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Module List

module List: sig .. end
Tail recursive version of standard List functions, plus additional operations.
type 'a t = 'a list 
include Container.S1
include Monad.S
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 Failure "nth" if the list is too short. Raise Invalid_argument "List.nth" if n is negative.
val rev : 'a t -> 'a t
List reversal.
val rev_append : 'a t -> 'a t -> 'a t
List.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.
val unordered_append : 'a t -> 'a t -> 'a t
val rev_map : 'a t -> f:('a -> 'b) -> 'b t
List.rev_map f l gives the same result as List.rev (ListLabels.map f l), but is more efficient.
val fold_left : 'a t -> init:'b -> f:('b -> 'a -> 'b) -> 'b
val iter2_exn : 'a t -> 'b t -> f:('a -> 'b -> unit) -> unit
List.iter2_exn f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn. Raise Invalid_argument if the two lists have different lengths.
val rev_map2_exn : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t
List.rev_map2_exn f l1 l2 gives the same result as List.rev (List.map2_exn f l1 l2), but is more efficient.
val fold2_exn : 'a t -> 'b t -> init:'c -> f:('c -> 'a -> 'b -> 'c) -> 'c
List.fold2_exn f a [b1; ...; bn] [c1; ...; cn] is f (... (f (f a b1 c1) b2 c2) ...) bn cn. Raise Invalid_argument if the two lists have different lengths.
val for_all2_exn : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool
Same as List.for_all, but for a two-argument predicate. Raise Invalid_argument if the two lists have different lengths.
val exists2_exn : 'a t -> 'b t -> f:('a -> 'b -> bool) -> bool
Same as List.exists, but for a two-argument predicate. Raise Invalid_argument if the end of one list is reached before the end of the other.
val filter : 'a t -> f:('a -> bool) -> 'a t
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 rev_filter : 'a t -> f:('a -> bool) -> 'a t
Like filter, but reverses the order of the input list
val filteri : 'a t -> f:(int -> 'a -> bool) -> 'a t
val partition_map : 'a t ->
       f:('a -> [ `Fst of 'b | `Snd of 'c ]) -> 'b t * 'c t
partition_map t ~f partitions t according to f.
val partition_tf : 'a t -> f:('a -> bool) -> 'a t * 'a t
partition_tf p l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate p, and l2 is the list of all the elements of l that do not satisfy p. The order of the elements in the input list is preserved. The "tf" suffix is mnemonic to remind readers at a call that the result is (trues, falses).
val split_n : 'a t -> int -> 'a t * 'a t
split_n n [e1; ...; em] is ([e1; ...; en], [en+1; ...; em]). If n > m, ([e1; ...; em], []) is returned. If n < 0, ([], [e1; ...; em]) is returned.
val sort : cmp:('a -> 'a -> int) -> 'a t -> 'a t
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, Pervasives.compare is a suitable comparison function.

The current implementation uses Merge Sort. It runs in constant 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.

val stable_sort : cmp:('a -> 'a -> int) -> 'a t -> 'a t
Same as sort, but guaranteed to be stable
val merge : 'a t -> 'a t -> cmp:('a -> 'a -> int) -> 'a t
Merge two lists: assuming that l1 and l2 are sorted according to the comparison function cmp, merge cmp l1 l2 will return a sorted list containting 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 tl : 'a t -> 'a t option
val hd_exn : 'a t -> 'a
Return the first element of the given list. Raise Failure "hd" if the list is empty.
val tl_exn : 'a t -> 'a t
Return the given list without its first element. Raise Failure "tl" if the list is empty.
val findi : 'a t -> f:(int -> 'a -> bool) -> (int * 'a) option
val find_exn : 'a t -> f:('a -> bool) -> 'a
find_exn t ~f returns the first element of t that satisfies f. It raises Not_found if there is no such element.

