Base.List
Immutable, singly-linked lists, giving fast access to the front of the list, and slow (i.e., O(n)) access to the back of the list. The comparison functions on lists are lexicographic.
val hash_fold_t :
(Hash.state -> 'a -> Hash.state) ->
Hash.state ->
'a t ->
Hash.state
include Sexplib0.Sexpable.S1 with type 'a t := 'a t
val t_of_sexp : (Sexplib0.Sexp.t -> 'a) -> Sexplib0.Sexp.t -> 'a t
val sexp_of_t : ('a -> Sexplib0.Sexp.t) -> 'a t -> Sexplib0.Sexp.t
val t_sexp_grammar : 'a Sexplib0.Sexp_grammar.t -> 'a t Sexplib0.Sexp_grammar.t
include Indexed_container.S1_with_creators with type 'a t := 'a t
include Container.S1_with_creators with type 'a t := 'a t
val of_list : 'a list -> 'a t
val of_array : 'a array -> 'a t
E.g., append (of_list [1; 2]) (of_list [3; 4; 5])
is of_list [1; 2; 3; 4; 5]
Concatenates a nested container. The elements of the inner containers are concatenated together in order to give the result.
filter t ~f
returns all the elements of t
that satisfy the predicate f
.
filter_map t ~f
applies f
to every x
in t
. The result contains every y
for which f x
returns Some y
.
partition_tf t ~f
returns a pair t1, t2
, where t1
is all elements of t
that satisfy f
, and t2
is all elements of t
that do not satisfy f
. The "tf" suffix is mnemonic to remind readers that the result is (trues, falses).
include Container.S1 with type 'a t := 'a t
val mem : 'a t -> 'a -> equal:('a -> 'a -> bool) -> bool
Checks whether the provided element is there, using equal
.
val length : 'a t -> int
val is_empty : 'a t -> bool
val iter : 'a t -> f:('a -> unit) -> unit
val fold : 'a t -> init:'acc -> f:('acc -> 'a -> 'acc) -> 'acc
fold t ~init ~f
returns f (... f (f (f init e1) e2) e3 ...) en
, where e1..en
are the elements of t
fold_result t ~init ~f
is a short-circuiting version of fold
that runs in the Result
monad. If f
returns an Error _
, that value is returned without any additional invocations of f
.
val fold_until :
'a t ->
init:'acc ->
f:('acc -> 'a -> ('acc, 'final) Container.Continue_or_stop.t) ->
finish:('acc -> 'final) ->
'final
fold_until t ~init ~f ~finish
is a short-circuiting version of fold
. If f
returns Stop _
the computation ceases and results in that value. If f
returns Continue _
, the fold will proceed. If f
never returns Stop _
, the final result is computed by finish
.
Example:
type maybe_negative =
| Found_negative of int
| All_nonnegative of { sum : int }
(** [first_neg_or_sum list] returns the first negative number in [list], if any,
otherwise returns the sum of the list. *)
let first_neg_or_sum =
List.fold_until ~init:0
~f:(fun sum x ->
if x < 0
then Stop (Found_negative x)
else Continue (sum + x))
~finish:(fun sum -> All_nonnegative { sum })
;;
let x = first_neg_or_sum [1; 2; 3; 4; 5]
val x : maybe_negative = All_nonnegative {sum = 15}
let y = first_neg_or_sum [1; 2; -3; 4; 5]
val y : maybe_negative = Found_negative -3
val exists : 'a t -> f:('a -> bool) -> bool
Returns true
if and only if there exists an element for which the provided function evaluates to true
. This is a short-circuiting operation.
val for_all : 'a t -> f:('a -> bool) -> bool
Returns true
if and only if the provided function evaluates to true
for all elements. This is a short-circuiting operation.
val count : 'a t -> f:('a -> bool) -> int
Returns the number of elements for which the provided function evaluates to true.
val sum :
(module Container.Summable with type t = 'sum) ->
'a t ->
f:('a -> 'sum) ->
'sum
Returns the sum of f i
for all i
in the container.
