Maintainer	[email protected]
Stability	provisional
Portability	portable (depends on ghc)
Safe Haskell	None
Language	Haskell2010

Domain.Math.Data.Relation

Contents

Type class
Relation data type
Constructor functions
Equation (or equality)
Inequality

Description

Synopsis

class Functor f => Relational f where
- leftHandSide :: f a -> a
- rightHandSide :: f a -> a
- flipSides :: f a -> f a
- constructor :: f a -> b -> b -> f b
- isSymmetric :: f a -> Bool
data Relation a
relationType :: Relation a -> RelationType
data RelationType
- = EqualTo
- | NotEqualTo
- | LessThan
- | GreaterThan
- | LessThanOrEqualTo
- | GreaterThanOrEqualTo
- | Approximately
relationSymbols :: [(RelationType, (String, Symbol))]
notRelation :: Relation a -> Relation a
eval :: (Ord a, Num a) => RelationType -> a -> a -> Bool
makeType :: RelationType -> a -> a -> Relation a
(.==.) :: a -> a -> Relation a
(./=.) :: a -> a -> Relation a
(.<.) :: a -> a -> Relation a
(.>.) :: a -> a -> Relation a
(.<=.) :: a -> a -> Relation a
(.>=.) :: a -> a -> Relation a
(.~=.) :: a -> a -> Relation a
type Equations a = [Equation a]
data Equation a = a :==: a
equationView :: View (Relation a) (Equation a)
data Inequality a
- = a :<: a
- | a :>: a
- | a :<=: a
- | a :>=: a
inequalityView :: View (Relation a) (Inequality a)

Type class

class Functor f => Relational f where Source #

Minimal complete definition

leftHandSide, rightHandSide, flipSides, constructor

Methods

leftHandSide :: f a -> a Source #

rightHandSide :: f a -> a Source #

flipSides :: f a -> f a Source #

constructor :: f a -> b -> b -> f b Source #

isSymmetric :: f a -> Bool Source #

Instances

Relational Inequality Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Inequality a -> a Source # rightHandSide :: Inequality a -> a Source # flipSides :: Inequality a -> Inequality a Source # constructor :: Inequality a -> b -> b -> Inequality b Source # isSymmetric :: Inequality a -> Bool Source #
Relational Equation Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Equation a -> a Source # rightHandSide :: Equation a -> a Source # flipSides :: Equation a -> Equation a Source # constructor :: Equation a -> b -> b -> Equation b Source # isSymmetric :: Equation a -> Bool Source #
Relational Relation Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Relation a -> a Source # rightHandSide :: Relation a -> a Source # flipSides :: Relation a -> Relation a Source # constructor :: Relation a -> b -> b -> Relation b Source # isSymmetric :: Relation a -> Bool Source #

Relation data type

data Relation a Source #

Instances

Functor Relation Source #
Instance details Defined in Domain.Math.Data.Relation Methods fmap :: (a -> b) -> Relation a -> Relation b # (<$) :: a -> Relation b -> Relation a #
Foldable Relation Source #
Instance details Defined in Domain.Math.Data.Relation Methods fold :: Monoid m => Relation m -> m # foldMap :: Monoid m => (a -> m) -> Relation a -> m # foldr :: (a -> b -> b) -> b -> Relation a -> b # foldr' :: (a -> b -> b) -> b -> Relation a -> b # foldl :: (b -> a -> b) -> b -> Relation a -> b # foldl' :: (b -> a -> b) -> b -> Relation a -> b # foldr1 :: (a -> a -> a) -> Relation a -> a # foldl1 :: (a -> a -> a) -> Relation a -> a # toList :: Relation a -> [a] # null :: Relation a -> Bool # length :: Relation a -> Int # elem :: Eq a => a -> Relation a -> Bool # maximum :: Ord a => Relation a -> a # minimum :: Ord a => Relation a -> a # sum :: Num a => Relation a -> a # product :: Num a => Relation a -> a #
Traversable Relation Source #
Instance details Defined in Domain.Math.Data.Relation Methods traverse :: Applicative f => (a -> f b) -> Relation a -> f (Relation b) # sequenceA :: Applicative f => Relation (f a) -> f (Relation a) # mapM :: Monad m => (a -> m b) -> Relation a -> m (Relation b) # sequence :: Monad m => Relation (m a) -> m (Relation a) #
Relational Relation Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Relation a -> a Source # rightHandSide :: Relation a -> a Source # flipSides :: Relation a -> Relation a Source # constructor :: Relation a -> b -> b -> Relation b Source # isSymmetric :: Relation a -> Bool Source #
Eq a => Eq (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods (==) :: Relation a -> Relation a -> Bool # (/=) :: Relation a -> Relation a -> Bool #
Ord a => Ord (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods compare :: Relation a -> Relation a -> Ordering # (<) :: Relation a -> Relation a -> Bool # (<=) :: Relation a -> Relation a -> Bool # (>) :: Relation a -> Relation a -> Bool # (>=) :: Relation a -> Relation a -> Bool # max :: Relation a -> Relation a -> Relation a # min :: Relation a -> Relation a -> Relation a #
Show a => Show (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods showsPrec :: Int -> Relation a -> ShowS # show :: Relation a -> String # showList :: [Relation a] -> ShowS #
Arbitrary a => Arbitrary (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods arbitrary :: Gen (Relation a) # shrink :: Relation a -> [Relation a] #
CoArbitrary a => CoArbitrary (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods coarbitrary :: Relation a -> Gen b -> Gen b #
IsTerm a => IsTerm (Relation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods toTerm :: Relation a -> Term # toTermList :: [Relation a] -> Term # fromTerm :: MonadPlus m => Term -> m (Relation a) # fromTermList :: MonadPlus m => Term -> m [Relation a] #

