Data.Algebra.Boolean

Documentation

class Boolean b where

A class for boolean algebras. Instances of this class are expected to obey all the laws of boolean algebra.

Minimal complete definition: true or false, not or <-->, || or &&.

Methods

true :: b

Truth value, defined as the top of the bounded lattice

false :: b

False value, defined as the bottom of the bounded lattice.

not :: b -> b

Logical negation.

(&&) :: b -> b -> b

Logical conjunction. (infxr 3)

(||) :: b -> b -> b

Logical inclusive disjunction. (infixr 2)

xor :: b -> b -> b

Logical exclusive disjunction. (infixr 1)

(-->) :: b -> b -> b

Logical implication. (infixr 1)

(<-->) :: b -> b -> b

Logical biconditional. (infixr 1)

Instances

Boolean Bool

Boolean All

Boolean Any

Boolean (Dual Bool)

Boolean (Endo Bool)

Bits a => Boolean (Bitwise a)

fromBool :: Boolean b => Bool -> b

Injection from Bool into a boolean algebra.

newtype Bitwise a

Constructors

Bitwise

Fields

getBits :: a

Instances

Typeable1 Bitwise

Bounded a => Bounded (Bitwise a)

Enum a => Enum (Bitwise a)

Eq a => Eq (Bitwise a)

Integral a => Integral (Bitwise a)

Data a => Data (Bitwise a)

Num a => Num (Bitwise a)

Ord a => Ord (Bitwise a)

Read a => Read (Bitwise a)

Real a => Real (Bitwise a)

Show a => Show (Bitwise a)

Ix a => Ix (Bitwise a)

PrintfArg a => PrintfArg (Bitwise a)

Storable a => Storable (Bitwise a)

Bits a => Bits (Bitwise a)

Bits a => Boolean (Bitwise a)