Safe Haskell	Safe
Language	Haskell2010

Math.Number.NumericExpression

Synopsis

data ctx :- a where
- ELam :: (Var a -> (ctx, a) :- b) -> ctx :- (a -> b)
- EApp :: (ctx :- (a -> b)) -> (ctx, a) :- b
- ECompose :: (b :- c) -> (a :- b) -> a :- c
- EVar :: Var a -> ctx :- a
- EPair :: (ctx :- a) -> (ctx :- b) -> ctx :- (a, b)
- EFst :: (ctx, a) :- ctx
- ESnd :: (ctx, a) :- a
- ECase :: (a :- c) -> (b :- c) -> Either a b :- c
- EIn1 :: a :- Either a b
- EIn2 :: b :- Either a b
- ETerminal :: ctx :- ()
- EInitial :: Contradiction :- b
- EVec :: VectorSpaceExpr v a -> () :- v a
- ENum :: NumExpr v a -> () :- a
data Contradiction
identity_expr :: ctx :- (b -> b)
pair_identity_expr :: (a, b) :- (a, b)
either_identity_expr :: Either a b :- Either a b
pair_expr :: ctx :- (a -> b -> (a, b))
var_intro :: (Var a -> (ctx, a) :- b) -> (ctx, a) :- b
data Var a
- = Var {
  - var_name :: !String
  - var_debruijn_index :: !Integer
  }
- | Val !a
varIso :: IsoA Var a b -> Var a :==: Var b
class Expression e ctx a where
- eval :: ctx a -> e a -> a
equal_in_context :: (Eq a, Expression f ctx a) => ctx a -> f a -> f a -> Bool
evalVar :: [a] -> Var a -> a
withCtx :: Functor f => [a] -> (f :*: Var) a -> f a
eVar :: Applicative f => String -> Integer -> (f :*: Var) a
expr :: Functor f => f a -> (f :*: Var) a
data VectorCtx v a = VectorCtx {
- vectorSpaceCtx :: Map String (VectorSpaceExpr v a)
- numCtx :: [a]
}
data VectorSpaceExpr v a
- = VZero
- | VNegate (VectorSpaceExpr v a)
- | VPlus (VectorSpaceExpr v a) (VectorSpaceExpr v a)
- | VScalar (NumExpr v a) (VectorSpaceExpr v a)
- | VVectorVar (Var (VectorSpaceExpr v a))
- | VPrim (v a)
reduceVectorSpaceExpr :: VectorSpaceExpr v a -> VectorSpaceExpr v a
vectorSpaceIso :: FunctorArrow v (->) (->) => IsoA (VectorSpaceExpr v) a b -> VectorSpaceExpr v a :==: VectorSpaceExpr v b
evalVectorSpaceExpr :: (VectorSpace (v a), IdVisitor a, Expression Var (Map String) (VectorSpaceExpr v a), Scalar (v a) ~ a) => VectorCtx v a -> VectorSpaceExpr v a -> v a
data NumExpr v a
- = Plus !(NumExpr v a) !(NumExpr v a)
- | Product !(NumExpr v a) !(NumExpr v a)
- | Subtract !(NumExpr v a) !(NumExpr v a)
- | Negate !(NumExpr v a)
- | Abs !(NumExpr v a)
- | Signum !(NumExpr v a)
- | NumPrim !(Var a)
- | FromInteger !Integer
- | InnerProduct !(VectorSpaceExpr v a) !(VectorSpaceExpr v a)
numIso :: FunctorArrow v (->) (->) => IsoA (NumExpr v) a b -> NumExpr v a :==: NumExpr v b
plus_assoc_iso :: NumExpr v a :==: NumExpr v a
product_assoc_iso :: NumExpr v a :==: NumExpr v a
data FracExpr v a
- = PrimFracExpr !(NumExpr v a)
- | Divide !(FracExpr v a) !(FracExpr v a)
- | Recip !(FracExpr v a)
- | FromRational !Rational
data FloatExpr v a
- = PrimPi
- | Exp !(FloatExpr v a)
- | Log !(FloatExpr v a)
- | Sqrt !(FloatExpr v a)
- | Power !(FloatExpr v a) !(FloatExpr v a)
- | Sin !(FloatExpr v a)
- | Cos !(FloatExpr v a)
- | Tan !(FloatExpr v a)
- | Asin !(FloatExpr v a)
- | Acos !(FloatExpr v a)
- | Atan !(FloatExpr v a)
- | Sinh !(FloatExpr v a)
- | Cosh !(FloatExpr v a)
- | Tanh !(FloatExpr v a)
- | Asinh !(FloatExpr v a)
- | Acosh !(FloatExpr v a)
- | Atanh !(FloatExpr v a)
- | PrimFloatExpr !(FracExpr v (FloatExpr v a))
pp_unary :: PpShow a => Text -> a -> Doc
class VectorShow v where
- show_vector :: Show a => v a -> String
liftNumFrac1 :: forall {k} {v :: Type -> Type} {a} {v :: Type -> Type} {a :: k}. (NumExpr v a -> NumExpr v (FloatExpr v a)) -> a -> FloatExpr v a
liftNumFrac2 :: forall {k} {v :: Type -> Type} {a} {v :: Type -> Type} {a} {v :: Type -> Type} {a :: k}. (NumExpr v a -> NumExpr v a -> NumExpr v (FloatExpr v a)) -> a -> a -> FloatExpr v a
data EnumExpr a
- = SuccExpr !(EnumExpr a)
- | PredExpr !(EnumExpr a)
- | ToEnumExpr !(Var a)
runEnumExpr :: Enum a => [a] -> EnumExpr a -> a
runNumExpr :: (Num a, IdVisitor a) => [a] -> NumExpr v a -> a
runFracExpr :: (Fractional a, IdVisitor a) => [a] -> FracExpr v a -> a
varFold :: [a] -> Fold (Var a) a
vecSpaceFold :: (Visitor (v a), VectorSpace b) => Fold (Var b) b -> Fold (NumExpr v a) (Scalar b) -> Fold (v a) b -> Fold (VectorSpaceExpr v a) b
numExprFold :: Num a => Fold (Var a) a -> Fold (NumExpr v a) a
fracExprFold :: Fractional b => Fold (NumExpr v a) b -> Fold (FracExpr v a) b
enumExprFold :: Enum b => Fold (Var a) b -> Fold (EnumExpr a) b

