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Module BatLazyList

module BatLazyList: sig .. end

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.

Exceptions 
exception Empty_list

Empty_list is raised when an operation applied on an empty list is invalid. For instance, hd nil will raise Empty_list.

exception Invalid_index of int

Invalid_index is raised when an indexed access on a list is out of list bounds.

exception Different_list_size of string

Different_list_size is raised when applying functions such as iter2 on two lists having different size.

exception No_more_elements

See BatLazyList.from and BatLazyList.from_loop for more information on this exception.

Type

Note The types are kept concrete so as to allow pattern-matching. However, it is generally easier to manipulate BatLazyList.nil and BatLazyList.cons.

type 'a t = 'a node_t Stdlib.Lazy.t

The type of a lazy list.

type 'a node_t =
| Nil
| Cons of 'a * 'a t (*

The type of an item in the list.

*) 
include BatEnum.Enumerable
include BatInterfaces.Mappable
Access 
val nil : 'a t

The empty list.

val cons : 'a -> 'a t -> 'a t

Build a list from a head and a tail.

val (^:^) : 'a -> 'a t -> 'a t

As cons: x^:^l is the lazy list with head x and tail l

val peek : 'a t -> 'a option

peek l returns the first element of l, if it exists.

val get : 'a t -> ('a * 'a t) option

get l returns the head and tail of l, if l is not empty.

List creation 
val from : (unit -> 'a) -> 'a t

from next creates a (possibly infinite) lazy list from the successive results of next.

val from_while : (unit -> 'a option) -> 'a t

from 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 t

seq 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 t

unfold 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 next

The 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 t

from_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 t

Similar 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 t

Similar to String.make, make n x returns a list containing n elements x.

val range : int -> int -> int t

Compute lazily a range of integers a .. b as a lazy list.

The range is empty if b <= a.

Higher-order functions 
val iter : ('a -> 'b) -> 'a t -> unit

Eager 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 -> unit

Eager 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.

val map : ('a -> 'b) -> 'a t -> 'b t

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.

val mapi : (int -> 'a -> 'b) -> 'a t -> 'b t

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 -> 'a

Eager 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 -> 'b

Eager 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 -> 'b

Eager 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.

val lazy_fold_right : ('a -> 'b Stdlib.Lazy.t -> 'b) ->
       'a t -> 'b Stdlib.Lazy.t -> 'b Stdlib.Lazy.t

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.

Finding 
val mem : 'a -> 'a t -> bool

mem x l determines if x is part of l. Evaluates all the elements of l which appear before x.

val memq : 'a -> 'a t -> bool

As mem, but with physical equality

val find : ('a -> bool) -> 'a t -> 'a

find p l returns the first element of l such as p x returns true.

val rfind : ('a -> bool) -> 'a t -> 'a

rfind p l returns the last element x of l such as p x returns true.

val find_exn : ('a -> bool) -> exn -> 'a t -> 'a

find_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 -> 'a

rfind_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 * 'a

findi 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 * 'a

rfindi 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 option

index_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 option

index_ofq e l behaves as index_of e l except it uses physical equality

val rindex_of : 'a -> 'a t -> int option

index_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 option

rindex_ofq e l behaves as rindex_of e l except it uses physical equality

Common functions 
val next : 'a t -> 'a node_t

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 -> int

Return the length (number of elements) of the given list.

Causes the evaluation of all the elements of the list.

val is_empty : 'a t -> bool

Returns true if the list is empty, false otherwise.

val would_at_fail : 'a t -> int -> bool

would_at_fail l n returns true if l contains strictly less than n elements, false otherwise

val hd : 'a t -> 'a

Return the first element of the given list.

val tl : 'a t -> 'a t

Return the given list without its first element.

val first : 'a t -> 'a

As hd

val last : 'a t -> 'a

Returns the last element of the list.

val at : 'a t -> int -> 'a

at l n returns the element at index n (starting from 0) in the list l.

val nth : 'a t -> int -> 'a

Obsolete. As at

Association lists

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 -> 'b

assoc 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 assq : 'a -> ('a * 'b) t -> 'b

As BatLazyList.assoc but with physical equality

val mem_assoc : 'a -> ('a * 'b) t -> bool

As BatLazyList.assoc but simply returns true if a binding exists, false otherwise.

val mem_assq : 'a -> ('a * 'b) t -> bool

As BatLazyList.mem_assoc but with physical equality.

val rev : 'a t -> 'a t

Eager list reversal.

Transformations 
val eager_append : 'a t -> 'a t -> 'a t

Evaluate a list and append another list after this one.

Cost is linear in the length of the first list, not tail-recursive.

val rev_append : 'a t -> 'a t -> 'a t

Eager reverse-and-append

Cost is linear in the length of the first list, tail-recursive.

val append : 'a t -> 'a t -> 'a t

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.

val (^@^) : 'a t -> 'a t -> 'a t

As lazy append

val concat : 'a t t -> 'a t

Lazy concatenation of a lazy list of lazy lists

val flatten : 'a t list -> 'a t

Lazy concatenation of a list of lazy lists

val split_at : int -> 'a t -> 'a t * 'a t

split_at n l returns two lists l1 and l2, l1 containing the first n elements of l and l2 the others.

val split_nth : int -> 'a t -> 'a t * 'a t

Obsolete. As split_at.

