Add two coercion optimisation perf tests

3 files changed, 1408 insertions, 1 deletions

diff --git a/testsuite/tests/perf/compiler/CoOpt_Read.hs b/testsuite/tests/perf/compiler/CoOpt_Read.hs
new file mode 100644
index 0000000000..e1df13b20e
--- /dev/null
+++ b/testsuite/tests/perf/compiler/CoOpt_Read.hs
@@ -0,0 +1,307 @@
+{-# LANGUAGE NoImplicitPrelude, ScopedTypeVariables #-}
+
+module CoOpt_Read where
+
+import Text.ParserCombinators.ReadP
+  ( ReadS
+  , readP_to_S
+  )
+import qualified Text.Read.Lex as L
+import Text.ParserCombinators.ReadPrec
+import GHC.Unicode
+import GHC.Num
+import GHC.Base
+
+class Read a where
+  {-# MINIMAL readsPrec | readPrec #-}
+
+  -- | attempts to parse a value from the front of the string, returning
+  -- a list of (parsed value, remaining string) pairs.  If there is no
+  -- successful parse, the returned list is empty.
+  --
+  -- Derived instances of 'Read' and 'Text.Show.Show' satisfy the following:
+  --
+  -- * @(x,\"\")@ is an element of
+  --   @('readsPrec' d ('Text.Show.showsPrec' d x \"\"))@.
+  --
+  -- That is, 'readsPrec' parses the string produced by
+  -- 'Text.Show.showsPrec', and delivers the value that
+  -- 'Text.Show.showsPrec' started with.
+
+  readsPrec    :: Int   -- ^ the operator precedence of the enclosing
+                        -- context (a number from @0@ to @11@).
+                        -- Function application has precedence @10@.
+                -> ReadS a
+
+  -- | The method 'readList' is provided to allow the programmer to
+  -- give a specialised way of parsing lists of values.
+  -- For example, this is used by the predefined 'Read' instance of
+  -- the 'Char' type, where values of type 'String' should be are
+  -- expected to use double quotes, rather than square brackets.
+  readList     :: ReadS [a]
+
+  -- | Proposed replacement for 'readsPrec' using new-style parsers (GHC only).
+  readPrec     :: ReadPrec a
+
+  -- | Proposed replacement for 'readList' using new-style parsers (GHC only).
+  -- The default definition uses 'readList'.  Instances that define 'readPrec'
+  -- should also define 'readListPrec' as 'readListPrecDefault'.
+  readListPrec :: ReadPrec [a]
+
+  -- default definitions
+  readsPrec    = readPrec_to_S readPrec
+  readList     = readPrec_to_S (list readPrec) 0
+  readPrec     = readS_to_Prec readsPrec
+  readListPrec = readS_to_Prec (\_ -> readList)
+
+readListDefault :: Read a => ReadS [a]
+-- ^ A possible replacement definition for the 'readList' method (GHC only).
+--   This is only needed for GHC, and even then only for 'Read' instances
+--   where 'readListPrec' isn't defined as 'readListPrecDefault'.
+readListDefault = readPrec_to_S readListPrec 0
+
+readListPrecDefault :: Read a => ReadPrec [a]
+-- ^ A possible replacement definition for the 'readListPrec' method,
+--   defined using 'readPrec' (GHC only).
+readListPrecDefault = list readPrec
+
+lex :: ReadS String             -- As defined by H2010
+lex s  = readP_to_S L.hsLex s
+
+------------------------------------------------------------------------
+-- utility parsers
+
+lexP :: ReadPrec L.Lexeme
+-- ^ Parse a single lexeme
+lexP = lift L.lex
+
+expectP :: L.Lexeme -> ReadPrec ()
+expectP lexeme = lift (L.expect lexeme)
+
+expectCharP :: Char -> ReadPrec a -> ReadPrec a
+expectCharP c a = do
+  q <- get
+  if q == c
+    then a
+    else pfail
+{-# INLINE expectCharP #-}
+
+skipSpacesThenP :: ReadPrec a -> ReadPrec a
+skipSpacesThenP m =
+  do s <- look
+     skip s
+ where
+   skip (c:s) | isSpace c = get *> skip s
+   skip _ = m
+
+paren :: ReadPrec a -> ReadPrec a
+-- ^ @(paren p)@ parses \"(P0)\"
+--      where @p@ parses \"P0\" in precedence context zero
+paren p = skipSpacesThenP (paren' p)
+
+paren' :: ReadPrec a -> ReadPrec a
+paren' p = expectCharP '(' $ reset p >>= \x ->
+              skipSpacesThenP (expectCharP ')' (pure x))
+
+parens :: ReadPrec a -> ReadPrec a
+-- ^ @(parens p)@ parses \"P\", \"(P0)\", \"((P0))\", etc,
+--      where @p@ parses \"P\"  in the current precedence context
+--          and parses \"P0\" in precedence context zero
+parens p = optional
+  where
+    optional = skipSpacesThenP (p +++ mandatory)
+    mandatory = paren' optional
+
+list :: ReadPrec a -> ReadPrec [a]
+-- ^ @(list p)@ parses a list of things parsed by @p@,
+-- using the usual square-bracket syntax.
+list readx =
+  parens
+  ( do expectP (L.Punc "[")
+       (listRest False +++ listNext)
+  )
+ where
+  listRest started =
+    do L.Punc c <- lexP
+       case c of
+         "]"           -> return []
+         "," | started -> listNext
+         _             -> pfail
+
+  listNext =
+    do x  <- reset readx
+       xs <- listRest True
+       return (x:xs)
+
+------------------------------------------------------------------------
+-- Tuple instances of Read, up to size 15
+------------------------------------------------------------------------
+
+-- | @since 2.01
+instance Read () where
+  readPrec =
+    parens
+    ( paren
+      ( return ()
+      )
+    )
+
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b) => Read (a,b) where
+  readPrec = wrap_tup read_tup2
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+wrap_tup :: ReadPrec a -> ReadPrec a
+wrap_tup p = parens (paren p)
+
+read_comma :: ReadPrec ()
+read_comma = expectP (L.Punc ",")
+
+read_tup2 :: (Read a, Read b) => ReadPrec (a,b)
+-- Reads "a , b"  no parens!
+read_tup2 = do x <- readPrec
+               read_comma
+               y <- readPrec
+               return (x,y)
+
+read_tup4 :: (Read a, Read b, Read c, Read d) => ReadPrec (a,b,c,d)
+read_tup4 = do  (a,b) <- read_tup2
+                read_comma
+                (c,d) <- read_tup2
+                return (a,b,c,d)
+
+
+read_tup8 :: (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h)
+          => ReadPrec (a,b,c,d,e,f,g,h)
+read_tup8 = do  (a,b,c,d) <- read_tup4
+                read_comma
+                (e,f,g,h) <- read_tup4
+                return (a,b,c,d,e,f,g,h)
+
+
+-- | @since 2.01
+instance (Read a, Read b, Read c) => Read (a, b, c) where
+  readPrec = wrap_tup (do { (a,b) <- read_tup2; read_comma
+                          ; c <- readPrec
+                          ; return (a,b,c) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d) => Read (a, b, c, d) where
+  readPrec = wrap_tup read_tup4
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) where
+  readPrec = wrap_tup (do { (a,b,c,d) <- read_tup4; read_comma
+                          ; e <- readPrec
+                          ; return (a,b,c,d,e) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f)
+        => Read (a, b, c, d, e, f) where
+  readPrec = wrap_tup (do { (a,b,c,d) <- read_tup4; read_comma
+                          ; (e,f) <- read_tup2
+                          ; return (a,b,c,d,e,f) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g)
+        => Read (a, b, c, d, e, f, g) where
+  readPrec = wrap_tup (do { (a,b,c,d) <- read_tup4; read_comma
+                          ; (e,f) <- read_tup2; read_comma
+                          ; g <- readPrec
+                          ; return (a,b,c,d,e,f,g) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h)
+        => Read (a, b, c, d, e, f, g, h) where
+  readPrec     = wrap_tup read_tup8
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i)
+        => Read (a, b, c, d, e, f, g, h, i) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; i <- readPrec
+                          ; return (a,b,c,d,e,f,g,h,i) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j)
+        => Read (a, b, c, d, e, f, g, h, i, j) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j) <- read_tup2
+                          ; return (a,b,c,d,e,f,g,h,i,j) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j, Read k)
+        => Read (a, b, c, d, e, f, g, h, i, j, k) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j) <- read_tup2; read_comma
+                          ; k <- readPrec
+                          ; return (a,b,c,d,e,f,g,h,i,j,k) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j, Read k, Read l)
+        => Read (a, b, c, d, e, f, g, h, i, j, k, l) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j,k,l) <- read_tup4
+                          ; return (a,b,c,d,e,f,g,h,i,j,k,l) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j, Read k, Read l, Read m)
+        => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j,k,l) <- read_tup4; read_comma
+                          ; m <- readPrec
+                          ; return (a,b,c,d,e,f,g,h,i,j,k,l,m) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j, Read k, Read l, Read m, Read n)
+        => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j,k,l) <- read_tup4; read_comma
+                          ; (m,n) <- read_tup2
+                          ; return (a,b,c,d,e,f,g,h,i,j,k,l,m,n) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
+
+-- | @since 2.01
+instance (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h,
+          Read i, Read j, Read k, Read l, Read m, Read n, Read o)
+        => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) where
+  readPrec = wrap_tup (do { (a,b,c,d,e,f,g,h) <- read_tup8; read_comma
+                          ; (i,j,k,l) <- read_tup4; read_comma
+                          ; (m,n) <- read_tup2; read_comma
+                          ; o <- readPrec
+                          ; return (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o) })
+  readListPrec = readListPrecDefault
+  readList     = readListDefault
diff --git a/testsuite/tests/perf/compiler/CoOpt_Singletons.hs b/testsuite/tests/perf/compiler/CoOpt_Singletons.hs
new file mode 100644
index 0000000000..593d1e4526
--- /dev/null
+++ b/testsuite/tests/perf/compiler/CoOpt_Singletons.hs
@@ -0,0 +1,1082 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE DefaultSignatures #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE InstanceSigs #-}
+{-# LANGUAGE NoNamedWildCards #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneKindSignatures #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE UndecidableInstances #-}
+
+{-# LANGUAGE Haskell2010 #-}
+
+{-# OPTIONS_GHC -Wno-unused-top-binds #-}
+
+module CoOpt_Singletons where
+
+-- base
+import Data.Kind
+  ( Type, Constraint )
+
+{-------------------------------------------------------------------------------
+This module extracts out everything needed to compile the following code
+from Data.Foldable.Singletons in singletons-base:
+
+$(singletonsOnly [d|
+  deriving instance Foldable ((,) a)
+  |])
+
+Except that we replace (,) with the custom Tuple2 datatype defined below.
+-}
+
+type Apply :: (k1 ~> k2) -> k1 -> k2
+type family Apply (f :: k1 ~> k2) (x :: k1) :: k2
+
+type (@@) :: (k1 ~> k2) -> k1 -> k2
+type a @@ b = Apply a b
+infixl 9 @@
+
+type TyFun :: Type -> Type -> Type
+data TyFun :: Type -> Type -> Type
+
+type (~>) :: Type -> Type -> Type
+type a ~> b = TyFun a b -> Type
+infixr 0 ~>
+
+type SameKind :: k -> k -> Constraint
+type SameKind (a :: k) (b :: k) = (() :: Constraint)
+
+type Sing :: k -> Type
+type family Sing :: k -> Type
+
+type SLambda :: (k1 ~> k2) -> Type
+newtype SLambda (f :: k1 ~> k2) =
+  SLambda { applySing :: forall t. Sing t -> Sing (f @@ t) }
+type instance Sing = SLambda
+
+type SingFunction1 :: (a1 ~> b) -> Type
+type SingFunction2 :: (a1 ~> a2 ~> b) -> Type
+type SingFunction3 :: (a1 ~> a2 ~> a3 ~> b) -> Type
+
+type SingFunction1 (f :: a1 ~> b) =
+  forall t. Sing t -> Sing (f @@ t)
+singFun1 :: forall f. SingFunction1 f -> Sing f
+singFun1 f = SLambda f
+
+type SingFunction2 (f :: a1 ~> a2 ~> b) =
+  forall t1 t2. Sing t1 -> Sing t2 -> Sing (f @@ t1 @@ t2)
+singFun2 :: forall f. SingFunction2 f -> Sing f
+singFun2 f = SLambda (\x -> singFun1 (f x))
+
+type SingFunction3 (f :: a1 ~> a2 ~> a3 ~> b) =
+     forall t1 t2 t3.