Documentation

data ctx :- a where Source #

Constructors

ELam :: (Var a -> (ctx, a) :- b) -> ctx :- (a -> b)
EApp :: (ctx :- (a -> b)) -> (ctx, a) :- b
ECompose :: (b :- c) -> (a :- b) -> a :- c
EVar :: Var a -> ctx :- a
EPair :: (ctx :- a) -> (ctx :- b) -> ctx :- (a, b)
EFst :: (ctx, a) :- ctx
ESnd :: (ctx, a) :- a
ECase :: (a :- c) -> (b :- c) -> Either a b :- c
EIn1 :: a :- Either a b
EIn2 :: b :- Either a b
ETerminal :: ctx :- ()
EInitial :: Contradiction :- b
EVec :: VectorSpaceExpr v a -> () :- v a
ENum :: NumExpr v a -> () :- a

data Contradiction Source #

identity_expr :: ctx :- (b -> b) Source #

pair_identity_expr :: (a, b) :- (a, b) Source #

either_identity_expr :: Either a b :- Either a b Source #

pair_expr :: ctx :- (a -> b -> (a, b)) Source #

var_intro :: (Var a -> (ctx, a) :- b) -> (ctx, a) :- b Source #

data Var a Source #

Constructors

Var
Fields var_name :: !String var_debruijn_index :: !Integer
Val !a

Instances

Instances details

Functor Var Source #
Instance details Defined in Math.Number.NumericExpression Methods fmap :: (a -> b) -> Var a -> Var b # (<$) :: a -> Var b -> Var a #
VectorShow Var Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => Var a -> String Source #
IsomorphicFunctor Var Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data IsoA Var a b Source # Methods transformIso :: IsoA Var a b -> Var a :==: Var b Source #
PpShowF Var Source #
Instance details Defined in Math.Number.NumericExpression Methods ppf :: PpShow a => Var a -> Doc Source #
Expression Var List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> Var a -> a Source #
FunctorArrow Var (->) (->) Source #
Instance details Defined in Math.Number.NumericExpression Methods amap :: forall (c :: k) (d :: k). (c -> d) -> Var c -> Var d Source #
Category (IsoA Var) Source #
Instance details Defined in Math.Number.NumericExpression Methods id :: forall (a :: k). IsoA Var a a # (.) :: forall (b :: k) (c :: k) (a :: k). IsoA Var b c -> IsoA Var a b -> IsoA Var a c #
Groupoid (IsoA Var) Source #
Instance details Defined in Math.Number.NumericExpression Methods invertA :: forall (a :: k) (b :: k). IsoA Var a b -> IsoA Var b a Source #
Expression Var (VectorCtx v) a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: VectorCtx v a -> Var a -> a Source #
Data a => Data (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Var a -> c (Var a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Var a) # toConstr :: Var a -> Constr # dataTypeOf :: Var a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Var a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Var a)) # gmapT :: (forall b. Data b => b -> b) -> Var a -> Var a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Var a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Var a -> r # gmapQ :: (forall d. Data d => d -> u) -> Var a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Var a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Var a -> m (Var a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Var a -> m (Var a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Var a -> m (Var a) #
Generic (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (Var a) :: Type -> Type # Methods from :: Var a -> Rep (Var a) x # to :: Rep (Var a) x -> Var a #
Show a => Show (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Methods showsPrec :: Int -> Var a -> ShowS # show :: Var a -> String # showList :: [Var a] -> ShowS #
BiArrow (IsoA Var) Source #
Instance details Defined in Math.Number.NumericExpression Methods (<->) :: (a -> b) -> (b -> a) -> IsoA Var a b Source #
PpShow a => PpShow (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pp :: Var a -> Doc Source #
Visitor (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (Var a) :: Type -> Type Source # Methods visit :: Fold (Var a) a0 -> Var a -> a0 Source #
Eq a => Eq (Var a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: Var a -> Var a -> Bool # (/=) :: Var a -> Var a -> Bool #
Num ((NumExpr v :*: Var) a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (+) :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # (-) :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # () :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # negate :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # abs :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # signum :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # fromInteger :: Integer -> (NumExpr v :*: Var) a #
data IsoA Var a b Source #
Instance details Defined in Math.Number.NumericExpression data IsoA Var a b = VarIso { var_nameIso :: String :==: String var_indexIso :: Integer :==: Integer var_valIso :: a :==: b }
type Rep (Var a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (Var a) = D1 ('MetaData "Var" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "Var" 'PrefixI 'True) (S1 ('MetaSel ('Just "var_name") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 String) :*: S1 ('MetaSel ('Just "var_debruijn_index") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Integer)) :+: C1 ('MetaCons "Val" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
data Fold (Var a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (Var a) b = VarFold [a] (String -> a -> b) (a -> b)

