Complexity O(1).

Complexity O(1).

Complexity O(log n).

Complexity O(1).

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

Complexity O(log n).

reverse xs returns the elements of xs in reverse order. xs must be finite.

Left-associative fold of a structure.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z `f` x1 in the above example) before applying them to the operator (e.g. to (`f` x2)). This results in a thunk chain \(\mathcal{O}(n)\) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl f z . toList

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite list to a single, monolithic result (e.g. length).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Determines whether any element of the structure satisfies the predicate.

Determines whether all elements of the structure satisfy the predicate.

The sum function computes the sum of the numbers of a structure.

Since: base-4.8.0.0

The product function computes the product of the numbers of a structure.

Since: base-4.8.0.0

The largest element of a non-empty structure.

Since: base-4.8.0.0

The least element of a non-empty structure.

Since: base-4.8.0.0

drop i l where l has length n has worst case complexity Complexity O(log n), Average case complexity should be O(min(log i, log n)).

Does the element occur in the structure?

Since: base-4.8.0.0

notElem is the negation of elem.

Change element at the given index. Complexity O(log n).

Apply a function to the value at the given index. Complexity O(log n).

List of elements of a structure, from left to right.

Since: base-4.8.0.0

Complexity O(n). toList :: RAList a -> [a] toList = foldr (:) [] toList ra = tops ra [] where flat (Leaf x) a = x : a flat (Node x l r) a = x : flat l (flat r a) tops RNil r = r tops (RCons _tot _ t xs) r = flat t (tops xs r)

Complexity O(n).