+     Sing t1 -> Sing t2 -> Sing t3
+  -> Sing (f @@ t1 @@ t2 @@ t3)
+singFun3 :: forall f. SingFunction3 f -> Sing f
+singFun3 f = SLambda (\x -> singFun2 (f x))
+
+------------------------------------------------------------
+
+data Tuple2 a b = Tuple2 a b
+
+type STuple2 :: Tuple2 a b -> Type
+data STuple2 tup where
+  STuple2 :: Sing a -> Sing b -> STuple2 ('Tuple2 a b)
+
+type instance Sing @(Tuple2 a b) = STuple2
+
+type Endo :: Type -> Type
+newtype Endo a = Endo (a ~> a)
+type SEndo :: Endo a -> Type
+data SEndo e where
+  SEndo :: Sing x -> SEndo ('Endo x)
+type instance Sing = SEndo
+type EndoSym0 :: (a ~> a) ~> Endo a
+data EndoSym0 tf
+type instance Apply EndoSym0 x = 'Endo x
+
+{-
+$(singletonsOnly [d|
+
+  id                      :: a -> a
+  id x                    =  x
+
+  flip                    :: (a -> b -> c) -> b -> a -> c
+  flip f x y              =  f y x
+
+  (.)    :: (b -> c) -> (a -> b) -> a -> c
+  (.) f g = \x -> f (g x)
+  infixr 9 .
+
+  ($!)                    :: (a -> b) -> a -> b
+  f $! x                  = let {-!-}vx = x in f vx
+  infixr 0 $!
+
+ |])
+-}
+
+data Let6989586621679038864VxSym0 f6989586621679038862
+  where
+    Let6989586621679038864VxSym0KindInference :: SameKind (Apply Let6989586621679038864VxSym0 arg_a7yV) (Let6989586621679038864VxSym1 arg_a7yV) =>
+                                                 Let6989586621679038864VxSym0 f6989586621679038862
+type instance Apply Let6989586621679038864VxSym0 f6989586621679038862 = Let6989586621679038864VxSym1 f6989586621679038862
+data Let6989586621679038864VxSym1 f6989586621679038862 x6989586621679038863
+  where
+    Let6989586621679038864VxSym1KindInference :: SameKind (Apply (Let6989586621679038864VxSym1 f6989586621679038862) arg_a7yV) (Let6989586621679038864VxSym2 f6989586621679038862 arg_a7yV) =>
+                                                 Let6989586621679038864VxSym1 f6989586621679038862 x6989586621679038863
+type instance Apply (Let6989586621679038864VxSym1 f6989586621679038862) x6989586621679038863 = Let6989586621679038864Vx f6989586621679038862 x6989586621679038863
+type family Let6989586621679038864VxSym2 f6989586621679038862 x6989586621679038863 where
+  Let6989586621679038864VxSym2 f6989586621679038862 x6989586621679038863 = Let6989586621679038864Vx f6989586621679038862 x6989586621679038863
+type family Let6989586621679038864Vx f_a7yS x_a7yT where
+  Let6989586621679038864Vx f_a7yS x_a7yT = x_a7yT
+type family Lambda_6989586621679038878_a7z9 f_a7z5 g_a7z6 a_6989586621679038866_a7z7 x_a7za where
+  Lambda_6989586621679038878_a7z9 f_a7z5 g_a7z6 a_6989586621679038866_a7z7 x_a7za = Apply f_a7z5 (Apply g_a7z6 x_a7za)
+data Lambda_6989586621679038878Sym0 f6989586621679038875
+  where
+    Lambda_6989586621679038878Sym0KindInference :: SameKind (Apply Lambda_6989586621679038878Sym0 arg_a7zb) (Lambda_6989586621679038878Sym1 arg_a7zb) =>
+                                                   Lambda_6989586621679038878Sym0 f6989586621679038875
+type instance Apply Lambda_6989586621679038878Sym0 f6989586621679038875 = Lambda_6989586621679038878Sym1 f6989586621679038875
+data Lambda_6989586621679038878Sym1 f6989586621679038875 g6989586621679038876
+  where
+    Lambda_6989586621679038878Sym1KindInference :: SameKind (Apply (Lambda_6989586621679038878Sym1 f6989586621679038875) arg_a7zb) (Lambda_6989586621679038878Sym2 f6989586621679038875 arg_a7zb) =>
+                                                   Lambda_6989586621679038878Sym1 f6989586621679038875 g6989586621679038876
+type instance Apply (Lambda_6989586621679038878Sym1 f6989586621679038875) g6989586621679038876 = Lambda_6989586621679038878Sym2 f6989586621679038875 g6989586621679038876
+data Lambda_6989586621679038878Sym2 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877
+  where
+    Lambda_6989586621679038878Sym2KindInference :: SameKind (Apply (Lambda_6989586621679038878Sym2 f6989586621679038875 g6989586621679038876) arg_a7zb) (Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 arg_a7zb) =>
+                                                   Lambda_6989586621679038878Sym2 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877
+type instance Apply (Lambda_6989586621679038878Sym2 f6989586621679038875 g6989586621679038876) a_69895866216790388666989586621679038877 = Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877
+data Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880
+  where
+    Lambda_6989586621679038878Sym3KindInference :: SameKind (Apply (Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877) arg_a7zb) (Lambda_6989586621679038878Sym4 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 arg_a7zb) =>
+                                                   Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880
+type instance Apply (Lambda_6989586621679038878Sym3 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877) x6989586621679038880 = Lambda_6989586621679038878_a7z9 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880
+type family Lambda_6989586621679038878Sym4 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880 where
+  Lambda_6989586621679038878Sym4 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880 = Lambda_6989586621679038878_a7z9 f6989586621679038875 g6989586621679038876 a_69895866216790388666989586621679038877 x6989586621679038880
+type ($!@#@$) :: (~>) ((~>) a_a7yq b_a7yr) ((~>) a_a7yq b_a7yr)
+data ($!@#@$) :: (~>) ((~>) a_a7yq b_a7yr) ((~>) a_a7yq b_a7yr)
+  where
+    (:$!@#@$###) :: SameKind (Apply ($!@#@$) arg_a7yP) (($!@#@$$) arg_a7yP) =>
+                    ($!@#@$) a6989586621679038860
+type instance Apply ($!@#@$) a6989586621679038860 = ($!@#@$$) a6989586621679038860
+infixr 0 $!@#@$
+type ($!@#@$$) :: (~>) a_a7yq b_a7yr -> (~>) a_a7yq b_a7yr
+data ($!@#@$$) (a6989586621679038860 :: (~>) a_a7yq b_a7yr) :: (~>) a_a7yq b_a7yr
+  where
+    (:$!@#@$$###) :: SameKind (Apply (($!@#@$$) a6989586621679038860) arg_a7yP) (($!@#@$$$) a6989586621679038860 arg_a7yP) =>
+                     ($!@#@$$) a6989586621679038860 a6989586621679038861
+type instance Apply (($!@#@$$) a6989586621679038860) a6989586621679038861 = ($!) a6989586621679038860 a6989586621679038861
+infixr 0 $!@#@$$
+type ($!@#@$$$) :: (~>) a_a7yq b_a7yr -> a_a7yq -> b_a7yr
+type family ($!@#@$$$) (a6989586621679038860 :: (~>) a_a7yq b_a7yr) (a6989586621679038861 :: a_a7yq) :: b_a7yr where
+  ($!@#@$$$) a6989586621679038860 a6989586621679038861 = ($!) a6989586621679038860 a6989586621679038861
+infixr 0 $!@#@$$$
+type (.@#@$) :: (~>) ((~>) b_a7ys c_a7yt) ((~>) ((~>) a_a7yu b_a7ys) ((~>) a_a7yu c_a7yt))
+data (.@#@$) :: (~>) ((~>) b_a7ys c_a7yt) ((~>) ((~>) a_a7yu b_a7ys) ((~>) a_a7yu c_a7yt))
+  where
+    (:.@#@$###) :: SameKind (Apply (.@#@$) arg_a7z1) ((.@#@$$) arg_a7z1) =>
+                   (.@#@$) a6989586621679038872
+type instance Apply (.@#@$) a6989586621679038872 = (.@#@$$) a6989586621679038872
+infixr 9 .@#@$
+type (.@#@$$) :: (~>) b_a7ys c_a7yt
+                 -> (~>) ((~>) a_a7yu b_a7ys) ((~>) a_a7yu c_a7yt)
+data (.@#@$$) (a6989586621679038872 :: (~>) b_a7ys c_a7yt) :: (~>) ((~>) a_a7yu b_a7ys) ((~>) a_a7yu c_a7yt)
+  where
+    (:.@#@$$###) :: SameKind (Apply ((.@#@$$) a6989586621679038872) arg_a7z1) ((.@#@$$$) a6989586621679038872 arg_a7z1) =>
+                    (.@#@$$) a6989586621679038872 a6989586621679038873
+type instance Apply ((.@#@$$) a6989586621679038872) a6989586621679038873 = (.@#@$$$) a6989586621679038872 a6989586621679038873
+infixr 9 .@#@$$
+type (.@#@$$$) :: (~>) b_a7ys c_a7yt
+                  -> (~>) a_a7yu b_a7ys -> (~>) a_a7yu c_a7yt
+data (.@#@$$$) (a6989586621679038872 :: (~>) b_a7ys c_a7yt) (a6989586621679038873 :: (~>) a_a7yu b_a7ys) :: (~>) a_a7yu c_a7yt
+  where
+    (:.@#@$$$###) :: SameKind (Apply ((.@#@$$$) a6989586621679038872 a6989586621679038873) arg_a7z1) ((.@#@$$$$) a6989586621679038872 a6989586621679038873 arg_a7z1) =>
+                     (.@#@$$$) a6989586621679038872 a6989586621679038873 a6989586621679038874
+type instance Apply ((.@#@$$$) a6989586621679038872 a6989586621679038873) a6989586621679038874 = (.) a6989586621679038872 a6989586621679038873 a6989586621679038874
+infixr 9 .@#@$$$
+type (.@#@$$$$) :: (~>) b_a7ys c_a7yt
+                   -> (~>) a_a7yu b_a7ys -> a_a7yu -> c_a7yt
+type family (.@#@$$$$) (a6989586621679038872 :: (~>) b_a7ys c_a7yt) (a6989586621679038873 :: (~>) a_a7yu b_a7ys) (a6989586621679038874 :: a_a7yu) :: c_a7yt where
+  (.@#@$$$$) a6989586621679038872 a6989586621679038873 a6989586621679038874 = (.) a6989586621679038872 a6989586621679038873 a6989586621679038874
+infixr 9 .@#@$$$$
+type FlipSym0 :: (~>) ((~>) a_a7yv ((~>) b_a7yw c_a7yx)) ((~>) b_a7yw ((~>) a_a7yv c_a7yx))
+data FlipSym0 :: (~>) ((~>) a_a7yv ((~>) b_a7yw c_a7yx)) ((~>) b_a7yw ((~>) a_a7yv c_a7yx))
+  where
+    FlipSym0KindInference :: SameKind (Apply FlipSym0 arg_a7zf) (FlipSym1 arg_a7zf) =>
+                             FlipSym0 a6989586621679038886
+type instance Apply FlipSym0 a6989586621679038886 = FlipSym1 a6989586621679038886
+type FlipSym1 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)
+                 -> (~>) b_a7yw ((~>) a_a7yv c_a7yx)
+data FlipSym1 (a6989586621679038886 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)) :: (~>) b_a7yw ((~>) a_a7yv c_a7yx)
+  where
+    FlipSym1KindInference :: SameKind (Apply (FlipSym1 a6989586621679038886) arg_a7zf) (FlipSym2 a6989586621679038886 arg_a7zf) =>
+                             FlipSym1 a6989586621679038886 a6989586621679038887
+type instance Apply (FlipSym1 a6989586621679038886) a6989586621679038887 = FlipSym2 a6989586621679038886 a6989586621679038887
+type FlipSym2 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)
+                 -> b_a7yw -> (~>) a_a7yv c_a7yx
+data FlipSym2 (a6989586621679038886 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)) (a6989586621679038887 :: b_a7yw) :: (~>) a_a7yv c_a7yx
+  where
+    FlipSym2KindInference :: SameKind (Apply (FlipSym2 a6989586621679038886 a6989586621679038887) arg_a7zf) (FlipSym3 a6989586621679038886 a6989586621679038887 arg_a7zf) =>
+                             FlipSym2 a6989586621679038886 a6989586621679038887 a6989586621679038888
+type instance Apply (FlipSym2 a6989586621679038886 a6989586621679038887) a6989586621679038888 = Flip a6989586621679038886 a6989586621679038887 a6989586621679038888
+type FlipSym3 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)
+                 -> b_a7yw -> a_a7yv -> c_a7yx
+type family FlipSym3 (a6989586621679038886 :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)) (a6989586621679038887 :: b_a7yw) (a6989586621679038888 :: a_a7yv) :: c_a7yx where
+  FlipSym3 a6989586621679038886 a6989586621679038887 a6989586621679038888 = Flip a6989586621679038886 a6989586621679038887 a6989586621679038888
+type IdSym0 :: (~>) a_a7yy a_a7yy
+data IdSym0 :: (~>) a_a7yy a_a7yy
+  where
+    IdSym0KindInference :: SameKind (Apply IdSym0 arg_a7zn) (IdSym1 arg_a7zn) =>
+                           IdSym0 a6989586621679038894
+type instance Apply IdSym0 a6989586621679038894 = Id a6989586621679038894
+type IdSym1 :: a_a7yy -> a_a7yy
+type family IdSym1 (a6989586621679038894 :: a_a7yy) :: a_a7yy where
+  IdSym1 a6989586621679038894 = Id a6989586621679038894
+type ($!) :: (~>) a_a7yq b_a7yr -> a_a7yq -> b_a7yr
+type family ($!) (a_a7yN :: (~>) a_a7yq b_a7yr) (a_a7yO :: a_a7yq) :: b_a7yr where
+  ($!) f_a7yS x_a7yT = Apply f_a7yS (Let6989586621679038864VxSym2 f_a7yS x_a7yT)
+type (.) :: (~>) b_a7ys c_a7yt
+            -> (~>) a_a7yu b_a7ys -> a_a7yu -> c_a7yt
+type family (.) (a_a7yY :: (~>) b_a7ys c_a7yt) (a_a7yZ :: (~>) a_a7yu b_a7ys) (a_a7z0 :: a_a7yu) :: c_a7yt where
+  (.) f_a7z5 g_a7z6 a_6989586621679038866_a7z7 = Apply (Apply (Apply (Apply Lambda_6989586621679038878Sym0 f_a7z5) g_a7z6) a_6989586621679038866_a7z7) a_6989586621679038866_a7z7
+type Flip :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)
+             -> b_a7yw -> a_a7yv -> c_a7yx
+type family Flip (a_a7zc :: (~>) a_a7yv ((~>) b_a7yw c_a7yx)) (a_a7zd :: b_a7yw) (a_a7ze :: a_a7yv) :: c_a7yx where
+  Flip f_a7zj x_a7zk y_a7zl = Apply (Apply f_a7zj y_a7zl) x_a7zk
+type Id :: a_a7yy -> a_a7yy
+type family Id (a_a7zm :: a_a7yy) :: a_a7yy where
+  Id x_a7zp = x_a7zp
+infixr 0 $!