varIso :: IsoA Var a b -> Var a :==: Var b Source #

class Expression e ctx a where Source #

Methods

eval :: ctx a -> e a -> a Source #

Instances

Instances details

Enum a => Expression EnumExpr List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> EnumExpr a -> a Source #
Expression Var List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> Var a -> a Source #
Expression Var (VectorCtx v) a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: VectorCtx v a -> Var a -> a Source #
(Fractional a, IdVisitor a) => Expression (FracExpr v) List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> FracExpr v a -> a Source #
(Num a, IdVisitor a) => Expression (NumExpr v) List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> NumExpr v a -> a Source #

equal_in_context :: (Eq a, Expression f ctx a) => ctx a -> f a -> f a -> Bool Source #

evalVar :: [a] -> Var a -> a Source #

withCtx :: Functor f => [a] -> (f :*: Var) a -> f a Source #

eVar :: Applicative f => String -> Integer -> (f :*: Var) a Source #

expr :: Functor f => f a -> (f :*: Var) a Source #

data VectorCtx v a Source #

Constructors

VectorCtx
Fields vectorSpaceCtx :: Map String (VectorSpaceExpr v a) numCtx :: [a]

Instances

Instances details

Expression Var (VectorCtx v) a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: VectorCtx v a -> Var a -> a Source #
(Typeable v, Data a, Data (v a)) => Data (VectorCtx v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> VectorCtx v a -> c (VectorCtx v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (VectorCtx v a) # toConstr :: VectorCtx v a -> Constr # dataTypeOf :: VectorCtx v a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (VectorCtx v a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (VectorCtx v a)) # gmapT :: (forall b. Data b => b -> b) -> VectorCtx v a -> VectorCtx v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> VectorCtx v a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> VectorCtx v a -> r # gmapQ :: (forall d. Data d => d -> u) -> VectorCtx v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> VectorCtx v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> VectorCtx v a -> m (VectorCtx v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> VectorCtx v a -> m (VectorCtx v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> VectorCtx v a -> m (VectorCtx v a) #
Generic (VectorCtx v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (VectorCtx v a) :: Type -> Type # Methods from :: VectorCtx v a -> Rep (VectorCtx v a) x # to :: Rep (VectorCtx v a) x -> VectorCtx v a #
(Eq a, Eq (v a)) => Eq (VectorCtx v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: VectorCtx v a -> VectorCtx v a -> Bool # (/=) :: VectorCtx v a -> VectorCtx v a -> Bool #
type Rep (VectorCtx v a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (VectorCtx v a) = D1 ('MetaData "VectorCtx" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "VectorCtx" 'PrefixI 'True) (S1 ('MetaSel ('Just "vectorSpaceCtx") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Map String (VectorSpaceExpr v a))) :*: S1 ('MetaSel ('Just "numCtx") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a])))

data VectorSpaceExpr v a Source #

Constructors

VZero
VNegate (VectorSpaceExpr v a)
VPlus (VectorSpaceExpr v a) (VectorSpaceExpr v a)
VScalar (NumExpr v a) (VectorSpaceExpr v a)
VVectorVar (Var (VectorSpaceExpr v a))
VPrim (v a)

