`module Enum: ``Extlib.Enum`

Enumeration over abstract collection of elements.
Enumerations are a representation of finite or infinite sequences of elements. In Batteries Included, enumerations are used pervasively, both as a uniform manner of reading and manipulating the contents of a data structure, or as a simple manner of reading or writing sequences of characters, numbers, strings, etc. from/to files, network connections or other inputs/outputs.

Enumerations are typically computed as needed, which allows the
definition and manipulation of huge (possibly infinite) sequences.
Manipulating an enumeration is a uniform and often comfortable way
of extracting subsequences (function `Enum.filter`

or operator `//`

et
al), converting sequences into other sequences (function `Enum.map`

or
operators `/@`

and `@/`

et al), gathering information (function
`Enum.scanl`

et al) or performing loops (functions `Enum.iter`

and
`Enum.map`

).

For instance, function `Random.enum_int`

creates an
infinite enumeration of random numbers. Combined with `//`

and `Enum.map`

, we may turn this into an infinite enumeration of
squares of random even numbers:
`map (fun x -> x * x) ( (Random.enum_int 100) // even )`

Similarly, to obtain an enumeration of 50 random integers,
we may use `Enum.take`

, as follows:
`take 50 (Random.enum_int 100)`

As most data structures in Batteries can be enumerated and built from enumerations, these operations may be used also on lists, arrays, hashtables, etc. When designing a new data structure, it is usuallly a good idea to allow enumeration and construction from an enumeration.

**Note** Enumerations are not thread-safe. You should not attempt
to access one enumeration from different threads.

**Author(s):** Nicolas Cannasse, David Rajchenbach-Teller

`type ``'a`

t

module type Enumerable =`sig`

..`end`

A signature for data structures which may be converted to and from

`enum`

.
`include Enum.Enumerable`

`include Enum.Mappable`

These functions consume the enumeration until
it ends or an exception is raised by the first
argument function.

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

`iter f e`

calls the function `f`

with each elements of `e`

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

`iter2 f e1 e2`

calls the function `f`

with the next elements of `e`

and
`e2`

repeatedly until one of the two enumerations ends.`val exists : ``('a -> bool) -> 'a t -> bool`

`exists f e`

returns `true`

if there is some `x`

in `e`

such
that `f x`

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

`for_all f e`

returns `true`

if for every `x`

in `e`

, `f x`

is true`val fold : ``('a -> 'b -> 'a) -> 'a -> 'b t -> 'a`

A general loop on an enumeration.

If `e`

is empty, `fold f v e`

returns `v`

. Otherwise, `fold v e`

returns `f (... (f (f v a1) a2) ...) aN`

where a1..N are the
elements of `e`

. This function may be used, for instance, to
compute the sum of all elements of an enumeration `e`

as follows:
`fold ( + ) 0 e`

.