relationType :: Relation a -> RelationType Source #

data RelationType Source #

Constructors

EqualTo
NotEqualTo
LessThan
GreaterThan
LessThanOrEqualTo
GreaterThanOrEqualTo
Approximately

Instances

Enum RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods succ :: RelationType -> RelationType # pred :: RelationType -> RelationType # toEnum :: Int -> RelationType # fromEnum :: RelationType -> Int # enumFrom :: RelationType -> [RelationType] # enumFromThen :: RelationType -> RelationType -> [RelationType] # enumFromTo :: RelationType -> RelationType -> [RelationType] # enumFromThenTo :: RelationType -> RelationType -> RelationType -> [RelationType] #
Eq RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods (==) :: RelationType -> RelationType -> Bool # (/=) :: RelationType -> RelationType -> Bool #
Ord RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods compare :: RelationType -> RelationType -> Ordering # (<) :: RelationType -> RelationType -> Bool # (<=) :: RelationType -> RelationType -> Bool # (>) :: RelationType -> RelationType -> Bool # (>=) :: RelationType -> RelationType -> Bool # max :: RelationType -> RelationType -> RelationType # min :: RelationType -> RelationType -> RelationType #
Show RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods showsPrec :: Int -> RelationType -> ShowS # show :: RelationType -> String # showList :: [RelationType] -> ShowS #
Arbitrary RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods arbitrary :: Gen RelationType # shrink :: RelationType -> [RelationType] #
CoArbitrary RelationType Source #
Instance details Defined in Domain.Math.Data.Relation Methods coarbitrary :: RelationType -> Gen b -> Gen b #

relationSymbols :: [(RelationType, (String, Symbol))] Source #

notRelation :: Relation a -> Relation a Source #

eval :: (Ord a, Num a) => RelationType -> a -> a -> Bool Source #

Constructor functions

makeType :: RelationType -> a -> a -> Relation a Source #

(.==.) :: a -> a -> Relation a infix 1 Source #

(./=.) :: a -> a -> Relation a infix 1 Source #

(.<.) :: a -> a -> Relation a infix 1 Source #

(.>.) :: a -> a -> Relation a infix 1 Source #

(.<=.) :: a -> a -> Relation a infix 1 Source #

(.>=.) :: a -> a -> Relation a infix 1 Source #

(.~=.) :: a -> a -> Relation a infix 1 Source #

Equation (or equality)