Instances

Instances details

FunctorArrow v (->) (->) => FunctorArrow (VectorSpaceExpr v :: Type -> Type) (->) (->) Source #
Instance details Defined in Math.Number.NumericExpression Methods amap :: forall (c :: k) (d :: k). (c -> d) -> VectorSpaceExpr v c -> VectorSpaceExpr v d Source #
FunctorArrow v (->) (->) => Category (IsoA (VectorSpaceExpr v) :: Type -> Type -> Type) Source #
Instance details Defined in Math.Number.NumericExpression Methods id :: forall (a :: k). IsoA (VectorSpaceExpr v) a a # (.) :: forall (b :: k) (c :: k) (a :: k). IsoA (VectorSpaceExpr v) b c -> IsoA (VectorSpaceExpr v) a b -> IsoA (VectorSpaceExpr v) a c #
FunctorArrow v (->) (->) => Groupoid (IsoA (VectorSpaceExpr v) :: Type -> Type -> Type) Source #
Instance details Defined in Math.Number.NumericExpression Methods invertA :: forall (a :: k) (b :: k). IsoA (VectorSpaceExpr v) a b -> IsoA (VectorSpaceExpr v) b a Source #
VectorShow v => VectorShow (VectorSpaceExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => VectorSpaceExpr v a -> String Source #
FunctorArrow v (->) (->) => BiArrow (IsoA (VectorSpaceExpr v)) Source #
Instance details Defined in Math.Number.NumericExpression Methods (<->) :: (a -> b) -> (b -> a) -> IsoA (VectorSpaceExpr v) a b Source #
FunctorArrow v (->) (->) => IsomorphicFunctor (VectorSpaceExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data IsoA (VectorSpaceExpr v) a b Source # Methods transformIso :: IsoA (VectorSpaceExpr v) a b -> VectorSpaceExpr v a :==: VectorSpaceExpr v b Source #
PpShowF v => PpShowF (VectorSpaceExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods ppf :: PpShow a => VectorSpaceExpr v a -> Doc Source #
(Typeable v, Data a, Data (v a)) => Data (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> VectorSpaceExpr v a -> c (VectorSpaceExpr v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (VectorSpaceExpr v a) # toConstr :: VectorSpaceExpr v a -> Constr # dataTypeOf :: VectorSpaceExpr v a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (VectorSpaceExpr v a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (VectorSpaceExpr v a)) # gmapT :: (forall b. Data b => b -> b) -> VectorSpaceExpr v a -> VectorSpaceExpr v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> VectorSpaceExpr v a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> VectorSpaceExpr v a -> r # gmapQ :: (forall d. Data d => d -> u) -> VectorSpaceExpr v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> VectorSpaceExpr v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> VectorSpaceExpr v a -> m (VectorSpaceExpr v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> VectorSpaceExpr v a -> m (VectorSpaceExpr v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> VectorSpaceExpr v a -> m (VectorSpaceExpr v a) #
Generic (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (VectorSpaceExpr v a) :: Type -> Type # Methods from :: VectorSpaceExpr v a -> Rep (VectorSpaceExpr v a) x # to :: Rep (VectorSpaceExpr v a) x -> VectorSpaceExpr v a #
(Show a, Show (v a)) => Show (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods showsPrec :: Int -> VectorSpaceExpr v a -> ShowS # show :: VectorSpaceExpr v a -> String # showList :: [VectorSpaceExpr v a] -> ShowS #
InnerProductSpace (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (%.) :: VectorSpaceExpr v a -> VectorSpaceExpr v a -> Scalar (VectorSpaceExpr v a) Source #
VectorSpace (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Scalar (VectorSpaceExpr v a) Source # Methods vzero :: VectorSpaceExpr v a Source # vnegate :: VectorSpaceExpr v a -> VectorSpaceExpr v a Source # (%+) :: VectorSpaceExpr v a -> VectorSpaceExpr v a -> VectorSpaceExpr v a Source # (%*) :: Scalar (VectorSpaceExpr v a) -> VectorSpaceExpr v a -> VectorSpaceExpr v a Source #
(PpShow a, PpShowF v) => PpShow (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pp :: VectorSpaceExpr v a -> Doc Source #
Visitor (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (VectorSpaceExpr v a) :: Type -> Type Source # Methods visit :: Fold (VectorSpaceExpr v a) a0 -> VectorSpaceExpr v a -> a0 Source #
(Eq a, Eq (v a)) => Eq (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: VectorSpaceExpr v a -> VectorSpaceExpr v a -> Bool # (/=) :: VectorSpaceExpr v a -> VectorSpaceExpr v a -> Bool #
data IsoA (VectorSpaceExpr v) a b Source #
Instance details Defined in Math.Number.NumericExpression data IsoA (VectorSpaceExpr v) a b = VectorSpaceIso { vnegate_iso :: IsoA (VectorSpaceExpr v) a b vplus_1_iso :: IsoA (VectorSpaceExpr v) a b vplus_2_iso :: IsoA (VectorSpaceExpr v) a b vscalar_1_iso :: IsoA (NumExpr v) a b vscalar_2_iso :: IsoA (VectorSpaceExpr v) a b vvector_1_iso :: IsoA Var (VectorSpaceExpr v a) (VectorSpaceExpr v b) vprim_iso :: v a :==: v b }
type Rep (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (VectorSpaceExpr v a) = D1 ('MetaData "VectorSpaceExpr" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) ((C1 ('MetaCons "VZero" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "VNegate" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (VectorSpaceExpr v a))) :+: C1 ('MetaCons "VPlus" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (VectorSpaceExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (VectorSpaceExpr v a))))) :+: (C1 ('MetaCons "VScalar" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (NumExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (VectorSpaceExpr v a))) :+: (C1 ('MetaCons "VVectorVar" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Var (VectorSpaceExpr v a)))) :+: C1 ('MetaCons "VPrim" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (v a))))))
type Scalar (VectorSpaceExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression type Scalar (VectorSpaceExpr v a) = NumExpr v a
data Fold (VectorSpaceExpr v a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (VectorSpaceExpr v a) b = VectorSpaceExprFold { vzero_fold :: b vnegate_fold :: b -> b vplus_fold :: b -> b -> b vscalar_fold :: NumExpr v a -> b -> b vvector_fold :: Var b -> b vprim_fold :: v a -> b }

reduceVectorSpaceExpr :: VectorSpaceExpr v a -> VectorSpaceExpr v a Source #

vectorSpaceIso :: FunctorArrow v (->) (->) => IsoA (VectorSpaceExpr v) a b -> VectorSpaceExpr v a :==: VectorSpaceExpr v b Source #

evalVectorSpaceExpr :: (VectorSpace (v a), IdVisitor a, Expression Var (Map String) (VectorSpaceExpr v a), Scalar (v a) ~ a) => VectorCtx v a -> VectorSpaceExpr v a -> v a Source #

data NumExpr v a Source #

Basically same as methods in Num type class from prelude, but as data.