`val reduce : ``('a -> 'a -> 'a) -> 'a t -> 'a`

A simplified version of

`fold`

, which uses the first element
of the enumeration as a default value.
`fold f e`

throws `Not_found`

if `e`

is empty, returns its only
element if e is a singleton, otherwise ```
f (... (f (f a1 a2)
a3)...) aN
```

where a1..N are the elements of `e`

.

`val fold2 : ``('a -> 'b -> 'c -> 'c) -> 'c -> 'a t -> 'b t -> 'c`

`fold2`

is similar to `fold`

but will fold over two enumerations at the
same time until one of the two enumerations ends.`val scanl : ``('a -> 'b -> 'a) -> 'a -> 'b t -> 'a t`

A variant of

`fold`

producing an enumeration of its intermediate values.
If `e`

contains `x1`

, `x2`

, ..., `scanl f init e`

is the enumeration
containing `init`

, `f init x1`

, `f (f init x1) x2`

...`val scan : ``('a -> 'a -> 'a) -> 'a t -> 'a t`

`scan`

is similar to `scanl`

but without the `init`

value: if `e`

contains `x1`

, `x2`

, `x3`

..., `scan f e`

is the enumeration containing
`x1`

, `f x1 x2`

, `f (f x1 x2) x3`

...
For instance, `scan ( * ) (1 -- 10)`

will produce an enumeration
containing the successive values of the factorial function.

Indexed functions : these functions are similar to previous ones except that they call the function with one additional argument which is an index starting at 0 and incremented after each call to the function.

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

`val iter2i : ``(int -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit`

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

`val fold2i : ``(int -> 'a -> 'b -> 'c -> 'c) ->`

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

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

`find f e`

returns the first element `x`

of `e`

such that `f x`

returns
`true`

, consuming the enumeration up to and including the
found element, or, raises `Not_found`

if no such element exists
in the enumeration, consuming the whole enumeration in the search.
Since `find`

consumes a prefix of the enumeration, it can be used several
times on the same enumeration to find the next element.

`val is_empty : ``'a t -> bool`

`is_empty e`

returns true if `e`

does not contains any element.`val peek : ``'a t -> 'a option`

`peek e`

returns `None`

if `e`

is empty or `Some x`

where `x`

is
the next element of `e`

. The element is not removed from the
enumeration.`val get : ``'a t -> 'a option`

`get e`

returns `None`

if `e`

is empty or `Some x`

where `x`

is
the next element of `e`

, in which case the element is removed
from the enumeration.`val push : ``'a t -> 'a -> unit`

`push e x`

will add `x`

at the beginning of `e`

.`val junk : ``'a t -> unit`

`junk e`

removes the first element from the enumeration, if any.`val clone : ``'a t -> 'a t`

`clone e`

creates a new enumeration that is copy of `e`

. If `e`

is consumed by later operations, the clone will not get affected.`val force : ``'a t -> unit`

`force e`

forces the application of all lazy functions and the
enumeration of all elements, exhausting the enumeration.
An efficient intermediate data structure
of enumerated elements is constructed and `e`

will now enumerate over
that data structure.

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

`take n e`

returns the prefix of `e`

of length `n`

, or `e`

itself if `n`

is greater than the length of `e`

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

`drop n e`

removes the first `n`

element from the enumeration, if any.`val skip : ``int -> 'a t -> 'a t`

`skip n e`

removes the first `n`

element from the enumeration, if any,
then returns `e`

.
This function has the same behavior as `drop`

but is often easier to
compose with, e.g., `skip 5 |- take 3`

is a new function which skips
5 elements and then returns the next 3 elements.

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

`take_while f e`

produces a new enumeration in which only remain
the first few elements `x`

of `e`

such that `f x`

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

`drop_while p e`

produces a new enumeration in which only
all the first elements such that `f e`

have been junked.`val span : ``('a -> bool) -> 'a t -> 'a t * 'a t`

`span test e`

produces two enumerations `(hd, tl)`

, such that
`hd`

is the same as `take_while test e`

and `tl`

is the same
as `drop_while test e`

.`val break : ``('a -> bool) -> 'a t -> 'a t * 'a t`

Negated span.

`break test e`

is equivalent to `span (fun x -> not (test x)) e`

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

`group test e`

devides `e`

into an enumeration of enumerations, where
each sub-enumeration is the longest continuous enumeration of elements whose `test`

results are the same.`val clump : ``int -> ('a -> unit) -> (unit -> 'b) -> 'a t -> 'b t`

`clump size add get e`

runs `add`

on `size`

(or less at the end)
elements of `e`

and then runs `get`

to produce value for the
result enumeration. Useful to convert a char enum into string
enum.These functions are lazy which means that they will create a new modified enumeration without actually enumerating any element until they are asked to do so by the programmer (using one of the functions above).

When the resulting enumerations of these functions are consumed, the
underlying enumerations they were created from are also consumed.

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

`map f e`

returns an enumeration over `(f a1, f a2, ... , f aN)`

where
a1...N are the elements of `e`

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

`mapi`

is similar to `map`

except that `f`

is passed one extra argument
