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 :: RuleOpts -> Literal -> Literal
  convFloating env (LitFloat  f) | not (roExcessRationalPrecision env) =
     LitFloat  (toRational (fromRational f :: Float ))
  convFloating env (LitDouble d) | not (roExcessRationalPrecision env) =
     LitDouble (toRational (fromRational d :: Double))
  convFloating _ l = l
  
  guardFloatDiv :: RuleM ()
  guardFloatDiv = do
    [Lit (LitFloat f1), Lit (LitFloat f2)] <- getArgs
    guard $ (f1 /=0 || f2 > 0) -- see Note [negative zero]
         && f2 /= 0            -- avoid NaN and Infinity/-Infinity
  
  guardDoubleDiv :: RuleM ()
  guardDoubleDiv = do
    [Lit (LitDouble d1), Lit (LitDouble 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 (primOpId 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 :: Platform -> Expr CoreBndr
  trueValInt  platform = Lit $ onei  platform -- see Note [What's true and false]
  falseValInt platform = Lit $ zeroi platform
  
  trueValBool, falseValBool :: Expr CoreBndr
  trueValBool   = Var trueDataConId -- see Note [What's true and false]
  falseValBool  = Var falseDataConId
  
  ltVal, eqVal, gtVal :: Expr CoreBndr
  ltVal = Var ordLTDataConId
  eqVal = Var ordEQDataConId
  gtVal = Var ordGTDataConId
  
  mkIntVal :: Platform -> Integer -> Expr CoreBndr
  mkIntVal platform i = Lit (mkLitInt platform i)
  mkFloatVal :: RuleOpts -> Rational -> Expr CoreBndr
  mkFloatVal env f = Lit (convFloating env (LitFloat  f))
  mkDoubleVal :: RuleOpts -> Rational -> Expr CoreBndr
  mkDoubleVal env d = Lit (convFloating env (LitDouble 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.
  
  We also do something similar if we can see that the argument of tagToEnum is out
  of bounds, e.g. `tagToEnum# 99# :: Bool`.
  Replacing this with an error expression is better for two reasons:
  * It allow us to eliminate more dead code in cases like `case tagToEnum# 99# :: Bool of ...`
  * Should we actually end up executing the relevant code at runtime the user will
    see a meaningful error message, instead of a segfault or incorrect result.
  See #25976.
  -}
  
  tagToEnumRule :: RuleM CoreExpr
  -- If     data T a = A | B | C
  -- then   tagToEnum# (T ty) 2# -->  B ty
  tagToEnumRule = do
    [Type ty, Lit (LitNumber LitNumInt i)] <- getArgs
    case splitTyConApp_maybe ty of
      Just (tycon, tc_args) | isEnumerationTyCon tycon -> do
        let tag = fromInteger i
            correct_tag dc = (dataConTagZ dc) == tag
        Just dataCons <- pure $ tyConDataCons_maybe tycon
        case filter correct_tag dataCons of
          (dc:rest) -> do
            massert (null rest)
            pure $ mkTyApps (Var (dataConWorkId dc)) tc_args
          -- Literal is out of range, e.g. tagToEnum @Bool #4
          [] -> pure $ mkImpossibleExpr ty "tagToEnum: Argument out of range"
  
      -- See Note [tagToEnum#]
      _ -> warnPprTrace True "tagToEnum# on non-enumeration type" (ppr ty) $
           return $ mkImpossibleExpr ty "tagToEnum# on non-enumeration type"
  
  ------------------------------
  dataToTagRule :: RuleM CoreExpr
  -- Used for both dataToTagSmall# and dataToTagLarge#.
  -- See Note [DataToTag overview] in GHC.Tc.Instance.Class,
  -- particularly wrinkle DTW5.
  dataToTagRule = a `mplus` b
    where
      -- dataToTag (tagToEnum x)   ==>   x
      a = do
        [Type _lev, 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 (K e1 e2)  ==>   tag-of K
      -- This also works (via exprIsConApp_maybe) for
      --   dataToTag x
      -- where x's unfolding is a constructor application
      b = do
        platform <- getPlatform
        [_lev, _ty, val_arg] <- getArgs
        in_scope <- getInScopeEnv
        (_,floats, dc,_,_) <- liftMaybe $ exprIsConApp_maybe in_scope val_arg
        massert (not (isNewTyCon (dataConTyCon dc)))
        return $ wrapFloats floats (mkIntVal platform (toInteger (dataConTagZ dc)))
  
  
  {- *********************************************************************
  *                                                                      *
               unsafeEqualityProof
  *                                                                      *
  ********************************************************************* -}
  
  -- unsafeEqualityProof k t t  ==>  UnsafeRefl (Refl t)
  -- That is, if the two types are equal, it's not unsafe!
  
  unsafeEqualityProofRule :: RuleM CoreExpr
  unsafeEqualityProofRule
    = do { [Type rep, Type t1, Type t2] <- getArgs
         ; guard (t1 `eqType` t2)
         ; fn <- getFunction
         ; let (_, ue) = splitForAllTyCoVars (idType fn)
               tc      = tyConAppTyCon ue  -- tycon:    UnsafeEquality
               dc      = tyConSingleDataCon tc  -- data con: UnsafeRefl
               -- UnsafeRefl :: forall (r :: RuntimeRep) (a :: TYPE r).
               --               UnsafeEquality r a a
         ; return (mkTyApps (Var (dataConWrapId dc)) [rep, t1]) }
  
  
  {- *********************************************************************
  *                                                                      *
               Rules for spark#
  *                                                                      *
  ********************************************************************* -}
  
  -- spark# :: forall a s . a -> State# s -> (# State# s, a #)
  sparkRule :: RuleM CoreExpr
  sparkRule = do -- reduce on HNF
    [Type _ty_a, Type _ty_s, a, s] <- getArgs
    guard $ exprIsHNF a
    return $ mkCoreUnboxedTuple [s, a]
      -- 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.  But the occurrence analyser does a GlomBinds
  step when necessary, that does a new SCC analysis on the whole set of
  bindings (see occurAnalysePgm), which sorts out the dependency, so all
  is fine.
  -}
  
  builtinRules :: [CoreRule]
  -- Rules for non-primops that can't be expressed using a RULE pragma
  builtinRules
    = [BuiltinRule { ru_name = fsLit "CStringFoldrLit",
                     ru_fn = unpackCStringFoldrName,
                     ru_nargs = 4, ru_try = match_cstring_foldr_lit_C },
       BuiltinRule { ru_name = fsLit "CStringFoldrLitUtf8",
                     ru_fn = unpackCStringFoldrUtf8Name,
                     ru_nargs = 4, ru_try = match_cstring_foldr_lit_utf8 },
       BuiltinRule { ru_name = fsLit "CStringAppendLit",
                     ru_fn = unpackCStringAppendName,
                     ru_nargs = 2, ru_try = match_cstring_append_lit_C },
       BuiltinRule { ru_name = fsLit "CStringAppendLitUtf8",
                     ru_fn = unpackCStringAppendUtf8Name,
                     ru_nargs = 2, ru_try = match_cstring_append_lit_utf8 },
       BuiltinRule { ru_name = fsLit "EqString", ru_fn = eqStringName,
                     ru_nargs = 2, ru_try = match_eq_string },
       BuiltinRule { ru_name = fsLit "CStringLength", ru_fn = cstringLengthName,
                     ru_nargs = 1, ru_try = match_cstring_length },
       BuiltinRule { ru_name = fsLit "Inline", ru_fn = inlineIdName,
                     ru_nargs = 2, ru_try = \_ _ _ -> match_inline },
  
       mkBasicRule unsafeEqualityProofName 3 unsafeEqualityProofRule,
  
       mkBasicRule divIntName 2 $ msum
          [ nonZeroLit 1 >> binaryLit (intOp2 div)
          , leftZero
          , do
            [arg, Lit (LitNumber LitNumInt d)] <- getArgs
            Just n <- return $ exactLog2 d
            platform <- getPlatform
            return $ Var (primOpId IntSraOp) `App` arg `App` mkIntVal platform n
          ],
  
       mkBasicRule modIntName 2 $ msum
          [ nonZeroLit 1 >> binaryLit (intOp2 mod)
          , leftZero
          , do
            [arg, Lit (LitNumber LitNumInt d)] <- getArgs
            Just _ <- return $ exactLog2 d
            platform <- getPlatform
            return $ Var (primOpId IntAndOp)
              `App` arg `App` mkIntVal platform (d - 1)
          ]
       ]
   ++ builtinBignumRules
  {-# NOINLINE builtinRules #-}
  -- there is no benefit to inlining these yet, despite this, GHC produces
  -- unfoldings for this regardless since the floated list entries look small.
  
  
  
  {- Note [Built-in bignum rules]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We have some built-in rules for operations on bignum types (Integer, Natural,
  BigNat). These rules implement the same kind of constant folding as we have for
  Int#/Word#/etc. primops. See builtinBignumRules.
  
