Modulenumeric-prelude-0.4.4Haskell98

Algebra.Laws

Define common properties that can be used e.g. for automated tests. Cf. to Test.QuickCheck.Utils.

Synopsis

valuecommutative :: Eq a => (b -> b -> a) -> b -> b -> Bool

valueassociative :: Eq a => (a -> a -> a) -> a -> a -> a -> Bool

valueleftIdentity :: Eq a => (b -> a -> a) -> b -> a -> Bool

valuerightIdentity :: Eq a => (a -> b -> a) -> b -> a -> Bool

valueidentity :: Eq a => (a -> a -> a) -> a -> a -> Bool

valueleftZero :: Eq a => (a -> a -> a) -> a -> a -> Bool

valuerightZero :: Eq a => (a -> a -> a) -> a -> a -> Bool

valuezero :: Eq a => (a -> a -> a) -> a -> a -> Bool

valueleftInverse :: Eq a => (b -> b -> a) -> (b -> b) -> a -> b -> Bool

valuerightInverse :: Eq a => (b -> b -> a) -> (b -> b) -> a -> b -> Bool

valueinverse :: Eq a => (b -> b -> a) -> (b -> b) -> a -> b -> Bool

valueleftDistributive

valuerightDistributive

valuehomomorphism

valuerightCascade

valueleftCascade :: Eq a => (b -> b -> b) -> (b -> a -> a) -> a -> b -> b -> Bool