Lazy lists of elements.
Lazy lists are similar to lists, with the exception that their contents are only computed whenever requested. This makes them particularly useful in contexts where streams of data are to be handled.
Note For this documentation, we will assume the existence of a lazy list syntax extension such that [^ ^] is the empty lazy list and [^ a;b;c ^] is the lazy list containing elements a, b, c.
Note Enumerations (as featured in module BatEnum) and lazy lists (as featured in this module) are quite similar in purpose. Lazy lists are slightly higher level, insofar as no cloning is required to get them to work, which makes them slightly more useful in contexts where backtracking is common. Enumerations, on the other hand, are closer to traditional stream processing, and require more low-level marking whenever backtracking is required, but may be faster and more memory-efficient when used properly. Either choice is recommended over OCaml's built-in Stream.
Empty_list is raised when an operation applied on an empty list is invalid. For instance, hd nil will raise Empty_list.
Invalid_index is raised when an indexed access on a list is out of list bounds.
Different_list_size is raised when applying functions such as iter2 on two lists having different size.
Note The types are kept concrete so as to allow pattern-matching. However, it is generally easier to manipulate nil and cons.
include BatEnum.Enumerable with type 'a enumerable = 'a ttype 'a enumerable = 'a tThe data structure, e.g. 'a List.t
include BatInterfaces.Mappable with type 'a mappable = 'a ttype 'a mappable = 'a tThe data structure, e.g. 'a List.t
val nil : 'a tThe empty list.
val peek : 'a t -> 'a optionpeek l returns the first element of l, if it exists.
val from : (unit -> 'a) -> 'a tfrom next creates a (possibly infinite) lazy list from the successive results of next.
val from_while : (unit -> 'a option) -> 'a tfrom next creates a (possibly infinite) lazy list from the successive results of next. The list ends whenever next returns None.
val seq : 'a -> ('a -> 'a) -> ('a -> bool) -> 'a tseq data next cond creates a lazy list from the successive results of applying next to data, then to the result, etc. The list continues until the condition cond fails. For example, seq 1 ((+) 1) ((>) 100) returns [^1, 2, ... 99^]. If cond init is false, the result is empty. To create an infinite lazy list, pass (fun _ -> true) as cond.
val unfold : 'b -> ('b -> ('a * 'b) option) -> 'a tunfold data next creates a (possibly infinite) lazy list from the successive results of applying next to data, then to the result, etc. The list ends whenever next returns None. The function next should return a pair option whose first element will be the current value of the sequence; the second element will be passed (lazily) to next in order to compute the following element. One example of a use of unfold is to make each element of the resulting sequence to depend on the previous two elements, as in this Fibonacci sequence definition:
let data = (1, 1)
let next (x, y) = Some (x, (y, x + y))
let fib = unfold data nextThe first element x of the pair within Some will be the current value of the sequence; the next value of the sequence, and the one after that, are recorded as y and x + y respectively.
val from_loop : 'b -> ('b -> 'a * 'b) -> 'a tfrom_loop data next creates a (possibly infinite) lazy list from the successive results of applying next to data, then to the result, etc. The list ends whenever the function raises LazyList.No_more_elements. (For further information see unfold; ignore references to option and Some.)
val init : int -> (int -> 'a) -> 'a tSimilar to Array.init, init n f returns the lazy list containing the results of (f 0),(f 1).... (f (n-1)).
val make : int -> 'a -> 'a tSimilar to String.make, make n x returns a list containing n elements x.
val range : int -> int -> int tCompute lazily a range of integers a .. b as a lazy list.
The range is empty if b <= a.
val iter : ('a -> 'b) -> 'a t -> unitEager iteration
iter f [^ a0; a1; ...; an ^] applies function f in turn to a0;
a1; ...; an. It is equivalent to begin f a0; f a1; ...; f an; ()
end. In particular, it causes all the elements of the list to be evaluated.
val iteri : (int -> 'a -> unit) -> 'a t -> unitEager iteration, with indices
iteri f [^ a0; a1; ...; an ^] applies function f in turn to a0; a1;...; an, along with the corresponding 0,1..n index. It is equivalent to begin f 0 a0; f 1 a1; ...; f n an; ()
end. In particular, it causes all the elements of the list to be evaluated.
Lazy map
map f [^ a0; a1; ... ^] builds the list [^ f a0; f a1; ... ^] with the results returned by f. Not tail-recursive. Evaluations of f take place only when the contents of the list are forced.