Tail-recursive implementations of standard List operations

val append : 'a t -> 'a t -> 'a t
E.g. append [1; 2] [3; 4; 5] is [1; 2; 3; 4; 5]
val map : 'a t -> f:('a -> 'b) -> 'b t
List.map f [a1; ...; an] applies function f to a1, ..., an, and builds the list [f a1; ...; f an] with the results returned by f.
val concat_map : 'a t -> f:('a -> 'b t) -> 'b t
concat_map t ~f is concat (map t ~f), except that there is no guarantee about the order in which f is applied to the elements of t.
val concat_mapi : 'a t -> f:(int -> 'a -> 'b t) -> 'b t
concat_mapi t ~f is like concat_map, but passes the index as an argument
val map2_exn : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t
List.map2_exn f [a1; ...; an] [b1; ...; bn] is [f a1 b1; ...; f an bn]. Raise Invalid_argument if the two lists have different lengths.
val rev_map3_exn : 'a t ->
       'b t ->
       'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t
val map3_exn : 'a t ->
       'b t ->
       'c t -> f:('a -> 'b -> 'c -> 'd) -> 'd t
val rev_map_append : 'a t -> 'b t -> f:('a -> 'b) -> 'b t
rev_map_append ~f l1 l2 reverses l1 mapping f over each element, and appends the result to the front of l2.
val fold_right : 'a t -> f:('a -> 'b -> 'b) -> init:'b -> 'b
List.fold_right f [a1; ...; an] b is f a1 (f a2 (... (f an b) ...)).
val unzip : ('a * 'b) t -> 'a t * 'b t
Transform a list of pairs into a pair of lists: unzip [(a1,b1); ...; (an,bn)] is ([a1; ...; an], [b1; ...; bn]).
val zip : 'a t -> 'b t -> ('a * 'b) t option
Transform a pair of lists into an (optional) list of pairs: zip [a1; ...; an] [b1; ...; bn] is [(a1,b1); ...; (an,bn)]. Returns None if the two lists have different lengths.
val zip_exn : 'a t -> 'b t -> ('a * 'b) t
val mapi : 'a t -> f:(int -> 'a -> 'b) -> 'b t
mapi is just like map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.
val rev_mapi : 'a t -> f:(int -> 'a -> 'b) -> 'b t
val iteri : 'a t -> f:(int -> 'a -> unit) -> unit
iteri is just like iter, but it also passes in the index of each element as the first argument to the iter'd function. Tail-recursive.
val foldi : 'a t -> f:(int -> 'b -> 'a -> 'b) -> init:'b -> 'b
foldi is just like fold, but it also passes in the index of each element as the first argument to the folded function. Tail-recursive.
val reduce_exn : 'a t -> f:('a -> 'a -> 'a) -> 'a
reduce_exn f [a1; ...; an] 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 group : 'a t -> break:('a -> 'a -> bool) -> 'a t t
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']

val groupi : 'a t ->
       break:(int -> 'a -> 'a -> bool) -> 'a t t
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']

val last : 'a t -> 'a option
The final element of a list. The _exn version raises Invalid_argument on the empty list.
val last_exn : 'a t -> 'a
val dedup : ?compare:('a -> 'a -> int) -> 'a t -> 'a t
dedup (de-duplicate). The same list with duplicates removed, but the order is not guaranteed.
val contains_dup : ?compare:('a -> 'a -> int) -> 'a t -> bool
contains_dup True if there are any two elements in the list which are the same.
val find_a_dup : ?compare:('a -> 'a -> int) -> 'a t -> 'a option
find_a_dup returns a duplicate from the list (no guarantees about which duplicate you get), or None if there are no dups.
exception Duplicate_found of (unit -> Sexplib.Sexp.t) * string
val exn_if_dup : ?compare:('a -> 'a -> int) ->
       ?context:string -> 'a t -> to_sexp:('a -> Sexplib.Sexp.t) -> unit
exn_if_dup ?compare ?context t ~to_sexp will run find_a_dup on t, and raise Duplicate_found if a duplicate is found. The context is the second argument of the exception
val count : 'a t -> f:('a -> bool) -> int
count f l is the number of elements in l that satisfy the predicate f.
val range : ?stride:int ->
       ?start:[ `exclusive | `inclusive ] ->
       ?stop:[ `exclusive | `inclusive ] -> 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 init : int -> f:(int -> 'a) -> 'a t
init f n is [(f 0); (f 1); ...; (f (n-1))]. It is an error if n < 0.
val rev_filter_map : 'a t -> f:('a -> 'b option) -> 'b t
rev_filter_map f l is the reversed sublist of l containing only elements for which f returns Some e.
val rev_filter_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b t
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.
val filter_map : 'a t -> f:('a -> 'b option) -> 'b t
filter_map f l is the sublist of l containing only elements for which f returns Some e.
val filter_mapi : 'a t -> f:(int -> 'a -> 'b option) -> 'b t
filter_mapi is just like filter_map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.
val filter_opt : 'a option t -> 'a t
filter_opt l is the sublist of l containing only elements which are Some e. In other words, filter_opt l = filter_map ~f:ident l.
module Assoc: sig .. end

