Data.Algebra.Boolean

Documentation

class Boolean b where

A class for boolean algebras. Instances of this class should obey all the axioms of boolean algebra.

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

Methods

true :: b

Truth value.

false :: b

False value.

not :: b -> b

Logical negation.

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

Logical conjunction.

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

Logical inclusive disjunction.

xor :: b -> b -> b

Logical exclusive disjunction.

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

Logical implication

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

Logical biconditional

Instances

Boolean Bool

Boolean All

Boolean Any

Boolean (Dual Bool)

Boolean (Endo Bool)

fromBool :: Boolean b => Bool -> b

Injection from Bool into a boolean algebra.