`module Lazy_list: ``Extlib.LazyList`

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 `Enum`

) 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`

.

**Author(s):** David Teller

`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`

**Note** The types are kept concrete so as to allow pattern-matching.
However, it is generally easier to manipulate `Lazy_list.nil`

and `Lazy_list.cons`

.

type`'a`

t =`'a node_t Lazy.t`

The type of a lazy list.

`type ``'a`

node_t =

`|` |
`Nil` |
|||

`|` |
`Cons of ` |
`(*` | The type of an item in the list. | `*)` |

`include Lazy_list.Enumerable`

`include Lazy_list.Mappable`

`val nil : ``'a t`

`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.`val from : ``(unit -> 'a) -> 'a t`

`from next`

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

.
The function `Lazy_list.No_more_elements`

to denote the end of the
list.`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 from_loop : ``'a -> ('a -> 'b * 'a) -> 'b 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
`Lazy_list.No_more_elements`

`val seq : ``'a -> ('a -> 'a) -> ('a -> bool) -> 'a t`

`seq init step cond`

creates a sequence of data, which starts
from `init`

, extends by `step`

, until the condition `cond`

fails. E.g. `seq 1 ((+) 1) ((>) 100)`

returns `^[1, 2, ... 99]^`

. If ```
cond
init
```

is false, the result is empty.`val unfold : ``'a -> ('a -> ('b * 'a) option) -> 'b 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 the function returns `None`

`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)).
Raise `Invalid_arg "LazyList.init"`

if n < 0.`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 a <= b.

`val iter : ``('a -> 'b) -> 'a t -> unit`

Eager iteration

`iter f [^ a1; ...; an ^]`

applies function `f`

in turn to `a1; ...; an`

.
It is equivalent to `begin f a1; f a2; ...; f an; () end`

. In particular, it
causes all the elements of the list to be evaluated.

`val iteri : ``(int -> 'a -> 'b) -> 'a t -> unit`

Eager iteration, with indices

`iteri f [^ a1; ...; an ^]`

applies function `f`

in turn to `a1 0; ...; an (n - 1)`

.
It is equivalent to `begin f a1 0; f a2 0; ...; f an (n-1); () 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 [^ a1; ...; an ^]`

applies function `f`

to `a1, ..., an`

, and builds the list
`^ f a1; ...; f an ^`

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

`map f [^ a1; ...; an ^]`

applies function `f`

to `a1, ..., an`

, and builds the list
`^ f 0 a1; ...; f ( n - 1) an ^`

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 [^ b1; ...; bn ^]`

is `f (... (f (f a b1) b2) ...) 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 a [^ b1; ...; bn ^]`

is `f ( f (... (f (f a bn) ...) b2) b1`

. This causes
evaluation of all the elements of the list. Not tail-recursive.

`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`

or raises `Not_found`

if such an element
has not been found.`val rfind : ``('a -> bool) -> 'a t -> 'a`

`rfind p l`

returns the last element `x`

of `l`

such as `p x`

returns
`true`

or raises `Not_found`

if such element as not been found.`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`

`find_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, or raises `Not_found`

if no
such element has been found.`val rfindi : ``(int -> 'a -> bool) -> 'a t -> int * 'a`

`findi p e l`

returns the last element `ai`

of `l`

along with its
index `i`

such that `p i ai`

is true, or raises `Not_found`

if no
such element has been found.`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`val next : ``'a t -> 'a node_t`

`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. Raise

`Empty_list`

if the list is empty.
Note: this function does not comply with the usual exceptionless error-management
recommendations, as doing so would essentially render it useless.

`val tl : ``'a t -> 'a t`

Return the given list without its first element. Raise

`Empty_list`

if the list is empty.
Note: this function does not comply with the usual exceptionless error-management
recommendations, as doing so would essentially render it useless.

`val first : ``'a t -> 'a`

As

`hd`

`val last : ``'a t -> 'a`

Returns the last element of the list, or raise

`Empty_list`

if
the list is empty. This function takes linear time and causes the
evaluation of all elements of the list`val at : ``'a t -> int -> 'a`

`at l n`

returns the n-th element of the list `l`

or raise
`Invalid_index`

is the index is outside of `l`

bounds.`val nth : ``'a t -> int -> 'a`

Obsolete. 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 -> '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`

.
Raise `Not_found`

if there is no value associated with `a`

in the
list `l`

.`val assq : ``'a -> ('a * 'b) t -> 'b`

As

`Lazy_list.assoc`

but with physical equality`val mem_assoc : ``'a -> ('a * 'b) t -> bool`

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

As

`Lazy_list.mem_assoc`

but with physical equality.`val rev : ``'a t -> 'a t`

Eager list reversal.

`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. Raise `Invalid_index`

if
`n`

is outside of `l`

size bounds.`val split_nth : ``int -> 'a t -> 'a t * 'a t`

Obsolete. As

`split_at`

.`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 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 l x`

is similar to `remove`

but removes all elements that
are equal to `x`

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.`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 Enum.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 Enum.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 `Lazy_list.of_list`

but will freeze on cyclic lists.

`val of_array : ``'a array -> 'a t`

Eager conversion from array

`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 [^ a1; ...; an ^]`

checks if at least one element of the list satisfies the predicate `p`

.
That is, it returns ` (p a1) || (p a2) || ... || (p an) `

.

`val for_all : ``('a -> bool) -> 'a t -> bool`

Eager universal.

`for_all p [^ a1; ...; an ^]`

checks if all elements of the list satisfy the predicate `p`

.
That is, it returns `(p a1) && (p a2) && ... && (p an)`

.

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

Lazily eliminate some elements and transform others.

`filter_map f [^ a1; a2; ... ;an ^]`

applies `f`

to each
`a1`

, ..., `an`

. 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 a1 with
| Some x1 -> x1 ^:^ (match f a2 with
|Some x2 -> x2 ^:^ (match ...
(match f an with
| Some xn -> [^ xn ^]
| None -> [^ ^]
) ... )
| ...)
| None -> ...
```