Lazy map, with indices
mapi f [^ a0; a1; ... ^] builds the list [^ f 0 a0; f 1 a1;
... ^] with the results returned by f. Not tail-recursive. Evaluations of f take place only when the contents of the list are forced.
val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'aEager fold_left
LazyList.fold_left f a [^ b0; b1; ...; bn ^] is f (... (f (f
a b0) b1) ...) bn. This causes evaluation of all the elements of the list.
val fold_right : ('a -> 'b -> 'b) -> 'b -> 'a t -> 'bEager fold_right
fold_right f b [^ a0; a1; ...; an ^] is f a0 (f a1 (... (f an b) ...)). This causes evaluation of all the elements of the list. Not tail-recursive.
Note that the argument order of this function is the same as fold_left above, but inconsistent with other fold_right functions in Batteries. We hope to fix this inconsistency in the next compatibility-breaking release, so you should rather use the more consistent eager_fold_right.
val eager_fold_right : ('a -> 'b -> 'b) -> 'a t -> 'b -> 'bEager fold_right
As fold_right above, but with the usual argument order for a fold_right.
Just as fold_left on a structure 'a t turns an element-level function of type ('b -> 'a -> 'b), with the accumulator argument 'b on the left, into a structure-level function 'b -> 'a t -> 'b, fold_right turns a function ('a -> 'b -> 'b) (accumulator on the right) into a 'a t -> 'b -> 'b.
Lazy fold_right lazy_fold_right f (Cons (a0, Cons (a1, Cons (a2, nil)))) b is lazy (f a0 (lazy (f a1 (lazy (f a2 b))))).
Forcing the result of lazy_fold_right forces the first element of the list; the rest is forced only if/when the function f forces its accumulator argument.
val mem : 'a -> 'a t -> boolmem x l determines if x is part of l. Evaluates all the elements of l which appear before x.
val memq : 'a -> 'a t -> boolAs mem, but with physical equality
val find : ('a -> bool) -> 'a t -> 'afind p l returns the first element of l such as p x returns true.
val rfind : ('a -> bool) -> 'a t -> 'arfind p l returns the last element x of l such as p x returns true.
val find_exn : ('a -> bool) -> exn -> 'a t -> 'afind_exn p e l returns the first element of l such as p x returns true or raises e if such an element has not been found.
val rfind_exn : ('a -> bool) -> exn -> 'a t -> 'arfind_exn p e l returns the last element of l such as p x returns true or raises e if such an element has not been found.
val findi : (int -> 'a -> bool) -> 'a t -> int * 'afindi p e l returns the first element ai of l along with its index i such that p i ai is true.
val rfindi : (int -> 'a -> bool) -> 'a t -> int * 'arfindi p e l returns the last element ai of l along with its index i such that p i ai is true.
val index_of : 'a -> 'a t -> int optionindex_of e l returns the index of the first occurrence of e in l, or None if there is no occurrence of e in l
val index_ofq : 'a -> 'a t -> int optionindex_ofq e l behaves as index_of e l except it uses physical equality
val rindex_of : 'a -> 'a t -> int optionindex_of e l returns the index of the last occurrence of e in l, or None if there is no occurrence of e in l
val rindex_ofq : 'a -> 'a t -> int optionrindex_ofq e l behaves as rindex_of e l except it uses physical equality
Compute and return the first node from the list as a Cons. This differs from hd, which returns the first element (the first component of the first node).
val length : 'a t -> intReturn the length (number of elements) of the given list.
Causes the evaluation of all the elements of the list.
val is_empty : 'a t -> boolReturns true if the list is empty, false otherwise.
val would_at_fail : 'a t -> int -> boolwould_at_fail l n returns true if l contains strictly less than n elements, false otherwise
val hd : 'a t -> 'aReturn the first element of the given list.
val first : 'a t -> 'aAs hd
val last : 'a t -> 'aReturns the last element of the list.
val at : 'a t -> int -> 'aat l n returns the element at index n (starting from 0) in the list l.
val nth : 'a t -> int -> 'aObsolete. As at
These lists behave essentially as HashMap, although they are typically faster for short number of associations, and much slower for for large number of associations.
val assoc : 'a -> ('a * 'b) t -> 'bassoc a l returns the value associated with key a in the list of pairs l. That is, assoc a [^ ...; (a,b); ...^] = b if (a,b) is the leftmost binding of a in list l.
val mem_assoc : 'a -> ('a * 'b) t -> boolAs assoc but simply returns true if a binding exists, false otherwise.
Evaluate a list and append another list after this one.
Cost is linear in the length of the first list, not tail-recursive.
Eager reverse-and-append
Cost is linear in the length of the first list, tail-recursive.