  These rules are built-in because they can't be expressed as regular rules for
  now. The reason is that due to the let-can-float invariant (see Note [Core
  let-can-float invariant] in GHC.Core), GHC is too conservative with some bignum
  operations and they don't match rules. For example:
  
    case integerAdd 1 x of r { _ -> integerAdd 1 r }
  
  doesn't constant-fold into `integerAdd 2 x` with a regular rule. That's because
  GHC never floats in `integerAdd 1 x` to form `integerAdd 1 (integerAdd 1 x)`
  because of the let-can-float invariant (it doesn't know if `integerAdd`
  terminates).
  
  In the built-in rule for `integerAdd` we can access the unfolding of `r` and we
  can perform the appropriate substitution.
  
  To support constant-folding, Bignum operations are not allowed to inline. As a
  consequence, some codes that would benefit from inlining of bignum operations
  don't. An idea to fix this was to only have built-in rules for BigNat#
  operations and to allow Integer and Natural operations to inline. However these
  operations are often too big to inline and we end up with broken
  constant-folding and still no inlining. This issue is tracked in #20361
  
  Bignum built-in rules can be disabled independently of other built-in rules by
  passing the -dno-bignum-rules flag or programmatically with the `roBignumRules` field of
  RuleOpts.
  
  -}
  
  -- | Built-in bignum rules (see Note [Built-in bignum rules])
  builtinBignumRules :: [CoreRule]
  builtinBignumRules =
    [ -- conversions
      lit_to_integer "Word# -> Integer"   integerFromWordName
    , lit_to_integer "Int64# -> Integer"  integerFromInt64Name
    , lit_to_integer "Word64# -> Integer" integerFromWord64Name
    , lit_to_integer "Natural -> Integer" integerFromNaturalName
  
    , integer_to_lit "Integer -> Word# (wrap)"   integerToWordName   mkWordLitWrap
    , integer_to_lit "Integer -> Int# (wrap)"    integerToIntName    mkIntLitWrap
    , integer_to_lit "Integer -> Word64# (wrap)" integerToWord64Name (\_ -> mkWord64LitWord64 . fromInteger)
    , integer_to_lit "Integer -> Int64# (wrap)"  integerToInt64Name  (\_ -> mkInt64LitInt64 . fromInteger)
    , integer_to_lit "Integer -> Float#"         integerToFloatName  (\_ -> mkFloatLitFloat . fromInteger)
    , integer_to_lit "Integer -> Double#"        integerToDoubleName (\_ -> mkDoubleLitDouble . fromInteger)
  
    , integer_to_natural "Integer -> Natural (clamp)" integerToNaturalClampName False True
    , integer_to_natural "Integer -> Natural (wrap)"  integerToNaturalName      False False
    , integer_to_natural "Integer -> Natural (throw)" integerToNaturalThrowName True False
  
    , natural_to_word "Natural -> Word# (wrap)"  naturalToWordName
  
      -- comparisons (return an unlifted Int#)
    , bignum_bin_pred "bigNatEq#"  bignatEqName (==)
  
      -- comparisons (return an Ordering)
    , bignum_compare "bignatCompare"      bignatCompareName
    , bignum_compare "bignatCompareWord#" bignatCompareWordName
  
      -- binary operations
    , integer_binop "integerAdd" integerAddName (+)
    , integer_binop "integerSub" integerSubName (-)
    , integer_binop "integerMul" integerMulName (*)
    , integer_binop "integerGcd" integerGcdName gcd
    , integer_binop "integerLcm" integerLcmName lcm
    , integer_binop "integerAnd" integerAndName (.&.)
    , integer_binop "integerOr"  integerOrName  (.|.)
    , integer_binop "integerXor" integerXorName xor
  
    , natural_binop "naturalAdd" naturalAddName (+)
    , natural_binop "naturalMul" naturalMulName (*)
    , natural_binop "naturalGcd" naturalGcdName gcd
    , natural_binop "naturalLcm" naturalLcmName lcm
    , natural_binop "naturalAnd" naturalAndName (.&.)
    , natural_binop "naturalOr"  naturalOrName  (.|.)
    , natural_binop "naturalXor" naturalXorName xor
  
      -- Natural subtraction: it's a binop but it can fail because of underflow so
      -- we have several primitives to handle here.
    , natural_sub "naturalSubUnsafe" naturalSubUnsafeName
    , natural_sub "naturalSubThrow"  naturalSubThrowName
    , mkRule "naturalSub" naturalSubName 2 $ do
          [a0,a1] <- getArgs
          x <- isNaturalLiteral a0
          y <- isNaturalLiteral a1
          -- return an unboxed sum: (# (# #) | Natural #)
          let ret n v = pure $ mkCoreUnboxedSum 2 n [unboxedUnitTy,naturalTy] v
          platform <- getPlatform
          if x < y
              then ret 1 unboxedUnitExpr
              else ret 2 $ mkNaturalExpr platform (x - y)
  
      -- unary operations
    , bignum_unop "integerNegate"     integerNegateName     mkIntegerExpr negate
    , bignum_unop "integerAbs"        integerAbsName        mkIntegerExpr abs
    , bignum_unop "integerComplement" integerComplementName mkIntegerExpr complement
  
    , bignum_popcount "integerPopCount" integerPopCountName mkLitIntWrap
    , bignum_popcount "naturalPopCount" naturalPopCountName mkLitWordWrap
  
      -- Bits.bit
    , bignum_bit "integerBit" integerBitName mkIntegerExpr
    , bignum_bit "naturalBit" naturalBitName mkNaturalExpr
  
      -- Bits.testBit
    , bignum_testbit "integerTestBit" integerTestBitName
    , bignum_testbit "naturalTestBit" naturalTestBitName
  
      -- Bits.shift
    , bignum_shift "integerShiftL" integerShiftLName shiftL mkIntegerExpr
    , bignum_shift "integerShiftR" integerShiftRName shiftR mkIntegerExpr
    , bignum_shift "naturalShiftL" naturalShiftLName shiftL mkNaturalExpr
    , bignum_shift "naturalShiftR" naturalShiftRName shiftR mkNaturalExpr
  
      -- division
    , divop_one  "integerQuot"    integerQuotName    quot    mkIntegerExpr
    , divop_one  "integerRem"     integerRemName     rem     mkIntegerExpr
    , divop_one  "integerDiv"     integerDivName     div     mkIntegerExpr
    , divop_one  "integerMod"     integerModName     mod     mkIntegerExpr
    , divop_both "integerDivMod"  integerDivModName  divMod  mkIntegerExpr
    , divop_both "integerQuotRem" integerQuotRemName quotRem mkIntegerExpr
  
    , divop_one  "naturalQuot"    naturalQuotName    quot    mkNaturalExpr
    , divop_one  "naturalRem"     naturalRemName     rem     mkNaturalExpr
    , divop_both "naturalQuotRem" naturalQuotRemName quotRem mkNaturalExpr
  
      -- conversions from Rational for Float/Double literals
    , rational_to "rationalToFloat"  rationalToFloatName  mkFloatExpr
    , rational_to "rationalToDouble" rationalToDoubleName mkDoubleExpr
  
      -- conversions from Integer for Float/Double literals
    , integer_encode_float "integerEncodeFloat"  integerEncodeFloatName  mkFloatLitFloat
    , integer_encode_float "integerEncodeDouble" integerEncodeDoubleName mkDoubleLitDouble
    ]
    where
      mkRule str name nargs f = BuiltinRule
        { ru_name = fsLit str
        , ru_fn = name
        , ru_nargs = nargs
        , ru_try = runRuleM $ do
            env <- getRuleOpts
            guard (roBignumRules env)
            f
        }
  
      integer_to_lit str name convert = mkRule str name 1 $ do
        [a0] <- getArgs
        platform <- getPlatform
        -- we only match on Big Integer literals. Small literals
        -- are matched by the "Int# -> Integer -> *" rules
        x <- isBigIntegerLiteral a0
        pure (convert platform x)
  
      natural_to_word str name = mkRule str name 1 $ do
        [a0] <- getArgs
        n <- isNaturalLiteral a0
        platform <- getPlatform
        pure (Lit (mkLitWordWrap platform n))
  
      integer_to_natural str name thrw clamp = mkRule str name 1 $ do
        [a0] <- getArgs
        x <- isIntegerLiteral a0
        platform <- getPlatform
        if | x >= 0    -> pure $ mkNaturalExpr platform x
           | thrw      -> mzero
           | clamp     -> pure $ mkNaturalExpr platform 0       -- clamp to 0
           | otherwise -> pure $ mkNaturalExpr platform (abs x) -- negate/wrap
  
      lit_to_integer str name = mkRule str name 1 $ do
        [a0] <- getArgs
        platform <- getPlatform
        i <- isBignumLiteral a0
        -- convert any numeric literal into an Integer literal
        pure (mkIntegerExpr platform i)
  
      integer_binop str name op = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isIntegerLiteral a0
        y <- isIntegerLiteral a1
        platform <- getPlatform
        pure (mkIntegerExpr platform (x `op` y))
  
      natural_binop str name op = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isNaturalLiteral a0
        y <- isNaturalLiteral a1
        platform <- getPlatform
        pure (mkNaturalExpr platform (x `op` y))
  
      natural_sub str name = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isNaturalLiteral a0
        y <- isNaturalLiteral a1
        guard (x >= y)
        platform <- getPlatform
        pure (mkNaturalExpr platform (x - y))
  