+infixr 9 .
+infixr 0 %$!
+infixr 9 %.
+(%$!) ::
+  forall a_a7yq
+         b_a7yr
+         (t_a7zq :: (~>) a_a7yq b_a7yr)
+         (t_a7zr :: a_a7yq). Sing t_a7zq
+                             -> Sing t_a7zr
+                                -> Sing (Apply (Apply ($!@#@$) t_a7zq) t_a7zr :: b_a7yr)
+(%.) ::
+  forall b_a7ys
+         c_a7yt
+         a_a7yu
+         (t_a7zv :: (~>) b_a7ys c_a7yt)
+         (t_a7zw :: (~>) a_a7yu b_a7ys)
+         (t_a7zx :: a_a7yu). Sing t_a7zv
+                             -> Sing t_a7zw
+                                -> Sing t_a7zx
+                                   -> Sing (Apply (Apply (Apply (.@#@$) t_a7zv) t_a7zw) t_a7zx :: c_a7yt)
+sFlip ::
+  forall a_a7yv
+         b_a7yw
+         c_a7yx
+         (t_a7zF :: (~>) a_a7yv ((~>) b_a7yw c_a7yx))
+         (t_a7zG :: b_a7yw)
+         (t_a7zH :: a_a7yv). Sing t_a7zF
+                             -> Sing t_a7zG
+                                -> Sing t_a7zH
+                                   -> Sing (Apply (Apply (Apply FlipSym0 t_a7zF) t_a7zG) t_a7zH :: c_a7yx)
+sId ::
+  forall a_a7yy (t_a7zP :: a_a7yy). Sing t_a7zP
+                                    -> Sing (Apply IdSym0 t_a7zP :: a_a7yy)
+(%$!) (sF :: Sing f_a7yS) (sX :: Sing x_a7yT)
+  = let
+      sVx :: Sing @_ (Let6989586621679038864VxSym2 f_a7yS x_a7yT)
+      sVx = sX
+    in (applySing sF) sVx
+(%.)
+  (sF :: Sing f_a7z5)
+  (sG :: Sing g_a7z6)
+  (sA_6989586621679038866 :: Sing a_6989586621679038866_a7z7)
+  = (applySing
+       ((singFun1
+           @(Apply (Apply (Apply Lambda_6989586621679038878Sym0 f_a7z5) g_a7z6) a_6989586621679038866_a7z7))
+          (\ sX
+             -> case sX of
+                  (_ :: Sing x_a7za) -> (applySing sF) ((applySing sG) sX))))
+      sA_6989586621679038866
+sFlip (sF :: Sing f_a7zj) (sX :: Sing x_a7zk) (sY :: Sing y_a7zl)
+  = (applySing ((applySing sF) sY)) sX
+sId (sX :: Sing x_a7zp) = sX
+
+------------------------------------------------------------
+
+newtype Dual a = Dual { getDual :: a }
+
+{-
+$(genSingletons [''Dual])
+-}
+
+type DualSym0 :: forall (a_a5fi :: Type). (~>) a_a5fi (Dual (a_a5fi :: Type))
+data DualSym0 :: (~>) a_a5fi (Dual (a_a5fi :: Type))
+  where
+    DualSym0KindInference :: SameKind (Apply DualSym0 arg_a9sh) (DualSym1 arg_a9sh) =>
+                             DualSym0 a6989586621679046142
+type instance Apply DualSym0 a6989586621679046142 = 'Dual a6989586621679046142
+type DualSym1 :: forall (a_a5fi :: Type). a_a5fi
+                                          -> Dual (a_a5fi :: Type)
+type family DualSym1 (a6989586621679046142 :: a_a5fi) :: Dual (a_a5fi :: Type) where
+  DualSym1 a6989586621679046142 = 'Dual a6989586621679046142
+type GetDualSym0 :: forall (a_a5fi :: Type). (~>) (Dual (a_a5fi :: Type)) a_a5fi
+data GetDualSym0 :: (~>) (Dual (a_a5fi :: Type)) a_a5fi
+  where
+    GetDualSym0KindInference :: SameKind (Apply GetDualSym0 arg_a9sk) (GetDualSym1 arg_a9sk) =>
+                                GetDualSym0 a6989586621679046145
+type instance Apply GetDualSym0 a6989586621679046145 = GetDual a6989586621679046145
+type GetDualSym1 :: forall (a_a5fi :: Type). Dual (a_a5fi :: Type)
+                                             -> a_a5fi
+type family GetDualSym1 (a6989586621679046145 :: Dual (a_a5fi :: Type)) :: a_a5fi where
+  GetDualSym1 a6989586621679046145 = GetDual a6989586621679046145
+type GetDual :: forall (a_a5fi :: Type). Dual (a_a5fi :: Type)
+                                         -> a_a5fi
+type family GetDual (a_a9sj :: Dual (a_a5fi :: Type)) :: a_a5fi where
+  GetDual ('Dual field_a9sm) = field_a9sm
+sGetDual ::
+  forall (a_a5fi :: Type)
+         (t_a9sn :: Dual (a_a5fi :: Type)). Sing t_a9sn
+                                            -> Sing (Apply GetDualSym0 t_a9sn :: a_a5fi)
+sGetDual (SDual (sField :: Sing field_a9sm)) = sField
+type SDual :: forall (a_a5fi :: Type). Dual a_a5fi -> Type
+data SDual :: forall (a_a5fi :: Type). Dual a_a5fi -> Type
+  where
+    SDual :: forall (a_a5fi :: Type) (n_a9sq :: a_a5fi).
+             (Sing n_a9sq) -> SDual ('Dual n_a9sq :: Dual (a_a5fi :: Type))
+type instance Sing @(Dual a_a5fi) = SDual
+
+{-
+$(singletonsOnly [d|
+  class Semigroup a where
+    (<>) :: a -> a -> a
+
+  class Semigroup a => Monoid a where
+        mempty  :: a
+
+        mappend :: a -> a -> a
+        mappend = (<>)
+
+  instance Semigroup a => Semigroup (Dual a) where
+    Dual a <> Dual b = Dual (b <> a)
+
+  instance Monoid a => Monoid (Dual a) where
+          mempty = Dual mempty
+  |])
+-}
+
+type (<>@#@$) :: forall a_a9GJ. (~>) a_a9GJ ((~>) a_a9GJ a_a9GJ)
+data (<>@#@$) :: (~>) a_a9GJ ((~>) a_a9GJ a_a9GJ)
+  where
+    (:<>@#@$###) :: SameKind (Apply (<>@#@$) arg_a9GZ) ((<>@#@$$) arg_a9GZ) =>
+                    (<>@#@$) a6989586621679047054
+type instance Apply (<>@#@$) a6989586621679047054 = (<>@#@$$) a6989586621679047054
+type (<>@#@$$) :: forall a_a9GJ. a_a9GJ -> (~>) a_a9GJ a_a9GJ
+data (<>@#@$$) (a6989586621679047054 :: a_a9GJ) :: (~>) a_a9GJ a_a9GJ
+  where
+    (:<>@#@$$###) :: SameKind (Apply ((<>@#@$$) a6989586621679047054) arg_a9GZ) ((<>@#@$$$) a6989586621679047054 arg_a9GZ) =>
+                     (<>@#@$$) a6989586621679047054 a6989586621679047055
+type instance Apply ((<>@#@$$) a6989586621679047054) a6989586621679047055 = (<>) a6989586621679047054 a6989586621679047055
+type (<>@#@$$$) :: forall a_a9GJ. a_a9GJ -> a_a9GJ -> a_a9GJ
+type family (<>@#@$$$) (a6989586621679047054 :: a_a9GJ) (a6989586621679047055 :: a_a9GJ) :: a_a9GJ where
+  (<>@#@$$$) a6989586621679047054 a6989586621679047055 = (<>) a6989586621679047054 a6989586621679047055
+class PSemigroup a_a9GJ where
+  type family (<>) (arg_a9GX :: a_a9GJ) (arg_a9GY :: a_a9GJ) :: a_a9GJ
+type MemptySym0 :: forall a_a9GK. a_a9GK
+type family MemptySym0 :: a_a9GK where
+  MemptySym0 = Mempty
+type MappendSym0 :: forall a_a9GK. (~>) a_a9GK ((~>) a_a9GK a_a9GK)
+data MappendSym0 :: (~>) a_a9GK ((~>) a_a9GK a_a9GK)
+  where
+    MappendSym0KindInference :: SameKind (Apply MappendSym0 arg_a9H5) (MappendSym1 arg_a9H5) =>
+                                MappendSym0 a6989586621679047060
+type instance Apply MappendSym0 a6989586621679047060 = MappendSym1 a6989586621679047060
+type MappendSym1 :: forall a_a9GK. a_a9GK -> (~>) a_a9GK a_a9GK
+data MappendSym1 (a6989586621679047060 :: a_a9GK) :: (~>) a_a9GK a_a9GK
+  where
+    MappendSym1KindInference :: SameKind (Apply (MappendSym1 a6989586621679047060) arg_a9H5) (MappendSym2 a6989586621679047060 arg_a9H5) =>
+                                MappendSym1 a6989586621679047060 a6989586621679047061
+type instance Apply (MappendSym1 a6989586621679047060) a6989586621679047061 = Mappend a6989586621679047060 a6989586621679047061
+type MappendSym2 :: forall a_a9GK. a_a9GK -> a_a9GK -> a_a9GK
+type family MappendSym2 (a6989586621679047060 :: a_a9GK) (a6989586621679047061 :: a_a9GK) :: a_a9GK where
+  MappendSym2 a6989586621679047060 a6989586621679047061 = Mappend a6989586621679047060 a6989586621679047061
+type Mappend_6989586621679047064 :: a_a9GK -> a_a9GK -> a_a9GK
+type family Mappend_6989586621679047064 (a_a9Hg :: a_a9GK) (a_a9Hh :: a_a9GK) :: a_a9GK where
+  Mappend_6989586621679047064 a_6989586621679047066_a9Hl a_6989586621679047068_a9Hm = Apply (Apply (<>@#@$) a_6989586621679047066_a9Hl) a_6989586621679047068_a9Hm
+type Mappend_6989586621679047064Sym0 :: (~>) a_a9GK ((~>) a_a9GK a_a9GK)
+data Mappend_6989586621679047064Sym0 :: (~>) a_a9GK ((~>) a_a9GK a_a9GK)
+  where
+    Mappend_6989586621679047064Sym0KindInference :: SameKind (Apply Mappend_6989586621679047064Sym0 arg_a9Hi) (Mappend_6989586621679047064Sym1 arg_a9Hi) =>
+                                                    Mappend_6989586621679047064Sym0 a6989586621679047073
+type instance Apply Mappend_6989586621679047064Sym0 a6989586621679047073 = Mappend_6989586621679047064Sym1 a6989586621679047073
+type Mappend_6989586621679047064Sym1 :: a_a9GK
+                                        -> (~>) a_a9GK a_a9GK
+data Mappend_6989586621679047064Sym1 (a6989586621679047073 :: a_a9GK) :: (~>) a_a9GK a_a9GK
+  where
+    Mappend_6989586621679047064Sym1KindInference :: SameKind (Apply (Mappend_6989586621679047064Sym1 a6989586621679047073) arg_a9Hi) (Mappend_6989586621679047064Sym2 a6989586621679047073 arg_a9Hi) =>
+                                                    Mappend_6989586621679047064Sym1 a6989586621679047073 a6989586621679047074
+type instance Apply (Mappend_6989586621679047064Sym1 a6989586621679047073) a6989586621679047074 = Mappend_6989586621679047064 a6989586621679047073 a6989586621679047074
+type Mappend_6989586621679047064Sym2 :: a_a9GK -> a_a9GK -> a_a9GK
+type family Mappend_6989586621679047064Sym2 (a6989586621679047073 :: a_a9GK) (a6989586621679047074 :: a_a9GK) :: a_a9GK where
+  Mappend_6989586621679047064Sym2 a6989586621679047073 a6989586621679047074 = Mappend_6989586621679047064 a6989586621679047073 a6989586621679047074
+class PMonoid a_a9GK where
+  type family Mempty :: a_a9GK
+  type family Mappend (arg_a9H3 :: a_a9GK) (arg_a9H4 :: a_a9GK) :: a_a9GK
+  type Mappend a_a9H8 a_a9H9 = Apply (Apply Mappend_6989586621679047064Sym0 a_a9H8) a_a9H9
+type TFHelper_6989586621679047079 :: Dual a_a9GL
+                                     -> Dual a_a9GL -> Dual a_a9GL
+type family TFHelper_6989586621679047079 (a_a9Hr :: Dual a_a9GL) (a_a9Hs :: Dual a_a9GL) :: Dual a_a9GL where
+  TFHelper_6989586621679047079 ('Dual a_a9Hw) ('Dual b_a9Hx) = Apply DualSym0 (Apply (Apply (<>@#@$) b_a9Hx) a_a9Hw)
+type TFHelper_6989586621679047079Sym0 :: (~>) (Dual a_a9GL) ((~>) (Dual a_a9GL) (Dual a_a9GL))
+data TFHelper_6989586621679047079Sym0 :: (~>) (Dual a_a9GL) ((~>) (Dual a_a9GL) (Dual a_a9GL))
+  where
+    TFHelper_6989586621679047079Sym0KindInference :: SameKind (Apply TFHelper_6989586621679047079Sym0 arg_a9Ht) (TFHelper_6989586621679047079Sym1 arg_a9Ht) =>
+                                                     TFHelper_6989586621679047079Sym0 a6989586621679047084
+type instance Apply TFHelper_6989586621679047079Sym0 a6989586621679047084 = TFHelper_6989586621679047079Sym1 a6989586621679047084
+type TFHelper_6989586621679047079Sym1 :: Dual a_a9GL
+                                         -> (~>) (Dual a_a9GL) (Dual a_a9GL)
+data TFHelper_6989586621679047079Sym1 (a6989586621679047084 :: Dual a_a9GL) :: (~>) (Dual a_a9GL) (Dual a_a9GL)
+  where
+    TFHelper_6989586621679047079Sym1KindInference :: SameKind (Apply (TFHelper_6989586621679047079Sym1 a6989586621679047084) arg_a9Ht) (TFHelper_6989586621679047079Sym2 a6989586621679047084 arg_a9Ht) =>
+                                                     TFHelper_6989586621679047079Sym1 a6989586621679047084 a6989586621679047085
+type instance Apply (TFHelper_6989586621679047079Sym1 a6989586621679047084) a6989586621679047085 = TFHelper_6989586621679047079 a6989586621679047084 a6989586621679047085
