module BatEnum:`sig`

..`end`

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 `BatEnum.filter`

or operator `//`

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

or
operators `/@`

and `@/`

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

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

and
`BatEnum.map`

).

For instance, function `BatRandom.enum_int`

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

and `BatEnum.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 `BatEnum.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 BatEnum.Enumerable`

`include BatInterfaces.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 `e1`

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

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 a0) a1) ...) aN`

where `a0,a1..aN`

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`

. Eager.

`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.
`reduce f e`

throws `Not_found`

if `e`

is empty, returns its only
element if e is a singleton, otherwise ```
f (... (f (f a0 a1)
a2)...) aN
```

where `a0,a1..aN`

are the elements of `e`

.

`val sum : ``int t -> int`

`sum`

returns the sum of the given int enum. If the argument is
empty, returns 0. Eager`val fsum : ``float t -> float`

`val kahan_sum : ``float t -> float`

`kahan_sum l`

returns a numerically-accurate sum of the floats of
`l`

. See `BatArray.fsum`

for more details.`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 : ``('b -> 'a -> 'b) -> 'b -> 'a t -> 'b t`

A variant of

`fold`

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

contains `x0`

, `x1`

, ..., `scanl f init e`

is the enumeration
containing `init`

, `f init x0`

, `f (f init x0) x1`

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

`scan`

is similar to `scanl`

but without the `init`

value: if `e`

contains `x0`

, `x1`

, `x2`

..., `scan f e`

is the enumeration containing
`x0`

, `f x0 x1`

, `f (f x0 x1) x2`

...
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.`Not_found`

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

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

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

`find_map f e`

finds the first element `x`

of `e`

such that `f x`

returns
`Some r`

, then returns r. It consumes the enumeration up to and including
the found element.`Not_found`

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

(eagerly) 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.
Forces at most one 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 get_exn : ``'a t -> 'a`

`get_exn e`

returns the first element of `e`

.`No_more_elements`

if `e`

is empty.`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 -> 'b) -> 'a t -> 'a t t`

`group test e`

divides `e`

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

results are the same.
`Enum.group (x -> x mod 2) [1;2;4;1] = [[1];[2;4];[1]]`

`Enum.group (fun x -> x mod 3) [1;2;4;1] = [[1];[2];[4;1]]`

`Enum.group (fun s -> s.[0]) ["cat"; "canary"; "dog"; "dodo"; "ant"; "cow"] = [["cat"; "canary"];["dog";"dodo"];["ant"];["cow"]]`

Warning: The result of this operation cannot be directly cloned
safely; instead, reify to a non-lazy structure and read from that
structure multiple times.

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

`group_by eq e`

divides `e`

into an enumeration of enumerations,
where each sub-enumeration is the longest continuous enumeration
of elements that are equal, as judged by `eq`

.
Warning: The result of this operation cannot be directly cloned
safely; instead, reify to a non-lazy structure and read from that
structure multiple times.

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

`cartesian_product e1 e2`

computes the cartesian product of `e1`

and `e2`

.
Pairs are enumerated in a non-specified order, but in fair enough an order
so that it works on infinite enums (i.e. even then, any pair is eventually
returned)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 a0, f a1, ...)`

where
`a0,a1...`

are the elements of `e`

. Lazy.`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 :
mapi f e returns an enumeration over `(f 0 a0, f 1 a1, ...)`

where
`a0,a1...`

are the elements of `e`

.`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`

. Lazy.
**Note** filter is lazy in that it returns a lazy enumeration, but
each element in the result is eagerly searched in the input
enumeration. Therefore, the access to a given element in the result
will diverge if it is preceded, in the input enumeration, by
infinitely many false elements (elements on which the predicate
`p`

returns `false`

).

Other functions that may drop an unbound number of elements
(`filter_map`

, `take_while`

, etc.) have the same behavior.

`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`

.
`filter_map`

works on infinite enumerations; see `filter`

.

`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`

. Lazy.
**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

`BatEnum.concat`

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

Synonym of

**Since** 2.2.0

`BatEnum.Monad.bind`

, with flipped arguments.
`concat_map f e`

is the same as `concat (map f e)`

.
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 `BatList.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 : ``'b -> ('b -> 'a * 'b) -> 'a 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
`BatEnum.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 : ``'b -> ('b -> ('a * 'b) option) -> 'a t`

As

`from_loop`

, except uses option type to signal the end of the enumeration.
`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`

Example: ```
Enum.unfold n (fun x -> if x = 1 then None else Some
(x, if x land 1 = 1 then 3 * x + 1 else x / 2))
```

returns the
hailstone sequence starting at `n`

.

