| Safe Haskell | Safe-Inferred |
|---|
Algebra.PartialOrd
- class Eq a => PartialOrd a where
- partialOrdEq :: PartialOrd a => a -> a -> Bool
- lfpFrom :: PartialOrd a => a -> (a -> a) -> a
- unsafeLfpFrom :: Eq a => a -> (a -> a) -> a
- gfpFrom :: PartialOrd a => a -> (a -> a) -> a
- unsafeGfpFrom :: Eq a => a -> (a -> a) -> a
Partial orderings
class Eq a => PartialOrd a whereSource
A partial ordering on sets: http://en.wikipedia.org/wiki/Partially_ordered_set
This can be defined using either |joinLeq| or |meetLeq|, or a more efficient definition can be derived directly.
Reflexive: a leq a
Antisymmetric: a leq b && b leq a ==> a == b
Transitive: a leq b && b leq c ==> a leq c
The superclass equality (which can be defined using |partialOrdEq|) must obey these laws:
Reflexive: a == a Transitive: a == b && b == c ==> a == b
Instances
| PartialOrd IntSet | |
| (Eq (IntMap v), PartialOrd v) => PartialOrd (IntMap v) | |
| (Eq (Set a), Ord a) => PartialOrd (Set a) | |
| (Eq (k -> v), PartialOrd v, Enumerable k) => PartialOrd (k -> v) | |
| (Eq (a, b), PartialOrd a, PartialOrd b) => PartialOrd (a, b) | |
| (Eq (Map k v), Ord k, PartialOrd v) => PartialOrd (Map k v) |
partialOrdEq :: PartialOrd a => a -> a -> BoolSource
The equality relation induced by the partial-order structure
Fixed points of chains in partial orders
lfpFrom :: PartialOrd a => a -> (a -> a) -> aSource
Least point of a partially ordered monotone function. Checks that the function is monotone.
unsafeLfpFrom :: Eq a => a -> (a -> a) -> aSource
Least point of a partially ordered monotone function. Does not checks that the function is monotone.
gfpFrom :: PartialOrd a => a -> (a -> a) -> aSource
Greatest fixed point of a partially ordered antinone function. Checks that the function is antinone.
unsafeGfpFrom :: Eq a => a -> (a -> a) -> aSource
Greatest fixed point of a partially ordered antinone function. Does not check that the function is antinone.