sequence

library sequence

library sequence.bigarray

module SequenceBigarray

Simple and Efficient Iterators
Version of Sequence
with labels
A sequence of values of type 'a
. If you give it a function 'a > unit
it will be applied to every element of the sequence successively.
type +'a sequence = 'a t
NOTE Type ('a, 'b) t2 = ('a > 'b > unit) > unit
has been removed and subsumed by ('a * 'b) t
Build a sequence
val from_iter : ( ( 'a > unit ) > unit ) > 'a t
Build a sequence from a iter function
val from_fun : ( unit > 'a option ) > 'a t
Call the function repeatedly until it returns None. This sequence is transient, use persistent
if needed!
val empty : 'a t
Empty sequence. It contains no element.
val singleton : 'a > 'a t
Singleton sequence, with exactly one element.
val doubleton : 'a > 'a > 'a t
Sequence with exactly two elements
val init : f:( int > 'a ) > 'a t
init f
is the infinite sequence f 0; f 1; f 2; …
.
val repeat : 'a > 'a t
Infinite sequence of the same element. You may want to look at take
and the likes if you iterate on it.
val iterate : ( 'a > 'a ) > 'a > 'a t
iterate f x
is the infinite sequence x, f(x), f(f(x)), ...
val forever : ( unit > 'b ) > 'b t
Sequence that calls the given function to produce elements. The sequence may be transient (depending on the function), and definitely is infinite. You may want to use take
and persistent
.
Cycle forever through the given sequence. Assume the given sequence can be traversed any amount of times (not transient). This yields an infinite sequence, you should use something like take
not to loop forever.
Consume a sequence
val iter : f:( 'a > unit ) > 'a t > unit
Consume the sequence, passing all its arguments to the function. Basically iter f seq
is just seq f
.
val iteri : f:( int > 'a > unit ) > 'a t > unit
Iterate on elements and their index in the sequence
val fold : f:( 'a > 'b > 'a ) > init:'a > 'b t > 'a
Fold over elements of the sequence, consuming it
val foldi : f:( 'a > int > 'b > 'a ) > init:'a > 'b t > 'a
Fold over elements of the sequence and their index, consuming it
fold_filter_map f acc l
is a fold_map
like function, but the function can choose to skip an element by retuning None
.
Map objects two by two. lazily. The last element is kept in the sequence if the count is odd.
val for_all : f:( 'a > bool ) > 'a t > bool
Do all elements satisfy the predicate?
val exists : f:( 'a > bool ) > 'a t > bool
Exists there some element satisfying the predicate?
val mem : ?eq:( 'a > 'a > bool ) > x:'a > 'a t > bool
Is the value a member of the sequence?
val find : ( 'a > 'b option ) > 'a t > 'b option
Find the first element on which the function doesn't return None
val find_pred : f:( 'a > bool ) > 'a t > 'a option
find_pred p l
finds the first element of l
that satisfies p
, or returns None
if no element satisfies p
val length : 'a t > int
How long is the sequence? Forces the sequence.
val is_empty : 'a t > bool
Is the sequence empty? Forces the sequence.
Transform a sequence
Append two sequences. Iterating on the result is like iterating on the first, then on the second.
Append sequences. Iterating on the result is like iterating on the each sequence of the list in order.
Map with indices, and only keep nonNone
elements
seq_list l
returns all the ways to pick one element in each subsequence in l
. Assumes the subsequences can be iterated on several times.
seq_list_map f l
maps f
over every element of l
, then calls seq_list
val filter_count : f:( 'a > bool ) > 'a t > int
Count how many elements satisfy the given predicate
Insert the single element between every element of the sequence
filter_some l
retains only elements of the form Some x
. Same as filter_map (fun x>x)
val keep_ok : ( 'a, _ ) Result.result t > 'a t
keep_ok l
retains only elements of the form Ok x
.
val keep_error : ( _, 'e ) Result.result t > 'e t
keep_error l
retains only elements of the form Error x
.
Caching
Iterate on the sequence, storing elements in an efficient internal structure.. The resulting sequence can be iterated on as many times as needed. Note: calling persistent on an already persistent sequence will still make a new copy of the sequence!
Lazy version of persistent
. When calling persistent_lazy s
, a new sequence s'
is immediately returned (without actually consuming s
) in constant time; the first time s'
is iterated on, it also consumes s
and caches its content into a inner data structure that will back s'
for future iterations.
warning: on the first traversal of s'
, if the traversal is interrupted prematurely (take
, etc.) then s'
will not be memorized, and the next call to s'
will traverse s
again.