+type TFHelper_6989586621679047079Sym2 :: Dual a_a9GL
+                                         -> Dual a_a9GL -> Dual a_a9GL
+type family TFHelper_6989586621679047079Sym2 (a6989586621679047084 :: Dual a_a9GL) (a6989586621679047085 :: Dual a_a9GL) :: Dual a_a9GL where
+  TFHelper_6989586621679047079Sym2 a6989586621679047084 a6989586621679047085 = TFHelper_6989586621679047079 a6989586621679047084 a6989586621679047085
+instance PSemigroup (Dual a_a9GL) where
+  type (<>) a_a9Hn a_a9Ho = Apply (Apply TFHelper_6989586621679047079Sym0 a_a9Hn) a_a9Ho
+type Mempty_6989586621679047088 :: Dual a_a9GO
+type family Mempty_6989586621679047088 :: Dual a_a9GO where
+  Mempty_6989586621679047088 = Apply DualSym0 MemptySym0
+type Mempty_6989586621679047088Sym0 :: Dual a_a9GO
+type family Mempty_6989586621679047088Sym0 :: Dual a_a9GO where
+  Mempty_6989586621679047088Sym0 = Mempty_6989586621679047088
+instance PMonoid (Dual a_a9GO) where
+  type Mempty = Mempty_6989586621679047088Sym0
+class SSemigroup a_a9GJ where
+  (%<>) ::
+    forall (t_a9HB :: a_a9GJ) (t_a9HC :: a_a9GJ). Sing t_a9HB
+                                                  -> Sing t_a9HC
+                                                     -> Sing (Apply (Apply (<>@#@$) t_a9HB) t_a9HC :: a_a9GJ)
+class SSemigroup a_a9GK => SMonoid a_a9GK where
+  sMempty :: Sing (MemptySym0 :: a_a9GK)
+  sMappend ::
+    forall (t_a9HG :: a_a9GK) (t_a9HH :: a_a9GK). Sing t_a9HG
+                                                  -> Sing t_a9HH
+                                                     -> Sing (Apply (Apply MappendSym0 t_a9HG) t_a9HH :: a_a9GK)
+  default sMappend ::
+            forall (t_a9HG :: a_a9GK)
+                   (t_a9HH :: a_a9GK). ((Apply (Apply MappendSym0 t_a9HG) t_a9HH :: a_a9GK)
+                                        ~
+                                        Apply (Apply Mappend_6989586621679047064Sym0 t_a9HG) t_a9HH) =>
+                                       Sing t_a9HG
+                                       -> Sing t_a9HH
+                                          -> Sing (Apply (Apply MappendSym0 t_a9HG) t_a9HH :: a_a9GK)
+  sMappend
+    (sA_6989586621679047066 :: Sing a_6989586621679047066_a9Hl)
+    (sA_6989586621679047068 :: Sing a_6989586621679047068_a9Hm)
+    = (applySing
+         ((applySing ((singFun2 @(<>@#@$)) (%<>))) sA_6989586621679047066))
+        sA_6989586621679047068
+instance SSemigroup a_a9GL => SSemigroup (Dual a_a9GL) where
+  (%<>) ::
+    forall (t_a9HN :: Dual a_a9GL) (t_a9HO :: Dual a_a9GL). Sing t_a9HN
+                                                            -> Sing t_a9HO
+                                                               -> Sing (Apply (Apply (<>@#@$) t_a9HN) t_a9HO :: Dual a_a9GL)
+  (%<>) (SDual (sA :: Sing a_a9Hw)) (SDual (sB :: Sing b_a9Hx))
+    = (applySing ((singFun1 @DualSym0) SDual))
+        ((applySing ((applySing ((singFun2 @(<>@#@$)) (%<>))) sB)) sA)
+instance SMonoid a_a9GO => SMonoid (Dual a_a9GO) where
+  sMempty :: Sing (MemptySym0 :: Dual a_a9GO)
+  sMempty = (applySing ((singFun1 @DualSym0) SDual)) sMempty
+
+{-
+$(singletonsOnly [d|
+  appEndo :: Endo a -> (a -> a)
+  appEndo (Endo x) = x
+
+  instance Semigroup (Endo a) where
+          Endo x <> Endo y = Endo (x . y)
+
+  instance Monoid (Endo a) where
+          mempty = Endo id
+  |])
+-}
+
+type AppEndoSym0 :: (~>) (Endo a_agCh) ((~>) a_agCh a_agCh)
+data AppEndoSym0 :: (~>) (Endo a_agCh) ((~>) a_agCh a_agCh)
+  where
+    AppEndoSym0KindInference :: SameKind (Apply AppEndoSym0 arg_agUE) (AppEndoSym1 arg_agUE) =>
+                                AppEndoSym0 a6989586621679074809
+type instance Apply AppEndoSym0 a6989586621679074809 = AppEndoSym1 a6989586621679074809
+type AppEndoSym1 :: Endo a_agCh -> (~>) a_agCh a_agCh
+data AppEndoSym1 (a6989586621679074809 :: Endo a_agCh) :: (~>) a_agCh a_agCh
+  where
+    AppEndoSym1KindInference :: SameKind (Apply (AppEndoSym1 a6989586621679074809) arg_agUE) (AppEndoSym2 a6989586621679074809 arg_agUE) =>
+                                AppEndoSym1 a6989586621679074809 a6989586621679074810
+type instance Apply (AppEndoSym1 a6989586621679074809) a6989586621679074810 = AppEndo a6989586621679074809 a6989586621679074810
+type AppEndoSym2 :: Endo a_agCh -> a_agCh -> a_agCh
+type family AppEndoSym2 (a6989586621679074809 :: Endo a_agCh) (a6989586621679074810 :: a_agCh) :: a_agCh where
+  AppEndoSym2 a6989586621679074809 a6989586621679074810 = AppEndo a6989586621679074809 a6989586621679074810
+type AppEndo :: Endo a_agCh -> a_agCh -> a_agCh
+type family AppEndo (a_agUC :: Endo a_agCh) (a_agUD :: a_agCh) :: a_agCh where
+  AppEndo ('Endo x_agUH) a_6989586621679074804_agUI = Apply x_agUH a_6989586621679074804_agUI
+type TFHelper_6989586621679075091 :: Endo a_agCk
+                                     -> Endo a_agCk -> Endo a_agCk
+type family TFHelper_6989586621679075091 (a_agZf :: Endo a_agCk) (a_agZg :: Endo a_agCk) :: Endo a_agCk where
+  TFHelper_6989586621679075091 ('Endo x_agZk) ('Endo y_agZl) = Apply EndoSym0 (Apply (Apply (.@#@$) x_agZk) y_agZl)
+type TFHelper_6989586621679075091Sym0 :: (~>) (Endo a_agCk) ((~>) (Endo a_agCk) (Endo a_agCk))
+data TFHelper_6989586621679075091Sym0 :: (~>) (Endo a_agCk) ((~>) (Endo a_agCk) (Endo a_agCk))
+  where
+    TFHelper_6989586621679075091Sym0KindInference :: SameKind (Apply TFHelper_6989586621679075091Sym0 arg_agZh) (TFHelper_6989586621679075091Sym1 arg_agZh) =>
+                                                     TFHelper_6989586621679075091Sym0 a6989586621679075096
+type instance Apply TFHelper_6989586621679075091Sym0 a6989586621679075096 = TFHelper_6989586621679075091Sym1 a6989586621679075096
+type TFHelper_6989586621679075091Sym1 :: Endo a_agCk
+                                         -> (~>) (Endo a_agCk) (Endo a_agCk)
+data TFHelper_6989586621679075091Sym1 (a6989586621679075096 :: Endo a_agCk) :: (~>) (Endo a_agCk) (Endo a_agCk)
+  where
+    TFHelper_6989586621679075091Sym1KindInference :: SameKind (Apply (TFHelper_6989586621679075091Sym1 a6989586621679075096) arg_agZh) (TFHelper_6989586621679075091Sym2 a6989586621679075096 arg_agZh) =>
+                                                     TFHelper_6989586621679075091Sym1 a6989586621679075096 a6989586621679075097
+type instance Apply (TFHelper_6989586621679075091Sym1 a6989586621679075096) a6989586621679075097 = TFHelper_6989586621679075091 a6989586621679075096 a6989586621679075097
+type TFHelper_6989586621679075091Sym2 :: Endo a_agCk
+                                         -> Endo a_agCk -> Endo a_agCk
+type family TFHelper_6989586621679075091Sym2 (a6989586621679075096 :: Endo a_agCk) (a6989586621679075097 :: Endo a_agCk) :: Endo a_agCk where
+  TFHelper_6989586621679075091Sym2 a6989586621679075096 a6989586621679075097 = TFHelper_6989586621679075091 a6989586621679075096 a6989586621679075097
+instance PSemigroup (Endo a_agCk) where
+  type (<>) a_agZb a_agZc = Apply (Apply TFHelper_6989586621679075091Sym0 a_agZb) a_agZc
+type Mempty_6989586621679075313 :: Endo a_agCn
+type family Mempty_6989586621679075313 :: Endo a_agCn where
+  Mempty_6989586621679075313 = Apply EndoSym0 IdSym0
+type Mempty_6989586621679075313Sym0 :: Endo a_agCn
+type family Mempty_6989586621679075313Sym0 :: Endo a_agCn where
+  Mempty_6989586621679075313Sym0 = Mempty_6989586621679075313
+instance PMonoid (Endo a_agCn) where
+  type Mempty = Mempty_6989586621679075313Sym0
+sAppEndo ::
+  forall a_agCh
+         (t_ah2Q :: Endo a_agCh)
+         (t_ah2R :: a_agCh). Sing t_ah2Q
+                             -> Sing t_ah2R
+                                -> Sing (Apply (Apply AppEndoSym0 t_ah2Q) t_ah2R :: a_agCh)
+sAppEndo
+  (SEndo (sX :: Sing x_agUH))
+  (sA_6989586621679074804 :: Sing a_6989586621679074804_agUI)
+  = (applySing sX) sA_6989586621679074804
+instance SSemigroup (Endo a_agCk) where
+  (%<>) ::
+    forall (t1_ih30 :: Endo a_agCk)
+           (t2_ih31 :: Endo a_agCk). Sing t1_ih30
+                                     -> Sing t2_ih31
+                                        -> Sing (Apply (Apply ((<>@#@$) :: TyFun (Endo a_agCk) ((~>) (Endo a_agCk) (Endo a_agCk))
+                                          -> Type) t1_ih30) t2_ih31)
+  (%<>) (SEndo (sX :: Sing x_agZk)) (SEndo (sY :: Sing y_agZl))
+    = (applySing ((singFun1 @EndoSym0) SEndo))
+        ((applySing ((applySing ((singFun3 @(.@#@$)) (%.))) sX)) sY)
+instance SMonoid (Endo a_agCn) where
+  sMempty :: Sing (MemptySym0 :: Endo a_agCn)
+  sMempty
+    = (applySing ((singFun1 @EndoSym0) SEndo)) ((singFun1 @IdSym0) sId)
+
+{-
+$(singletonsOnly [d|
+
+  class Foldable t where
+
+      foldMap :: Monoid m => (a -> m) -> t a -> m
+      foldr   :: (a -> b -> b) -> b -> t a -> b
+
+      foldr' :: (a -> b -> b) -> b -> t a -> b
+      foldr' f z0 xs = foldl f' id xs z0
+        where f' k x z = k $! f x z
+
+      foldl :: (b -> a -> b) -> b -> t a -> b
+      foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
+
+  |])
+-}
+
+type FoldMapSym0 :: forall a_ahBz
+                           m_ahBy
+                           t_ahBx. (~>) ((~>) a_ahBz m_ahBy) ((~>) (t_ahBx a_ahBz) m_ahBy)
+data FoldMapSym0 :: (~>) ((~>) a_ahBz m_ahBy) ((~>) (t_ahBx a_ahBz) m_ahBy)
+  where
+    FoldMapSym0KindInference :: SameKind (Apply FoldMapSym0 arg_ahBS) (FoldMapSym1 arg_ahBS) =>
+                                FoldMapSym0 a6989586621679077489
+type instance Apply FoldMapSym0 a6989586621679077489 = FoldMapSym1 a6989586621679077489
+type FoldMapSym1 :: forall a_ahBz m_ahBy t_ahBx. (~>) a_ahBz m_ahBy
+                                                 -> (~>) (t_ahBx a_ahBz) m_ahBy
+data FoldMapSym1 (a6989586621679077489 :: (~>) a_ahBz m_ahBy) :: (~>) (t_ahBx a_ahBz) m_ahBy
+  where
+    FoldMapSym1KindInference :: SameKind (Apply (FoldMapSym1 a6989586621679077489) arg_ahBS) (FoldMapSym2 a6989586621679077489 arg_ahBS) =>
+                                FoldMapSym1 a6989586621679077489 a6989586621679077490
+type instance Apply (FoldMapSym1 a6989586621679077489) a6989586621679077490 = FoldMap a6989586621679077489 a6989586621679077490
+type FoldMapSym2 :: forall a_ahBz m_ahBy t_ahBx. (~>) a_ahBz m_ahBy
+                                                 -> t_ahBx a_ahBz -> m_ahBy
+type family FoldMapSym2 (a6989586621679077489 :: (~>) a_ahBz m_ahBy) (a6989586621679077490 :: t_ahBx a_ahBz) :: m_ahBy where
+  FoldMapSym2 a6989586621679077489 a6989586621679077490 = FoldMap a6989586621679077489 a6989586621679077490
+type FoldrSym0 :: forall a_ahBA
+                         b_ahBB
+                         t_ahBx. (~>) ((~>) a_ahBA ((~>) b_ahBB b_ahBB)) ((~>) b_ahBB ((~>) (t_ahBx a_ahBA) b_ahBB))
+data FoldrSym0 :: (~>) ((~>) a_ahBA ((~>) b_ahBB b_ahBB)) ((~>) b_ahBB ((~>) (t_ahBx a_ahBA) b_ahBB))