Constructors

Plus !(NumExpr v a) !(NumExpr v a)
Product !(NumExpr v a) !(NumExpr v a)
Subtract !(NumExpr v a) !(NumExpr v a)
Negate !(NumExpr v a)
Abs !(NumExpr v a)
Signum !(NumExpr v a)
NumPrim !(Var a)
FromInteger !Integer
InnerProduct !(VectorSpaceExpr v a) !(VectorSpaceExpr v a)

Instances

Instances details

FunctorArrow v (->) (->) => FunctorArrow (NumExpr v :: Type -> Type) (->) (->) Source #
Instance details Defined in Math.Number.NumericExpression Methods amap :: forall (c :: k) (d :: k). (c -> d) -> NumExpr v c -> NumExpr v d Source #
FunctorArrow v (->) (->) => Category (IsoA (NumExpr v) :: Type -> Type -> Type) Source #
Instance details Defined in Math.Number.NumericExpression Methods id :: forall (a :: k). IsoA (NumExpr v) a a # (.) :: forall (b :: k) (c :: k) (a :: k). IsoA (NumExpr v) b c -> IsoA (NumExpr v) a b -> IsoA (NumExpr v) a c #
FunctorArrow v (->) (->) => Groupoid (IsoA (NumExpr v) :: Type -> Type -> Type) Source #
Instance details Defined in Math.Number.NumericExpression Methods invertA :: forall (a :: k) (b :: k). IsoA (NumExpr v) a b -> IsoA (NumExpr v) b a Source #
Functor (NumExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods fmap :: (a -> b) -> NumExpr v a -> NumExpr v b # (<$) :: a -> NumExpr v b -> NumExpr v a #
VectorShow v => VectorShow (NumExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => NumExpr v a -> String Source #
FunctorArrow v (->) (->) => BiArrow (IsoA (NumExpr v)) Source #
Instance details Defined in Math.Number.NumericExpression Methods (<->) :: (a -> b) -> (b -> a) -> IsoA (NumExpr v) a b Source #
FunctorArrow v (->) (->) => IsomorphicFunctor (NumExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data IsoA (NumExpr v) a b Source # Methods transformIso :: IsoA (NumExpr v) a b -> NumExpr v a :==: NumExpr v b Source #
PpShowF v => PpShowF (NumExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods ppf :: PpShow a => NumExpr v a -> Doc Source #
(Num a, IdVisitor a) => Expression (NumExpr v) List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> NumExpr v a -> a Source #
(Typeable v, Data a, Data (v a)) => Data (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NumExpr v a -> c (NumExpr v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NumExpr v a) # toConstr :: NumExpr v a -> Constr # dataTypeOf :: NumExpr v a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NumExpr v a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NumExpr v a)) # gmapT :: (forall b. Data b => b -> b) -> NumExpr v a -> NumExpr v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NumExpr v a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NumExpr v a -> r # gmapQ :: (forall d. Data d => d -> u) -> NumExpr v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> NumExpr v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> NumExpr v a -> m (NumExpr v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NumExpr v a -> m (NumExpr v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NumExpr v a -> m (NumExpr v a) #
Generic (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (NumExpr v a) :: Type -> Type # Methods from :: NumExpr v a -> Rep (NumExpr v a) x # to :: Rep (NumExpr v a) x -> NumExpr v a #
Num (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (+) :: NumExpr v a -> NumExpr v a -> NumExpr v a # (-) :: NumExpr v a -> NumExpr v a -> NumExpr v a # (*) :: NumExpr v a -> NumExpr v a -> NumExpr v a # negate :: NumExpr v a -> NumExpr v a # abs :: NumExpr v a -> NumExpr v a # signum :: NumExpr v a -> NumExpr v a # fromInteger :: Integer -> NumExpr v a #
(Show a, Show (v a)) => Show (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods showsPrec :: Int -> NumExpr v a -> ShowS # show :: NumExpr v a -> String # showList :: [NumExpr v a] -> ShowS #
(Eq a, Show a) => ConjugateSymmetric (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods conj :: NumExpr v a -> NumExpr v a Source #
(PpShow a, PpShowF v) => PpShow (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pp :: NumExpr v a -> Doc Source #
Visitor (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (NumExpr v a) :: Type -> Type Source # Methods visit :: Fold (NumExpr v a) a0 -> NumExpr v a -> a0 Source #
(Eq a, Eq (v a)) => Eq (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: NumExpr v a -> NumExpr v a -> Bool # (/=) :: NumExpr v a -> NumExpr v a -> Bool #
Num ((NumExpr v :*: Var) a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (+) :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # (-) :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # () :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a -> (NumExpr v :: Var) a # negate :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # abs :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # signum :: (NumExpr v :: Var) a -> (NumExpr v :: Var) a # fromInteger :: Integer -> (NumExpr v :*: Var) a #
data IsoA (NumExpr v) a b Source #
Instance details Defined in Math.Number.NumericExpression data IsoA (NumExpr v) a b = NumIso { plusIso_1 :: IsoA (NumExpr v) a b plusIso_2 :: IsoA (NumExpr v) a b prodIso_1 :: IsoA (NumExpr v) a b prodIso_2 :: IsoA (NumExpr v) a b subtractIso_1 :: IsoA (NumExpr v) a b subtractIso_2 :: IsoA (NumExpr v) a b negateIso :: IsoA (NumExpr v) a b numAbsIso :: IsoA (NumExpr v) a b signumIso :: IsoA (NumExpr v) a b numPrimIso :: IsoA Var a b fromIntegerIso :: Integer :==: Integer innerProductIso_1 :: IsoA (VectorSpaceExpr v) a b innerProductIso_2 :: IsoA (VectorSpaceExpr v) a b }
type Rep (NumExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (NumExpr v a) = D1 ('MetaData "NumExpr" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (((C1 ('MetaCons "Plus" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a))) :+: C1 ('MetaCons "Product" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a)))) :+: (C1 ('MetaCons "Subtract" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a))) :+: C1 ('MetaCons "Negate" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a))))) :+: ((C1 ('MetaCons "Abs" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a))) :+: C1 ('MetaCons "Signum" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a)))) :+: (C1 ('MetaCons "NumPrim" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Var a))) :+: (C1 ('MetaCons "FromInteger" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Integer)) :+: C1 ('MetaCons "InnerProduct" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (VectorSpaceExpr v a)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (VectorSpaceExpr v a)))))))
data Fold (NumExpr v a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (NumExpr v a) b = NumExprFold { exprfold_plus :: b -> b -> b exprfold_product :: b -> b -> b exprfold_subtract :: b -> b -> b exprfold_negate :: b -> b exprfold_abs :: b -> b exprfold_signum :: b -> b exprfold_prim :: Fold (Var a) b exprfold_frominteger :: Integer -> b }