`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 of 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. When `~times`

is absent the
result is an infinite 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 -> BatEnum.empty ()
| Node (n, l, r) -> BatEnum.append (BatEnum.singleton n)
(BatEnum.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 : 'b; count : int; next : 'a > as 'b) -> 'a 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 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 `xa`

of
`a`

and the first element `xb`

of `b`

to determine which should get first
into resulting enumeration. If `test xa xb`

returns `true`

, `xa`

(the
first element of `a`

) is used, otherwise `xb`

is used. If `a`

or `b`

runs
out of elements, the process will append all elements of the other
enumeration to the result.
For example, if `a`

and `b`

are enumerations of integers sorted
in increasing order, then `merge (<) a b`

will also be sorted.

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

`interleave enums`

creates a new enumeration from an array of enumerations.
The new enumeration first yields the first elements of the enumerations in
the supplied order, then second elements, etc. Thus, a sequence
` [| [x11 ; x12 ; ...] ; [x21 ; x22, ...] , ... [xN1 ; xN2 ; ...] |] `

becomes
`[ x11 ; x12 ; ... ; xN1 ; x21 ; x22 ; ... ; xN2 ; x31 ; ... ]`

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

`uniq e`

returns a duplicate of `e`

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

command).
It uses structural equality to compare consecutive elements.`val uniqq : ``'a t -> 'a t`

`uniqq e`

behaves as `uniq e`

except it uses physical equality
to compare consecutive elements.`val uniq_by : ``('a -> 'a -> bool) -> 'a t -> 'a t`

`uniqq cmp e`

behaves as `uniq e`

except it allows to specify a
comparison function.`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 partition : ``('a -> bool) -> 'a t -> 'a t * 'a t`

as

`switch`

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

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

`arg_min f xs`

returns the `x`

in `xs`

for which `f x`

is minimum.
Similarly for `arg_max`

, except it returns the maximum. If
multiple values reach the maximum, one of them is
returned. (currently the first, but this is not guaranteed)
Example: `-5 -- 5 |> arg_min (fun x -> x * x + 6 * x - 5) = -3`

Example: `List.enum ["cat"; "canary"; "dog"; "dodo"; "ant"; "cow"] |> arg_max String.length = "canary"`

**Raises** `Invalid_argument`

if the input enum is empty

`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 `x0`

, `x1`

, `x2`

..., then if `cont x0`

is `false`

,
`x0`

is returned as such and treatment stops. On the other hand, if `cont x0`

is `true`

, `f x0`

is returned and the loop proceeds with `x1`

...

Note that f is used as halting condition *after* the
corresponding element has been added to the result stream.

Infix versions of some functions

This module groups together all infix operators so that
you can open it without opening the whole batEnum module.

module Infix:`sig`

..`end`

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

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

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

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

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

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

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

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

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

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

module WithMonad:

Monadic operations on Enumerations containing monadic elements

module Monad:`sig`

..`end`

The BatEnum Monad

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

?last:string ->

?sep:string ->

('a BatInnerIO.output -> 'b -> unit) ->

'a BatInnerIO.output -> 'b t -> unit

Print and consume the contents of an enumeration.

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

?last:string ->

?sep:string ->

limit:int ->

('a BatInnerIO.output -> 'b -> unit) ->

'a BatInnerIO.output -> 'b t -> unit

`print_at_most pp limit out enum`

consumes `enum`

to print its elements
into `out`

(using `pp`

to print individual elements).
At most `limit`

arguments are printed, if more elements are
available an ellipsis "..." is added.`Invalid_argument`

if the limit is <= 0.`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 ord : ``('a -> 'a -> BatOrd.order) -> 'a t -> 'a t -> BatOrd.order`

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

`equal eq a b`

returns `true`

when `a`

and `b`

contain
the same sequence of elements.The following modules replace functions defined in

`BatEnum`

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

.module Exceptionless:`sig`

..`end`

Operations on

`BatEnum`

without exceptions.
module Labels:`sig`

..`end`

Operations on

`BatEnum`

with labels.