      bignum_bin_pred str name op = mkRule str name 2 $ do
        platform <- getPlatform
        [a0,a1] <- getArgs
        x <- isBignumLiteral a0
        y <- isBignumLiteral a1
        pure $ if x `op` y
                then trueValInt platform
                else falseValInt platform
  
      bignum_compare str name = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isBignumLiteral a0
        y <- isBignumLiteral a1
        pure $ case x `compare` y of
                LT -> ltVal
                EQ -> eqVal
                GT -> gtVal
  
      bignum_unop str name mk_lit op = mkRule str name 1 $ do
        [a0] <- getArgs
        x <- isBignumLiteral a0
        platform <- getPlatform
        pure $ mk_lit platform (op x)
  
      bignum_popcount str name mk_lit = mkRule str name 1 $ do
        platform <- getPlatform
        -- We use a host Int to compute the popCount. If we compile on a 32-bit
        -- host for a 64-bit target, the result may be different than if computed
        -- by the target. So we disable this rule if sizes don't match.
        guard (platformWordSizeInBits platform <= finiteBitSize (0 :: Word))
        [a0] <- getArgs
        x <- isBignumLiteral a0
        pure $ Lit (mk_lit platform (fromIntegral (popCount x)))
  
      bignum_bit str name mk_lit = mkRule str name 1 $ do
        [a0] <- getArgs
        platform <- getPlatform
        n <- isNumberLiteral a0
        -- Make sure n is positive and small enough to yield a decently
        -- small number. Attempting to construct the Integer for
        --    (integerBit 9223372036854775807#)
        -- would be a bad idea (#14959)
        guard (n >= 0 && n <= fromIntegral (platformWordSizeInBits platform))
        -- it's safe to convert a target Int value into a host Int value
        -- to perform the "bit" operation because n is very small (<= 64).
        pure $ mk_lit platform (bit (fromIntegral n))
  
      bignum_testbit str name = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        platform <- getPlatform
        x <- isBignumLiteral a0
        n <- isNumberLiteral a1
        -- ensure that we can store 'n' in a host Int
        guard (n >= 0 && n <= fromIntegral (maxBound :: Int))
        pure $ if testBit x (fromIntegral n)
                then trueValInt platform
                else falseValInt platform
  
      bignum_shift str name shift_op mk_lit = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isBignumLiteral a0
        n <- isNumberLiteral a1
        -- See Note [Guarding against silly shifts]
        -- Restrict constant-folding of shifts on Integers, somewhat arbitrary.
        -- We can get huge shifts in inaccessible code (#15673)
        guard (n <= 4)
        platform <- getPlatform
        pure $ mk_lit platform (x `shift_op` fromIntegral n)
  
      divop_one str name divop mk_lit = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        n <- isBignumLiteral a0
        d <- isBignumLiteral a1
        guard (d /= 0)
        platform <- getPlatform
        pure $ mk_lit platform (n `divop` d)
  
      divop_both str name divop mk_lit = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        n <- isBignumLiteral a0
        d <- isBignumLiteral a1
        guard (d /= 0)
        let (r,s) = n `divop` d
        platform <- getPlatform
        pure $ mkCoreUnboxedTuple [mk_lit platform r, mk_lit platform s]
  
      integer_encode_float :: RealFloat a => String -> Name -> (a -> CoreExpr) -> CoreRule
      integer_encode_float str name mk_lit = mkRule str name 2 $ do
        [a0,a1] <- getArgs
        x <- isIntegerLiteral a0
        y <- isNumberLiteral a1
        -- check that y (a target Int) is in the host Int range
        guard (y <= fromIntegral (maxBound :: Int))
        pure (mk_lit $ encodeFloat x (fromInteger y))
  
      rational_to :: RealFloat a => String -> Name -> (a -> CoreExpr) -> CoreRule
      rational_to str name mk_lit = mkRule str name 2 $ do
        -- This turns `rationalToFloat n d` where `n` and `d` are literals into
        -- a literal Float (and similarly for Double).
        [a0,a1] <- getArgs
        n <- isIntegerLiteral a0
        d <- isIntegerLiteral a1
        -- 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
        guard (d /= 0)
        pure $ mk_lit (fromRational (n % d))
  
  
  ---------------------------------------------------
  -- The rules are:
  --      unpackAppendCString*# "foo"# (unpackCString*# "baz"#)
  --      =  unpackCString*# "foobaz"#
  --
  --      unpackAppendCString*# "foo"# (unpackAppendCString*# "baz"# e)
  --      =  unpackAppendCString*# "foobaz"# e
  --
  
  -- CString version
  match_cstring_append_lit_C :: RuleFun
  match_cstring_append_lit_C = match_cstring_append_lit unpackCStringAppendIdKey unpackCStringIdKey
  
  -- CStringUTF8 version
  match_cstring_append_lit_utf8 :: RuleFun
  match_cstring_append_lit_utf8 = match_cstring_append_lit unpackCStringAppendUtf8IdKey unpackCStringUtf8IdKey
  
  {-# INLINE match_cstring_append_lit #-}
  match_cstring_append_lit :: Unique -> Unique -> RuleFun
  match_cstring_append_lit append_key unpack_key _ env _ [lit1, e2]
    | Just (LitString s1) <- exprIsLiteral_maybe env lit1
    , (strTicks, Var unpk `App` lit2) <- stripStrTopTicks env e2
    , unpk `hasKey` unpack_key
    , Just (LitString s2) <- exprIsLiteral_maybe env lit2
    = Just $ mkTicks strTicks
           $ Var unpk `App` Lit (LitString (s1 `BS.append` s2))
  
    | Just (LitString s1) <- exprIsLiteral_maybe env lit1
    , (strTicks, Var appnd `App` lit2 `App` e) <- stripStrTopTicks env e2
    , appnd `hasKey` append_key
    , Just (LitString s2) <- exprIsLiteral_maybe env lit2
    = Just $ mkTicks strTicks
           $ Var appnd `App` Lit (LitString (s1 `BS.append` s2)) `App` e
  
  match_cstring_append_lit _ _ _ _ _ _ = Nothing
  
  ---------------------------------------------------
  -- The rule is this:
  --      unpackFoldrCString*# "foo"# c (unpackFoldrCString*# "baz"# c n)
  --      =  unpackFoldrCString*# "foobaz"# c n
  --
  -- See also Note [String literals in GHC] in CString.hs
  
  -- CString version
  match_cstring_foldr_lit_C :: RuleFun
  match_cstring_foldr_lit_C = match_cstring_foldr_lit unpackCStringFoldrIdKey
  
  -- CStringUTF8 version
  match_cstring_foldr_lit_utf8 :: RuleFun
  match_cstring_foldr_lit_utf8 = match_cstring_foldr_lit unpackCStringFoldrUtf8IdKey
  
  {-# INLINE match_cstring_foldr_lit #-}
  match_cstring_foldr_lit :: Unique -> RuleFun
  match_cstring_foldr_lit foldVariant _ env _
          [ Type ty1
          , lit1
          , c1
          , e2
          ]
    | (strTicks, Var unpk `App` Type ty2
                          `App` lit2
                          `App` c2
                          `App` n) <- stripStrTopTicks env e2
    , unpk `hasKey` foldVariant
    , Just (LitString s1) <- exprIsLiteral_maybe env lit1
    , Just (LitString s2) <- exprIsLiteral_maybe env lit2
    , eqCoreExpr c1 c2
    , (c1Ticks, c1') <- stripStrTopTicks env c1
    , c2Ticks <- stripStrTopTicksT c2
    = assert (ty1 `eqType` ty2) $
      Just $ mkTicks strTicks
           $ Var unpk `App` Type ty1
                      `App` Lit (LitString (s1 `BS.append` s2))
                      `App` mkTicks (c1Ticks ++ c2Ticks) c1'
                      `App` n
  
  match_cstring_foldr_lit _ _ _ _ _ = Nothing
  
  
  -- N.B. Ensure that we strip off any ticks (e.g. source notes) from the
  -- argument, lest this may fail to fire when building with -g3. See #16740.
  --
  -- Also, look into variable's unfolding just in case the expression we look for
  -- is in a top-level thunk.
  stripStrTopTicks :: InScopeEnv -> CoreExpr -> ([CoreTickish], CoreExpr)
  stripStrTopTicks (ISE _ id_unf) e = case e of
    Var v
      | Just rhs <- expandUnfolding_maybe (id_unf v)
      -> stripTicksTop tickishFloatable rhs
    _ -> stripTicksTop tickishFloatable e
  
  stripStrTopTicksT :: CoreExpr -> [CoreTickish]
  stripStrTopTicksT e = stripTicksTopT tickishFloatable e
  