numIso :: FunctorArrow v (->) (->) => IsoA (NumExpr v) a b -> NumExpr v a :==: NumExpr v b Source #

plus_assoc_iso :: NumExpr v a :==: NumExpr v a Source #

product_assoc_iso :: NumExpr v a :==: NumExpr v a Source #

data FracExpr v a Source #

basically same as Fractional class in Prelude.

Constructors

PrimFracExpr !(NumExpr v a)
Divide !(FracExpr v a) !(FracExpr v a)
Recip !(FracExpr v a)
FromRational !Rational

Instances

Instances details

Functor (FracExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods fmap :: (a -> b) -> FracExpr v a -> FracExpr v b # (<$) :: a -> FracExpr v b -> FracExpr v a #
VectorShow v => VectorShow (FracExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => FracExpr v a -> String Source #
PpShowF v => PpShowF (FracExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods ppf :: PpShow a => FracExpr v a -> Doc Source #
(Fractional a, IdVisitor a) => Expression (FracExpr v) List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> FracExpr v a -> a Source #
(Typeable v, Data a, Data (v a)) => Data (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> FracExpr v a -> c (FracExpr v a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (FracExpr v a) # toConstr :: FracExpr v a -> Constr # dataTypeOf :: FracExpr v a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (FracExpr v a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (FracExpr v a)) # gmapT :: (forall b. Data b => b -> b) -> FracExpr v a -> FracExpr v a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FracExpr v a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FracExpr v a -> r # gmapQ :: (forall d. Data d => d -> u) -> FracExpr v a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> FracExpr v a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> FracExpr v a -> m (FracExpr v a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> FracExpr v a -> m (FracExpr v a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> FracExpr v a -> m (FracExpr v a) #
Generic (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (FracExpr v a) :: Type -> Type # Methods from :: FracExpr v a -> Rep (FracExpr v a) x # to :: Rep (FracExpr v a) x -> FracExpr v a #
(Show a, Show (v a)) => Show (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods showsPrec :: Int -> FracExpr v a -> ShowS # show :: FracExpr v a -> String # showList :: [FracExpr v a] -> ShowS #
(PpShow a, PpShowF v) => PpShow (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pp :: FracExpr v a -> Doc Source #
Visitor (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (FracExpr v a) :: Type -> Type Source # Methods visit :: Fold (FracExpr v a) a0 -> FracExpr v a -> a0 Source #
(Eq a, Eq (v a)) => Eq (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: FracExpr v a -> FracExpr v a -> Bool # (/=) :: FracExpr v a -> FracExpr v a -> Bool #
type Rep (FracExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (FracExpr v a) = D1 ('MetaData "FracExpr" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) ((C1 ('MetaCons "PrimFracExpr" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (NumExpr v a))) :+: C1 ('MetaCons "Divide" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FracExpr v a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FracExpr v a)))) :+: (C1 ('MetaCons "Recip" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FracExpr v a))) :+: C1 ('MetaCons "FromRational" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Rational))))
data Fold (FracExpr v a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (FracExpr v a) b = FracExprFold { fracexprfold_prim :: Fold (NumExpr v a) b fracexprfold_divide :: b -> b -> b fracexprfold_recip :: b -> b fracexprfold_fromrational :: Rational -> b }

data FloatExpr v a Source #

basically same as Floating class in Prelude, but as data.

