Ideas.Common.Algebra.Boolean

Boolean algebra

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

BoolValue a => BoolValue (Smart a)

BoolValue (Predicate a)

BoolValue b => BoolValue (a -> b)

class BoolValue a => Boolean a where

Methods

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

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

complement :: a -> a

Instances

Boolean Bool

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

Boolean (Predicate a)

Boolean b => Boolean (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

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)

Boolean a => DualMonoid (And a)

newtype And a

Constructors

And

Fields

fromAnd :: a

Instances

Functor And

Applicative And

Eq a => Eq (And a)

Ord a => Ord (And a)

Show a => Show (And a)

Arbitrary a => Arbitrary (And a)

CoArbitrary a => CoArbitrary (And a)

Boolean a => Monoid (And a)

CoBoolean a => CoMonoidZero (And a)

CoBoolean a => CoMonoid (And a)

Boolean a => MonoidZero (And a)

Boolean a => DualMonoid (And a)

newtype Or a

Constructors

Or

Fields

fromOr :: a

Instances

Functor Or

Applicative Or

Eq a => Eq (Or a)

Ord a => Ord (Or a)

Show a => Show (Or a)

Arbitrary a => Arbitrary (Or a)

CoArbitrary a => CoArbitrary (Or a)

Boolean a => Monoid (Or a)

CoBoolean a => CoMonoidZero (Or a)

CoBoolean a => CoMonoid (Or a)

Boolean a => MonoidZero (Or a)

Boolean a => DualMonoid (Or a)