Domain.Algebra.SmartGroup

Smart datatypes

newtype Smart a

Constructors

Smart

Fields

• fromSmart :: a

Instances

Functor Smart

Defined in Domain.Algebra.SmartGroup

Methods

fmap :: (a -> b) -> Smart a -> Smart b

(<$) :: a -> Smart b -> Smart a

Applicative Smart

Defined in Domain.Algebra.SmartGroup

Methods

pure :: a -> Smart a

(<*>) :: Smart (a -> b) -> Smart a -> Smart b

liftA2 :: (a -> b -> c) -> Smart a -> Smart b -> Smart c

(*>) :: Smart a -> Smart b -> Smart b

(<*) :: Smart a -> Smart b -> Smart a

Eq a => Eq (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

(==) :: Smart a -> Smart a -> Bool

(/=) :: Smart a -> Smart a -> Bool

Ord a => Ord (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

compare :: Smart a -> Smart a -> Ordering

(<) :: Smart a -> Smart a -> Bool

(<=) :: Smart a -> Smart a -> Bool

(>) :: Smart a -> Smart a -> Bool

(>=) :: Smart a -> Smart a -> Bool

max :: Smart a -> Smart a -> Smart a

min :: Smart a -> Smart a -> Smart a

Show a => Show (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

showsPrec :: Int -> Smart a -> ShowS

show :: Smart a -> String

showList :: [Smart a] -> ShowS

(CoMonoid a, Semigroup a) => Semigroup (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

(<>) :: Smart a -> Smart a -> Smart a

sconcat :: NonEmpty (Smart a) -> Smart a

stimes :: Integral b => b -> Smart a -> Smart a

(CoMonoid a, Monoid a) => Monoid (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

mempty :: Smart a

mappend :: Smart a -> Smart a -> Smart a

mconcat :: [Smart a] -> Smart a

BoolValue a => BoolValue (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

true :: Smart a

false :: Smart a

fromBool :: Bool -> Smart a

isTrue :: Smart a -> Bool

isFalse :: Smart a -> Bool

(Boolean a, CoBoolean a) => Boolean (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

(<&&>) :: Smart a -> Smart a -> Smart a

(<||>) :: Smart a -> Smart a -> Smart a

complement :: Smart a -> Smart a

CoMonoidZero a => CoMonoidZero (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

isMonoidZero :: Smart a -> Bool

CoMonoid a => CoMonoid (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

isEmpty :: Smart a -> Bool

isAppend :: Smart a -> Maybe (Smart a, Smart a)

(MonoidZero a, CoMonoid a) => MonoidZero (Smart a)

Defined in Domain.Algebra.SmartGroup

Methods

mzero :: Smart a

newtype SmartZero a

Constructors

SmartZero

Fields

• fromSmartZero :: a

Instances

Functor SmartZero

Defined in Domain.Algebra.SmartGroup

Methods

fmap :: (a -> b) -> SmartZero a -> SmartZero b

(<$) :: a -> SmartZero b -> SmartZero a

Applicative SmartZero

Defined in Domain.Algebra.SmartGroup

Methods

pure :: a -> SmartZero a

(<*>) :: SmartZero (a -> b) -> SmartZero a -> SmartZero b

liftA2 :: (a -> b -> c) -> SmartZero a -> SmartZero b -> SmartZero c

(*>) :: SmartZero a -> SmartZero b -> SmartZero b

(<*) :: SmartZero a -> SmartZero b -> SmartZero a

Eq a => Eq (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

(==) :: SmartZero a -> SmartZero a -> Bool

(/=) :: SmartZero a -> SmartZero a -> Bool

Ord a => Ord (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

compare :: SmartZero a -> SmartZero a -> Ordering

(<) :: SmartZero a -> SmartZero a -> Bool

(<=) :: SmartZero a -> SmartZero a -> Bool

(>) :: SmartZero a -> SmartZero a -> Bool

(>=) :: SmartZero a -> SmartZero a -> Bool

max :: SmartZero a -> SmartZero a -> SmartZero a

min :: SmartZero a -> SmartZero a -> SmartZero a

Show a => Show (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

showsPrec :: Int -> SmartZero a -> ShowS

show :: SmartZero a -> String

showList :: [SmartZero a] -> ShowS

(CoMonoidZero a, MonoidZero a, Semigroup a) => Semigroup (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

(<>) :: SmartZero a -> SmartZero a -> SmartZero a

sconcat :: NonEmpty (SmartZero a) -> SmartZero a

stimes :: Integral b => b -> SmartZero a -> SmartZero a

(CoMonoidZero a, MonoidZero a) => Monoid (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

mempty :: SmartZero a

mappend :: SmartZero a -> SmartZero a -> SmartZero a

mconcat :: [SmartZero a] -> SmartZero a

CoMonoidZero a => CoMonoidZero (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

isMonoidZero :: SmartZero a -> Bool

CoMonoid a => CoMonoid (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

isEmpty :: SmartZero a -> Bool

isAppend :: SmartZero a -> Maybe (SmartZero a, SmartZero a)

(MonoidZero a, CoMonoidZero a) => MonoidZero (SmartZero a)

