interface Hat.Complex where {

{-# NEED #-}
instance NHC.FFI.Storable NHC.FFI.CChar;

{-# NEED #-}
instance NHC.FFI.Storable (NHC.FFI.Ptr a);

{-# NEED #-}
instance Prelude.Functor NHC.Internal.IO;

{-# NEED #-}
instance Prelude.Monad NHC.Internal.IO;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a) => Hat.Hat.WrapVal (Complex a);

{-# NEED #-}
instance Hat.Hat.WrapVal (Hat.PreludeBasic.Either a b);

{-# NEED #-}
instance Hat.Hat.WrapVal (Hat.PreludeBasic.Maybe a);

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.Hat.WrapVal (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.Hat.WrapVal Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.RealFloat Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.RealFloat Prelude.Double;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.RealFrac (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.RealFrac Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.RealFrac Prelude.Double;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a) => Hat.PreludeBasic.Floating (Complex a);

{-# NEED #-}
instance Hat.PreludeBasic.Floating Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Floating Prelude.Double;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a) => Hat.PreludeBasic.Fractional (Complex a);

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Fractional (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Fractional Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Fractional Prelude.Double;

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Fractional (Ratio.Ratio a);

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.RealFrac (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Bounded IO.IOMode;

{-# NEED #-}
instance Prelude.Bounded IO.SeekMode;

{-# NEED #-}
instance Prelude.Bounded NHC.FFI.CChar;

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Num (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Num NHC.FFI.CChar;

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Real (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Real NHC.FFI.CChar;

{-# NEED #-}
instance (Prelude.Read a,Prelude.Integral a) => Prelude.Read (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Read IO.IOMode;

{-# NEED #-}
instance Prelude.Read IO.SeekMode;

{-# NEED #-}
instance Prelude.Read IO.BufferMode;

{-# NEED #-}
instance Prelude.Read NHC.FFI.CChar;

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Enum (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Enum IO.IOMode;

{-# NEED #-}
instance Prelude.Enum IO.SeekMode;

{-# NEED #-}
instance Prelude.Enum NHC.FFI.CChar;

{-# NEED #-}
instance Prelude.Enum DErrNo.ErrNo;

{-# NEED #-}
instance Prelude.Enum (NHC.FFI.Ptr a);

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Ord (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Ord IO.IOMode;

{-# NEED #-}
instance Prelude.Ord IO.SeekMode;

{-# NEED #-}
instance Prelude.Ord IO.BufferMode;

{-# NEED #-}
instance Prelude.Ord NHC.FFI.CChar;

{-# NEED #-}
instance Prelude.Ord (NHC.FFI.Ptr a);

{-# NEED #-}
instance (Prelude.Show a) => Prelude.Show (NHC.Internal.IO a);

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Show (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Show IO.IOMode;

{-# NEED #-}
instance Prelude.Show IO.SeekMode;

{-# NEED #-}
instance Prelude.Show IO.BufferMode;

{-# NEED #-}
instance Prelude.Show NHC.FFI.CChar;

{-# NEED #-}
instance Prelude.Show IO.Handle;

{-# NEED #-}
instance Prelude.Show IO.HandlePosn;

{-# NEED #-}
instance Prelude.Show DErrNo.ErrNo;

{-# NEED #-}
instance Prelude.Show (NHC.FFI.Ptr a);

{-# NEED #-}
instance Prelude.Integral NHC.FFI.CChar;

{-# NEED #-}
instance (Prelude.Integral a) => Prelude.Eq (Ratio.Ratio a);

{-# NEED #-}
instance Prelude.Eq IO.IOMode;

{-# NEED #-}
instance Prelude.Eq IO.SeekMode;

{-# NEED #-}
instance Prelude.Eq IO.BufferMode;

{-# NEED #-}
instance Prelude.Eq NHC.FFI.CChar;

{-# NEED #-}
instance Prelude.Eq IO.Handle;

