ToySolver.Data.Boolean

Type classes for lattices and boolean algebras.

Boolean algebra

class MonotoneBoolean a where

Minimal complete definition

(true, (.&&.) | andB), (false, (.||.) | orB)

Methods

true, false :: a

(.&&.) :: a -> a -> a infixr 3

(.||.) :: a -> a -> a infixr 2

andB :: [a] -> a

orB :: [a] -> a

Instances

MonotoneBoolean Bool

MonotoneBoolean (GenFormula a)

MonotoneBoolean (DNF lit)

MonotoneBoolean (BoolExpr a)

MonotoneBoolean (Formula c)

MonotoneBoolean a => MonotoneBoolean (b -> a)

(MonotoneBoolean a, MonotoneBoolean b) => MonotoneBoolean (a, b)

class Complement a where

types that can be negated.

Methods

notB :: a -> a

Instances

Complement Bool

Complement Lit

Complement (GenFormula a)

Complement (GenLit a)

Complement lit => Complement (DNF lit)

Complement (BoolExpr a)

Complement (Formula a)

Complement (ArithRel c)

Complement a => Complement (b -> a)

(Complement a, Complement b) => Complement (a, b)

class (MonotoneBoolean a, Complement a) => Boolean a where

types that can be combined with boolean operations.

Minimal complete definition

Nothing

Methods

(.=>.), (.<=>.) :: a -> a -> a infix 1 .=>., .<=>.

ite :: a -> a -> a -> a

Instances

Boolean Bool

Boolean (GenFormula a)

Complement lit => Boolean (DNF lit)

Boolean (BoolExpr a)

Boolean (Formula c)

Boolean a => Boolean (b -> a)

(Boolean a, Boolean b) => Boolean (a, b)