val find : 'a t -> f:('a -> bool) -> 'a option
Returns as an option
the first element for which f
evaluates to true.
val find_map : 'a t -> f:('a -> 'b option) -> 'b option
Returns the first evaluation of f
that returns Some
, and returns None
if there is no such element.
val to_list : 'a t -> 'a list
val to_array : 'a t -> 'a array
val min_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option
Returns a minimum (resp maximum) element from the collection using the provided compare
function, or None
if the collection is empty. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold
so it has the same complexity as fold
.
val max_elt : 'a t -> compare:('a -> 'a -> int) -> 'a option
These are all like their equivalents in Container
except that an index starting at 0 is added as the first argument to f
.
val foldi : 'a t -> init:_ -> f:(int -> _ -> 'a -> _) -> _
val iteri : 'a t -> f:(int -> 'a -> unit) -> unit
val existsi : 'a t -> f:(int -> 'a -> bool) -> bool
val for_alli : 'a t -> f:(int -> 'a -> bool) -> bool
val counti : 'a t -> f:(int -> 'a -> bool) -> int
val findi : 'a t -> f:(int -> 'a -> bool) -> (int * 'a) option
val find_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b option
val init : int -> f:(int -> 'a) -> 'a t
init n ~f
is equivalent to of_list [f 0; f 1; ...; f (n-1)]
. It raises an exception if n < 0
.
mapi
is like map. Additionally, it passes in the index of each element as the first argument to the mapped function.
filter_mapi is like filter_map
. Additionally, it passes in the index of each element as the first argument to the mapped function.
val invariant : ('a -> unit) -> 'a t -> unit
module Cartesian_product : sig ... end
Implements cartesian-product behavior for map
and bind
. *
The monad portion of Cartesian_product
is re-exported at top level.
include Monad.S_local with type 'a t := 'a t
t >>= f
returns a computation that sequences the computations represented by two monad elements. The resulting computation first does t
to yield a value v
, and then runs the computation returned by f v
.
module Monad_infix : sig ... end
val return : 'a -> 'a t
return v
returns the (trivial) computation that returns v.
ignore_m t
is map t ~f:(fun _ -> ())
. ignore_m
used to be called ignore
, but we decided that was a bad name, because it shadowed the widely used Stdlib.ignore
. Some monads still do let ignore = ignore_m
for historical reasons.
Like all
, but ensures that every monadic value in the list produces a unit value, all of which are discarded rather than being collected into a list.
module Let_syntax : sig ... end
These are convenient to have in scope when programming with a monad:
module Or_unequal_lengths : sig ... end
Or_unequal_lengths
is used for functions that take multiple lists and that only make sense if all the lists have the same length, e.g., iter2
, map3
. Such functions check the list lengths prior to doing anything else, and return Unequal_lengths
if not all the lists have the same length.
val nth : 'a t -> int -> 'a option
val nth_exn : 'a t -> int -> 'a
Return the n
-th element of the given list. The first element (head of the list) is at position 0. Raise if the list is too short or n
is negative.
rev_append l1 l2
reverses l1
and concatenates it to l2
. This is equivalent to (
List.rev
l1) @ l2
, but rev_append
is more efficient.
unordered_append l1 l2
has the same elements as l1 @ l2
, but in some unspecified order. Generally takes time proportional to length of first list, but is O(1) if either list is empty.
rev_map l ~f
gives the same result as List.rev
(
ListLabels.map
f l)
, but is more efficient.
iter2 [a1; ...; an] [b1; ...; bn] ~f
calls in turn f a1 b1; ...; f an bn
. The exn version will raise if the two lists have different lengths.
val iter2 : 'a t -> 'b t -> f:('a -> 'b -> unit) -> unit Or_unequal_lengths.t
rev_map2_exn l1 l2 ~f
gives the same result as List.rev (List.map2_exn l1 l2
~f)
, but is more efficient.
val rev_map2 : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t Or_unequal_lengths.t
fold2 ~f ~init:a [b1; ...; bn] [c1; ...; cn]
is f (... (f (f a b1 c1) b2 c2)
...) bn cn
. The exn version will raise if the two lists have different lengths.
val fold2 :
'a t ->
'b t ->
init:'acc ->
f:('acc -> 'a -> 'b -> 'acc) ->
'acc Or_unequal_lengths.t
fold_right2 ~f [a1; ...; an] [b1; ...; bn] ~init:c
is f a1 b1 (f a2 b2 (... (f an bn c) ...))
