Domain.Algebra.Boolean

Boolean algebra (re-exported)

class BoolValue a where

Minimal complete definition

isTrue, isFalse

Methods

true :: a

false :: a

fromBool :: Bool -> a

isTrue :: a -> Bool

isFalse :: a -> Bool

Instances

BoolValue Bool

Defined in Ideas.Common.Classes

Methods

true :: Bool

false :: Bool

fromBool :: Bool -> Bool

isTrue :: Bool -> Bool

isFalse :: Bool -> Bool

BoolValue (Predicate a)

Defined in Ideas.Common.Predicate

Methods

true :: Predicate a

false :: Predicate a

fromBool :: Bool -> Predicate a

isTrue :: Predicate a -> Bool

isFalse :: Predicate a -> Bool

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

BoolValue (Logic a)

Defined in Domain.Logic.Formula

Methods

true :: Logic a

false :: Logic a

fromBool :: Bool -> Logic a

isTrue :: Logic a -> Bool

isFalse :: Logic a -> Bool

Ord a => BoolValue (Interval a)

Defined in Domain.Math.Data.Interval

Methods

true :: Interval a

false :: Interval a

fromBool :: Bool -> Interval a

isTrue :: Interval a -> Bool

isFalse :: Interval a -> Bool

Ord a => BoolValue (OrSet a)

Defined in Domain.Math.Data.OrList

Methods

true :: OrSet a

false :: OrSet a

fromBool :: Bool -> OrSet a

isTrue :: OrSet a -> Bool

isFalse :: OrSet a -> Bool

BoolValue (OrList a)

Defined in Domain.Math.Data.OrList

Methods

true :: OrList a

false :: OrList a

fromBool :: Bool -> OrList a

isTrue :: OrList a -> Bool

isFalse :: OrList a -> Bool

BoolValue (WithBool a)

Defined in Domain.Math.Data.WithBool

Methods

true :: WithBool a

false :: WithBool a

fromBool :: Bool -> WithBool a

isTrue :: WithBool a -> Bool

isFalse :: WithBool a -> Bool

BoolValue b => BoolValue (a -> b)

Defined in Ideas.Common.Classes

Methods

true :: a -> b

false :: a -> b

fromBool :: Bool -> a -> b

isTrue :: (a -> b) -> Bool

isFalse :: (a -> b) -> Bool

class BoolValue a => Boolean a where

Methods

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

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

complement :: a -> a

Instances

Boolean Bool

Defined in Ideas.Common.Classes

Methods

(<&&>) :: Bool -> Bool -> Bool

(<||>) :: Bool -> Bool -> Bool

complement :: Bool -> Bool

Boolean (Predicate a)

Defined in Ideas.Common.Predicate

Methods

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

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

complement :: Predicate a -> Predicate a

(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

Boolean (Logic a)

Defined in Domain.Logic.Formula

Methods

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

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

complement :: Logic a -> Logic a

Ord a => Boolean (Interval a)

Defined in Domain.Math.Data.Interval

Methods

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

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

complement :: Interval a -> Interval a

Boolean b => Boolean (a -> b)

Defined in Ideas.Common.Classes

Methods

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

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

complement :: (a -> b) -> a -> b

ands :: Boolean a => [a] -> a

ors :: Boolean a => [a] -> a

implies :: Boolean a => a -> a -> a

equivalent :: Boolean a => a -> a -> a

CoBoolean (matching)

class BoolValue a => CoBoolean a where

Methods

isAnd :: a -> Maybe (a, a)

isOr :: a -> Maybe (a, a)

isComplement :: a -> Maybe a

Instances

CoBoolean (Logic a)

Defined in Domain.Logic.Formula

Methods

isAnd :: Logic a -> Maybe (Logic a, Logic a)

isOr :: Logic a -> Maybe (Logic a, Logic a)

isComplement :: Logic a -> Maybe (Logic a)

conjunctions :: CoBoolean a => a -> [a]

disjunctions :: CoBoolean a => a -> [a]

Monoids monoid

class MonoidZero a => DualMonoid a where

Methods

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

dualCompl :: a -> a

Instances

Boolean a => DualMonoid (Or a)

Defined in Domain.Algebra.Boolean

Methods

(><) :: Or a -> Or a -> Or a

dualCompl :: Or a -> Or a

Boolean a => DualMonoid (And a)