Dropping elements 
val unique : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

unique cmp l returns the list l without any duplicate element. Default comparator ( = ) is used if no comparison function specified.

val unique_eq : ?eq:('a -> 'a -> bool) -> 'a t -> 'a t

as unique except only uses an equality function. Use for short lists when comparing is expensive compared to equality testing

val remove : 'a -> 'a t -> 'a t

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 ( = ).

val remove_if : ('a -> bool) -> 'a t -> 'a t

remove_if cmp l is similar to remove, but with cmp used instead of ( = ).

val remove_all : 'a -> 'a t -> 'a t

remove_all l x is similar to remove but removes all elements that are equal to x and not only the first one.

val remove_all_such : ('a -> bool) -> 'a t -> 'a t

remove_all_such f l is similar to remove but removes all elements that satisfy the predicate f and not only the first one.

val take : int -> 'a t -> 'a t

take n l returns up to the n first elements from list l, if available.

val drop : int -> 'a t -> 'a t

drop n l returns l without the first n elements, or the empty list if l have less than n elements.

val take_while : ('a -> bool) -> 'a t -> 'a t

take_while f xs returns the first elements of list xs which satisfy the predicate f.

val drop_while : ('a -> bool) -> 'a t -> 'a t

drop_while f xs returns the list xs with the first elements satisfying the predicate f dropped.

Combinatorics 
val combinations : 'a list -> 'a list t

combinations 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 t

permutations 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.

Conversions 
val to_list : 'a t -> 'a list

Eager conversion to string.

val to_stream : 'a t -> 'a Stream.t

Lazy conversion to stream.

val to_array : 'a t -> 'a array

Eager conversion to array.

val enum : 'a t -> 'a BatEnum.t

Lazy conversion to enumeration

val of_list : 'a list -> 'a t

Lazy 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 of_stream : 'a Stream.t -> 'a t

Lazy conversion from stream.

val of_enum : 'a BatEnum.t -> 'a t

Lazy conversion from enum.

val eager_of_list : 'a list -> 'a t

Eager conversion from lists.

This function is much faster than BatLazyList.of_list but will freeze on cyclic lists.

val of_array : 'a array -> 'a t

Eager conversion from array

Predicates 
val filter : ('a -> bool) -> 'a t -> 'a t

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 -> bool

Eager 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 -> bool

Eager 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) && ... .

val filter_map : ('a -> 'b option) -> 'a t -> 'b t

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   -> [^ ^] .

Misc. 
val eternity : unit t

An infinite list of nothing

Sorting 
val sort : ?cmp:('a -> 'a -> int) -> 'a t -> 'a t

Sort the list using optional comparator (by default compare).

val stable_sort : ('a -> 'a -> int) -> 'a t -> 'a t
Operations on two lists 
val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

map2 f [^ a0; a1; ...^] [^ b0; b1; ... ^] is [^ f a0 b0; f a1
    b1; ... ^].

val iter2 : ('a -> 'b -> unit) -> 'a t -> 'b t -> unit

iter2 f [^ a0; ...; an ^] [^ b0; ...; bn ^] calls in turn f a0 b0; ...; f an bn. Tail-recursive, eager.

val fold_left2 : ('a -> 'b -> 'c -> 'a) -> 'a -> 'b t -> 'c t -> 'a

fold_left2 f a [^ b0; b1; ...; bn ^] [^ c0; c1; ...; cn ^] is f (... (f (f a b0 c0) b1 c1) ...) bn cn. Eager.

val fold_right2 : ('a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c

fold_right2 f [^ a0; a1; ...; an ^] [^ b0; b1; ...; bn ^] c is f a0 b0 (f a1 b1 (... (f an bn c) ...)). Eager.

val for_all2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Same as BatLazyList.for_all, but for a two-argument predicate.

val equal : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

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.

val exists2 : ('a -> 'b -> bool) -> 'a t -> 'b t -> bool

Same as BatLazyList.exists, but for a two-argument predicate.

val combine : 'a t -> 'b t -> ('a * 'b) t

Transform a pair of lists into a list of pairs: combine [^ a0; a1; ... ^] [^ b0; b1; ... ^] is [^ (a0, b0); (a1, b1); ... ^].

val uncombine : ('a * 'b) t -> 'a t * 'b t

Divide a list of pairs into a pair of lists.

module Infix: sig .. end

Infix submodule regrouping all infix operators

Boilerplate code
Printing
val print : ?first:string ->
       ?last:string ->
       ?sep:string ->
       ('a BatInnerIO.output -> 'b -> unit) ->
       'a BatInnerIO.output -> 'b t -> unit
Override modules

The 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 .. end

Exceptionless counterparts for error-raising operations

module Labels: sig .. end

Operations on LazyList with labels.