{-# NEED #-}
instance Prelude.Eq IO.HandlePosn;

{-# NEED #-}
instance Prelude.Eq DErrNo.ErrNo;

{-# NEED #-}
instance Prelude.Eq (NHC.FFI.Ptr a);

{-# NEED #-}
instance Prelude.Eq Hat.Hat.RefExp;

{-# NEED #-}
instance Hat.PreludeBasic.Monad Hat.Hat.IO;

{-# NEED #-}
instance Hat.PreludeBasic.Monad Hat.PreludeBasic.Maybe;

{-# NEED #-}
instance Hat.PreludeBasic.Monad Hat.Hat.List;

{-# NEED #-}
instance Hat.PreludeBasic.Functor Hat.Hat.IO;

{-# NEED #-}
instance Hat.PreludeBasic.Functor Hat.PreludeBasic.Maybe;

{-# NEED #-}
instance Hat.PreludeBasic.Functor Hat.Hat.List;

{-# NEED #-}
instance Hat.PreludeBasic.Integral Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Integral Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Real (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Real Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Real Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Real Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Real Prelude.Integer;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Hat.Hat.Tuple0;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Enum (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Enum Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Char;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Bool;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Enum Prelude.Integer;

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i,Ix.Ix j,Ix.Ix k,Ix.Ix l,Ix.Ix m,Ix.Ix n,Ix.Ix o) => Ix.Ix (a,b,c,d,e,f,g,h,i,j,k,l,m,n,o);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i,Ix.Ix j,Ix.Ix k,Ix.Ix l,Ix.Ix m) => Ix.Ix (a,b,c,d,e,f,g,h,i,j,k,l,m);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i,Ix.Ix j,Ix.Ix k,Ix.Ix l) => Ix.Ix (a,b,c,d,e,f,g,h,i,j,k,l);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i,Ix.Ix j,Ix.Ix k) => Ix.Ix (a,b,c,d,e,f,g,h,i,j,k);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i,Ix.Ix j) => Ix.Ix (a,b,c,d,e,f,g,h,i,j);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h,Ix.Ix i) => Ix.Ix (a,b,c,d,e,f,g,h,i);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g,Ix.Ix h) => Ix.Ix (a,b,c,d,e,f,g,h);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f,Ix.Ix g) => Ix.Ix (a,b,c,d,e,f,g);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e,Ix.Ix f) => Ix.Ix (a,b,c,d,e,f);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d,Ix.Ix e) => Ix.Ix (a,b,c,d,e);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c,Ix.Ix d) => Ix.Ix (a,b,c,d);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b,Ix.Ix c) => Ix.Ix (a,b,c);

{-# NEED #-}
instance (Ix.Ix a,Ix.Ix b) => Ix.Ix (a,b);

{-# NEED #-}
instance Ix.Ix Prelude.Ordering;

{-# NEED #-}
instance Ix.Ix IO.IOMode;

{-# NEED #-}
instance Ix.Ix IO.SeekMode;

{-# NEED #-}
instance Ix.Ix Prelude.Char;

{-# NEED #-}
instance Ix.Ix Prelude.Bool;

{-# NEED #-}
instance Ix.Ix Prelude.Int;

{-# NEED #-}
instance Ix.Ix Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a,Hat.PreludeBasic.Read a) => Hat.PreludeBasic.Read (Complex a);

{-# NEED #-}
instance (Hat.PreludeBasic.Read a,Hat.PreludeBasic.Read b) => Hat.PreludeBasic.Read (Hat.PreludeBasic.Either a b);

{-# NEED #-}
instance (Hat.PreludeBasic.Read a,Hat.PreludeBasic.Read b,Hat.PreludeBasic.Read c) => Hat.PreludeBasic.Read (Hat.Hat.Tuple3 a b c);

{-# NEED #-}
instance (Hat.PreludeBasic.Read a) => Hat.PreludeBasic.Read (Hat.PreludeBasic.Maybe a);

