:: [Bool] -> Bool -package:extra

and returns the conjunction of a Boolean list. For the result to be True, the list must be finite; False, however, results from a False value at a finite index of a finite or infinite list.

Examples

>>> and []
True

>>> and [True]
True

>>> and [False]
False

>>> and [True, True, False]
False

>>> and (False : repeat True) -- Infinite list [False,True,True,True,True,True,True...
False

>>> and (repeat True)
* Hangs forever *

or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.

Examples

>>> or []
False

>>> or [True]
True

>>> or [False]
False

>>> or [True, True, False]
True

>>> or (True : repeat False) -- Infinite list [True,False,False,False,False,False,False...
True

>>> or (repeat False)
* Hangs forever *

Test whether a list is empty.

>>> null []
True

>>> null [1]
False

>>> null [1..]
False

A version specialized to lists to avoid errors such as taking null of Maybe [a] instead of [a]. Such errors are hard to detect, because the type of elements of the list is not constrained.

Is the given list not null? Equivalent to not . null

>>> allEqual "aab"
False

>>> allEqual "aaa"
True

>>> allEqual "aa"
True

>>> allEqual "a"
True

>>> allEqual ""
True

Check whether all elements in a list are distinct from each other. Assumes that the Eq instance stands for an equivalence relation. O(n²) in the worst case distinct xs == True.

Checks if all the elements in the list are equal. Assumes that the Eq instance stands for an equivalence relation. O(n).

Test if all elements of a list are equal; returns True for empty list.

Test whether an index is a diagonal one.

>>> isDiag [2,2,2]
True

>>> isDiag [1,2]
False

Check if all elements in a list are distinct. Note that empty or singleton lists are always distinct.

>>> distinct []
True

>>> distinct [1]
True

>>> distinct [1, 2, 3]
True

>>> distinct [1, 2, 2]
False

Checks if all elements of a list are equal.

Checks if all elements of a list are equal. Exceptionally this function returns false for an empty or unit list. This returns true when all elements are equal and the list has a length greater than or equal to two.

O(n). Whether the elements are all equal.

>>> allEqual [1..]
False

>>> allEqual [3, 3, 3, 3]
True

>>> allEqual []
True

>>> allEqual [1]
True

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

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

>>> isAscending "abc"
True

>>> isAscending "abb"
True

>>> isAscending "aba"
False

>>> isAscending "cba"
False

>>> isAscending "a"
True

>>> isAscending ""
True

The isSorted predicate returns True if the elements of a list occur in non-descending order, equivalent to isSortedBy (<=).

Are all of the items in a list (which have an ordering) distinct? This uses Set (as opposed to nub) for better asymptotic time complexity.