Misc
Sort the sequence. Eager, O(n) ram and O(n ln(n)) time. It iterates on elements of the argument sequence immediately, before it sorts them.
Sort the sequence and remove duplicates. Eager, same as sort
val sorted : ?cmp:( 'a > 'a > int ) > 'a t > bool
Checks whether the sequence is sorted. Eager, same as sort
.
Group equal consecutive elements. Formerly synonym to group
.
Group equal elements, disregarding their order of appearance. The result sequence is traversable as many times as required. precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
Map each distinct element to its number of occurrences in the whole seq. Similar to group_by seq > map (fun l>List.hd l, List.length l)
Remove consecutive duplicate elements. Basically this is like fun seq > map List.hd (group seq)
.
Cartesian product of the sequences. When calling product a b
, the caller MUST ensure that b
can be traversed as many times as required (several times), possibly by calling persistent
on it beforehand.
val diagonal_l : 'a list > ('a * 'a) t
All pairs of distinct positions of the list. diagonal l
will return the sequence of all List.nth i l, List.nth j l
if i < j
.
All pairs of distinct positions of the sequence. Iterates only once on the sequence, which must be finite.
join ~join_row a b
combines every element of a
with every element of b
using join_row
. If join_row
returns None, then the two elements do not combine. Assume that b
allows for multiple iterations.
val join_by :
?eq:'key equal >
?hash:'key hash >
( 'a > 'key ) >
( 'b > 'key ) >
merge:( 'key > 'a > 'b > 'c option ) >
'a t >
'b t >
'c t
join key1 key2 ~merge
is a binary operation that takes two sequences a
and b
, projects their elements resp. with key1
and key2
, and combine values (x,y)
from (a,b)
with the same key
using merge
. If merge
returns None
, the combination of values is discarded. precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
val join_all_by :
?eq:'key equal >
?hash:'key hash >
( 'a > 'key ) >
( 'b > 'key ) >
merge:( 'key > 'a list > 'b list > 'c option ) >
'a t >
'b t >
'c t
join_all_by key1 key2 ~merge
is a binary operation that takes two sequences a
and b
, projects their elements resp. with key1
and key2
, and, for each key k
occurring in at least one of them:
 compute the list
l1
of elements ofa
that map tok
 compute the list
l2
of elements ofb
that map tok
 call
merge k l1 l2
. Ifmerge
returnsNone
, the combination of values is discarded, otherwise it returnsSome c
andc
is inserted in the result.
val group_join_by :
?eq:'a equal >
?hash:'a hash >
( 'b > 'a ) >
'a t >
'b t >
('a * 'b list) t
group_join_by key2
associates to every element x
of the first sequence, all the elements y
of the second sequence such that eq x (key y)
. Elements of the first sequences without corresponding values in the second one are mapped to []
precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
Intersection of two collections. Each element will occur at most once in the result. Eager. precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
Union of two collections. Each element will occur at most once in the result. Eager. precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
subset a b
returns true
if all elements of a
belong to b
. Eager. precondition: for any x
and y
, if eq x y
then hash x=hash y
must hold.
val unfoldr : ( 'b > ('a * 'b) option ) > 'b > 'a t
unfoldr f b
will apply f
to b
. If it yields Some (x,b')
then x
is returned and unfoldr recurses with b'
.
val max : ?lt:( 'a > 'a > bool ) > 'a t > 'a option
Max element of the sequence, using the given comparison function.
val min : ?lt:( 'a > 'a > bool ) > 'a t > 'a option
Min element of the sequence, using the given comparison function. see max
for more details.
val sum : int t > int
Sum of elements
val sumf : float t > float
Sum of elements, using Kahan summation
val head : 'a t > 'a option
First element, if any, otherwise None
val head_exn : 'a t > 'a
First element, if any, fails
Take at most n
elements from the sequence. Works on infinite sequences.
Take elements while they satisfy the predicate, then stops iterating. Will work on an infinite sequence s
if the predicate is false for at least one element of s
.
val fold_while :
f:( 'a > 'b > 'a * [ `Stop  `Continue ] ) >
init:'a >
'b t >
'a
Folds over elements of the sequence, stopping early if the accumulator returns ('a, `Stop)
Reverse the sequence. O(n) memory and time, needs the sequence to be finite. The result is persistent and does not depend on the input being repeatable.