Constructors

PrimPi
Exp !(FloatExpr v a)
Log !(FloatExpr v a)
Sqrt !(FloatExpr v a)
Power !(FloatExpr v a) !(FloatExpr v a)
Sin !(FloatExpr v a)
Cos !(FloatExpr v a)
Tan !(FloatExpr v a)
Asin !(FloatExpr v a)
Acos !(FloatExpr v a)
Atan !(FloatExpr v a)
Sinh !(FloatExpr v a)
Cosh !(FloatExpr v a)
Tanh !(FloatExpr v a)
Asinh !(FloatExpr v a)
Acosh !(FloatExpr v a)
Atanh !(FloatExpr v a)
PrimFloatExpr !(FracExpr v (FloatExpr v a))

Instances

Instances details

Floating (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pi :: FloatExpr v a # exp :: FloatExpr v a -> FloatExpr v a # log :: FloatExpr v a -> FloatExpr v a # sqrt :: FloatExpr v a -> FloatExpr v a # (**) :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # logBase :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # sin :: FloatExpr v a -> FloatExpr v a # cos :: FloatExpr v a -> FloatExpr v a # tan :: FloatExpr v a -> FloatExpr v a # asin :: FloatExpr v a -> FloatExpr v a # acos :: FloatExpr v a -> FloatExpr v a # atan :: FloatExpr v a -> FloatExpr v a # sinh :: FloatExpr v a -> FloatExpr v a # cosh :: FloatExpr v a -> FloatExpr v a # tanh :: FloatExpr v a -> FloatExpr v a # asinh :: FloatExpr v a -> FloatExpr v a # acosh :: FloatExpr v a -> FloatExpr v a # atanh :: FloatExpr v a -> FloatExpr v a # log1p :: FloatExpr v a -> FloatExpr v a # expm1 :: FloatExpr v a -> FloatExpr v a # log1pexp :: FloatExpr v a -> FloatExpr v a # log1mexp :: FloatExpr v a -> FloatExpr v a #
Generic (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (FloatExpr v a) :: Type -> Type # Methods from :: FloatExpr v a -> Rep (FloatExpr v a) x # to :: Rep (FloatExpr v a) x -> FloatExpr v a #
Num (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (+) :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # (-) :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # (*) :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # negate :: FloatExpr v a -> FloatExpr v a # abs :: FloatExpr v a -> FloatExpr v a # signum :: FloatExpr v a -> FloatExpr v a # fromInteger :: Integer -> FloatExpr v a #
Fractional (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (/) :: FloatExpr v a -> FloatExpr v a -> FloatExpr v a # recip :: FloatExpr v a -> FloatExpr v a # fromRational :: Rational -> FloatExpr v a #
VectorShow v => Show (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods showsPrec :: Int -> FloatExpr v a -> ShowS # show :: FloatExpr v a -> String # showList :: [FloatExpr v a] -> ShowS #
PpShowF v => PpShow (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods pp :: FloatExpr v a -> Doc Source #
Visitor (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (FloatExpr v a) :: Type -> Type Source # Methods visit :: Fold (FloatExpr v a) a0 -> FloatExpr v a -> a0 Source #
Eq (v (FloatExpr v a)) => Eq (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: FloatExpr v a -> FloatExpr v a -> Bool # (/=) :: FloatExpr v a -> FloatExpr v a -> Bool #
type Rep (FloatExpr v a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (FloatExpr v a) = D1 ('MetaData "FloatExpr" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) ((((C1 ('MetaCons "PrimPi" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "Exp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a)))) :+: (C1 ('MetaCons "Log" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Sqrt" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))))) :+: ((C1 ('MetaCons "Power" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Sin" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a)))) :+: (C1 ('MetaCons "Cos" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: (C1 ('MetaCons "Tan" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Asin" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))))))) :+: (((C1 ('MetaCons "Acos" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Atan" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a)))) :+: (C1 ('MetaCons "Sinh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Cosh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))))) :+: ((C1 ('MetaCons "Tanh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "Asinh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a)))) :+: (C1 ('MetaCons "Acosh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: (C1 ('MetaCons "Atanh" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FloatExpr v a))) :+: C1 ('MetaCons "PrimFloatExpr" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (FracExpr v (FloatExpr v a)))))))))
data Fold (FloatExpr v a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (FloatExpr v a) b = FloatExprFold { floatfold_pi :: b floatfold_exp :: b -> b floatfold_log :: b -> b floatfold_sqrt :: b -> b floatfold_power :: b -> b -> b floatfold_sin :: b -> b floatfold_cos :: b -> b floatfold_tan :: b -> b floatfold_asin :: b -> b floatfold_acos :: b -> b floatfold_atan :: b -> b floatfold_sinh :: b -> b floatfold_cosh :: b -> b floatfold_tanh :: b -> b floatfold_asinh :: b -> b floatfold_acosh :: b -> b floatfold_atanh :: b -> b floatfold_prim :: Fold (FracExpr v (FloatExpr v a)) b }