Note that sub, unlike slice, doesn't use python-style indices!
val sub : 'a t -> pos:int -> len:int -> 'a t
sub pos len l is the len-element sublist of l, starting at pos.
val slice : 'a t -> int -> int -> 'a t
slice l start stop returns a new list including elements l.(start) through l.(stop-1), normalized python-style.
val take : 'a t -> int -> 'a t
take l n is fst (split_n n l). drop l n is snd (split_n n l).
val drop : 'a t -> int -> 'a t
val take_while : 'a t -> f:('a -> bool) -> 'a t
take_while l ~f returns the longest prefix of l for which f is true.
val drop_while : 'a t -> f:('a -> bool) -> 'a t
drop_while l ~f drops the longest prefix of l for which f is true.
val concat : 'a t t -> 'a t
Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Tail recursive over outer and inner lists.
val concat_no_order : 'a t t -> 'a t
Same as concat but faster and without preserving any ordering (ie for lists that are essentially viewed as multi-sets.
val cons : 'a -> 'a t -> 'a t
val cartesian_product : 'a t -> 'b t -> ('a * 'b) t
val to_string : f:('a -> string) -> 'a t -> string
val permute : ?random_state:Random.State.t -> 'a t -> 'a t
permute ?random_state t returns a permutation of t.

permute side affects random_state by repeated calls to Random.State.int. If random_state is not supplied, permute uses Random.State.default.

val is_sorted : 'a t -> compare:('a -> 'a -> int) -> bool
val compare : 'a t -> 'a t -> cmp:('a -> 'a -> int) -> int
lexicographic
val equal : 'a t -> 'a t -> equal:('a -> 'a -> bool) -> bool
module Infix: sig .. end
val transpose : 'a t t -> 'a t t option
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. *

val transpose_exn : 'a t t -> 'a t t
transpose_exn transposes the rows and columns of its argument, throwing exception if the list is not rectangular. *
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 bin_t : 'a Bin_prot.Type_class.t -> 'a t Bin_prot.Type_class.t
val bin_read_t : 'a Bin_prot.Unsafe_read_c.reader -> 'a t Bin_prot.Read_ml.reader
val bin_read_t_ : 'a Bin_prot.Unsafe_read_c.reader ->
       'a t Bin_prot.Unsafe_read_c.reader
val bin_read_t__ : 'a Bin_prot.Unsafe_read_c.reader ->
       (int -> 'a t) Bin_prot.Unsafe_read_c.reader
val bin_reader_t : 'a Bin_prot.Type_class.reader -> 'a t Bin_prot.Type_class.reader
val bin_size_t : 'a Bin_prot.Size.sizer -> 'a t Bin_prot.Size.sizer
val bin_write_t : 'a Bin_prot.Unsafe_write_c.writer -> 'a t Bin_prot.Write_ml.writer
val bin_write_t_ : 'a Bin_prot.Unsafe_write_c.writer ->
       'a t Bin_prot.Unsafe_write_c.writer
val bin_writer_t : 'a Bin_prot.Type_class.writer -> 'a t Bin_prot.Type_class.writer

Return the n-th element of the given list. The first element (head of the list) is at position 0. Raise Failure "nth" if the list is too short. Raise Invalid_argument "List.nth" if n is negative.

List reversal.

List.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.

List.rev_map f l gives the same result as List.rev (ListLabels.map f l), but is more efficient.

List.iter2_exn f [a1; ...; an] [b1; ...; bn] calls in turn f a1 b1; ...; f an bn. Raise Invalid_argument if the two lists have different lengths.

List.rev_map2_exn f l1 l2 gives the same result as List.rev (List.map2_exn f l1 l2), but is more efficient.

List.fold2_exn f a [b1; ...; bn] [c1; ...; cn] is f (... (f (f a b1 c1) b2 c2) ...) bn cn. Raise Invalid_argument if the two lists have different lengths.