  ---------------------------------------------------
  -- The rule is this:
  --      eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2)) = s1==s2
  -- Also  matches unpackCStringUtf8#
  
  match_eq_string :: RuleFun
  match_eq_string _ env _ [e1, e2]
    | (ticks1, Var unpk1 `App` lit1) <- stripStrTopTicks env e1
    , (ticks2, Var unpk2 `App` lit2) <- stripStrTopTicks env e2
    , unpk_key1 <- getUnique unpk1
    , unpk_key2 <- getUnique unpk2
    , unpk_key1 == unpk_key2
    -- For now we insist the literals have to agree in their encoding
    -- to keep the rule simple. But we could check if the decoded strings
    -- compare equal in here as well.
    , unpk_key1 `elem` [unpackCStringUtf8IdKey, unpackCStringIdKey]
    , Just (LitString s1) <- exprIsLiteral_maybe env lit1
    , Just (LitString s2) <- exprIsLiteral_maybe env lit2
    = Just $ mkTicks (ticks1 ++ ticks2)
           $ (if s1 == s2 then trueValBool else falseValBool)
  
  match_eq_string _ _ _ _ = Nothing
  
  -----------------------------------------------------------------------
  -- Illustration of this rule:
  --
  -- cstringLength# "foobar"# --> 6
  -- cstringLength# "fizz\NULzz"# --> 4
  --
  -- Nota bene: Addr# literals are suffixed by a NUL byte when they are
  -- compiled to read-only data sections. That's why cstringLength# is
  -- well defined on Addr# literals that do not explicitly have an embedded
  -- NUL byte.
  --
  -- See GHC issue #5218, MR 2165, and bytestring PR 191. This is particularly
  -- helpful when using OverloadedStrings to create a ByteString since the
  -- function computing the length of such ByteStrings can often be constant
  -- folded.
  match_cstring_length :: RuleFun
  match_cstring_length rule_env env _ [lit1]
    | Just (LitString str) <- exprIsLiteral_maybe env lit1
      -- If elemIndex returns Just, it has the index of the first embedded NUL
      -- in the string. If no NUL bytes are present (the common case) then use
      -- full length of the byte string.
    = let len = fromMaybe (BS.length str) (BS.elemIndex 0 str)
       in Just (Lit (mkLitInt (roPlatform rule_env) (fromIntegral len)))
  match_cstring_length _ _ _ _ = Nothing
  