Defined in Domain.Algebra.Boolean

Methods

(><) :: And a -> And a -> And a

dualCompl :: And a -> And a

newtype And a

Constructors

And

Fields

• fromAnd :: a

Instances

Functor And

Defined in Domain.Algebra.Boolean

Methods

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

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

Applicative And

Defined in Domain.Algebra.Boolean

Methods

pure :: a -> And a

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

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

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

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

Eq a => Eq (And a)

Defined in Domain.Algebra.Boolean

Methods

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

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

Ord a => Ord (And a)

Defined in Domain.Algebra.Boolean

Methods

compare :: And a -> And a -> Ordering

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

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

(>) :: And a -> And a -> Bool

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

max :: And a -> And a -> And a

min :: And a -> And a -> And a

Show a => Show (And a)

Defined in Domain.Algebra.Boolean

Methods

showsPrec :: Int -> And a -> ShowS

show :: And a -> String

showList :: [And a] -> ShowS

Boolean a => Semigroup (And a)

Defined in Domain.Algebra.Boolean

Methods

(<>) :: And a -> And a -> And a

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

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

Boolean a => Monoid (And a)

Defined in Domain.Algebra.Boolean

Methods

mempty :: And a

mappend :: And a -> And a -> And a

mconcat :: [And a] -> And a

Arbitrary a => Arbitrary (And a)

Defined in Domain.Algebra.Boolean

Methods

arbitrary :: Gen (And a)

shrink :: And a -> [And a]

CoArbitrary a => CoArbitrary (And a)

Defined in Domain.Algebra.Boolean

Methods

coarbitrary :: And a -> Gen b -> Gen b

CoBoolean a => CoMonoidZero (And a)

Defined in Domain.Algebra.Boolean

Methods

isMonoidZero :: And a -> Bool

CoBoolean a => CoMonoid (And a)

Defined in Domain.Algebra.Boolean

Methods

isEmpty :: And a -> Bool

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

Boolean a => MonoidZero (And a)

Defined in Domain.Algebra.Boolean

Methods

mzero :: And a

Boolean a => DualMonoid (And a)

Defined in Domain.Algebra.Boolean

Methods

(><) :: And a -> And a -> And a

dualCompl :: And a -> And a

newtype Or a

Constructors

Or

Fields

• fromOr :: a

Instances

Functor Or

Defined in Domain.Algebra.Boolean

Methods

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

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

Applicative Or

Defined in Domain.Algebra.Boolean

Methods

pure :: a -> Or a

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

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

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

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

Eq a => Eq (Or a)

Defined in Domain.Algebra.Boolean

Methods

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

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

Ord a => Ord (Or a)

Defined in Domain.Algebra.Boolean

Methods

compare :: Or a -> Or a -> Ordering

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

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

(>) :: Or a -> Or a -> Bool

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

max :: Or a -> Or a -> Or a

min :: Or a -> Or a -> Or a

Show a => Show (Or a)

Defined in Domain.Algebra.Boolean

Methods

showsPrec :: Int -> Or a -> ShowS

show :: Or a -> String

showList :: [Or a] -> ShowS

Boolean a => Semigroup (Or a)

Defined in Domain.Algebra.Boolean

Methods

(<>) :: Or a -> Or a -> Or a

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

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

Boolean a => Monoid (Or a)

Defined in Domain.Algebra.Boolean

Methods

mempty :: Or a

mappend :: Or a -> Or a -> Or a

mconcat :: [Or a] -> Or a

Arbitrary a => Arbitrary (Or a)

Defined in Domain.Algebra.Boolean

Methods

arbitrary :: Gen (Or a)

shrink :: Or a -> [Or a]

CoArbitrary a => CoArbitrary (Or a)

Defined in Domain.Algebra.Boolean

Methods

coarbitrary :: Or a -> Gen b -> Gen b

CoBoolean a => CoMonoidZero (Or a)

Defined in Domain.Algebra.Boolean

Methods

isMonoidZero :: Or a -> Bool

CoBoolean a => CoMonoid (Or a)

Defined in Domain.Algebra.Boolean

Methods

isEmpty :: Or a -> Bool

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

Boolean a => MonoidZero (Or a)

Defined in Domain.Algebra.Boolean

Methods

mzero :: Or a

Boolean a => DualMonoid (Or a)

Defined in Domain.Algebra.Boolean

Methods

(><) :: Or a -> Or a -> Or a

dualCompl :: Or a -> Or a