.

`val eternity : ``unit t`

An infinite list of nothing

`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`

`val map2 : ``('a -> 'b -> 'c) ->`

'a t -> 'b t -> 'c t

`map2 f [^a1; ...; an^] [^b1; ...; bn^]`

is
`[f a1 b1; ...; f an bn]`

.
Raise `Different_list_size`

if the two lists have
different lengths. Not tail-recursive, lazy.

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

`iter2 f [a1; ...; an] [b1; ...; bn]`

calls in turn
`f a1 b1; ...; f an bn`

. Tail-recursive, eager.
Raise `Different_list_size`

if the two lists have
different lengths.`val fold_left2 : ``('a -> 'b -> 'c -> 'a) ->`

'a -> 'b t -> 'c t -> 'a

`fold_left2 f a [b1; ...; bn] [c1; ...; cn]`

is
`f (... (f (f a b1 c1) b2 c2) ...) bn cn`

. Eager.
Raise `Different_list_size`

if the two lists have
different lengths.`val fold_right2 : ``('a -> 'b -> 'c -> 'c) ->`

'a t -> 'b t -> 'c -> 'c

`fold_right2 f [a1; ...; an] [b1; ...; bn] c`

is
`f a1 b1 (f a2 b2 (... (f an bn c) ...))`

. Eager.
Raise `Different_list_size`

if the two lists have
different lengths. Tail-recursive.`val for_all2 : ``('a -> 'b -> bool) -> 'a t -> 'b t -> bool`

Same as

`Lazy_list.for_all`

, but for a two-argument predicate.
Raise `Different_list_size`

if the two lists have
different lengths.`val exists2 : ``('a -> 'b -> bool) -> 'a t -> 'b t -> bool`

Same as

`Lazy_list.exists`

, but for a two-argument predicate.
Raise `Different_list_size`

if the two lists have
different lengths.`val combine : ``'a t -> 'b t -> ('a * 'b) t`

Transform a pair of lists into a list of pairs:

`combine [a1; ...; an] [b1; ...; bn]`

is
`[(a1,b1); ...; (an,bn)]`

.
Raise `Different_list_size`

if the two lists
have different lengths. Tail-recursive.`val uncombine : ``('a * 'b) t -> 'a t * 'b t`

Divide a list of pairs into a pair of lists.

S-Expressions

`val t_of_sexp : ``(Sexplib.Sexp.t -> 'a) -> Sexplib.Sexp.t -> 'a t`

`val sexp_of_t : ``('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t`

`val node_t_of_sexp : ``(Sexplib.Sexp.t -> 'a) -> Sexplib.Sexp.t -> 'a node_t`

`val sexp_of_node_t : ``('a -> Sexplib.Sexp.t) -> 'a node_t -> Sexplib.Sexp.t`

Printing

`val print : ``?first:string ->`

?last:string ->

?sep:string ->

('a Extlib.InnerIO.output -> 'b -> unit) ->

'a Extlib.InnerIO.output -> 'b t -> unit

The following modules replace functions defined in

`Lazy_list`

with functions
behaving slightly differently but having the same name. This is by design:
the functions meant to override the corresponding functions of `Lazy_list`

.
To take advantage of these overrides, you probably want to
or . For instance, to open a version of `List`

with exceptionless error management, you may write

open LazyList, ExceptionLess. To locally replace module

`Lazy_list`

with a module of
the same name but with exceptionless error management, you may
write `module LazyList = LazyList include ExceptionLess`

module Lazy_list.Exceptionless:`sig`

..`end`

Exceptionless counterparts for error-raising operations

module Lazy_list.Labels:`sig`

..`end`

Operations on

`Lazy_list`

with labels.