Zip elements of the sequence with their index in the sequence. Changed type
val fold2 : f:( 'c > 'a > 'b > 'c ) > init:'c > ('a * 'b) t > 'c
val iter2 : f:( 'a > 'b > unit ) > ('a * 'b) t > unit
map2_2 f g seq2
maps each x, y
of seq2 into f x y, g x y
Basic data structures converters
val to_list : 'a t > 'a list
Convert the sequence into a list. Preserves order of elements. This function is tailrecursive, but consumes 2*n memory. If order doesn't matter to you, consider to_rev_list
.
val to_rev_list : 'a t > 'a list
Get the list of the reversed sequence (more efficient than to_list
)
val of_list : 'a list > 'a t
on_list f l
is equivalent to to_list @@ f @@ of_list l
.
val to_array : 'a t > 'a array
Convert to an array. Currently not very efficient because an intermediate list is used.
val of_array : 'a array > 'a t
val of_array_i : 'a array > (int * 'a) t
Elements of the array, with their index
val array_slice : 'a array > int > int > 'a t
array_slice a i j
Sequence of elements whose indexes range from i
to j
val of_opt : 'a option > 'a t
Iterate on 0 or 1 values.
Convert to a stream. linear in memory and time (a copy is made in memory)
Add elements of the sequence to the hashtable, with Hashtbl.add
Add elements of the sequence to the hashtable, with Hashtbl.replace (erases conflicting bindings)
Build a hashtable from a sequence of key/value pairs
val of_str : string > char t
val to_str : char t > string
val concat_str : string t > string
Concatenate strings together, eagerly. Also see intersperse
to add a separator.
Raised when the user tries to iterate several times on a transient iterator
val of_in_channel : in_channel > char t
Iterates on characters of the input (can block when one iterates over the sequence). If you need to iterate several times on this sequence, use persistent
.
val int_range : start:int > stop:int > int t
Iterator on integers in start...stop
by steps 1. Also see ()
for an infix version.
val int_range_dec : start:int > stop:int > int t
Iterator on decreasing integers in stop...start
by steps 1. See (^)
for an infix version
val int_range_by : step:int > start:int > stop:int > int t
int_range_by ~step ~start:i ~stop:j
is the range starting at i
, including j
, where the difference between successive elements is step
. use a negative step
for a decreasing sequence.
val bools : bool t
Iterates on true
and false
Convert the given set to a sequence. The set module must be provided.
Convert the sequence to a set, given the proper set module
type 'a klist = unit > [ `Nil  `Cons of 'a * 'a klist ]
Functorial conversions between sets and sequences
module Set : sig ... end
Conversion between maps and sequences.
module Map : sig ... end
Infinite sequences of random values
val random_int : int > int t
Infinite sequence of random integers between 0 and the given higher bound (see Random.int)
val random_bool : bool t
Infinite sequence of random bool values
val random_float : float > float t
val random_array : 'a array > 'a t
Sequence of choices of an element in the array
val random_list : 'a list > 'a t
Infinite sequence of random elements of the list. Basically the same as random_array
.
shuffle seq
returns a perfect shuffle of seq
. Uses O(length seq) memory and time. Eager.
shuffle_buffer n seq
returns a sequence of element of seq
in random order. The shuffling is not uniform. Uses O(n) memory.
The first n
elements of the sequence are consumed immediately. The rest is consumed lazily.
Sampling
val sample : n:int > 'a t > 'a array
sample n seq
returns k samples of seq
, with uniform probability. It will consume the sequence and use O(n) memory.
It returns an array of size min (length seq) n
.
Infix functions
module Infix : sig ... end
include module type of Infix
val () : int > int > int t
a  b
is the range of integers from a
to b
, both included, in increasing order. It will therefore be empty if a > b
.
val (^) : int > int > int t
a ^ b
is the range of integers from b
to a
, both included, in decreasing order (starts from a
). It will therefore be empty if a < b
.
Pretty printing of sequences
val pp_seq :
?sep:string >
( Format.formatter > 'a > unit ) >
Format.formatter >
'a t >
unit
Pretty print a sequence of 'a
, using the given pretty printer to print each elements. An optional separator string can be provided.
Print into a buffer
val to_string : ?sep:string > ( 'a > string ) > 'a t > string
Print into a string
Basic IO
Very basic interface to manipulate files as sequence of chunks/lines. The sequences take care of opening and closing files properly; every time one iterates over a sequence, the file is opened/closed again.
Example: copy a file "a"
into file "b"
, removing blank lines:
Sequence.(IO.lines_of "a" > filter (fun l> l<> "") > IO.write_lines "b");;
By chunks of 4096
bytes:
Sequence.IO.(chunks_of ~size:4096 "a" > write_to "b");;
Read the lines of a file into a list:
Sequence.IO.lines "a" > Sequence.to_list
module IO : sig ... end