pp_unary :: PpShow a => Text -> a -> Doc Source #

class VectorShow v where Source #

Methods

show_vector :: Show a => v a -> String Source #

Instances

Instances details

VectorShow Var Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => Var a -> String Source #
VectorShow v => VectorShow (FracExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => FracExpr v a -> String Source #
VectorShow v => VectorShow (NumExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => NumExpr v a -> String Source #
VectorShow v => VectorShow (VectorSpaceExpr v) Source #
Instance details Defined in Math.Number.NumericExpression Methods show_vector :: Show a => VectorSpaceExpr v a -> String Source #

liftNumFrac1 :: forall {k} {v :: Type -> Type} {a} {v :: Type -> Type} {a :: k}. (NumExpr v a -> NumExpr v (FloatExpr v a)) -> a -> FloatExpr v a Source #

liftNumFrac2 :: forall {k} {v :: Type -> Type} {a} {v :: Type -> Type} {a} {v :: Type -> Type} {a :: k}. (NumExpr v a -> NumExpr v a -> NumExpr v (FloatExpr v a)) -> a -> a -> FloatExpr v a Source #

data EnumExpr a Source #

Constructors

SuccExpr !(EnumExpr a)
PredExpr !(EnumExpr a)
ToEnumExpr !(Var a)

Instances

Instances details

Enum a => Expression EnumExpr List a Source #
Instance details Defined in Math.Number.NumericExpression Methods eval :: [a] -> EnumExpr a -> a Source #
Data a => Data (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> EnumExpr a -> c (EnumExpr a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (EnumExpr a) # toConstr :: EnumExpr a -> Constr # dataTypeOf :: EnumExpr a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (EnumExpr a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (EnumExpr a)) # gmapT :: (forall b. Data b => b -> b) -> EnumExpr a -> EnumExpr a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> EnumExpr a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> EnumExpr a -> r # gmapQ :: (forall d. Data d => d -> u) -> EnumExpr a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> EnumExpr a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> EnumExpr a -> m (EnumExpr a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> EnumExpr a -> m (EnumExpr a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> EnumExpr a -> m (EnumExpr a) #
Enum a => Enum (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression Methods succ :: EnumExpr a -> EnumExpr a # pred :: EnumExpr a -> EnumExpr a # toEnum :: Int -> EnumExpr a # fromEnum :: EnumExpr a -> Int # enumFrom :: EnumExpr a -> [EnumExpr a] # enumFromThen :: EnumExpr a -> EnumExpr a -> [EnumExpr a] # enumFromTo :: EnumExpr a -> EnumExpr a -> [EnumExpr a] # enumFromThenTo :: EnumExpr a -> EnumExpr a -> EnumExpr a -> [EnumExpr a] #
Generic (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types type Rep (EnumExpr a) :: Type -> Type # Methods from :: EnumExpr a -> Rep (EnumExpr a) x # to :: Rep (EnumExpr a) x -> EnumExpr a #
Visitor (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression Associated Types data Fold (EnumExpr a) :: Type -> Type Source # Methods visit :: Fold (EnumExpr a) a0 -> EnumExpr a -> a0 Source #
Eq a => Eq (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression Methods (==) :: EnumExpr a -> EnumExpr a -> Bool # (/=) :: EnumExpr a -> EnumExpr a -> Bool #
type Rep (EnumExpr a) Source #
Instance details Defined in Math.Number.NumericExpression type Rep (EnumExpr a) = D1 ('MetaData "EnumExpr" "Math.Number.NumericExpression" "cifl-math-library-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "SuccExpr" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EnumExpr a))) :+: (C1 ('MetaCons "PredExpr" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (EnumExpr a))) :+: C1 ('MetaCons "ToEnumExpr" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 (Var a)))))
data Fold (EnumExpr a) b Source #
Instance details Defined in Math.Number.NumericExpression data Fold (EnumExpr a) b = EnumExprFold { enumfold_succ :: b -> b enumfold_pred :: b -> b enumfold_toenum :: Fold (Var a) b }

runEnumExpr :: Enum a => [a] -> EnumExpr a -> a Source #

runNumExpr :: (Num a, IdVisitor a) => [a] -> NumExpr v a -> a Source #

runFracExpr :: (Fractional a, IdVisitor a) => [a] -> FracExpr v a -> a Source #

varFold :: [a] -> Fold (Var a) a Source #

vecSpaceFold :: (Visitor (v a), VectorSpace b) => Fold (Var b) b -> Fold (NumExpr v a) (Scalar b) -> Fold (v a) b -> Fold (VectorSpaceExpr v a) b Source #

numExprFold :: Num a => Fold (Var a) a -> Fold (NumExpr v a) a Source #

fracExprFold :: Fractional b => Fold (NumExpr v a) b -> Fold (FracExpr v a) b Source #

enumExprFold :: Enum b => Fold (Var a) b -> Fold (EnumExpr a) b Source #