Defined in Domain.Algebra.SmartGroup

Methods

mzero :: SmartZero a

newtype SmartGroup a

Constructors

SmartGroup

Fields

• fromSmartGroup :: a

Instances

Functor SmartGroup

Defined in Domain.Algebra.SmartGroup

Methods

fmap :: (a -> b) -> SmartGroup a -> SmartGroup b

(<$) :: a -> SmartGroup b -> SmartGroup a

Applicative SmartGroup

Defined in Domain.Algebra.SmartGroup

Methods

pure :: a -> SmartGroup a

(<*>) :: SmartGroup (a -> b) -> SmartGroup a -> SmartGroup b

liftA2 :: (a -> b -> c) -> SmartGroup a -> SmartGroup b -> SmartGroup c

(*>) :: SmartGroup a -> SmartGroup b -> SmartGroup b

(<*) :: SmartGroup a -> SmartGroup b -> SmartGroup a

Eq a => Eq (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

(==) :: SmartGroup a -> SmartGroup a -> Bool

(/=) :: SmartGroup a -> SmartGroup a -> Bool

Ord a => Ord (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

compare :: SmartGroup a -> SmartGroup a -> Ordering

(<) :: SmartGroup a -> SmartGroup a -> Bool

(<=) :: SmartGroup a -> SmartGroup a -> Bool

(>) :: SmartGroup a -> SmartGroup a -> Bool

(>=) :: SmartGroup a -> SmartGroup a -> Bool

max :: SmartGroup a -> SmartGroup a -> SmartGroup a

min :: SmartGroup a -> SmartGroup a -> SmartGroup a

Show a => Show (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

showsPrec :: Int -> SmartGroup a -> ShowS

show :: SmartGroup a -> String

showList :: [SmartGroup a] -> ShowS

(CoGroup a, Group a) => Semigroup (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

(<>) :: SmartGroup a -> SmartGroup a -> SmartGroup a

sconcat :: NonEmpty (SmartGroup a) -> SmartGroup a

stimes :: Integral b => b -> SmartGroup a -> SmartGroup a

(CoGroup a, Group a) => Monoid (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

mempty :: SmartGroup a

mappend :: SmartGroup a -> SmartGroup a -> SmartGroup a

mconcat :: [SmartGroup a] -> SmartGroup a

CoMonoidZero a => CoMonoidZero (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

isMonoidZero :: SmartGroup a -> Bool

CoGroup a => CoGroup (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

isInverse :: SmartGroup a -> Maybe (SmartGroup a)

isAppendInv :: SmartGroup a -> Maybe (SmartGroup a, SmartGroup a)

CoMonoid a => CoMonoid (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

isEmpty :: SmartGroup a -> Bool

isAppend :: SmartGroup a -> Maybe (SmartGroup a, SmartGroup a)

(MonoidZero a, CoGroup a, Group a) => MonoidZero (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

mzero :: SmartGroup a

(CoGroup a, Group a) => Group (SmartGroup a)

Defined in Domain.Algebra.SmartGroup

Methods

inverse :: SmartGroup a -> SmartGroup a

appendInv :: SmartGroup a -> SmartGroup a -> SmartGroup a

newtype SmartField a

Constructors

SmartField

Fields

• fromSmartField :: a

Instances

Functor SmartField

Defined in Domain.Algebra.SmartGroup

Methods

fmap :: (a -> b) -> SmartField a -> SmartField b

(<$) :: a -> SmartField b -> SmartField a

Applicative SmartField

Defined in Domain.Algebra.SmartGroup

Methods

pure :: a -> SmartField a

(<*>) :: SmartField (a -> b) -> SmartField a -> SmartField b

liftA2 :: (a -> b -> c) -> SmartField a -> SmartField b -> SmartField c

(*>) :: SmartField a -> SmartField b -> SmartField b

(<*) :: SmartField a -> SmartField b -> SmartField a

CoField a => CoField (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

isRecip :: SmartField a -> Maybe (SmartField a)

isDivision :: SmartField a -> Maybe (SmartField a, SmartField a)

CoRing a => CoRing (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

isNegate :: SmartField a -> Maybe (SmartField a)

isMinus :: SmartField a -> Maybe (SmartField a, SmartField a)

CoSemiRing a => CoSemiRing (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

isPlus :: SmartField a -> Maybe (SmartField a, SmartField a)

isZero :: SmartField a -> Bool

isTimes :: SmartField a -> Maybe (SmartField a, SmartField a)

isOne :: SmartField a -> Bool

(CoField a, Field a) => Field (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

timesInverse :: SmartField a -> SmartField a

(|/|) :: SmartField a -> SmartField a -> SmartField a

(CoField a, Field a) => Ring (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

plusInverse :: SmartField a -> SmartField a

(|-|) :: SmartField a -> SmartField a -> SmartField a

(CoField a, Field a) => SemiRing (SmartField a)

Defined in Domain.Algebra.SmartGroup

Methods

(|+|) :: SmartField a -> SmartField a -> SmartField a

zero :: SmartField a

sum :: [SmartField a] -> SmartField a

(|*|) :: SmartField a -> SmartField a -> SmartField a

one :: SmartField a

product :: [SmartField a] -> SmartField a

(.+.) :: (CoField a, Field a) => a -> a -> a infixl 6

(.-.) :: (CoField a, Field a) => a -> a -> a infixl 6

neg :: (CoField a, Field a) => a -> a

(.*.) :: (CoField a, Field a) => a -> a -> a infixl 7

(./.) :: (CoField a, Field a) => a -> a -> a infixl 7

Smart booleans

(.&&.) :: (Boolean a, CoBoolean a) => a -> a -> a infixr 5

(.||.) :: (Boolean a, CoBoolean a) => a -> a -> a infixr 4