{-# NEED #-}
instance Hat.PreludeBasic.Read Hat.Hat.Tuple0;

{-# NEED #-}
instance (Hat.PreludeBasic.Read a,Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Read (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Read Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Char;

{-# NEED #-}
instance (Hat.PreludeBasic.Read a,Hat.PreludeBasic.Read b) => Hat.PreludeBasic.Read (Hat.Hat.Tuple2 a b);

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Bool;

{-# NEED #-}
instance (Hat.PreludeBasic.Read a) => Hat.PreludeBasic.Read (Hat.Hat.List a);

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Read Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.Bounded a,Hat.PreludeBasic.Bounded b,Hat.PreludeBasic.Bounded c) => Hat.PreludeBasic.Bounded (Hat.Hat.Tuple3 a b c);

{-# NEED #-}
instance Hat.PreludeBasic.Bounded Hat.Hat.Tuple0;

{-# NEED #-}
instance Hat.PreludeBasic.Bounded Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Bounded Prelude.Char;

{-# NEED #-}
instance (Hat.PreludeBasic.Bounded a,Hat.PreludeBasic.Bounded b) => Hat.PreludeBasic.Bounded (Hat.Hat.Tuple2 a b);

{-# NEED #-}
instance Hat.PreludeBasic.Bounded Prelude.Bool;

{-# NEED #-}
instance Hat.PreludeBasic.Bounded Prelude.Int;

{-# NEED #-}
instance (Hat.PreludeBasic.Ord a,Hat.PreludeBasic.Ord b) => Hat.PreludeBasic.Ord (Hat.PreludeBasic.Either a b);

{-# NEED #-}
instance (Hat.PreludeBasic.Ord a,Hat.PreludeBasic.Ord b,Hat.PreludeBasic.Ord c) => Hat.PreludeBasic.Ord (Hat.Hat.Tuple3 a b c);

{-# NEED #-}
instance (Hat.PreludeBasic.Ord a) => Hat.PreludeBasic.Ord (Hat.PreludeBasic.Maybe a);

{-# NEED #-}
instance Hat.PreludeBasic.Ord Hat.Hat.Tuple0;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Ord (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Ord Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Char;

{-# NEED #-}
instance (Hat.PreludeBasic.Ord a,Hat.PreludeBasic.Ord b) => Hat.PreludeBasic.Ord (Hat.Hat.Tuple2 a b);

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Bool;

{-# NEED #-}
instance (Hat.PreludeBasic.Ord a) => Hat.PreludeBasic.Ord (Hat.Hat.List a);

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Ord Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a) => Hat.PreludeBasic.Num (Complex a);

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Num (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Num Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Num Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Num Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Num Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a,Hat.PreludeBasic.Show a) => Hat.PreludeBasic.Show (Complex a);

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.IOError;

{-# NEED #-}
instance (Hat.PreludeBasic.Show a,Hat.PreludeBasic.Show b) => Hat.PreludeBasic.Show (Hat.PreludeBasic.Either a b);

{-# NEED #-}
instance (Hat.PreludeBasic.Show a,Hat.PreludeBasic.Show b,Hat.PreludeBasic.Show c) => Hat.PreludeBasic.Show (Hat.Hat.Tuple3 a b c);

{-# NEED #-}
instance (Hat.PreludeBasic.Show a) => Hat.PreludeBasic.Show (Hat.PreludeBasic.Maybe a);

{-# NEED #-}
instance Hat.PreludeBasic.Show Hat.Hat.Tuple0;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a) => Hat.PreludeBasic.Show (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Show Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Char;

{-# NEED #-}
instance (Hat.PreludeBasic.Show a,Hat.PreludeBasic.Show b) => Hat.PreludeBasic.Show (Hat.Hat.Tuple2 a b);

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Bool;

{-# NEED #-}
instance (Hat.PreludeBasic.Show a) => Hat.PreludeBasic.Show (Hat.Hat.List a);