+  where
+    FoldrSym0KindInference :: SameKind (Apply FoldrSym0 arg_ahBY) (FoldrSym1 arg_ahBY) =>
+                              FoldrSym0 a6989586621679077495
+type instance Apply FoldrSym0 a6989586621679077495 = FoldrSym1 a6989586621679077495
+type FoldrSym1 :: forall a_ahBA
+                         b_ahBB
+                         t_ahBx. (~>) a_ahBA ((~>) b_ahBB b_ahBB)
+                                 -> (~>) b_ahBB ((~>) (t_ahBx a_ahBA) b_ahBB)
+data FoldrSym1 (a6989586621679077495 :: (~>) a_ahBA ((~>) b_ahBB b_ahBB)) :: (~>) b_ahBB ((~>) (t_ahBx a_ahBA) b_ahBB)
+  where
+    FoldrSym1KindInference :: SameKind (Apply (FoldrSym1 a6989586621679077495) arg_ahBY) (FoldrSym2 a6989586621679077495 arg_ahBY) =>
+                              FoldrSym1 a6989586621679077495 a6989586621679077496
+type instance Apply (FoldrSym1 a6989586621679077495) a6989586621679077496 = FoldrSym2 a6989586621679077495 a6989586621679077496
+type FoldrSym2 :: forall a_ahBA
+                         b_ahBB
+                         t_ahBx. (~>) a_ahBA ((~>) b_ahBB b_ahBB)
+                                 -> b_ahBB -> (~>) (t_ahBx a_ahBA) b_ahBB
+data FoldrSym2 (a6989586621679077495 :: (~>) a_ahBA ((~>) b_ahBB b_ahBB)) (a6989586621679077496 :: b_ahBB) :: (~>) (t_ahBx a_ahBA) b_ahBB
+  where
+    FoldrSym2KindInference :: SameKind (Apply (FoldrSym2 a6989586621679077495 a6989586621679077496) arg_ahBY) (FoldrSym3 a6989586621679077495 a6989586621679077496 arg_ahBY) =>
+                              FoldrSym2 a6989586621679077495 a6989586621679077496 a6989586621679077497
+type instance Apply (FoldrSym2 a6989586621679077495 a6989586621679077496) a6989586621679077497 = Foldr a6989586621679077495 a6989586621679077496 a6989586621679077497
+type FoldrSym3 :: forall a_ahBA
+                         b_ahBB
+                         t_ahBx. (~>) a_ahBA ((~>) b_ahBB b_ahBB)
+                                 -> b_ahBB -> t_ahBx a_ahBA -> b_ahBB
+type family FoldrSym3 (a6989586621679077495 :: (~>) a_ahBA ((~>) b_ahBB b_ahBB)) (a6989586621679077496 :: b_ahBB) (a6989586621679077497 :: t_ahBx a_ahBA) :: b_ahBB where
+  FoldrSym3 a6989586621679077495 a6989586621679077496 a6989586621679077497 = Foldr a6989586621679077495 a6989586621679077496 a6989586621679077497
+type Foldr'Sym0 :: forall a_ahBC
+                          b_ahBD
+                          t_ahBx. (~>) ((~>) a_ahBC ((~>) b_ahBD b_ahBD)) ((~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD))
+data Foldr'Sym0 :: (~>) ((~>) a_ahBC ((~>) b_ahBD b_ahBD)) ((~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD))
+  where
+    Foldr'Sym0KindInference :: SameKind (Apply Foldr'Sym0 arg_ahC5) (Foldr'Sym1 arg_ahC5) =>
+                               Foldr'Sym0 a6989586621679077502
+type instance Apply Foldr'Sym0 a6989586621679077502 = Foldr'Sym1 a6989586621679077502
+type Foldr'Sym1 :: forall a_ahBC
+                          b_ahBD
+                          t_ahBx. (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                  -> (~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD)
+data Foldr'Sym1 (a6989586621679077502 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) :: (~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD)
+  where
+    Foldr'Sym1KindInference :: SameKind (Apply (Foldr'Sym1 a6989586621679077502) arg_ahC5) (Foldr'Sym2 a6989586621679077502 arg_ahC5) =>
+                               Foldr'Sym1 a6989586621679077502 a6989586621679077503
+type instance Apply (Foldr'Sym1 a6989586621679077502) a6989586621679077503 = Foldr'Sym2 a6989586621679077502 a6989586621679077503
+type Foldr'Sym2 :: forall a_ahBC
+                          b_ahBD
+                          t_ahBx. (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                  -> b_ahBD -> (~>) (t_ahBx a_ahBC) b_ahBD
+data Foldr'Sym2 (a6989586621679077502 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (a6989586621679077503 :: b_ahBD) :: (~>) (t_ahBx a_ahBC) b_ahBD
+  where
+    Foldr'Sym2KindInference :: SameKind (Apply (Foldr'Sym2 a6989586621679077502 a6989586621679077503) arg_ahC5) (Foldr'Sym3 a6989586621679077502 a6989586621679077503 arg_ahC5) =>
+                               Foldr'Sym2 a6989586621679077502 a6989586621679077503 a6989586621679077504
+type instance Apply (Foldr'Sym2 a6989586621679077502 a6989586621679077503) a6989586621679077504 = Foldr' a6989586621679077502 a6989586621679077503 a6989586621679077504
+type Foldr'Sym3 :: forall a_ahBC
+                          b_ahBD
+                          t_ahBx. (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                  -> b_ahBD -> t_ahBx a_ahBC -> b_ahBD
+type family Foldr'Sym3 (a6989586621679077502 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (a6989586621679077503 :: b_ahBD) (a6989586621679077504 :: t_ahBx a_ahBC) :: b_ahBD where
+  Foldr'Sym3 a6989586621679077502 a6989586621679077503 a6989586621679077504 = Foldr' a6989586621679077502 a6989586621679077503 a6989586621679077504
+type FoldlSym0 :: forall b_ahBE
+                         a_ahBF
+                         t_ahBx. (~>) ((~>) b_ahBE ((~>) a_ahBF b_ahBE)) ((~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE))
+data FoldlSym0 :: (~>) ((~>) b_ahBE ((~>) a_ahBF b_ahBE)) ((~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE))
+  where
+    FoldlSym0KindInference :: SameKind (Apply FoldlSym0 arg_ahCc) (FoldlSym1 arg_ahCc) =>
+                              FoldlSym0 a6989586621679077509
+type instance Apply FoldlSym0 a6989586621679077509 = FoldlSym1 a6989586621679077509
+type FoldlSym1 :: forall b_ahBE
+                         a_ahBF
+                         t_ahBx. (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                 -> (~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE)
+data FoldlSym1 (a6989586621679077509 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) :: (~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE)
+  where
+    FoldlSym1KindInference :: SameKind (Apply (FoldlSym1 a6989586621679077509) arg_ahCc) (FoldlSym2 a6989586621679077509 arg_ahCc) =>
+                              FoldlSym1 a6989586621679077509 a6989586621679077510
+type instance Apply (FoldlSym1 a6989586621679077509) a6989586621679077510 = FoldlSym2 a6989586621679077509 a6989586621679077510
+type FoldlSym2 :: forall b_ahBE
+                         a_ahBF
+                         t_ahBx. (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                 -> b_ahBE -> (~>) (t_ahBx a_ahBF) b_ahBE
+data FoldlSym2 (a6989586621679077509 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (a6989586621679077510 :: b_ahBE) :: (~>) (t_ahBx a_ahBF) b_ahBE
+  where
+    FoldlSym2KindInference :: SameKind (Apply (FoldlSym2 a6989586621679077509 a6989586621679077510) arg_ahCc) (FoldlSym3 a6989586621679077509 a6989586621679077510 arg_ahCc) =>
+                              FoldlSym2 a6989586621679077509 a6989586621679077510 a6989586621679077511
+type instance Apply (FoldlSym2 a6989586621679077509 a6989586621679077510) a6989586621679077511 = Foldl a6989586621679077509 a6989586621679077510 a6989586621679077511
+type FoldlSym3 :: forall b_ahBE
+                         a_ahBF
+                         t_ahBx. (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                 -> b_ahBE -> t_ahBx a_ahBF -> b_ahBE
+type family FoldlSym3 (a6989586621679077509 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (a6989586621679077510 :: b_ahBE) (a6989586621679077511 :: t_ahBx a_ahBF) :: b_ahBE where
+  FoldlSym3 a6989586621679077509 a6989586621679077510 a6989586621679077511 = Foldl a6989586621679077509 a6989586621679077510 a6989586621679077511
+data Let6989586621679077527F'Sym0 f6989586621679077524
+  where
+    Let6989586621679077527F'Sym0KindInference :: SameKind (Apply Let6989586621679077527F'Sym0 arg_ahCz) (Let6989586621679077527F'Sym1 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym0 f6989586621679077524
+type instance Apply Let6989586621679077527F'Sym0 f6989586621679077524 = Let6989586621679077527F'Sym1 f6989586621679077524
+data Let6989586621679077527F'Sym1 f6989586621679077524 z06989586621679077525
+  where
+    Let6989586621679077527F'Sym1KindInference :: SameKind (Apply (Let6989586621679077527F'Sym1 f6989586621679077524) arg_ahCz) (Let6989586621679077527F'Sym2 f6989586621679077524 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym1 f6989586621679077524 z06989586621679077525
+type instance Apply (Let6989586621679077527F'Sym1 f6989586621679077524) z06989586621679077525 = Let6989586621679077527F'Sym2 f6989586621679077524 z06989586621679077525
+data Let6989586621679077527F'Sym2 f6989586621679077524 z06989586621679077525 xs6989586621679077526
+  where
+    Let6989586621679077527F'Sym2KindInference :: SameKind (Apply (Let6989586621679077527F'Sym2 f6989586621679077524 z06989586621679077525) arg_ahCz) (Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym2 f6989586621679077524 z06989586621679077525 xs6989586621679077526
+type instance Apply (Let6989586621679077527F'Sym2 f6989586621679077524 z06989586621679077525) xs6989586621679077526 = Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 xs6989586621679077526
+data Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528
+  where
+    Let6989586621679077527F'Sym3KindInference :: SameKind (Apply (Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 xs6989586621679077526) arg_ahCz) (Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528
+type instance Apply (Let6989586621679077527F'Sym3 f6989586621679077524 z06989586621679077525 xs6989586621679077526) a6989586621679077528 = Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528
+data Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529
+  where
+    Let6989586621679077527F'Sym4KindInference :: SameKind (Apply (Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528) arg_ahCz) (Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529
+type instance Apply (Let6989586621679077527F'Sym4 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528) a6989586621679077529 = Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529
+data Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530
+  where
+    Let6989586621679077527F'Sym5KindInference :: SameKind (Apply (Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529) arg_ahCz) (Let6989586621679077527F'Sym6 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 arg_ahCz) =>
+                                                 Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530
+type instance Apply (Let6989586621679077527F'Sym5 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529) a6989586621679077530 = Let6989586621679077527F' f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530
+type family Let6989586621679077527F'Sym6 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530 where