which is the index of the element in the enumeration, starting from 0.`val filter : ``('a -> bool) -> 'a t -> 'a t`

`filter f e`

returns an enumeration over all elements `x`

of `e`

such
as `f x`

returns `true`

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

`filter_map f e`

returns an enumeration over all elements `x`

such as
`f y`

returns `Some x`

, where `y`

is an element of `e`

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

`append e1 e2`

returns an enumeration that will enumerate over all
elements of `e1`

followed by all elements of `e2`

.
**Note** The behavior of appending `e`

to itself or to something
derived from `e`

is not specified. In particular, cloning `append e e`

may destroy any sharing between the first and the second argument.

`val prefix_action : ``(unit -> unit) -> 'a t -> 'a t`

`prefix_action f e`

will behave as `e`

but guarantees that `f ()`

will be invoked exactly once before the current first element of `e`

is read.
If `prefix_action f e`

is cloned, `f`

is invoked only once, during
the cloning. If `prefix_action f e`

is counted, `f`

is invoked
only once, during the counting.

May be used for signalling that reading starts or for performing
delayed evaluations.

`val suffix_action : ``(unit -> unit) -> 'a t -> 'a t`

`suffix_action f e`

will behave as `e`

but guarantees that `f ()`

will be invoked after the contents of `e`

are exhausted.
If `suffix_action f e`

is cloned, `f`

is invoked only once, when
the original enumeration is exhausted. If `suffix_action f e`

is counted, `f`

is only invoked if the act of counting
requires a call to `force`

.

May be used for signalling that reading stopped or for performing
delayed evaluations.

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

`concat e`

returns an enumeration over all elements of all enumerations
of `e`

.`val flatten : ``'a t t -> 'a t`

Synonym of

`Enum.concat`

In this section the word *shall* denotes a semantic
requirement. The correct operation of the functions in this
interface are conditional on the client meeting these
requirements.

`exception No_more_elements`

This exception *shall* be raised by the *shall not*
be raised by any function which is an argument to any
other function specified in the interface.

`next`

function of `make`

or `from`

when no more elements can be enumerated, it `exception Infinite_enum`

As a convenience for debugging, this exception *may* be raised by
the

`count`

function of `make`

when attempting to count an infinite enum.`val empty : ``unit -> 'a t`

The empty enumeration : contains no element

`val make : ``next:(unit -> 'a) ->`

count:(unit -> int) -> clone:(unit -> 'a t) -> 'a t

This function creates a fully defined enumeration.

- the
`next`

function*shall*return the next element of the enumeration or raise`No_more_elements`

if the underlying data structure does not have any more elements to enumerate. - the
`count`

function*shall*return the actual number of remaining elements in the enumeration or*may*raise`Infinite_enum`

if it is known that the enumeration is infinite. - the
`clone`

function*shall*create a clone of the enumeration such as operations on the original enumeration will not affect the clone.

For some samples on how to correctly use `make`

, you can have a look
at implementation of `ExtList.enum`

.

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

`from next`

creates an enumeration from the `next`

function.
`next`

`No_more_elements`

when no more elements can be enumerated. Since the
enumeration definition is incomplete, a call to `count`

will result in
a call to `force`

that will enumerate all elements in order to
return a correct value.`val from_while : ``(unit -> 'a option) -> 'a t`

`from_while next`

creates an enumeration from the `next`

function.
`next`

`Some x`

where `x`

is the next element of the
enumeration or `None`

when no more elements can be enumerated. Since the
enumeration definition is incomplete, a call to `clone`

or `count`

will
result in a call to `force`

that will enumerate all elements in order to
return a correct value.`val from_loop : ``'a -> ('a -> 'b * 'a) -> 'b t`

`from_loop data next`

creates a (possibly infinite) enumeration from
the successive results of applying `next`

to `data`

, then to the
result, etc. The list ends whenever the function raises
`Enum.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`

More powerful version of

`seq`

, with the ability of hiding data.
`unfold data next`

creates a (possibly infinite) enumeration from
the successive results of applying `next`

to `data`

, then to the
result, etc. The enumeration ends whenever the function returns `None`

`val init : ``int -> (int -> 'a) -> 'a t`

`init n f`

creates a new enumeration over elements
`f 0, f 1, ..., f (n-1)`

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

Create an enumeration consisting in exactly one element.

`val repeat : ``?times:int -> 'a -> 'a t`

`repeat ~times:n x`

creates a enum sequence filled with `n`

times of
`x`

. It return infinite enum when `~times`

is absent. It returns empty
enum when `times <= 0`

`val cycle : ``?times:int -> 'a t -> 'a t`

`cycle`

is similar to `repeat`

, except that the content to fill is a
subenum rather than a single element. Note that `times`

represents the
times of repeating not the length of enum.`val delay : ``(unit -> 'a t) -> 'a t`

`delay (fun () -> e)`

produces an enumeration which behaves as `e`

.
The enumeration itself will only be computed when consumed.
A typical use of this function is to explore lazily non-trivial data structures, as follows:

```
type 'a tree = Leaf
| Node of 'a * 'a tree * 'a tree
let enum_tree =
let rec aux = function
| Leaf -> Enum.empty ()
| Node (n, l, r) -> Enum.append (Enum.singleton n)
(Enum.append (delay (fun () -> aux l))
(delay (fun () -> aux r)))
```

`val to_object : ``'a t -> (< clone : 'b; count : int; next : 'a > as 'b)`

`to_object e`

returns a representation of `e`

as an object.`val of_object : ``(< clone : 'a; count : int; next : 'b > as 'a) -> 'b t`

`of_object e`

returns a representation of an object as an enumeration`val enum : ``'a t -> 'a t`

identity : added for consistency with the other data structures

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

identity : added for consistency with the other data structures

`val count : ``'a t -> int`

`count e`

returns the number of remaining elements in `e`

without
consuming the enumeration.
Depending of the underlying data structure that is implementing the
enumeration functions, the count operation can be costly, and even sometimes
can cause a call to `force`

.

`val fast_count : ``'a t -> bool`

For users worried about the speed of

`count`

you can call the `fast_count`

function that will give an hint about `count`

implementation. Basically, if
the enumeration has been created with `make`

or `init`

or if `force`

has
been called on it, then `fast_count`

will return true.`val hard_count : ``'a t -> int`

`hard_count`

returns the number of remaining in elements in `e`

,
consuming the whole enumeration somewhere along the way. This
function is always at least as fast as the fastest of either
`count`

or a `fold`

on the elements of `t`

.
This function is useful when you have opened an enumeration for
the sole purpose of counting its elements (e.g. the number of
lines in a file).

`val range : ``?until:int -> int -> int t`

`range p until:q`

creates an enumeration of integers `[p, p+1, ..., q]`

.
If `until`

is omitted, the enumeration is not bounded. Behaviour is
not-specified once `max_int`

has been reached.

`val (--) : ``int -> int -> int t`

As

`range`

, without the label.
`5 -- 10`

is the enumeration 5,6,7,8,9,10.
`10 -- 5`

is the empty enumeration

`val (--.) : ``float * float -> float -> float t`

`(a, step) --. b)`

creates a float enumeration from `a`

to `b`

with an
increment of `step`

between elements.
`(5.0, 1.0) --. 10.0`

is the enumeration 5.0,6.0,7.0,8.0,9.0,10.0.
`(10.0, -1.0) --. 5.0`

is the enumeration 10.0,9.0,8.0,7.0,6.0,5.0.
`(10.0, 1.0) --. 1.0`

is the empty enumeration.

`val (---) : ``int -> int -> int t`

As

`--`

, but accepts enumerations in reverse order.
`5 --- 10`

is the enumeration 5,6,7,8,9,10.
`10 --- 5`

is the enumeration 10,9,8,7,6,5.

`val (--~) : ``char -> char -> char t`

As ( -- ), but for characters.

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

Filtering (pronounce this operator name "such that").

For instance, `(1 -- 37) // odd`

is the enumeration of all odd
numbers between 1 and 37.

`val (/@) : ``'a t -> ('a -> 'b) -> 'b t`

`val (@/) : ``('a -> 'b) -> 'a t -> 'b t`

Mapping operators.

These operators have the same meaning as function `Enum.map`

but are
sometimes more readable than this function, when chaining
several transformations in a row.

`val dup : ``'a t -> 'a t * 'a t`

`dup stream`

returns a pair of streams which are identical to `stream`

. Note
that stream is a destructive data structure, the point of `dup`

is to
return two streams can be used independently.`val combine : ``'a t * 'b t -> ('a * 'b) t`

`combine`

transform a pair of stream into a stream of pairs of corresponding
elements. If one stream is short, excess elements of the longer stream are
ignored.`val uncombine : ``('a * 'b) t -> 'a t * 'b t`

`uncombine`

is the opposite of `combine`

`val merge : ``('a -> 'a -> bool) ->`

'a t -> 'a t -> 'a t

`merge test (a, b)`

merge the elements from `a`

and `b`

into a single
enumeration. At each step, `test`

is applied to the first element of
`a`

and the first element of `b`

to determine which should get first
into resulting enumeration. If `a`

or `b`

runs out of elements,
the process will append all elements of the other enumeration to
the result.`val uniq : ``'a t -> 'a t`

`uniq e`

returns a duplicate of `e`

with repeated values
omitted. (similar to unix's `uniq`

command)`val compare : ``('a -> 'a -> int) -> 'a t -> 'a t -> int`

`compare cmp a b`

compares enumerations `a`

and `b`

by lexicographical order using comparison `cmp`

.`compare cmp a' b'`

, where `a'`

and `b'`

are
respectively equal to `a`

and `b`

without their first
element, if both `a`

and `b`

are non-empty and `cmp x y = 0`

,
where `x`

is the first element of `a`

and `y`

is the first
element of `b`

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

`switch test enum`

splits `enum`

into two enums, where the first enum have
all the elements satisfying `test`

, the second enum is opposite. The
order of elements in the source enum is preserved.`val while_do : ``('a -> bool) ->`

('a t -> 'a t) ->

'a t -> 'a t

`while_do cont f e`

is a loop on `e`

using `f`

as body and `cont`

as
condition for continuing.

If `e`

contains elements `x1`

, `x2`

, `x3`

..., then if `cont x1`

is `false`

,
`x1`

is returned as such and treatment stops. On the other hand, if `cont x1`

is `true`

, `f x1`

is returned and the loop proceeds with `x2`

...

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

?last:string ->

?sep:string ->

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

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

Print and consume the contents of an enumeration.

`val t_printer : ``'a Value_printer.t -> 'a t Value_printer.t`

The following modules replace functions defined in

`Enum`

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

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

with exceptionless error management, you may write ```
open Enum,
Exceptionless
```

. To locally replace module `Enum`

with a module of
the same name but with exceptionless error management, you may
write

module Enum = Enum include Exceptionless.

module Enum.Exceptionless:`sig`

..`end`

Operations on

`Enum`

without exceptions.
module Enum.Labels:`sig`

..`end`

Operations on

`Enum`

with labels.