| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Test.Property.Relation.Connex
Description
Synopsis
- connex :: (r -> r -> Bool) -> r -> r -> Bool
- semiconnex :: Eq r => (r -> r -> Bool) -> r -> r -> Bool
- semiconnex_on :: (r -> r -> Bool) -> (r -> r -> Bool) -> r -> r -> Bool
- trichotomous :: Eq r => (r -> r -> Bool) -> r -> r -> Bool
- trichotomous_on :: (r -> r -> Bool) -> (r -> r -> Bool) -> r -> r -> Bool
Documentation
connex :: (r -> r -> Bool) -> r -> r -> Bool Source #
\( \forall a, b: ((a \# b) \vee (b \# a)) \)
For example, ≥ is a connex relation, while 'divides evenly' is not.
A connex relation cannot be symmetric, except for the universal relation.
semiconnex :: Eq r => (r -> r -> Bool) -> r -> r -> Bool Source #
\( \forall a, b: \neg (a \equiv b) \Rightarrow ((a \# b) \vee (b \# a)) \)
A binary relation is semiconnex if it relates all pairs of _distinct_ elements in some way.
A relation is connex if and only if it is semiconnex and reflexive.
semiconnex_on :: (r -> r -> Bool) -> (r -> r -> Bool) -> r -> r -> Bool Source #
\( \forall a, b: \neg (a \doteq b) \Rightarrow ((a \# b) \vee (b \# a)) \)
trichotomous :: Eq r => (r -> r -> Bool) -> r -> r -> Bool Source #
\( \forall a, b, c: ((a \# b) \vee (a \equiv b) \vee (b \# a)) \wedge \neg ((a \# b) \wedge (a \equiv b) \wedge (b \# a)) \)
Note that trichotomous (>) should hold for any Ord instance.
trichotomous_on :: (r -> r -> Bool) -> (r -> r -> Bool) -> r -> r -> Bool Source #
\( \forall a, b, c: ((a \# b) \vee (a \doteq b) \vee (b \# a)) \wedge \neg ((a \# b) \wedge (a \doteq b) \wedge (b \# a)) \)
In other words, exactly one of \(a \# b\), \(a \doteq b\), or \(b \# a\) holds.
For example, > is a trichotomous relation, while ≥ is not.