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Show Prelude.Integer;

{-# NEED #-}
instance (Hat.PreludeBasic.RealFloat a,Hat.PreludeBasic.Eq a) => Hat.PreludeBasic.Eq (Complex a);

{-# NEED #-}
instance (Hat.PreludeBasic.Eq a,Hat.PreludeBasic.Eq b) => Hat.PreludeBasic.Eq (Hat.PreludeBasic.Either a b);

{-# NEED #-}
instance (Hat.PreludeBasic.Eq a,Hat.PreludeBasic.Eq b,Hat.PreludeBasic.Eq c) => Hat.PreludeBasic.Eq (Hat.Hat.Tuple3 a b c);

{-# NEED #-}
instance (Hat.PreludeBasic.Eq a) => Hat.PreludeBasic.Eq (Hat.PreludeBasic.Maybe a);

{-# NEED #-}
instance Hat.PreludeBasic.Eq Hat.Hat.Tuple0;

{-# NEED #-}
instance (Hat.PreludeBasic.Integral a,Hat.PreludeBasic.Eq a) => Hat.PreludeBasic.Eq (Hat.PreludeBasic.Ratio a);

{-# NEED #-}
instance Hat.PreludeBasic.Eq Hat.PreludeBasic.Ordering;

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Float;

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Double;

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Char;

{-# NEED #-}
instance (Hat.PreludeBasic.Eq a,Hat.PreludeBasic.Eq b) => Hat.PreludeBasic.Eq (Hat.Hat.Tuple2 a b);

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Bool;

{-# NEED #-}
instance (Hat.PreludeBasic.Eq a) => Hat.PreludeBasic.Eq (Hat.Hat.List a);

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Int;

{-# NEED #-}
instance Hat.PreludeBasic.Eq Prelude.Integer;
interface Ratio
{-# NEED Ratio #-}
data Ratio a;
interface IO
{-# NEED BufferMode #-}
data BufferMode;
interface NHC.FFI
{-# NEED CChar #-}
newtype {-#  #-} CChar;
interface IO
{-# NEED Handle #-}
newtype {-#  #-} Handle;

{-# NEED HandlePosn #-}
data HandlePosn;
interface DErrNo
{-# NEED ErrNo #-}
data ErrNo;
interface NHC.FFI
{-# NEED Ptr #-}
data Ptr a;
interface Hat.Hat
{-# NEED IO #-}
newtype {-#  #-} IO a;
interface NHC.Internal
{-# NEED IO #-}
newtype {-#  #-} IO a;

{-# NEED World #-}
data World;
interface Ix
{-# NEED Ix #-}
class (Prelude.Ord a) => Ix a;
interface IO
{-# NEED IOMode #-}
data IOMode;

{-# NEED SeekMode #-}
data SeekMode;
interface Hat.PreludeBasic
{-# NEED Read #-}
class Read a;

{-# NEED Bounded #-}
class Bounded a;

{-# NEED Either #-}
data Either a b;
interface Hat.Hat
{-# NEED Tuple3 #-}
data Tuple3 a b c;
interface Hat.PreludeBasic
{-# NEED Maybe #-}
data Maybe a;
interface Hat.Hat
{-# NEED Tuple0 #-}
data Tuple0;
interface Hat.PreludeBasic
{-# NEED Ratio #-}
data (Integral a) => Ratio a;

{-# NEED Integral #-}
class (Hat.PreludeBasic.Real a,Hat.PreludeBasic.Enum a) => Integral a;

{-# NEED Enum #-}
class Enum a;

{-# NEED Ordering #-}
data Ordering;
interface Hat.Hat
{-# NEED List #-}
data List a;
interface ! Hat.Complex
{-# NEED aphase #-}
aphase{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED amagnitude #-}
amagnitude{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED apolar #-}
apolar{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED acis #-}
acis{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED amkPolar #-}
amkPolar{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED aconjugate #-}
aconjugate{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED aimagPart #-}
aimagPart{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED arealPart #-}
arealPart{-# 0 #-}::Hat.Hat.RefAtom;