  {- Note [inlineId magic]
  ~~~~~~~~~~~~~~~~~~~~~~~~
  The call 'inline f' arranges that 'f' is inlined, regardless of
  its size. More precisely, the call 'inline f' rewrites to the
  right-hand side of 'f's definition. This allows the programmer to
  control inlining from a particular call site rather than the
  definition site of the function.
  
  The moving parts are simple:
  
  * A very simple definition in the library base:GHC.Magic
       {-# NOINLINE[0] inline #-}
       inline :: a -> a
       inline x = x
    So in phase 0, 'inline' will be inlined, so its use imposes
    no overhead.
  
  * A rewrite rule, in GHC.Core.Opt.ConstantFold, which makes
    (inline f) inline, implemented by match_inline.
    The rule for the 'inline' function 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)
  
    Additionally the rule looks through ticks/casts as well (#24808):
        inline f_ty (f a b c |> co) = <f's unfolding> a b c |> co
        inline f_ty <tick> ( f a b c ) = <tick> <f's unfolding> a b c
  
    It's important to allow the argument to 'inline' to have args itself
    (a) because its more forgiving to allow the programmer to write
        either  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, so the call may look like
          inline (map @Int @Bool) g xs
  
    Also, don't forget about 'inline's type argument!
  -}
  
  match_inline :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
  match_inline (Type _ : e : _) = go e
    -- Maybe Monad ahead:
    where
      go (Var f)      = -- Ignore the IdUnfoldingFun here!
                        (maybeUnfoldingTemplate (realIdUnfolding f))
      go (App f a)    = do { f' <- go f; pure $ App f' a }
      -- inline (f |> co)
      go (Cast e co)  = do { app <- go e; pure (Cast app co) }
      -- inline (<tick> f)
      go (Tick t e)   = do { app <- go e; pure (Tick t app) }
      go _            = Nothing
  
  match_inline _ = Nothing
  
  --------------------------------------------------------
  -- Note [Constant folding through nested expressions]
  -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  -- GHC has some support for constant folding through nested expressions (i.e.
  -- when constants are not only arguments of the considered App node but to one
  -- of its own argument (an App node too), see examples below).
  --
  -- For performance reason, this optimization is only enabled with -O1 and above.
  -- As with all optimizations, it can also be independently enabled with its own
  -- command-line flag too: -fnum-constant-folding (grep Opt_NumConstantFolding).
  --
  -- We use rewrites rules to perform constant folding. It means that we don't
  -- have a global view of the expression we are trying to optimise. As a
  -- consequence we only perform local (small-step) transformations that either:
  --    1) reduce the number of operations
  --    2) rearrange the expression to increase the odds that other rules will
  --    match
  --
  -- We don't try to handle more complex expression optimisation cases that would
  -- require a global view. For example, rewriting expressions to increase
  -- sharing (e.g., Horner's method); optimisations that require local
  -- transformations increasing the number of operations; rearrangements to
  -- cancel/factorize terms (e.g., (a+b-a-b) isn't rearranged to reduce to 0).
  --
  -- We already have rules to perform constant folding on expressions with the
  -- following shape (where a and/or b are literals):
  --
  --          D)    op
  --                /\
  --               /  \
  --              /    \
  --             a      b
  --
  -- To support nested expressions, we match three other shapes of expression
  -- trees:
  --
  -- A)   op1          B)       op1       C)       op1
  --      /\                    /\                 /\
  --     /  \                  /  \               /  \
  --    /    \                /    \             /    \
  --   a     op2            op2     c          op2    op3
  --          /\            /\                 /\      /\
  --         /  \          /  \               /  \    /  \
  --        b    c        a    b             a    b  c    d
  --
  --
  -- R1) +/- simplification:
  --    ops = + or -, two literals (not siblings)
  --
  --    Examples:
  --       A: 5 + (10-x)  ==> 15-x
  --       B: (10+x) + 5  ==> 15+x
  --       C: (5+a)-(5-b) ==> 0+(a+b)
  --
  -- R2) *, `and`, `or`  simplification
  --    ops = *, `and`, `or` two literals (not siblings)
  --
  --    Examples:
  --       A: 5 * (10*x)  ==> 50*x
  --       B: (10*x) * 5  ==> 50*x
  --       C: (5*a)*(5*b) ==> 25*(a*b)
  --
  -- R3) * distribution over +/-
  --    op1 = *, op2 = + or -, two literals (not siblings)
  --
  --    This transformation doesn't reduce the number of operations but switches
  --    the outer and the inner operations so that the outer is (+) or (-) instead
  --    of (*). It increases the odds that other rules will match after this one.
  --
  --    Examples:
  --       A: 5 * (10-x)  ==> 50 - (5*x)
  --       B: (10+x) * 5  ==> 50 + (5*x)
  --       C: Not supported as it would increase the number of operations:
  --          (5+a)*(5-b) ==> 25 - 5*b + 5*a - a*b
  --
  -- R4) Simple factorization
  --
  --    op1 = + or -, op2/op3 = *,
  --    one literal for each innermost * operation (except in the D case),
  --    the two other terms are equals
  --
  --    Examples:
  --       A: x - (10*x)  ==> (-9)*x
  --       B: (10*x) + x  ==> 11*x
  --       C: (5*x)-(x*3) ==> 2*x
  --       D: x+x         ==> 2*x
  --
  -- R5) +/- propagation
  --
  --    ops = + or -, one literal
  --
  --    This transformation doesn't reduce the number of operations but propagates
  --    the constant to the outer level. It increases the odds that other rules
  --    will match after this one.
  --
  --    Examples:
  --       A: x - (10-y)  ==> (x+y) - 10
  --       B: (10+x) - y  ==> 10 + (x-y)
  --       C: N/A (caught by the A and B cases)
  --
  --------------------------------------------------------
  
  -- Rules to perform constant folding into nested expressions
  --
  --See Note [Constant folding through nested expressions]
  
  addFoldingRules :: PrimOp -> NumOps -> RuleM CoreExpr
  addFoldingRules op num_ops = do
     massert (op == numAdd num_ops)
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe
        -- commutativity for + is handled here
        (addFoldingRules' platform arg1 arg2 num_ops
         <|> addFoldingRules' platform arg2 arg1 num_ops)
  
  subFoldingRules :: PrimOp -> NumOps -> RuleM CoreExpr
  subFoldingRules op num_ops = do
     massert (op == numSub num_ops)
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe (subFoldingRules' platform arg1 arg2 num_ops)
  
  mulFoldingRules :: PrimOp -> NumOps -> RuleM CoreExpr
  mulFoldingRules op num_ops = do
     massert (op == numMul num_ops)
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe
        -- commutativity for * is handled here
        (mulFoldingRules' platform arg1 arg2 num_ops
         <|> mulFoldingRules' platform arg2 arg1 num_ops)
  
  andFoldingRules :: NumOps -> RuleM CoreExpr
  andFoldingRules num_ops = do
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe
        -- commutativity for `and` is handled here
        (andFoldingRules' platform arg1 arg2 num_ops
         <|> andFoldingRules' platform arg2 arg1 num_ops)
  
  orFoldingRules :: NumOps -> RuleM CoreExpr
  orFoldingRules num_ops = do
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe
        -- commutativity for `or` is handled here
        (orFoldingRules' platform arg1 arg2 num_ops
         <|> orFoldingRules' platform arg2 arg1 num_ops)
  
  quotFoldingRules :: NumOps -> RuleM CoreExpr
  quotFoldingRules num_ops = do
     env <- getRuleOpts
     guard (roNumConstantFolding env)
     [arg1,arg2] <- getArgs
     platform <- getPlatform
     liftMaybe (quotFoldingRules' platform arg1 arg2 num_ops)
  
  addFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  addFoldingRules' platform arg1 arg2 num_ops = case (arg1, arg2) of
  
        -- x + (-y) ==> x-y
        (x, is_neg num_ops -> Just y)
           -> Just (x `sub` y)
  
        -- R1) +/- simplification
  
        -- l1 + (l2 + x) ==> (l1+l2) + x
        (L l1, is_lit_add num_ops -> Just (l2,x))
           -> Just (mkL (l1+l2) `add` x)
  
        -- l1 + (l2 - x) ==> (l1+l2) - x
        (L l1, is_sub num_ops -> Just (L l2,x))
           -> Just (mkL (l1+l2) `sub` x)
  
        -- l1 + (x - l2) ==> (l1-l2) + x
        (L l1, is_sub num_ops -> Just (x,L l2))
           -> Just (mkL (l1-l2) `add` x)
  
        -- (l1 + x) + (l2 + y) ==> (l1+l2) + (x+y)
        (is_lit_add num_ops -> Just (l1,x), is_lit_add num_ops -> Just (l2,y))
           -> Just (mkL (l1+l2) `add` (x `add` y))
  
        -- (l1 + x) + (l2 - y) ==> (l1+l2) + (x-y)
        (is_lit_add num_ops -> Just (l1,x), is_sub num_ops -> Just (L l2,y))
           -> Just (mkL (l1+l2) `add` (x `sub` y))
  
        -- (l1 + x) + (y - l2) ==> (l1-l2) + (x+y)
        (is_lit_add num_ops -> Just (l1,x), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (l1-l2) `add` (x `add` y))
  
        -- (l1 - x) + (l2 - y) ==> (l1+l2) - (x+y)
        (is_sub num_ops -> Just (L l1,x), is_sub num_ops -> Just (L l2,y))
           -> Just (mkL (l1+l2) `sub` (x `add` y))
  
        -- (l1 - x) + (y - l2) ==> (l1-l2) + (y-x)