+  Let6989586621679077527F'Sym6 f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530 = Let6989586621679077527F' f6989586621679077524 z06989586621679077525 xs6989586621679077526 a6989586621679077528 a6989586621679077529 a6989586621679077530
+type family Let6989586621679077527F' f_ahCs z0_ahCt xs_ahCu a_ahCw a_ahCx a_ahCy where
+  Let6989586621679077527F' f_ahCs z0_ahCt xs_ahCu k_ahCA x_ahCB z_ahCC = Apply (Apply ($!@#@$) k_ahCA) (Apply (Apply f_ahCs x_ahCB) z_ahCC)
+type Foldr'_6989586621679077515 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                   -> b_ahBD -> t_ahBx a_ahBC -> b_ahBD
+type family Foldr'_6989586621679077515 (a_ahCl :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (a_ahCm :: b_ahBD) (a_ahCn :: t_ahBx a_ahBC) :: b_ahBD where
+  Foldr'_6989586621679077515 f_ahCs z0_ahCt xs_ahCu = Apply (Apply (Apply (Apply FoldlSym0 (Let6989586621679077527F'Sym3 f_ahCs z0_ahCt xs_ahCu)) IdSym0) xs_ahCu) z0_ahCt
+type Foldr'_6989586621679077515Sym0 :: (~>) ((~>) a_ahBC ((~>) b_ahBD b_ahBD)) ((~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD))
+data Foldr'_6989586621679077515Sym0 :: (~>) ((~>) a_ahBC ((~>) b_ahBD b_ahBD)) ((~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD))
+  where
+    Foldr'_6989586621679077515Sym0KindInference :: SameKind (Apply Foldr'_6989586621679077515Sym0 arg_ahCo) (Foldr'_6989586621679077515Sym1 arg_ahCo) =>
+                                                   Foldr'_6989586621679077515Sym0 a6989586621679077521
+type instance Apply Foldr'_6989586621679077515Sym0 a6989586621679077521 = Foldr'_6989586621679077515Sym1 a6989586621679077521
+type Foldr'_6989586621679077515Sym1 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                       -> (~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD)
+data Foldr'_6989586621679077515Sym1 (a6989586621679077521 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) :: (~>) b_ahBD ((~>) (t_ahBx a_ahBC) b_ahBD)
+  where
+    Foldr'_6989586621679077515Sym1KindInference :: SameKind (Apply (Foldr'_6989586621679077515Sym1 a6989586621679077521) arg_ahCo) (Foldr'_6989586621679077515Sym2 a6989586621679077521 arg_ahCo) =>
+                                                   Foldr'_6989586621679077515Sym1 a6989586621679077521 a6989586621679077522
+type instance Apply (Foldr'_6989586621679077515Sym1 a6989586621679077521) a6989586621679077522 = Foldr'_6989586621679077515Sym2 a6989586621679077521 a6989586621679077522
+type Foldr'_6989586621679077515Sym2 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                       -> b_ahBD -> (~>) (t_ahBx a_ahBC) b_ahBD
+data Foldr'_6989586621679077515Sym2 (a6989586621679077521 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (a6989586621679077522 :: b_ahBD) :: (~>) (t_ahBx a_ahBC) b_ahBD
+  where
+    Foldr'_6989586621679077515Sym2KindInference :: SameKind (Apply (Foldr'_6989586621679077515Sym2 a6989586621679077521 a6989586621679077522) arg_ahCo) (Foldr'_6989586621679077515Sym3 a6989586621679077521 a6989586621679077522 arg_ahCo) =>
+                                                   Foldr'_6989586621679077515Sym2 a6989586621679077521 a6989586621679077522 a6989586621679077523
+type instance Apply (Foldr'_6989586621679077515Sym2 a6989586621679077521 a6989586621679077522) a6989586621679077523 = Foldr'_6989586621679077515 a6989586621679077521 a6989586621679077522 a6989586621679077523
+type Foldr'_6989586621679077515Sym3 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)
+                                       -> b_ahBD -> t_ahBx a_ahBC -> b_ahBD
+type family Foldr'_6989586621679077515Sym3 (a6989586621679077521 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (a6989586621679077522 :: b_ahBD) (a6989586621679077523 :: t_ahBx a_ahBC) :: b_ahBD where
+  Foldr'_6989586621679077515Sym3 a6989586621679077521 a6989586621679077522 a6989586621679077523 = Foldr'_6989586621679077515 a6989586621679077521 a6989586621679077522 a6989586621679077523
+type Foldl_6989586621679077538 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                  -> b_ahBE -> t_ahBx a_ahBF -> b_ahBE
+type family Foldl_6989586621679077538 (a_ahCI :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (a_ahCJ :: b_ahBE) (a_ahCK :: t_ahBx a_ahBF) :: b_ahBE where
+  Foldl_6989586621679077538 f_ahCP z_ahCQ t_ahCR = Apply (Apply AppEndoSym0 (Apply GetDualSym0 (Apply (Apply FoldMapSym0 (Apply (Apply (.@#@$) DualSym0) (Apply (Apply (.@#@$) EndoSym0) (Apply FlipSym0 f_ahCP)))) t_ahCR))) z_ahCQ
+type Foldl_6989586621679077538Sym0 :: (~>) ((~>) b_ahBE ((~>) a_ahBF b_ahBE)) ((~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE))
+data Foldl_6989586621679077538Sym0 :: (~>) ((~>) b_ahBE ((~>) a_ahBF b_ahBE)) ((~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE))
+  where
+    Foldl_6989586621679077538Sym0KindInference :: SameKind (Apply Foldl_6989586621679077538Sym0 arg_ahCL) (Foldl_6989586621679077538Sym1 arg_ahCL) =>
+                                                  Foldl_6989586621679077538Sym0 a6989586621679077544
+type instance Apply Foldl_6989586621679077538Sym0 a6989586621679077544 = Foldl_6989586621679077538Sym1 a6989586621679077544
+type Foldl_6989586621679077538Sym1 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                      -> (~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE)
+data Foldl_6989586621679077538Sym1 (a6989586621679077544 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) :: (~>) b_ahBE ((~>) (t_ahBx a_ahBF) b_ahBE)
+  where
+    Foldl_6989586621679077538Sym1KindInference :: SameKind (Apply (Foldl_6989586621679077538Sym1 a6989586621679077544) arg_ahCL) (Foldl_6989586621679077538Sym2 a6989586621679077544 arg_ahCL) =>
+                                                  Foldl_6989586621679077538Sym1 a6989586621679077544 a6989586621679077545
+type instance Apply (Foldl_6989586621679077538Sym1 a6989586621679077544) a6989586621679077545 = Foldl_6989586621679077538Sym2 a6989586621679077544 a6989586621679077545
+type Foldl_6989586621679077538Sym2 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                      -> b_ahBE -> (~>) (t_ahBx a_ahBF) b_ahBE
+data Foldl_6989586621679077538Sym2 (a6989586621679077544 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (a6989586621679077545 :: b_ahBE) :: (~>) (t_ahBx a_ahBF) b_ahBE
+  where
+    Foldl_6989586621679077538Sym2KindInference :: SameKind (Apply (Foldl_6989586621679077538Sym2 a6989586621679077544 a6989586621679077545) arg_ahCL) (Foldl_6989586621679077538Sym3 a6989586621679077544 a6989586621679077545 arg_ahCL) =>
+                                                  Foldl_6989586621679077538Sym2 a6989586621679077544 a6989586621679077545 a6989586621679077546
+type instance Apply (Foldl_6989586621679077538Sym2 a6989586621679077544 a6989586621679077545) a6989586621679077546 = Foldl_6989586621679077538 a6989586621679077544 a6989586621679077545 a6989586621679077546
+type Foldl_6989586621679077538Sym3 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)
+                                      -> b_ahBE -> t_ahBx a_ahBF -> b_ahBE
+type family Foldl_6989586621679077538Sym3 (a6989586621679077544 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (a6989586621679077545 :: b_ahBE) (a6989586621679077546 :: t_ahBx a_ahBF) :: b_ahBE where
+  Foldl_6989586621679077538Sym3 a6989586621679077544 a6989586621679077545 a6989586621679077546 = Foldl_6989586621679077538 a6989586621679077544 a6989586621679077545 a6989586621679077546
+class PFoldable t_ahBx where
+  type family FoldMap (arg_ahBQ :: (~>) a_ahBz m_ahBy) (arg_ahBR :: t_ahBx a_ahBz) :: m_ahBy
+  type family Foldr (arg_ahBV :: (~>) a_ahBA ((~>) b_ahBB b_ahBB)) (arg_ahBW :: b_ahBB) (arg_ahBX :: t_ahBx a_ahBA) :: b_ahBB
+  type family Foldr' (arg_ahC2 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD)) (arg_ahC3 :: b_ahBD) (arg_ahC4 :: t_ahBx a_ahBC) :: b_ahBD
+  type family Foldl (arg_ahC9 :: (~>) b_ahBE ((~>) a_ahBF b_ahBE)) (arg_ahCa :: b_ahBE) (arg_ahCb :: t_ahBx a_ahBF) :: b_ahBE
+  type Foldr' a_ahCg a_ahCh a_ahCi = Apply (Apply (Apply Foldr'_6989586621679077515Sym0 a_ahCg) a_ahCh) a_ahCi
+  type Foldl a_ahCD a_ahCE a_ahCF = Apply (Apply (Apply Foldl_6989586621679077538Sym0 a_ahCD) a_ahCE) a_ahCF
+class SFoldable t_ahBx where
+  sFoldMap ::
+    forall a_ahBz
+           m_ahBy
+           (t_ahCS :: (~>) a_ahBz m_ahBy)
+           (t_ahCT :: t_ahBx a_ahBz). SMonoid m_ahBy =>
+                                      Sing t_ahCS
+                                      -> Sing t_ahCT
+                                         -> Sing (Apply (Apply FoldMapSym0 t_ahCS) t_ahCT :: m_ahBy)
+  sFoldr ::
+    forall a_ahBA
+           b_ahBB
+           (t_ahCX :: (~>) a_ahBA ((~>) b_ahBB b_ahBB))
+           (t_ahCY :: b_ahBB)
+           (t_ahCZ :: t_ahBx a_ahBA). Sing t_ahCX
+                                      -> Sing t_ahCY
+                                         -> Sing t_ahCZ
+                                            -> Sing (Apply (Apply (Apply FoldrSym0 t_ahCX) t_ahCY) t_ahCZ :: b_ahBB)
+  sFoldr' ::
+    forall a_ahBC
+           b_ahBD
+           (t_ahD7 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD))
+           (t_ahD8 :: b_ahBD)
+           (t_ahD9 :: t_ahBx a_ahBC). Sing t_ahD7
+                                      -> Sing t_ahD8
+                                         -> Sing t_ahD9
+                                            -> Sing (Apply (Apply (Apply Foldr'Sym0 t_ahD7) t_ahD8) t_ahD9 :: b_ahBD)
+  sFoldl ::
+    forall b_ahBE
+           a_ahBF
+           (t_ahDh :: (~>) b_ahBE ((~>) a_ahBF b_ahBE))
+           (t_ahDi :: b_ahBE)
+           (t_ahDj :: t_ahBx a_ahBF). Sing t_ahDh
+                                      -> Sing t_ahDi
+                                         -> Sing t_ahDj
+                                            -> Sing (Apply (Apply (Apply FoldlSym0 t_ahDh) t_ahDi) t_ahDj :: b_ahBE)
+  default sFoldr' ::
+            forall a_ahBC
+                   b_ahBD
+                   (t_ahD7 :: (~>) a_ahBC ((~>) b_ahBD b_ahBD))
+                   (t_ahD8 :: b_ahBD)
+                   (t_ahD9 :: t_ahBx a_ahBC). ((Apply (Apply (Apply Foldr'Sym0 t_ahD7) t_ahD8) t_ahD9 :: b_ahBD)
+                                               ~
+                                               Apply (Apply (Apply Foldr'_6989586621679077515Sym0 t_ahD7) t_ahD8) t_ahD9) =>
+                                              Sing t_ahD7
+                                              -> Sing t_ahD8
+                                                 -> Sing t_ahD9
+                                                    -> Sing (Apply (Apply (Apply Foldr'Sym0 t_ahD7) t_ahD8) t_ahD9 :: b_ahBD)
+  default sFoldl ::
+            forall b_ahBE
+                   a_ahBF