{-# NEED (+:+) #-}
(+:+){-# 0 #-}::Hat.Hat.RefAtom;
interface Hat.Hat
{-# NEED RefAtom #-}
newtype {-#  #-} RefAtom;
interface ! Hat.Complex
{-# NEED hphase #-}
hphase{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R a)));

{-# NEED gphase #-}
gphase{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) a))));

{-# NEED hmagnitude #-}
hmagnitude{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R a)));

{-# NEED gmagnitude #-}
gmagnitude{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) a))));

{-# NEED hpolar #-}
hpolar{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Tuple2 a a))));

{-# NEED gpolar #-}
gpolar{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) (Hat.Hat.Tuple2 a a)))));
interface Hat.Hat
{-# NEED Tuple2 #-}
data Tuple2 a b;
interface ! Hat.Complex
{-# NEED hcis #-}
hcis{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R a) -> (Hat.Hat.RefExp -> (Hat.Hat.R (Complex a))));

{-# NEED gcis #-}
gcis{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun a (Complex a)))));

{-# NEED hmkPolar #-}
hmkPolar{-# 3 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R a) -> ((Hat.Hat.R a) -> (Hat.Hat.RefExp -> (Hat.Hat.R (Complex a)))));

{-# NEED gmkPolar #-}
gmkPolar{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun a (Hat.Hat.Fun a (Complex a))))));

{-# NEED hconjugate #-}
hconjugate{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R (Complex a))));

{-# NEED gconjugate #-}
gconjugate{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) (Complex a)))));

{-# NEED himagPart #-}
himagPart{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R a)));

{-# NEED gimagPart #-}
gimagPart{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) a))));

{-# NEED hrealPart #-}
hrealPart{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => ((Hat.Hat.R (Complex a)) -> (Hat.Hat.RefExp -> (Hat.Hat.R a)));

{-# NEED grealPart #-}
grealPart{-# 2 #-}::(Hat.PreludeBasic.RealFloat a) => (Hat.Hat.RefSrcPos -> (Hat.Hat.RefExp -> (Hat.Hat.R (Hat.Hat.Fun (Complex a) a))));
interface Hat.Hat
{-# NEED Fun #-}
newtype {-#  #-} Fun a b;

{-# NEED RefSrcPos #-}
newtype {-#  #-} RefSrcPos;
interface ! Hat.Complex
{-# NEED {Complex (:+)} #-}
data (Hat.PreludeBasic.RealFloat a) => Complex a
  = (:+) !(Hat.Hat.R a) !(Hat.Hat.R a);
interface Hat.Hat
{-# NEED R #-}
data R a;

{-# NEED RefExp #-}
newtype {-#  #-} RefExp;
interface Hat.PreludeBasic
{-# NEED RealFloat #-}
class (Hat.PreludeBasic.RealFrac a,Hat.PreludeBasic.Floating a) => RealFloat a;

{-# NEED Floating #-}
class (Hat.PreludeBasic.Fractional a) => Floating a;

{-# NEED RealFrac #-}
class (Hat.PreludeBasic.Real a,Hat.PreludeBasic.Fractional a) => RealFrac a;

{-# NEED Fractional #-}
class (Hat.PreludeBasic.Num a) => Fractional a;

{-# NEED Real #-}
class (Hat.PreludeBasic.Num a,Hat.PreludeBasic.Ord a) => Real a;

{-# NEED Ord #-}
class (Hat.PreludeBasic.Eq a) => Ord a;

{-# NEED Num #-}
class (Hat.PreludeBasic.Eq a,Hat.PreludeBasic.Show a) => Num a;

{-# NEED Show #-}
class Show a;

{-# NEED Eq #-}
class Eq a;
}