        (is_sub num_ops -> Just (L l1,x), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (l1-l2) `add` (y `sub` x))
  
        -- (x - l1) + (y - l2) ==> (0-l1-l2) + (x+y)
        (is_sub num_ops -> Just (x,L l1), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (0-l1-l2) `add` (x `add` y))
  
        -- R4) Simple factorization
  
        -- x + x ==> 2 * x
        _ | Just l1 <- is_expr_mul num_ops arg1 arg2
          -> Just (mkL (l1+1) `mul` arg1)
  
        -- (l1 * x) + x ==> (l1+1) * x
        _ | Just l1 <- is_expr_mul num_ops arg2 arg1
          -> Just (mkL (l1+1) `mul` arg2)
  
        -- (l1 * x) + (l2 * x) ==> (l1+l2) * x
        (is_lit_mul num_ops -> Just (l1,x), is_expr_mul num_ops x -> Just l2)
           -> Just (mkL (l1+l2) `mul` x)
  
        -- R5) +/- propagation: these transformations push literals outwards
        -- with the hope that other rules can then be applied.
  
        -- In the following rules, x can't be a literal otherwise another
        -- rule would have combined it with the other literal in arg2. So we
        -- don't have to check this to avoid loops here.
  
        -- x + (l1 + y) ==> l1 + (x + y)
        (_, is_lit_add num_ops -> Just (l1,y))
           -> Just (mkL l1 `add` (arg1 `add` y))
  
        -- x + (l1 - y) ==> l1 + (x - y)
        (_, is_sub num_ops -> Just (L l1,y))
           -> Just (mkL l1 `add` (arg1 `sub` y))
  
        -- x + (y - l1) ==> (x + y) - l1
        (_, is_sub num_ops -> Just (y,L l1))
           -> Just ((arg1 `add` y) `sub` mkL l1)
  
        _ -> Nothing
  
     where
        mkL = Lit . mkNumLiteral platform num_ops
        add x y = BinOpApp x (numAdd num_ops) y
        sub x y = BinOpApp x (numSub num_ops) y
        mul x y = BinOpApp x (numMul num_ops) y
  
  subFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  subFoldingRules' platform arg1 arg2 num_ops = case (arg1,arg2) of
        -- x - (-y) ==> x+y
        (x, is_neg num_ops -> Just y)
           -> Just (x `add` y)
  
        -- R1) +/- simplification
  
        -- l1 - (l2 + x) ==> (l1-l2) - x
        (L l1, is_lit_add num_ops -> Just (l2,x))
           -> Just (mkL (l1-l2) `sub` x)
  
        -- l1 - (l2 - x) ==> (l1-l2) + x
        (L l1, is_sub num_ops -> Just (L l2,x))
           -> Just (mkL (l1-l2) `add` x)
  
        -- l1 - (x - l2) ==> (l1+l2) - x
        (L l1, is_sub num_ops -> Just (x, L l2))
           -> Just (mkL (l1+l2) `sub` x)
  
        -- (l1 + x) - l2 ==> (l1-l2) + x
        (is_lit_add num_ops -> Just (l1,x), L l2)
           -> Just (mkL (l1-l2) `add` x)
  
        -- (l1 - x) - l2 ==> (l1-l2) - x
        (is_sub num_ops -> Just (L l1,x), L l2)
           -> Just (mkL (l1-l2) `sub` x)
  
        -- (x - l1) - l2 ==> x - (l1+l2)
        (is_sub num_ops -> Just (x,L l1), L l2)
           -> Just (x `sub` mkL (l1+l2))
  
  
        -- (l1 + x) - (l2 + y) ==> (l1-l2) + (x-y)
        (is_lit_add num_ops -> Just (l1,x), is_lit_add num_ops -> Just (l2,y))
           -> Just (mkL (l1-l2) `add` (x `sub` y))
  
        -- (l1 + x) - (l2 - y) ==> (l1-l2) + (x+y)
        (is_lit_add num_ops -> Just (l1,x), is_sub num_ops -> Just (L l2,y))
           -> Just (mkL (l1-l2) `add` (x `add` y))
  
        -- (l1 + x) - (y - l2) ==> (l1+l2) + (x-y)
        (is_lit_add num_ops -> Just (l1,x), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (l1+l2) `add` (x `sub` y))
  
        -- (l1 - x) - (l2 + y) ==> (l1-l2) - (x+y)
        (is_sub num_ops -> Just (L l1,x), is_lit_add num_ops -> Just (l2,y))
           -> Just (mkL (l1-l2) `sub` (x `add` y))
  
        -- (x - l1) - (l2 + y) ==> (0-l1-l2) + (x-y)
        (is_sub num_ops -> Just (x,L l1), is_lit_add num_ops -> Just (l2,y))
           -> Just (mkL (0-l1-l2) `add` (x `sub` y))
  
        -- (l1 - x) - (l2 - y) ==> (l1-l2) + (y-x)
        (is_sub num_ops -> Just (L l1,x), is_sub num_ops -> Just (L l2,y))
           -> Just (mkL (l1-l2) `add` (y `sub` x))
  
        -- (l1 - x) - (y - l2) ==> (l1+l2) - (x+y)
        (is_sub num_ops -> Just (L l1,x), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (l1+l2) `sub` (x `add` y))
  
        -- (x - l1) - (l2 - y) ==> (0-l1-l2) + (x+y)
        (is_sub num_ops -> Just (x,L l1), is_sub num_ops -> Just (L l2,y))
           -> Just (mkL (0-l1-l2) `add` (x `add` y))
  
        -- (x - l1) - (y - l2) ==> (l2-l1) + (x-y)
        (is_sub num_ops -> Just (x,L l1), is_sub num_ops -> Just (y,L l2))
           -> Just (mkL (l2-l1) `add` (x `sub` y))
  
         -- R4) Simple factorization
  
        -- x - (l1 * x) ==> (1-l1) * x
        _ | Just l1 <- is_expr_mul num_ops arg1 arg2
          -> Just (mkL (1-l1) `mul` arg1)
  
        -- (l1 * x) - x ==> (l1-1) * x
        _ | Just l1 <- is_expr_mul num_ops arg2 arg1
          -> Just (mkL (l1-1) `mul` arg2)
  
        -- (l1 * x) - (l2 * x) ==> (l1-l2) * x
        (is_lit_mul num_ops -> Just (l1,x), is_expr_mul num_ops x -> Just l2)
           -> Just (mkL (l1-l2) `mul` x)
  
        -- R5) +/- propagation: these transformations push literals outwards
        -- with the hope that other rules can then be applied.
  
        -- In the following rules, x can't be a literal otherwise another
        -- rule would have combined it with the other literal in arg2. So we
        -- don't have to check this to avoid loops here.
  
        -- x - (l1 + y) ==> (x - y) - l1
        (_, is_lit_add num_ops -> Just (l1,y))
           -> Just ((arg1 `sub` y) `sub` mkL l1)
  
        -- (l1 + x) - y ==> l1 + (x - y)
        (is_lit_add num_ops -> Just (l1,x), _)
           -> Just (mkL l1 `add` (x `sub` arg2))
  
        -- x - (l1 - y) ==> (x + y) - l1
        (_, is_sub num_ops -> Just (L l1,y))
           -> Just ((arg1 `add` y) `sub` mkL l1)
  
        -- x - (y - l1) ==> l1 + (x - y)
        (_, is_sub num_ops -> Just (y,L l1))
           -> Just (mkL l1 `add` (arg1 `sub` y))
  
        -- (l1 - x) - y ==> l1 - (x + y)
        (is_sub num_ops -> Just (L l1,x), _)
           -> Just (mkL l1 `sub` (x `add` arg2))
  
        -- (x - l1) - y ==> (x - y) - l1
        (is_sub num_ops -> Just (x,L l1), _)
           -> Just ((x `sub` arg2) `sub` mkL l1)
  
        _ -> Nothing
     where
        mkL = Lit . mkNumLiteral platform num_ops
        add x y = BinOpApp x (numAdd num_ops) y
        sub x y = BinOpApp x (numSub num_ops) y
        mul x y = BinOpApp x (numMul num_ops) y
  
  mulFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  mulFoldingRules' platform arg1 arg2 num_ops = case (arg1,arg2) of
     -- (-x) * (-y) ==> x*y
     (is_neg num_ops -> Just x, is_neg num_ops -> Just y)
        -> Just (x `mul` y)
  
     -- l1 * (-x) ==> (-l1) * x
     (L l1, is_neg num_ops -> Just x)
        -> Just (mkL (-l1) `mul` x)
  
     -- l1 * (l2 * x) ==> (l1*l2) * x
     (L l1, is_lit_mul num_ops -> Just (l2,x))
        -> Just (mkL (l1*l2) `mul` x)
  
     -- l1 * (l2 + x) ==> (l1*l2) + (l1 * x)
     (L l1, is_lit_add num_ops -> Just (l2,x))
        -> Just (mkL (l1*l2) `add` (arg1 `mul` x))
  
     -- l1 * (l2 - x) ==> (l1*l2) - (l1 * x)
     (L l1, is_sub num_ops -> Just (L l2,x))
        -> Just (mkL (l1*l2) `sub` (arg1 `mul` x))
  
     -- l1 * (x - l2) ==> (l1 * x) - (l1*l2)
     (L l1, is_sub num_ops -> Just (x, L l2))
        -> Just ((arg1 `mul` x) `sub` mkL (l1*l2))
  
     -- (l1 * x) * (l2 * y) ==> (l1*l2) * (x * y)
     (is_lit_mul num_ops -> Just (l1,x), is_lit_mul num_ops -> Just (l2,y))
        -> Just (mkL (l1*l2) `mul` (x `mul` y))
  
     _ -> Nothing
     where
        mkL = Lit . mkNumLiteral platform num_ops
        add x y = BinOpApp x (numAdd num_ops) y
        sub x y = BinOpApp x (numSub num_ops) y
        mul x y = BinOpApp x (numMul num_ops) y
  
  andFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  andFoldingRules' platform arg1 arg2 num_ops = case (arg1, arg2) of
      -- R2) * `or` `and` simplifications
      -- l1 and (l2 and x) ==> (l1 and l2) and x
      (L l1, is_lit_and num_ops -> Just (l2, x))
         -> Just (mkL (l1 .&. l2) `and` x)
  
      -- l1 and (l2 or x) ==> (l1 and l2) or (l1 and x)
      -- does not decrease operations
  
      -- (l1 and x) and (l2 and y) ==> (l1 and l2) and (x and y)
      (is_lit_and num_ops -> Just (l1, x), is_lit_and num_ops -> Just (l2, y))
         -> Just (mkL (l1 .&. l2) `and` (x `and` y))
  
      -- (l1 and x) and (l2 or y) ==> (l1 and l2 and x) or (l1 and x and y)
      -- (l1 or x) and (l2 or y) ==> (l1 and l2) or (x and l2) or (l1 and y) or (x and y)
      -- increase operation numbers
  
      -- x and (y or ... or x or ... or z) ==> x
      (x, is_or_list num_ops -> Just xs)
        | any (cheapEqExpr x) xs
        -> Just x
  
      _ -> Nothing
      where
        mkL = Lit . mkNumLiteral platform num_ops
        and x y = BinOpApp x (fromJust (numAnd num_ops)) y
  
  orFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  orFoldingRules' platform arg1 arg2 num_ops = case (arg1, arg2) of
      -- R2) *  `or` `and` simplifications
      -- l1 or (l2 or x) ==> (l1 or l2) or x
      (L l1, is_lit_or num_ops -> Just (l2, x))
         -> Just (mkL (l1 .|. l2) `or` x)
  
      -- l1 or (l2 and x) ==> (l1 or l2) and (l1 and x)
      -- does not decrease operations
  
      -- (l1 or x) or (l2 or y) ==> (l1 or l2) or (x or y)
      (is_lit_or num_ops -> Just (l1, x), is_lit_or num_ops -> Just (l2, y))