+                   (t_ahDh :: (~>) b_ahBE ((~>) a_ahBF b_ahBE))
+                   (t_ahDi :: b_ahBE)
+                   (t_ahDj :: t_ahBx a_ahBF). ((Apply (Apply (Apply FoldlSym0 t_ahDh) t_ahDi) t_ahDj :: b_ahBE)
+                                               ~
+                                               Apply (Apply (Apply Foldl_6989586621679077538Sym0 t_ahDh) t_ahDi) t_ahDj) =>
+                                              Sing t_ahDh
+                                              -> Sing t_ahDi
+                                                 -> Sing t_ahDj
+                                                    -> Sing (Apply (Apply (Apply FoldlSym0 t_ahDh) t_ahDi) t_ahDj :: b_ahBE)
+  sFoldr'
+    (sF :: Sing f_ahCs)
+    (sZ0 :: Sing z0_ahCt)
+    (sXs :: Sing xs_ahCu)
+    = let
+        sF' ::
+          forall arg_ahDr arg_ahDs arg_ahDt. Sing arg_ahDr
+                                             -> Sing arg_ahDs
+                                                -> Sing arg_ahDt
+                                                   -> Sing (Apply (Apply (Apply (Let6989586621679077527F'Sym3 f_ahCs z0_ahCt xs_ahCu) arg_ahDr) arg_ahDs) arg_ahDt)
+        sF' (sK :: Sing k_ahCA) (sX :: Sing x_ahCB) (sZ :: Sing z_ahCC)
+          = (applySing ((applySing ((singFun2 @($!@#@$)) (%$!))) sK))
+              ((applySing ((applySing sF) sX)) sZ)
+      in
+        (applySing
+           ((applySing
+               ((applySing
+                   ((applySing ((singFun3 @FoldlSym0) sFoldl))
+                      ((singFun3
+                          @(Let6989586621679077527F'Sym3 f_ahCs z0_ahCt xs_ahCu))
+                         sF')))
+                  ((singFun1 @IdSym0) sId)))
+              sXs))
+          sZ0
+  sFoldl (sF :: Sing f_ahCP) (sZ :: Sing z_ahCQ) (sT :: Sing t_ahCR)
+    = (applySing
+         ((applySing ((singFun2 @AppEndoSym0) sAppEndo))
+            ((applySing ((singFun1 @GetDualSym0) sGetDual))
+               ((applySing
+                   ((applySing ((singFun2 @FoldMapSym0) sFoldMap))
+                      ((applySing
+                          ((applySing ((singFun3 @(.@#@$)) (%.)))
+                             ((singFun1 @DualSym0) SDual)))
+                         ((applySing
+                             ((applySing ((singFun3 @(.@#@$)) (%.)))
+                                ((singFun1 @EndoSym0) SEndo)))
+                            ((applySing ((singFun3 @FlipSym0) sFlip)) sF)))))
+                  sT))))
+        sZ
+
+{-
+$(singletonsOnly [d|
+  deriving instance Foldable (Tuple2 a)
+  |])
+-}
+
+type family Lambda_6989586621679081147_aiyU _f_6989586621679081117_aiyQ a_6989586621679081123_aiyR a_6989586621679081125_aiyS n_6989586621679081121_aiyV where
+  Lambda_6989586621679081147_aiyU _f_6989586621679081117_aiyQ a_6989586621679081123_aiyR a_6989586621679081125_aiyS n_6989586621679081121_aiyV = MemptySym0
+data Lambda_6989586621679081147Sym0 _f_69895866216790811176989586621679081144
+  where
+    Lambda_6989586621679081147Sym0KindInference :: SameKind (Apply Lambda_6989586621679081147Sym0 arg_aiyW) (Lambda_6989586621679081147Sym1 arg_aiyW) =>
+                                                   Lambda_6989586621679081147Sym0 _f_69895866216790811176989586621679081144
+type instance Apply Lambda_6989586621679081147Sym0 _f_69895866216790811176989586621679081144 = Lambda_6989586621679081147Sym1 _f_69895866216790811176989586621679081144
+data Lambda_6989586621679081147Sym1 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145
+  where
+    Lambda_6989586621679081147Sym1KindInference :: SameKind (Apply (Lambda_6989586621679081147Sym1 _f_69895866216790811176989586621679081144) arg_aiyW) (Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 arg_aiyW) =>
+                                                   Lambda_6989586621679081147Sym1 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145
+type instance Apply (Lambda_6989586621679081147Sym1 _f_69895866216790811176989586621679081144) a_69895866216790811236989586621679081145 = Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145
+data Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146
+  where
+    Lambda_6989586621679081147Sym2KindInference :: SameKind (Apply (Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145) arg_aiyW) (Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 arg_aiyW) =>
+                                                   Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146
+type instance Apply (Lambda_6989586621679081147Sym2 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145) a_69895866216790811256989586621679081146 = Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146
+data Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149
+  where
+    Lambda_6989586621679081147Sym3KindInference :: SameKind (Apply (Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146) arg_aiyW) (Lambda_6989586621679081147Sym4 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 arg_aiyW) =>
+                                                   Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149
+type instance Apply (Lambda_6989586621679081147Sym3 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146) n_69895866216790811216989586621679081149 = Lambda_6989586621679081147_aiyU _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149
+type family Lambda_6989586621679081147Sym4 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149 where
+  Lambda_6989586621679081147Sym4 _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149 = Lambda_6989586621679081147_aiyU _f_69895866216790811176989586621679081144 a_69895866216790811236989586621679081145 a_69895866216790811256989586621679081146 n_69895866216790811216989586621679081149
+type FoldMap_6989586621679081137 :: (~>) a_ahBz_acmX m_ahBy_acmY
+                                    -> Tuple2 a_aikY a_ahBz_acmX -> m_ahBy_acmY
+type family FoldMap_6989586621679081137 (a_aiyL :: (~>) a_ahBz_acmX m_ahBy_acmY) (a_aiyM :: Tuple2 a_aikY a_ahBz_acmX) :: m_ahBy_acmY where
+  FoldMap_6989586621679081137 _f_6989586621679081117_aiyQ ('Tuple2 a_6989586621679081123_aiyR a_6989586621679081125_aiyS) = Apply (Apply MappendSym0 (Apply (Apply (Apply (Apply Lambda_6989586621679081147Sym0 _f_6989586621679081117_aiyQ) a_6989586621679081123_aiyR) a_6989586621679081125_aiyS) a_6989586621679081123_aiyR)) (Apply _f_6989586621679081117_aiyQ a_6989586621679081125_aiyS)
+type FoldMap_6989586621679081137Sym0 :: (~>) ((~>) a_ahBz_acmX m_ahBy_acmY) ((~>) (Tuple2 a_aikY a_ahBz_acmX) m_ahBy_acmY)
+data FoldMap_6989586621679081137Sym0 :: (~>) ((~>) a_ahBz_acmX m_ahBy_acmY) ((~>) (Tuple2 a_aikY a_ahBz_acmX) m_ahBy_acmY)
+  where
+    FoldMap_6989586621679081137Sym0KindInference :: SameKind (Apply FoldMap_6989586621679081137Sym0 arg_aiyN) (FoldMap_6989586621679081137Sym1 arg_aiyN) =>
+                                                    FoldMap_6989586621679081137Sym0 a6989586621679081142
+type instance Apply FoldMap_6989586621679081137Sym0 a6989586621679081142 = FoldMap_6989586621679081137Sym1 a6989586621679081142
+type FoldMap_6989586621679081137Sym1 :: (~>) a_ahBz_acmX m_ahBy_acmY
+                                        -> (~>) (Tuple2 a_aikY a_ahBz_acmX) m_ahBy_acmY
+data FoldMap_6989586621679081137Sym1 (a6989586621679081142 :: (~>) a_ahBz_acmX m_ahBy_acmY) :: (~>) (Tuple2 a_aikY a_ahBz_acmX) m_ahBy_acmY
+  where
+    FoldMap_6989586621679081137Sym1KindInference :: SameKind (Apply (FoldMap_6989586621679081137Sym1 a6989586621679081142) arg_aiyN) (FoldMap_6989586621679081137Sym2 a6989586621679081142 arg_aiyN) =>
+                                                    FoldMap_6989586621679081137Sym1 a6989586621679081142 a6989586621679081143
+type instance Apply (FoldMap_6989586621679081137Sym1 a6989586621679081142) a6989586621679081143 = FoldMap_6989586621679081137 a6989586621679081142 a6989586621679081143
+type FoldMap_6989586621679081137Sym2 :: (~>) a_ahBz_acmX m_ahBy_acmY
+                                        -> Tuple2 a_aikY a_ahBz_acmX -> m_ahBy_acmY
+type family FoldMap_6989586621679081137Sym2 (a6989586621679081142 :: (~>) a_ahBz_acmX m_ahBy_acmY) (a6989586621679081143 :: Tuple2 a_aikY a_ahBz_acmX) :: m_ahBy_acmY where
+  FoldMap_6989586621679081137Sym2 a6989586621679081142 a6989586621679081143 = FoldMap_6989586621679081137 a6989586621679081142 a6989586621679081143
+type family Lambda_6989586621679081167_aize _f_6989586621679081117_aiz9 _z_6989586621679081119_aiza a_6989586621679081131_aizb a_6989586621679081133_aizc n1_6989586621679081127_aizf n2_6989586621679081129_aizg where
+  Lambda_6989586621679081167_aize _f_6989586621679081117_aiz9 _z_6989586621679081119_aiza a_6989586621679081131_aizb a_6989586621679081133_aizc n1_6989586621679081127_aizf n2_6989586621679081129_aizg = n2_6989586621679081129_aizg
+data Lambda_6989586621679081167Sym0 _f_69895866216790811176989586621679081163
+  where
+    Lambda_6989586621679081167Sym0KindInference :: SameKind (Apply Lambda_6989586621679081167Sym0 arg_aizh) (Lambda_6989586621679081167Sym1 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym0 _f_69895866216790811176989586621679081163
+type instance Apply Lambda_6989586621679081167Sym0 _f_69895866216790811176989586621679081163 = Lambda_6989586621679081167Sym1 _f_69895866216790811176989586621679081163
+data Lambda_6989586621679081167Sym1 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164
+  where
+    Lambda_6989586621679081167Sym1KindInference :: SameKind (Apply (Lambda_6989586621679081167Sym1 _f_69895866216790811176989586621679081163) arg_aizh) (Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym1 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164
+type instance Apply (Lambda_6989586621679081167Sym1 _f_69895866216790811176989586621679081163) _z_69895866216790811196989586621679081164 = Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164
+data Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165
+  where
+    Lambda_6989586621679081167Sym2KindInference :: SameKind (Apply (Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164) arg_aizh) (Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165
+type instance Apply (Lambda_6989586621679081167Sym2 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164) a_69895866216790811316989586621679081165 = Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165
+data Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166
+  where
+    Lambda_6989586621679081167Sym3KindInference :: SameKind (Apply (Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165) arg_aizh) (Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166
+type instance Apply (Lambda_6989586621679081167Sym3 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165) a_69895866216790811336989586621679081166 = Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166