Same as List.for_all, but for a two-argument predicate. Raise Invalid_argument if the two lists have different lengths.

Same as List.exists, but for a two-argument predicate. Raise Invalid_argument if the end of one list is reached before the end of the other.

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.

Like filter, but reverses the order of the input list

partition_map t ~f partitions t according to f.

partition_tf p l returns a pair of lists (l1, l2), where l1 is the list of all the elements of l that satisfy the predicate p, and l2 is the list of all the elements of l that do not satisfy p. The order of the elements in the input list is preserved. The "tf" suffix is mnemonic to remind readers at a call that the result is (trues, falses).

split_n n [e1; ...; em] is ([e1; ...; en], [en+1; ...; em]). If n > m, ([e1; ...; em], []) is returned. If 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, Pervasives.compare is a suitable comparison function.

The current implementation uses Merge Sort. It runs in constant 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.

Same as sort, but guaranteed to be stable

Merge two lists: assuming that l1 and l2 are sorted according to the comparison function cmp, merge cmp l1 l2 will return a sorted list containting all the elements of l1 and l2. If several elements compare equal, the elements of l1 will be before the elements of l2.

Return the first element of the given list. Raise Failure "hd" if the list is empty.

Return the given list without its first element. Raise Failure "tl" if the list is empty.

find_exn t ~f returns the first element of t that satisfies f. It raises Not_found if there is no such element.

Tail-recursive implementations of standard List operations


E.g. append [1; 2] [3; 4; 5] is [1; 2; 3; 4; 5]

List.map f [a1; ...; an] applies function f to a1, ..., an, and builds the list [f a1; ...; f an] with the results returned by f.

concat_map t ~f is concat (map t ~f), except that there is no guarantee about the order in which f is applied to the elements of t.

concat_mapi t ~f is like concat_map, but passes the index as an argument

List.map2_exn f [a1; ...; an] [b1; ...; bn] is [f a1 b1; ...; f an bn]. Raise Invalid_argument if the two lists have different lengths.

rev_map_append ~f l1 l2 reverses l1 mapping f over each element, and appends the result to the front of l2.

List.fold_right f [a1; ...; an] b is f a1 (f a2 (... (f an b) ...)).

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 None if the two lists have different lengths.

mapi is just like map, but it also passes in the index of each element as the first argument to the mapped function. Tail-recursive.

iteri is just like iter, but it also passes in the index of each element as the first argument to the iter'd function. Tail-recursive.

foldi is just like fold, but it also passes in the index of each element as the first argument to the folded function. Tail-recursive.

reduce_exn f [a1; ...; an] is f (... (f (f a1 a2) a3) ...) an. It fails on the empty list. Tail recursive.

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']

The final element of a list. The _exn version raises Invalid_argument on the empty list.

dedup (de-duplicate). The same list with duplicates removed, but the order is not guaranteed.

contains_dup True if there are any two elements in the list which are the same.

find_a_dup returns a duplicate from the list (no guarantees about which duplicate you get), or None if there are no dups.

exn_if_dup ?compare ?context t ~to_sexp will run find_a_dup on t, and raise Duplicate_found if a duplicate is found. The context is the second argument of the exception

count f l is the number of elements in l that satisfy the predicate f.

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).

init f n is [(f 0); (f 1); ...; (f (n-1))]. It is an error if n < 0.

rev_filter_map f l 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_map f l is the sublist of l containing only elements for which f returns Some e.

filter_mapi is just like 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:ident l.

Note that sub, unlike slice, doesn't use python-style indices!

sub pos len l is the len-element sublist of l, starting at pos.

slice l start stop returns a new list including elements l.(start) through l.(stop-1), normalized python-style.

take l n is fst (split_n n l). drop l n is snd (split_n n l).

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.

Concatenate a list of lists. The elements of the argument are all concatenated together (in the same order) to give the result. Tail recursive over outer and inner lists.

Same as concat but faster and without preserving any ordering (ie for lists that are essentially viewed as multi-sets.

permute ?random_state t returns a permutation of t.

permute side affects random_state by repeated calls to Random.State.int. If random_state is not supplied, permute uses Random.State.default.

lexicographic

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 exception if the list is not rectangular. *