         -> Just (mkL (l1 .|. l2) `or` (x `or` y))
  
      -- (l1 and x) or (l2 or y) ==> (l1 and l2 and x) or (l1 and x and y)
      -- (l1 and x) or (l2 and y) ==> (l1 and l2) or (x and l2) or (l1 and y) or (x and y)
      -- increase operation numbers
  
      -- x or (y and ... and x and ... and z) ==> x
      (x, is_and_list num_ops -> Just xs)
        | any (cheapEqExpr x) xs
        -> Just x
  
      _ -> Nothing
      where
        mkL = Lit . mkNumLiteral platform num_ops
        or x y = BinOpApp x (fromJust (numOr num_ops)) y
  
  quotFoldingRules' :: Platform -> CoreExpr -> CoreExpr -> NumOps -> Maybe CoreExpr
  quotFoldingRules' platform arg1 arg2 num_ops = case (arg1, arg2) of
  
    -- (x / l1) / l2
    -- l1 and l2 /= 0
    -- l1*l2 doesn't overflow
    -- ==> x / (l1 * l2)
    (is_div num_ops -> Just (x, L l1), L l2)
      | l1 /= 0
      , l2 /= 0
      -- check that the result of the multiplication is in range
      , Just l <- mkNumLiteralMaybe platform num_ops (l1 * l2)
      -> Just (div x (Lit l))
        -- NB: we could directly return 0 or (-1) in case of overflow,
        -- but we would need to know
        --  (1) if we're dealing with a quot or a div operation
        --  (2) if it's an underflow or an overflow.
        -- Left as future work for now.
  
    _ -> Nothing
    where
      div x y = BinOpApp x (fromJust (numDiv num_ops)) y
  
  is_binop :: PrimOp -> CoreExpr -> Maybe (Arg CoreBndr, Arg CoreBndr)
  is_binop op e = case e of
   BinOpApp x op' y | op == op' -> Just (x,y)
   _                            -> Nothing
  
  is_op :: PrimOp -> CoreExpr -> Maybe (Arg CoreBndr)
  is_op op e = case e of
   App (OpVal op') x | op == op' -> Just x
   _                             -> Nothing
  
  is_add, is_sub, is_mul, is_and, is_or, is_div :: NumOps -> CoreExpr -> Maybe (CoreArg, CoreArg)
  is_add num_ops e = is_binop (numAdd num_ops) e
  is_sub num_ops e = is_binop (numSub num_ops) e
  is_mul num_ops e = is_binop (numMul num_ops) e
  is_and num_ops e = numAnd num_ops >>= \op -> is_binop op e
  is_or  num_ops e = numOr  num_ops >>= \op -> is_binop op e
  is_div num_ops e = numDiv num_ops >>= \op -> is_binop op e
  
  is_neg :: NumOps -> CoreExpr -> Maybe (Arg CoreBndr)
  is_neg num_ops e = numNeg num_ops >>= \op -> is_op op e
  
  -- Return a list of operands for a given operation.
  -- E.e. is_and_list (a and ... and z) => [a,...,z] for any nesting of the and
  -- operation
  is_list :: (CoreExpr -> Maybe (CoreArg,CoreArg)) -> CoreExpr -> Maybe [CoreArg]
  is_list f e_org = case f e_org of -- do we have the operator at all?
    Just (a,b) -> Just (go [a,b])
    Nothing    -> Nothing
    where
      go = \case
        []     -> []
        (e:es) -> case f e of
          -- we can't split any more: add to the result list
          Nothing    -> e : go es
          Just (a,b) -> go (a:b:es)
  
  is_and_list, is_or_list :: NumOps -> CoreExpr -> Maybe [CoreArg]
  is_and_list ops = is_list (is_and ops)
  is_or_list  ops = is_list (is_or  ops)
  
  -- match operation with a literal (handles commutativity)
  is_lit_add, is_lit_mul, is_lit_and, is_lit_or :: NumOps -> CoreExpr -> Maybe (Integer, Arg CoreBndr)
  is_lit_add num_ops e = is_lit' is_add num_ops e
  is_lit_mul num_ops e = is_lit' is_mul num_ops e
  is_lit_and num_ops e = is_lit' is_and num_ops e
  is_lit_or  num_ops e = is_lit' is_or  num_ops e
  
  is_lit' :: (NumOps -> CoreExpr -> Maybe (Arg CoreBndr, Arg CoreBndr)) -> NumOps -> CoreExpr -> Maybe (Integer, Arg CoreBndr)
  is_lit' f num_ops e = case f num_ops e of
    Just (L l, x  ) -> Just (l,x)
    Just (x  , L l) -> Just (l,x)
    _               -> Nothing
  
  -- match given "x": return 1
  -- match "lit * x": return lit value (handles commutativity)
  is_expr_mul :: NumOps -> Expr CoreBndr -> Expr CoreBndr -> Maybe Integer
  is_expr_mul num_ops x e = if
     | x `cheapEqExpr` e
     -> Just 1
     | Just (k,x') <- is_lit_mul num_ops e
     , x `cheapEqExpr` x'
     -> return k
     | otherwise
     -> Nothing
  
  
  -- | Match the application of a binary primop
  pattern BinOpApp :: Arg CoreBndr -> PrimOp -> Arg CoreBndr -> CoreExpr
  pattern BinOpApp x op y = OpVal op `App` x `App` y
  
  -- | Match a primop
  pattern OpVal:: PrimOp  -> Arg CoreBndr
  pattern OpVal op <- Var (isPrimOpId_maybe -> Just op) where
     OpVal op = Var (primOpId op)
  
  -- | Match a literal
  pattern L :: Integer -> Arg CoreBndr
  pattern L i <- Lit (LitNumber _ i)
  
  -- | Explicit "type-class"-like dictionary for numeric primops
  data NumOps = NumOps
     { numAdd     :: !PrimOp         -- ^ Add two numbers
     , numSub     :: !PrimOp         -- ^ Sub two numbers
     , numMul     :: !PrimOp         -- ^ Multiply two numbers
     , numDiv     :: !(Maybe PrimOp) -- ^ Divide two numbers
     , numAnd     :: !(Maybe PrimOp) -- ^ And two numbers
     , numOr      :: !(Maybe PrimOp) -- ^ Or two numbers
     , numNeg     :: !(Maybe PrimOp) -- ^ Negate a number
     , numLitType :: !LitNumType     -- ^ Literal type
     }
  
  -- | Create a numeric literal
  mkNumLiteral :: Platform -> NumOps -> Integer -> Literal
  mkNumLiteral platform ops i = mkLitNumberWrap platform (numLitType ops) i
  
  -- | Create a numeric literal if it is in range
  mkNumLiteralMaybe :: Platform -> NumOps -> Integer -> Maybe Literal
  mkNumLiteralMaybe platform ops i = mkLitNumberMaybe platform (numLitType ops) i
  
  int8Ops :: NumOps
  int8Ops = NumOps
     { numAdd     = Int8AddOp
     , numSub     = Int8SubOp
     , numMul     = Int8MulOp
     , numDiv     = Just Int8QuotOp
     , numAnd     = Nothing
     , numOr      = Nothing
     , numNeg     = Just Int8NegOp
     , numLitType = LitNumInt8
     }
  
  word8Ops :: NumOps
  word8Ops = NumOps
     { numAdd     = Word8AddOp
     , numSub     = Word8SubOp
     , numMul     = Word8MulOp
     , numDiv     = Just Word8QuotOp
     , numAnd     = Just Word8AndOp
     , numOr      = Just Word8OrOp
     , numNeg     = Nothing
     , numLitType = LitNumWord8
     }
  
  int16Ops :: NumOps
  int16Ops = NumOps
     { numAdd     = Int16AddOp
     , numSub     = Int16SubOp
     , numMul     = Int16MulOp
     , numDiv     = Just Int16QuotOp
     , numAnd     = Nothing
     , numOr      = Nothing
     , numNeg     = Just Int16NegOp
     , numLitType = LitNumInt16
     }
  
  word16Ops :: NumOps
  word16Ops = NumOps
     { numAdd     = Word16AddOp
     , numSub     = Word16SubOp
     , numMul     = Word16MulOp
     , numDiv     = Just Word16QuotOp
     , numAnd     = Just Word16AndOp
     , numOr      = Just Word16OrOp
     , numNeg     = Nothing
     , numLitType = LitNumWord16
     }
  
  int32Ops :: NumOps
  int32Ops = NumOps
     { numAdd     = Int32AddOp
     , numSub     = Int32SubOp
     , numMul     = Int32MulOp
     , numDiv     = Just Int32QuotOp
     , numAnd     = Nothing
     , numOr      = Nothing
     , numNeg     = Just Int32NegOp
     , numLitType = LitNumInt32
     }
  
  word32Ops :: NumOps
  word32Ops = NumOps
     { numAdd     = Word32AddOp
     , numSub     = Word32SubOp
     , numMul     = Word32MulOp
     , numDiv     = Just Word32QuotOp
     , numAnd     = Just Word32AndOp
     , numOr      = Just Word32OrOp
     , numNeg     = Nothing
     , numLitType = LitNumWord32
     }
  
  int64Ops :: NumOps
  int64Ops = NumOps
     { numAdd     = Int64AddOp
     , numSub     = Int64SubOp
     , numMul     = Int64MulOp
     , numDiv     = Just Int64QuotOp
     , numAnd     = Nothing
     , numOr      = Nothing
     , numNeg     = Just Int64NegOp
     , numLitType = LitNumInt64
     }
  
  word64Ops :: NumOps
  word64Ops = NumOps
     { numAdd     = Word64AddOp
     , numSub     = Word64SubOp
     , numMul     = Word64MulOp
     , numDiv     = Just Word64QuotOp
     , numAnd     = Just Word64AndOp
     , numOr      = Just Word64OrOp
     , numNeg     = Nothing
     , numLitType = LitNumWord64
     }
  
  intOps :: NumOps
  intOps = NumOps
     { numAdd     = IntAddOp
     , numSub     = IntSubOp
     , numMul     = IntMulOp
     , numDiv     = Just IntQuotOp
     , numAnd     = Just IntAndOp
     , numOr      = Just IntOrOp
     , numNeg     = Just IntNegOp
     , numLitType = LitNumInt
     }
  
  wordOps :: NumOps
  wordOps = NumOps
     { numAdd     = WordAddOp
     , numSub     = WordSubOp
     , numMul     = WordMulOp
     , numDiv     = Just WordQuotOp
     , numAnd     = Just WordAndOp
     , numOr      = Just WordOrOp
     , numNeg     = Nothing
     , numLitType = LitNumWord
     }
  
  --------------------------------------------------------
  -- Constant folding through case-expressions
  --
  -- cf Scrutinee Constant Folding in simplCore/GHC.Core.Opt.Simplify.Utils
  --------------------------------------------------------
  
  -- | Match the scrutinee of a case and potentially return a new scrutinee and a
  -- function to apply to each literal alternative.
  caseRules :: Platform
            -> CoreExpr                       -- Scrutinee
            -> Maybe ( CoreExpr               -- New scrutinee
                     , AltCon -> Maybe AltCon -- How to fix up the alt pattern
                                              --   Nothing <=> Unreachable
                                              -- See Note [Unreachable caseRules alternatives]
                     , Id -> CoreExpr)        -- How to reconstruct the original scrutinee