. The exn version will raise if the two lists have different lengths.
val fold_right2 :
'a t ->
'b t ->
f:('a -> 'b -> 'acc -> 'acc) ->
init:'acc ->
'acc Or_unequal_lengths.t
Like List.for_all
, but for a two-argument predicate. The exn version will raise if the two lists have different lengths.
val for_all2 :
'a t ->
'b t ->
f:('a -> 'b -> bool) ->
bool Or_unequal_lengths.t
Like List.exists
, but for a two-argument predicate. The exn version will raise if the two lists have different lengths.
val exists2 : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool Or_unequal_lengths.t
Like filter
, but reverses the order of the input list.
partition_result l
returns a pair of lists (l1, l2)
, where l1
is the list of all Ok
elements in l
and l2
is the list of all Error
elements. The order of elements in the input list is preserved.
split_n [e1; ...; em] n
is ([e1; ...; en], [en+1; ...; em])
.
n > m
, ([e1; ...; em], [])
is returned.n < 0
, ([], [e1; ...; em])
is returned.Sort a list in increasing order according to a comparison function. The comparison function must return 0 if its arguments compare as equal, a positive integer if the first is greater, and a negative integer if the first is smaller (see Array.sort
for a complete specification). For example, Poly.compare
is a suitable comparison function.
The current implementation uses Merge Sort. It runs in linear heap space and logarithmic stack space.
Presently, the sort is stable, meaning that two equal elements in the input will be in the same order in the output.
Merges two lists: assuming that l1
and l2
are sorted according to the comparison function compare
, merge compare l1 l2
will return a sorted list containing all the elements of l1
and l2
. If several elements compare equal, the elements of l1
will be before the elements of l2
.
val hd : 'a t -> 'a option
val hd_exn : 'a t -> 'a
Returns the first element of the given list. Raises if the list is empty.
Returns the given list without its first element. Raises if the list is empty.
val findi_exn : 'a t -> f:(int -> 'a -> bool) -> int * 'a
Like find_exn
, but passes the index as an argument.
val find_exn : 'a t -> f:('a -> bool) -> 'a
find_exn t ~f
returns the first element of t
that satisfies f
. It raises Stdlib.Not_found
or Not_found_s
if there is no such element.
val find_map_exn : 'a t -> f:('a -> 'b option) -> 'b
Returns the first evaluation of f
that returns Some
. Raises Stdlib.Not_found
or Not_found_s
if f
always returns None
.
val find_mapi_exn : 'a t -> f:(int -> 'a -> 'b option) -> 'b
Like find_map_exn
, but passes the index as an argument.
folding_map
is a version of map
that threads an accumulator through calls to f
.
fold_map
is a combination of fold
and map
that threads an accumulator through calls to f
.
map2 [a1; ...; an] [b1; ...; bn] ~f
is [f a1 b1; ...; f an bn]
. The exn version will raise if the two lists have different lengths.
val map2 : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t Or_unequal_lengths.t
Analogous to rev_map2
.
val rev_map3 :
'a t ->
'b t ->
'c t ->
f:('a -> 'b -> 'c -> 'd) ->
'd t Or_unequal_lengths.t
Analogous to map2
.
val map3 :
'a t ->
'b t ->
'c t ->
f:('a -> 'b -> 'c -> 'd) ->
'd t Or_unequal_lengths.t
rev_map_append l1 l2 ~f
reverses l1
mapping f
over each element, and appends the result to the front of l2
.
val fold_right : 'a t -> f:('a -> 'acc -> 'acc) -> init:'acc -> 'acc
fold_right [a1; ...; an] ~f ~init:b
is f a1 (f a2 (... (f an b) ...))
