-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Predicates on lists -- -- Please see the README on GitHub at -- https://github.com/pgujjula/list-utilities#readme @package list-predicate @version 0.1.0.0 -- | Predicates (True/False queries) on lists. -- -- The functions in this module are as lazy as possible. For example, -- sortedBy undefined [undefined] == True, since a list -- of one element must be sorted, no matter the comparison function, or -- the value of the element. module Data.List.Predicate -- | O(n). Whether the elements are all equal. -- -- 
--   >>> allEqual [1..]
--   False
--   
--   >>> allEqual [3, 3, 3, 3]
--   True
--   
--   >>> allEqual []
--   True
--   
--   >>> allEqual [1]
--   True
--
allEqual :: Eq a => [a] -> Bool -- | O(n). Like allEqual, with a custom equality test. -- -- 
--   >>> allEqualBy ((==) `on` (`mod` 10)) [3, 13, 23]
--   True
--   
--   >>> allEqualBy ((==) `on` (`mod` 10)) [3, 13, 24]
--   False
--
allEqualBy :: (a -> a -> Bool) -> [a] -> Bool -- | O(n). Whether the elements are in sorted order. -- -- 
--   >>> sorted [1, 2, 3, 3]
--   True
--   
--   >>> sorted [1, 2, 3, 2]
--   False
--   
--   >>> sorted []
--   True
--   
--   >>> sorted [1]
--   True
--
sorted :: Ord a => [a] -> Bool -- | O(n). Like sorted, with a custom comparison test. -- -- 
--   >>> sortedBy (comparing Down) [3, 2, 1]
--   True
--   
--   >>> sortedBy (comparing Down) [3, 2, 1, 2]
--   False
--
sortedBy :: (a -> a -> Ordering) -> [a] -> Bool -- | O(n log(n)). Whether the elements are all unique. -- -- 
--   >>> allUnique [1, 2, 5, 7]
--   True
--   
--   >>> allUnique [1, 2, 5, 2]
--   False
--   
--   >>> allUnique []
--   True
--   
--   >>> allUnique [1]
--   True
--
allUnique :: Ord a => [a] -> Bool -- | O(n log(n)). Like allUnique, with a custom comparison -- test. -- -- 
--   >>> allUniqueBy (comparing head) ["apple", "bow", "cat"]
--   True
--   
--   >>> allUniqueBy (comparing head) ["apple", "bow", "ant"]
--   False
--
allUniqueBy :: (a -> a -> Ordering) -> [a] -> Bool -- | O(n). Whether all adjacent pairs of elements are different. -- Useful for determining whether a sorted list is all unique. -- -- 
--   >>> allAdjUnique [1, 2, 3, 2]
--   True
--   
--   >>> allAdjUnique [1, 2, 2, 3]
--   False
--   
--   >>> allAdjUnique []
--   True
--   
--   >>> allAdjUnique [1]
--   True
--
allAdjUnique :: Eq a => [a] -> Bool -- | O(n). Like allAdjUnique, with a custom equality test. -- -- 
--   >>> allAdjUniqueBy ((==) `on` head) ["apple", "bow", "cat", "ant"]
--   True
--   
--   >>> allAdjUniqueBy ((==) `on` head) ["apple", "ant", "bow", "cat"]
--   False
--
allAdjUniqueBy :: (a -> a -> Bool) -> [a] -> Bool -- | O(n). Whether the list is increasing sequentially (one-by-one). -- -- 
--   >>> ascSequential [1, 2, 3, 4, 5]
--   True
--   
--   >>> ascSequential [1, 2, 3, 4, 8]
--   False
--   
--   >>> ascSequential ([] :: [Int])
--   True
--   
--   >>> ascSequential [1]
--   True
--
ascSequential :: Enum a => [a] -> Bool -- | O(n). Whether the list is descending sequentially (one-by-one). -- -- 
--   >>> descSequential [5, 4, 3, 2, 1]
--   True
--   
--   >>> descSequential [5, 4, 3, 3, 1]
--   False
--   
--   >>> descSequential ([] :: [Int])
--   True
--   
--   >>> descSequential [1]
--   True
--
descSequential :: Enum a => [a] -> Bool -- | O(n). Whether the input is a palindrome, i.e., the same -- forwards and backwards. -- -- 
--   >>> palindrome "rotor"
--   True
--   
--   >>> palindrome "rover"
--   False
--   
--   >>> palindrome ""
--   True
--   
--   >>> palindrome "a"
--   True
--
palindrome :: Eq a => [a] -> Bool