Lazy append
Cost is constant. All evaluation is delayed until the contents of the list are actually read. Reading itself is delayed by a constant.
split_at n l returns two lists l1 and l2, l1 containing the first n elements of l and l2 the others.
unique cmp l returns the list l without any duplicate element. Default comparator ( = ) is used if no comparison function specified.
as unique except only uses an equality function. Use for short lists when comparing is expensive compared to equality testing
remove l x returns the list l without the first element x found or returns l if no element is equal to x. Elements are compared using ( = ).
remove_if cmp l is similar to remove, but with cmp used instead of ( = ).
remove_all l x is similar to remove but removes all elements that are equal to x and not only the first one.
remove_all_such f l is similar to remove but removes all elements that satisfy the predicate f and not only the first one.
take n l returns up to the n first elements from list l, if available.
drop n l returns l without the first n elements, or the empty list if l have less than n elements.
take_while f xs returns the first elements of list xs which satisfy the predicate f.
drop_while f xs returns the list xs with the first elements satisfying the predicate f dropped.
val combinations : 'a list -> 'a list tcombinations l yields a list of all combinations of elements of l. Each combination selects a "subset" of the elements of l (duplicates are considered as distinct elements).
val permutations : 'a list -> 'a list tpermutations l yields a lazy list of all permutations of the list l. Every permutation has the same elements as l, but in a different order. There are factorial (length l) permutations.
val to_list : 'a t -> 'a listEager conversion to string.
val to_array : 'a t -> 'a arrayEager conversion to array.
val of_list : 'a list -> 'a tLazy conversion from lists
Albeit slower than eager conversion, this is the default mechanism for converting from regular lists to lazy lists. This for two reasons : * if you're using lazy lists, total speed probably isn't as much an issue as start-up speed * this will let you convert regular infinite lists to lazy lists.
val eager_of_list : 'a list -> 'a tEager conversion from lists.
This function is much faster than of_list but will freeze on cyclic lists.
val of_array : 'a array -> 'a tEager conversion from array
Lazy filtering.
filter p l returns all the elements of the list l that satisfy the predicate p. The order of the elements in the input list is preserved.
val exists : ('a -> bool) -> 'a t -> boolEager existential.
exists p [^ a0; a1; ... ^] checks if at least one element of the list satisfies the predicate p. That is, it returns (p a0) || (p a1) || ... .
val for_all : ('a -> bool) -> 'a t -> boolEager universal.
for_all p [^ a0; a1; ... ^] checks if all elements of the list satisfy the predicate p. That is, it returns (p a0) && (p a1) && ... .
Lazily eliminate some elements and transform others.
filter_map f [^ a0; a1; ... ^] applies lazily f to each a0, a1... If f ai evaluates to None, the element is not included in the result. Otherwise, if f ai evaluates to Some x, element x is included in the result.
This is equivalent to match f a0 with
| Some x0 -> x0 ^:^ (match f a1 with
| Some x1 -> x1 ^:^ ...
| None -> [^ ^])
| None -> [^ ^] .
val eternity : unit tAn infinite list of nothing
Sort the list using optional comparator (by default compare).
map2 f [^ a0; a1; ...^] [^ b0; b1; ... ^] is [^ f a0 b0; f a1
b1; ... ^].
iter2 f [^ a0; ...; an ^] [^ b0; ...; bn ^] calls in turn f a0 b0; ...; f an bn. Tail-recursive, eager.
fold_left2 f a [^ b0; b1; ...; bn ^] [^ c0; c1; ...; cn ^] is f (... (f (f a b0 c0) b1 c1) ...) bn cn. Eager.
fold_right2 f [^ a0; a1; ...; an ^] [^ b0; b1; ...; bn ^] c is f a0 b0 (f a1 b1 (... (f an bn c) ...)). Eager.
Same as for_all, but for a two-argument predicate.
equal eq s1 s2 compares elements of s1 and s2 pairwise using eq and returns true if all elements pass the test and the lists have the same length; otherwise it returns false. Examples:
equal (=) (range 0 4) (range 0 4) (* true *)
(* Make lazy lists of lazy lists: *)
let s1 = init 5 (range 0)
let s2 = init 5 (range 0)
equal (equal (=)) s1 s2 (* true *)(Calling = directly on a pair of lazy lists may succeed but is not guaranteed to behave consistently.)
Note that on lists of equal length, equal and for_all2 can perform the same function; their intended uses differ, however, as signaled by behavior on lists of different lengths.
Same as exists, but for a two-argument predicate.
Transform a pair of lists into a list of pairs: combine [^ a0; a1; ... ^] [^ b0; b1; ... ^] is [^ (a0, b0); (a1, b1); ... ^].
module Infix : sig ... endval print :
?first:string ->
?last:string ->
?sep:string ->
('a BatInnerIO.output -> 'b -> unit) ->
'a BatInnerIO.output ->
'b t ->
unitThe following modules replace functions defined in LazyList with functions behaving slightly differently but having the same name. This is by design: the functions meant to override the corresponding functions of LazyList.
module Exceptionless : sig ... endExceptionless counterparts for error-raising operations
module Labels : sig ... endOperations on LazyList with labels.