type Equations a = [Equation a] Source #

data Equation a Source #

Constructors

a :==: a infix 1

Instances

Functor Equation Source #
Instance details Defined in Domain.Math.Data.Relation Methods fmap :: (a -> b) -> Equation a -> Equation b # (<$) :: a -> Equation b -> Equation a #
Foldable Equation Source #
Instance details Defined in Domain.Math.Data.Relation Methods fold :: Monoid m => Equation m -> m # foldMap :: Monoid m => (a -> m) -> Equation a -> m # foldr :: (a -> b -> b) -> b -> Equation a -> b # foldr' :: (a -> b -> b) -> b -> Equation a -> b # foldl :: (b -> a -> b) -> b -> Equation a -> b # foldl' :: (b -> a -> b) -> b -> Equation a -> b # foldr1 :: (a -> a -> a) -> Equation a -> a # foldl1 :: (a -> a -> a) -> Equation a -> a # toList :: Equation a -> [a] # null :: Equation a -> Bool # length :: Equation a -> Int # elem :: Eq a => a -> Equation a -> Bool # maximum :: Ord a => Equation a -> a # minimum :: Ord a => Equation a -> a # sum :: Num a => Equation a -> a # product :: Num a => Equation a -> a #
Traversable Equation Source #
Instance details Defined in Domain.Math.Data.Relation Methods traverse :: Applicative f => (a -> f b) -> Equation a -> f (Equation b) # sequenceA :: Applicative f => Equation (f a) -> f (Equation a) # mapM :: Monad m => (a -> m b) -> Equation a -> m (Equation b) # sequence :: Monad m => Equation (m a) -> m (Equation a) #
Relational Equation Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Equation a -> a Source # rightHandSide :: Equation a -> a Source # flipSides :: Equation a -> Equation a Source # constructor :: Equation a -> b -> b -> Equation b Source # isSymmetric :: Equation a -> Bool Source #
Eq a => Eq (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods (==) :: Equation a -> Equation a -> Bool # (/=) :: Equation a -> Equation a -> Bool #
Ord a => Ord (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods compare :: Equation a -> Equation a -> Ordering # (<) :: Equation a -> Equation a -> Bool # (<=) :: Equation a -> Equation a -> Bool # (>) :: Equation a -> Equation a -> Bool # (>=) :: Equation a -> Equation a -> Bool # max :: Equation a -> Equation a -> Equation a # min :: Equation a -> Equation a -> Equation a #
Show a => Show (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods showsPrec :: Int -> Equation a -> ShowS # show :: Equation a -> String # showList :: [Equation a] -> ShowS #
Arbitrary a => Arbitrary (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods arbitrary :: Gen (Equation a) # shrink :: Equation a -> [Equation a] #
CoArbitrary a => CoArbitrary (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods coarbitrary :: Equation a -> Gen b -> Gen b #
IsTerm a => IsTerm (Equation a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods toTerm :: Equation a -> Term # toTermList :: [Equation a] -> Term # fromTerm :: MonadPlus m => Term -> m (Equation a) # fromTermList :: MonadPlus m => Term -> m [Equation a] #

equationView :: View (Relation a) (Equation a) Source #

Inequality

data Inequality a Source #

Constructors

a :<: a infix 1
a :>: a infix 1
a :<=: a infix 1
a :>=: a infix 1

Instances

Functor Inequality Source #
Instance details Defined in Domain.Math.Data.Relation Methods fmap :: (a -> b) -> Inequality a -> Inequality b # (<$) :: a -> Inequality b -> Inequality a #
Foldable Inequality Source #
Instance details Defined in Domain.Math.Data.Relation Methods fold :: Monoid m => Inequality m -> m # foldMap :: Monoid m => (a -> m) -> Inequality a -> m # foldr :: (a -> b -> b) -> b -> Inequality a -> b # foldr' :: (a -> b -> b) -> b -> Inequality a -> b # foldl :: (b -> a -> b) -> b -> Inequality a -> b # foldl' :: (b -> a -> b) -> b -> Inequality a -> b # foldr1 :: (a -> a -> a) -> Inequality a -> a # foldl1 :: (a -> a -> a) -> Inequality a -> a # toList :: Inequality a -> [a] # null :: Inequality a -> Bool # length :: Inequality a -> Int # elem :: Eq a => a -> Inequality a -> Bool # maximum :: Ord a => Inequality a -> a # minimum :: Ord a => Inequality a -> a # sum :: Num a => Inequality a -> a # product :: Num a => Inequality a -> a #
Traversable Inequality Source #
Instance details Defined in Domain.Math.Data.Relation Methods traverse :: Applicative f => (a -> f b) -> Inequality a -> f (Inequality b) # sequenceA :: Applicative f => Inequality (f a) -> f (Inequality a) # mapM :: Monad m => (a -> m b) -> Inequality a -> m (Inequality b) # sequence :: Monad m => Inequality (m a) -> m (Inequality a) #
Relational Inequality Source #
Instance details Defined in Domain.Math.Data.Relation Methods leftHandSide :: Inequality a -> a Source # rightHandSide :: Inequality a -> a Source # flipSides :: Inequality a -> Inequality a Source # constructor :: Inequality a -> b -> b -> Inequality b Source # isSymmetric :: Inequality a -> Bool Source #
Show a => Show (Inequality a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods showsPrec :: Int -> Inequality a -> ShowS # show :: Inequality a -> String # showList :: [Inequality a] -> ShowS #
Arbitrary a => Arbitrary (Inequality a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods arbitrary :: Gen (Inequality a) # shrink :: Inequality a -> [Inequality a] #
CoArbitrary a => CoArbitrary (Inequality a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods coarbitrary :: Inequality a -> Gen b -> Gen b #
IsTerm a => IsTerm (Inequality a) Source #
Instance details Defined in Domain.Math.Data.Relation Methods toTerm :: Inequality a -> Term # toTermList :: [Inequality a] -> Term # fromTerm :: MonadPlus m => Term -> m (Inequality a) # fromTermList :: MonadPlus m => Term -> m [Inequality a] #

inequalityView :: View (Relation a) (Inequality a) Source #