.
val fold_left : 'a t -> init:'acc -> f:('acc -> 'a -> 'acc) -> 'acc
fold_left
is the same as Container.S1.fold
, and one should always use fold
rather than fold_left
, except in functors that are parameterized over a more general signature where this equivalence does not hold.
Transform a list of pairs into a pair of lists: unzip [(a1,b1); ...; (an,bn)]
is ([a1; ...; an], [b1; ...; bn])
.
Transform a pair of lists into an (optional) list of pairs: zip [a1; ...; an] [b1;
...; bn]
is [(a1,b1); ...; (an,bn)]
. Returns Unequal_lengths
if the two lists have different lengths.
val zip : 'a t -> 'b t -> ('a * 'b) t Or_unequal_lengths.t
val reduce_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a
reduce_exn [a1; ...; an] ~f
is f (... (f (f a1 a2) a3) ...) an
. It fails on the empty list. Tail recursive.
val reduce : 'a t -> f:('a -> 'a -> 'a) -> 'a option
val reduce_balanced : 'a t -> f:('a -> 'a -> 'a) -> 'a option
reduce_balanced
returns the same value as reduce
when f
is associative, but differs in that the tree of nested applications of f
has logarithmic depth.
This is useful when your 'a
grows in size as you reduce it and f
becomes more expensive with bigger inputs. For example, reduce_balanced ~f:(^)
takes n*log(n)
time, while reduce ~f:(^)
takes quadratic time.
val reduce_balanced_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a
group l ~break
returns a list of lists (i.e., groups) whose concatenation is equal to the original list. Each group is broken where break
returns true on a pair of successive elements.
Example:
group ~break:(<>) ['M';'i';'s';'s';'i';'s';'s';'i';'p';'p';'i'] ->
[['M'];['i'];['s';'s'];['i'];['s';'s'];['i'];['p';'p'];['i']]
This is just like group
, except that you get the index in the original list of the current element along with the two elements.
Example, group the chars of "Mississippi"
into triples:
groupi ~break:(fun i _ _ -> i mod 3 = 0)
['M';'i';'s';'s';'i';'s';'s';'i';'p';'p';'i'] ->
[['M'; 'i'; 's']; ['s'; 'i'; 's']; ['s'; 'i'; 'p']; ['p'; 'i']]
Group equal elements into the same buckets. Sorting is stable.
chunks_of l ~length
returns a list of lists whose concatenation is equal to the original list. Every list has length
elements, except for possibly the last list, which may have fewer. chunks_of
raises if length <= 0
.
val last : 'a t -> 'a option
The final element of a list. The _exn
version raises on the empty list.
val last_exn : 'a t -> 'a
is_prefix xs ~prefix
returns true
if xs
starts with prefix
.
is_suffix xs ~suffix
returns true
if xs
ends with suffix
.
val find_consecutive_duplicate :
'a t ->
equal:('a -> 'a -> bool) ->
('a * 'a) option
find_consecutive_duplicate t ~equal
returns the first pair of consecutive elements (a1, a2)
in t
such that equal a1 a2
. They are returned in the same order as they appear in t
. equal
need not be an equivalence relation; it is simply used as a predicate on consecutive elements.
val remove_consecutive_duplicates :
?which_to_keep:[ `First | `Last ] ->
'a t ->
equal:('a -> 'a -> bool) ->
'a t
Returns the given list with consecutive duplicates removed. The relative order of the other elements is unaffected. The element kept from a run of duplicates is determined by which_to_keep
.
