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)

and :: Foldable t => t b -> b

The logical conjunction of several values.

or :: Foldable t => t b -> b

The logical disjunction of several values.

nand :: Foldable t => t b -> b

The negated logical conjunction of several values.

nand = not . and

all :: Foldable t => (a -> b) -> t a -> b

The logical conjunction of the mapping of a function over several values.

any :: Foldable t => (a -> b) -> t a -> b

The logical disjunction of the mapping of a function over several values.

nor :: Foldable t => t b -> b

The negated logical disjunction of several values.

nor = not . or

Instances

Boolean Bool

Boolean All

Boolean Any

Boolean (Dual Bool)

Boolean (Endo Bool)

(Num a, Bits a) => Boolean (Bitwise a)

(Boolean x, Boolean y) => Boolean (x, y)

fromBool :: Boolean b => Bool -> b

Injection from Bool into a boolean algebra.

newtype Bitwise a

A newtype wrapper that derives a Boolean instance from any type that is both a Bits instance and a Num instance, such that boolean logic operations on the Bitwise wrapper correspond to bitwise logic operations on the inner type. It should be noted that false is defined as Bitwise 0 and true is defined as not false.

In addition, a number of other classes are automatically derived from the inner type. These classes were chosen on the basis that many other Bits instances defined in base are also instances of these classes.

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)

(Num a, Bits a) => Boolean (Bitwise a)