                                              -- from the new case-binder
  -- e.g  case e of b {
  --         ...;
  --         con bs -> rhs;
  --         ... }
  --  ==>
  --      case e' of b' {
  --         ...;
  --         fixup_altcon[con] bs -> let b = mk_orig[b] in rhs;
  --         ... }
  
  caseRules platform (App (App (Var f) v) (Lit l))   -- v `op` x#
    | Just op <- isPrimOpId_maybe f
    , LitNumber _ x <- l
    , Just adjust_lit <- adjustDyadicRight op x
    = Just (v, tx_lit_con platform adjust_lit
             , \v -> (App (App (Var f) (Var v)) (Lit l)))
  
  caseRules platform (App (App (Var f) (Lit l)) v)   -- x# `op` v
    | Just op <- isPrimOpId_maybe f
    , LitNumber _ x <- l
    , Just adjust_lit <- adjustDyadicLeft x op
    = Just (v, tx_lit_con platform adjust_lit
             , \v -> (App (App (Var f) (Lit l)) (Var v)))
  
  
  caseRules platform (App (Var f) v              )   -- op v
    | Just op <- isPrimOpId_maybe f
    , Just adjust_lit <- adjustUnary op
    = Just (v, tx_lit_con platform adjust_lit
             , \v -> App (Var f) (Var v))
  
  -- See Note [caseRules for tagToEnum]
  caseRules platform (App (App (Var f) type_arg) v)
    | Just TagToEnumOp <- isPrimOpId_maybe f
    = Just (v, tx_con_tte platform
             , \v -> (App (App (Var f) type_arg) (Var v)))
  
  -- See Note [caseRules for dataToTag]
  caseRules _ (Var f `App` Type lev `App` Type ty `App` v) -- dataToTag x
    | Just op <- isPrimOpId_maybe f
    , op == DataToTagSmallOp || op == DataToTagLargeOp
    = case splitTyConApp_maybe ty of
        Just (tc, _) | isValidDTT2TyCon tc
          -> Just (v, tx_con_dtt tc
                  , \v' -> Var f `App` Type lev `App` Type ty `App` Var v')
        _ -> pprTraceUserWarning warnMsg Nothing
    where
      warnMsg = vcat $ map text
        [ "Found dataToTag primop applied to a non-ADT type. This could"
        , "be a future bug in GHC, or it may be caused by an unsupported"
        , "use of the ghc-internal primops dataToTagSmall# and dataToTagLarge#."
        , "In either case, the GHC developers would like to know about it!"
        , "Please report this as a GHC bug:  http://www.haskell.org/ghc/reportabug"
        ]
  
  caseRules _ _ = Nothing
  
  
  -- | Case rules
  --
  -- It's important that occurrence info are present, hence the use of In* types.
  caseRules2
     :: InExpr  -- ^ Scutinee
     -> InId    -- ^ Case-binder
     -> [InAlt] -- ^ Alternatives in standard (increasing) order
     -> Maybe (InExpr, InId, [InAlt])
  caseRules2 scrut bndr alts
  
    -- case quotRem# x y of
    --    (# q, _ #) -> body
    -- ====>
    --  case quot# x y of
    --    q -> body
    --
    -- case quotRem# x y of
    --    (# _, r #) -> body
    -- ====>
    --  case rem# x y of
    --    r -> body
    | BinOpApp x op y <- scrut
    , Just (quot,rem) <- is_any_quot_rem op
    , [Alt (DataAlt _) [q,r] body] <- alts
    , isDeadBinder bndr
    , dead_q <- isDeadBinder q
    , dead_r <- isDeadBinder r
    , dead_q || dead_r
    = if
        | dead_q    -> Just $ (BinOpApp x rem  y, r, [Alt DEFAULT [] body])
        | dead_r    -> Just $ (BinOpApp x quot y, q, [Alt DEFAULT [] body])
        | otherwise -> Nothing
  
    | otherwise
    = Nothing
  
  
  -- | If the given primop is a quotRem, return the corresponding (quot,rem).
  is_any_quot_rem :: PrimOp -> Maybe (PrimOp, PrimOp)
  is_any_quot_rem = \case
    IntQuotRemOp    -> Just (IntQuotOp ,  IntRemOp)
    Int8QuotRemOp   -> Just (Int8QuotOp,  Int8RemOp)
    Int16QuotRemOp  -> Just (Int16QuotOp, Int16RemOp)
    Int32QuotRemOp  -> Just (Int32QuotOp, Int32RemOp)
    -- Int64QuotRemOp doesn't exist (yet)
  
    WordQuotRemOp   -> Just (WordQuotOp,   WordRemOp)
    Word8QuotRemOp  -> Just (Word8QuotOp,  Word8RemOp)
    Word16QuotRemOp -> Just (Word16QuotOp, Word16RemOp)
    Word32QuotRemOp -> Just (Word32QuotOp, Word32RemOp)
    -- Word64QuotRemOp doesn't exist (yet)
  
    _ -> Nothing
  
  
  tx_lit_con :: Platform -> (Integer -> Integer) -> AltCon -> Maybe AltCon
  tx_lit_con _        _      DEFAULT    = Just DEFAULT
  tx_lit_con platform adjust (LitAlt l) = Just $ LitAlt (mapLitValue platform adjust l)
  tx_lit_con _        _      alt        = pprPanic "caseRules" (ppr alt)
     -- NB: mapLitValue uses mkLitIntWrap etc, to ensure that the
     -- literal alternatives remain in Word/Int target ranges
     -- (See Note [Word/Int underflow/overflow] in GHC.Types.Literal and #13172).
  
  adjustDyadicRight :: PrimOp -> Integer -> Maybe (Integer -> Integer)
  -- Given (x `op` lit) return a function 'f' s.t.  f (x `op` lit) = x
  adjustDyadicRight op lit
    = case op of
           WordAddOp -> Just (\y -> y-lit      )
           IntAddOp  -> Just (\y -> y-lit      )
           WordSubOp -> Just (\y -> y+lit      )
           IntSubOp  -> Just (\y -> y+lit      )
           WordXorOp -> Just (\y -> y `xor` lit)
           IntXorOp  -> Just (\y -> y `xor` lit)
           _         -> Nothing
  
  adjustDyadicLeft :: Integer -> PrimOp -> Maybe (Integer -> Integer)
  -- Given (lit `op` x) return a function 'f' s.t.  f (lit `op` x) = x
  adjustDyadicLeft lit op
    = case op of
           WordAddOp -> Just (\y -> y-lit      )
           IntAddOp  -> Just (\y -> y-lit      )
           WordSubOp -> Just (\y -> lit-y      )
           IntSubOp  -> Just (\y -> lit-y      )
           WordXorOp -> Just (\y -> y `xor` lit)
           IntXorOp  -> Just (\y -> y `xor` lit)
           _         -> Nothing
  
  
  adjustUnary :: PrimOp -> Maybe (Integer -> Integer)
  -- Given (op x) return a function 'f' s.t.  f (op x) = x
  adjustUnary op
    = case op of
           WordNotOp -> Just (\y -> complement y)
           IntNotOp  -> Just (\y -> complement y)
           IntNegOp  -> Just (\y -> negate y    )
           _         -> Nothing
  
  tx_con_tte :: Platform -> AltCon -> Maybe AltCon
  tx_con_tte _        DEFAULT         = Just DEFAULT
  tx_con_tte _        alt@(LitAlt {}) = pprPanic "caseRules" (ppr alt)
  tx_con_tte platform (DataAlt dc)  -- See Note [caseRules for tagToEnum]
    = Just $ LitAlt $ mkLitInt platform $ toInteger $ dataConTagZ dc
  
  tx_con_dtt :: TyCon -> AltCon -> Maybe AltCon
  tx_con_dtt _  DEFAULT = Just DEFAULT
  tx_con_dtt tc (LitAlt (LitNumber LitNumInt i))
     | tag >= 0
     , tag < n_data_cons
     = Just (DataAlt (data_cons !! tag))   -- tag is zero-indexed, as is (!!)
     | otherwise
     = Nothing
     where
       tag         = fromInteger i :: ConTagZ
       n_data_cons = tyConFamilySize tc
       data_cons   = tyConDataCons tc
  
  tx_con_dtt _ alt = pprPanic "caseRules/dataToTag: bad alt" (ppr alt)
  
  
  {- Note [caseRules for tagToEnum]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We want to transform
     case tagToEnum# x of
       False -> e1
       True  -> e2
  into
     case x of
       0# -> e1
       1# -> e2
  
  See #8317.   This rule eliminates a lot of boilerplate. For
    if (x>y) then e2 else e1
  we generate
    case tagToEnum# (x ># y) of
      False -> e1
      True  -> e2
  and it is nice to then get rid of the tagToEnum#.
  
  Beware (#14768): avoid the temptation to map constructor 0 to
  DEFAULT, in the hope of getting this
    case (x ># y) of
      DEFAULT -> e1
      1#      -> e2
  That fails utterly in the case of
     data Colour = Red | Green | Blue
     case tagToEnum x of
        DEFAULT -> e1
        Red     -> e2
  
  We don't want to get this!
     case x of
        DEFAULT -> e1
        DEFAULT -> e2
  
  Instead, when possible, we turn one branch into DEFAULT in
  GHC.Core.Opt.Simplify.Utils.mkCase2; see Note [Literal cases]
  in that module.
  
  Note [caseRules for dataToTag]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  See also Note [DataToTag overview] in GHC.Tc.Instance.Class.
  
  We want to transform
    case dataToTagSmall# x of
      DEFAULT -> e1
      1# -> e2
  into
    case x of
      DEFAULT -> e1
      (:) _ _ -> e2
  
  (Note the need for some wildcard binders in the 'cons' case.)
  
  This transformation often enables further optimisation via
  case-flattening and case-of-known-constructor and can be very
  important for code using derived Eq instances.
  
  We can apply this transformation only when we can easily get the
  constructors from the type at which dataToTagSmall# is used.  And we
  cannot apply this transformation at "type data"-related types without
  breaking invariant I1 from Note [Type data declarations] in
  GHC.Rename.Module.  That leaves exactly the types satisfying condition
  DTT2 from Note [DataToTag overview] in GHC.Tc.Instance.Class.
  
  All of the above applies identically for `dataToTagLarge#`.  And
  thanks to wrinkle DTW5, there is no need to worry about large-tag
  arguments for `dataToTagSmall#`; those cause undefined behavior anyway.
  
  
  Note [Unreachable caseRules alternatives]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Take care if we see something like
    case dataToTag x of
      DEFAULT -> e1
      -1# -> e2
      100 -> e3
  because there isn't a data constructor with tag -1 or 100. In this case the
  out-of-range alternative is dead code -- we know the range of tags for x.
  
  Hence caseRules returns (AltCon -> Maybe AltCon), with Nothing indicating
  an alternative that is unreachable.
  
  You may wonder how this can happen: check out #15436.
  -}
  