cond-0.4.1.1: Basic conditional and boolean operators with monadic variants.

Data.Algebra.Boolean

Synopsis

# Documentation

class Boolean b where Source

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 &&.

Minimal complete definition

Nothing

Methods

true :: b Source

Truth value, defined as the top of the bounded lattice

false :: b Source

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

not :: b -> b Source

Logical negation.

(&&) :: b -> b -> b infixr 3 Source

Logical conjunction. (infxr 3)

(||) :: b -> b -> b infixr 2 Source

Logical inclusive disjunction. (infixr 2)

xor :: b -> b -> b infixr 1 Source

Logical exclusive disjunction. (infixr 1)

(-->) :: b -> b -> b infixr 1 Source

Logical implication. (infixr 1)

(<-->) :: b -> b -> b infixr 1 Source

Logical biconditional. (infixr 1)

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

The logical conjunction of several values.

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

The logical disjunction of several values.

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

The negated logical conjunction of several values.

nand = not . and

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

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

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

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

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

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 Source

Injection from Bool into a boolean algebra.

newtype Bitwise a Source

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 FieldsgetBits :: a

Instances

 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) Typeable (* -> *) Bitwise