+data Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169
+  where
+    Lambda_6989586621679081167Sym4KindInference :: SameKind (Apply (Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166) arg_aizh) (Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169
+type instance Apply (Lambda_6989586621679081167Sym4 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166) n1_69895866216790811276989586621679081169 = Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169
+data Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170
+  where
+    Lambda_6989586621679081167Sym5KindInference :: SameKind (Apply (Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169) arg_aizh) (Lambda_6989586621679081167Sym6 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 arg_aizh) =>
+                                                   Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170
+type instance Apply (Lambda_6989586621679081167Sym5 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169) n2_69895866216790811296989586621679081170 = Lambda_6989586621679081167_aize _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170
+type family Lambda_6989586621679081167Sym6 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170 where
+  Lambda_6989586621679081167Sym6 _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170 = Lambda_6989586621679081167_aize _f_69895866216790811176989586621679081163 _z_69895866216790811196989586621679081164 a_69895866216790811316989586621679081165 a_69895866216790811336989586621679081166 n1_69895866216790811276989586621679081169 n2_69895866216790811296989586621679081170
+type Foldr_6989586621679081154 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)
+                                  -> b_ahBB_acn2 -> Tuple2 a_aikY a_ahBA_acn1 -> b_ahBB_acn2
+type family Foldr_6989586621679081154 (a_aiz2 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) (a_aiz3 :: b_ahBB_acn2) (a_aiz4 :: Tuple2 a_aikY a_ahBA_acn1) :: b_ahBB_acn2 where
+  Foldr_6989586621679081154 _f_6989586621679081117_aiz9 _z_6989586621679081119_aiza ('Tuple2 a_6989586621679081131_aizb a_6989586621679081133_aizc) = Apply (Apply (Apply (Apply (Apply (Apply Lambda_6989586621679081167Sym0 _f_6989586621679081117_aiz9) _z_6989586621679081119_aiza) a_6989586621679081131_aizb) a_6989586621679081133_aizc) a_6989586621679081131_aizb) (Apply (Apply _f_6989586621679081117_aiz9 a_6989586621679081133_aizc) _z_6989586621679081119_aiza)
+type Foldr_6989586621679081154Sym0 :: (~>) ((~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) ((~>) b_ahBB_acn2 ((~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2))
+data Foldr_6989586621679081154Sym0 :: (~>) ((~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) ((~>) b_ahBB_acn2 ((~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2))
+  where
+    Foldr_6989586621679081154Sym0KindInference :: SameKind (Apply Foldr_6989586621679081154Sym0 arg_aiz5) (Foldr_6989586621679081154Sym1 arg_aiz5) =>
+                                                  Foldr_6989586621679081154Sym0 a6989586621679081160
+type instance Apply Foldr_6989586621679081154Sym0 a6989586621679081160 = Foldr_6989586621679081154Sym1 a6989586621679081160
+type Foldr_6989586621679081154Sym1 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)
+                                      -> (~>) b_ahBB_acn2 ((~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2)
+data Foldr_6989586621679081154Sym1 (a6989586621679081160 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) :: (~>) b_ahBB_acn2 ((~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2)
+  where
+    Foldr_6989586621679081154Sym1KindInference :: SameKind (Apply (Foldr_6989586621679081154Sym1 a6989586621679081160) arg_aiz5) (Foldr_6989586621679081154Sym2 a6989586621679081160 arg_aiz5) =>
+                                                  Foldr_6989586621679081154Sym1 a6989586621679081160 a6989586621679081161
+type instance Apply (Foldr_6989586621679081154Sym1 a6989586621679081160) a6989586621679081161 = Foldr_6989586621679081154Sym2 a6989586621679081160 a6989586621679081161
+type Foldr_6989586621679081154Sym2 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)
+                                      -> b_ahBB_acn2
+                                         -> (~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2
+data Foldr_6989586621679081154Sym2 (a6989586621679081160 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) (a6989586621679081161 :: b_ahBB_acn2) :: (~>) (Tuple2 a_aikY a_ahBA_acn1) b_ahBB_acn2
+  where
+    Foldr_6989586621679081154Sym2KindInference :: SameKind (Apply (Foldr_6989586621679081154Sym2 a6989586621679081160 a6989586621679081161) arg_aiz5) (Foldr_6989586621679081154Sym3 a6989586621679081160 a6989586621679081161 arg_aiz5) =>
+                                                  Foldr_6989586621679081154Sym2 a6989586621679081160 a6989586621679081161 a6989586621679081162
+type instance Apply (Foldr_6989586621679081154Sym2 a6989586621679081160 a6989586621679081161) a6989586621679081162 = Foldr_6989586621679081154 a6989586621679081160 a6989586621679081161 a6989586621679081162
+type Foldr_6989586621679081154Sym3 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)
+                                      -> b_ahBB_acn2 -> Tuple2 a_aikY a_ahBA_acn1 -> b_ahBB_acn2
+type family Foldr_6989586621679081154Sym3 (a6989586621679081160 :: (~>) a_ahBA_acn1 ((~>) b_ahBB_acn2 b_ahBB_acn2)) (a6989586621679081161 :: b_ahBB_acn2) (a6989586621679081162 :: Tuple2 a_aikY a_ahBA_acn1) :: b_ahBB_acn2 where
+  Foldr_6989586621679081154Sym3 a6989586621679081160 a6989586621679081161 a6989586621679081162 = Foldr_6989586621679081154 a6989586621679081160 a6989586621679081161 a6989586621679081162
+instance PFoldable (Tuple2 a_aikY) where
+  type FoldMap a_aiyH a_aiyI = Apply (Apply FoldMap_6989586621679081137Sym0 a_aiyH) a_aiyI
+  type Foldr a_aiyX a_aiyY a_aiyZ = Apply (Apply (Apply Foldr_6989586621679081154Sym0 a_aiyX) a_aiyY) a_aiyZ
+instance SFoldable (Tuple2 a_aikY) where
+  sFoldMap ::
+    forall (a_ahBz_acm7 :: Type)
+           (m_ahBy_acm8 :: Type)
+           (t_ahCS_acm9 :: (~>) a_ahBz_acm7 m_ahBy_acm8)
+           (t_ahCT_acma :: Tuple2 a_aikY a_ahBz_acm7). SMonoid m_ahBy_acm8 =>
+                                                       Sing t_ahCS_acm9
+                                                       -> Sing t_ahCT_acma
+                                                          -> Sing (Apply (Apply (FoldMapSym0 :: TyFun ((~>) a_ahBz_acm7 m_ahBy_acm8) ((~>) (Tuple2 a_aikY a_ahBz_acm7) m_ahBy_acm8)
+                                                                                                -> Type) t_ahCS_acm9) t_ahCT_acma)
+  sFoldr ::
+    forall (a_ahBA_acmb :: Type)
+           (b_ahBB_acmc :: Type)
+           (t_ahCX_acmd :: (~>) a_ahBA_acmb ((~>) b_ahBB_acmc b_ahBB_acmc))
+           (t_ahCY_acme :: b_ahBB_acmc)
+           (t_ahCZ_acmf :: Tuple2 a_aikY a_ahBA_acmb). Sing t_ahCX_acmd
+                                                       -> Sing t_ahCY_acme
+                                                          -> Sing t_ahCZ_acmf
+                                                             -> Sing (Apply (Apply (Apply (FoldrSym0 :: TyFun ((~>) a_ahBA_acmb ((~>) b_ahBB_acmc b_ahBB_acmc)) ((~>) b_ahBB_acmc ((~>) (Tuple2 a_aikY a_ahBA_acmb) b_ahBB_acmc))
+                                                                                                        -> Type) t_ahCX_acmd) t_ahCY_acme) t_ahCZ_acmf)
+  sFoldMap
+    (_sf_6989586621679081117 :: Sing _f_6989586621679081117_aiyQ)
+    (STuple2 (sA_6989586621679081123 :: Sing a_6989586621679081123_aiyR)
+             (sA_6989586621679081125 :: Sing a_6989586621679081125_aiyS))
+    = (applySing
+         ((applySing ((singFun2 @MappendSym0) sMappend))
+            ((applySing
+                ((singFun1
+                    @(Apply (Apply (Apply Lambda_6989586621679081147Sym0 _f_6989586621679081117_aiyQ) a_6989586621679081123_aiyR) a_6989586621679081125_aiyS))
+                   (\ sN_6989586621679081121
+                      -> case sN_6989586621679081121 of
+                           (_ :: Sing n_6989586621679081121_aiyV) -> sMempty)))
+               sA_6989586621679081123)))
+        ((applySing _sf_6989586621679081117) sA_6989586621679081125)
+  sFoldr
+    (_sf_6989586621679081117 :: Sing _f_6989586621679081117_aiz9)
+    (_sz_6989586621679081119 :: Sing _z_6989586621679081119_aiza)
+    (STuple2 (sA_6989586621679081131 :: Sing a_6989586621679081131_aizb)
+             (sA_6989586621679081133 :: Sing a_6989586621679081133_aizc))
+    = (applySing
+         ((applySing
+             ((singFun2
+                 @(Apply (Apply (Apply (Apply Lambda_6989586621679081167Sym0 _f_6989586621679081117_aiz9) _z_6989586621679081119_aiza) a_6989586621679081131_aizb) a_6989586621679081133_aizc))
+                (\ sN1_6989586621679081127 sN2_6989586621679081129
+                   -> case ((,) sN1_6989586621679081127) sN2_6989586621679081129 of
+                        (,) (_ :: Sing n1_6989586621679081127_aizf)
+                            (_ :: Sing n2_6989586621679081129_aizg)
+                          -> sN2_6989586621679081129)))
+            sA_6989586621679081131))
+        ((applySing
+            ((applySing _sf_6989586621679081117) sA_6989586621679081133))
+           _sz_6989586621679081119)
diff --git a/testsuite/tests/perf/compiler/all.T b/testsuite/tests/perf/compiler/all.T
index d7222696dd..e424639e7a 100644
--- a/testsuite/tests/perf/compiler/all.T
+++ b/testsuite/tests/perf/compiler/all.T
@@ -175,6 +175,11 @@ test ('T13386',
         collect_compiler_stats('bytes allocated',1) ],
       compile,
       ['-v0 -O0'])
+
+#########
+# The following tests are very sensitive
+# to coercion optimisation.
+
 test ('T15703',
       [ only_ways(['normal']),
         collect_compiler_stats('bytes allocated',1)
@@ -182,6 +187,19 @@ test ('T15703',
       ],
       multimod_compile,
       ['T15703', '-v0 -O'])
+
+test ('CoOpt_Read',
+      [ collect_compiler_stats('bytes allocated',2) ],
+      compile,
+      ['-v0 -O'])
+
+test('CoOpt_Singletons',
+     [ collect_compiler_stats('bytes allocated',2) ],
+     compile,
+     ['-v0 -O'])
+
+#########
+
 test ('LargeRecord',
       [ only_ways(['normal']),
         collect_compiler_stats('bytes allocated',1)
@@ -614,8 +632,8 @@ test('hard_hole_fits', # Testing multiple hole-fits with lots in scope for #1687
 test('T16875',  # Testing one hole-fit with a lot in scope for #16875
      collect_compiler_stats('bytes allocated', 2),
      compile, ['-fdefer-type-errors -fno-max-valid-hole-fits -package ghc'])
+
 test ('T20261',
       [collect_compiler_stats('all')],
       compile,
       [''])
-