Returns the given list with duplicates removed and in sorted order.
val find_a_dup : 'a t -> compare:('a -> 'a -> int) -> 'a option
find_a_dup
returns a duplicate from the list (with no guarantees about which duplicate you get), or None
if there are no dups.
val contains_dup : 'a t -> compare:('a -> 'a -> int) -> bool
Returns true if there are any two elements in the list which are the same. O(n log n) time complexity.
val find_all_dups : 'a t -> compare:('a -> 'a -> int) -> 'a list
find_all_dups
returns a list of all elements that occur more than once, with no guarantees about order. O(n log n) time complexity.
val all_equal : 'a t -> equal:('a -> 'a -> bool) -> 'a option
all_equal
returns a single element of the list that is equal to all other elements, or None
if no such element exists.
val range :
?stride:int ->
?start:[ `inclusive | `exclusive ] ->
?stop:[ `inclusive | `exclusive ] ->
int ->
int ->
int t
range ?stride ?start ?stop start_i stop_i
is the list of integers from start_i
to stop_i
, stepping by stride
. If stride
< 0 then we need start_i
> stop_i
for the result to be nonempty (or start_i
= stop_i
in the case where both bounds are inclusive).
val range' :
compare:('a -> 'a -> int) ->
stride:('a -> 'a) ->
?start:[ `inclusive | `exclusive ] ->
?stop:[ `inclusive | `exclusive ] ->
'a ->
'a ->
'a t
range'
is analogous to range
for general start/stop/stride types. range'
raises if stride x
returns x
or if the direction that stride x
moves x
changes from one call to the next.
rev_filter_map l ~f
is the reversed sublist of l
containing only elements for which f
returns Some e
.
rev_filter_mapi is just like rev_filter_map
, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.
filter_opt l
is the sublist of l
containing only elements which are Some e
. In other words, filter_opt l
= filter_map ~f:Fn.id l
.
module Assoc : sig ... end
Interpret a list of (key, value) pairs as a map in which only the first occurrence of a key affects the semantics, i.e.:
sub pos len l
is the len
-element sublist of l
, starting at pos
.
take l n
returns the first n
elements of l
, or all of l
if n > length l
. take l n = fst (split_n l n)
.
drop l n
returns l
without the first n
elements, or the empty list if n >
length l
. drop l n
is equivalent to snd (split_n l n)
.
take_while l ~f
returns the longest prefix of l
for which f
is true
.
drop_while l ~f
drops the longest prefix of l
for which f
is true
.
split_while xs ~f = (take_while xs ~f, drop_while xs ~f)
.
drop_last l
drops the last element of l
, returning None
if l
is empty
.
Like concat
, but faster and without preserving any ordering (i.e., for lists that are essentially viewed as multi-sets).
Returns a list with all possible pairs -- if the input lists have length len1
and len2
, the resulting list will have length len1 * len2
.
val permute : ?random_state:Random.State.t -> 'a t -> 'a t
permute ?random_state t
returns a permutation of t
.
permute
side-effects random_state
by repeated calls to Random.State.int
. If random_state
is not supplied, permute
uses Random.State.default
.
val random_element : ?random_state:Random.State.t -> 'a t -> 'a option
random_element ?random_state t
is None
if t
is empty, else it is Some x
for some x
chosen uniformly at random from t
.
random_element
side-effects random_state
by calling Random.State.int
. If random_state
is not supplied, random_element
uses Random.State.default
.
val random_element_exn : ?random_state:Random.State.t -> 'a t -> 'a
val is_sorted : 'a t -> compare:('a -> 'a -> int) -> bool
is_sorted t ~compare
returns true
iff for all adjacent a1; a2
in t
, compare
a1 a2 <= 0
.
is_sorted_strictly
is similar, except it uses <
instead of <=
.
val is_sorted_strictly : 'a t -> compare:('a -> 'a -> int) -> bool
module Infix : sig ... end
transpose m
transposes the rows and columns of the matrix m
, considered as either a row of column lists or (dually) a column of row lists.
Example:
transpose [[1;2;3];[4;5;6]] = [[1;4];[2;5];[3;6]]
On non-empty rectangular matrices, transpose
is an involution (i.e., transpose
(transpose m) = m
). Transpose returns None
when called on lists of lists with non-uniform lengths.
transpose_exn
transposes the rows and columns of its argument, throwing an exception if the list is not rectangular.