Simple sequence abstract datatype, intended to iterate efficiently on collections while performing some transformations.
Common operations supported by Sequence include
Sequence is not designed to be as general-purpose or flexible as, say,
'a Enum.t. Rather, it aims at providing a very simple and efficient
way of iterating on a finite number of values, only allocating (most of the time)
one intermediate closure to do so. For instance, iterating on keys, or values,
Hashtbl.t, without creating a list.
There is only one important type,
'a Sequence.t, and lots of functions built
around this type.
To get an overview of sequence, its origins and why it was created,
you can start with the slides of a talk
I (@c-cube) made at some OCaml meeting.
See the online API for more details on the set of available functions.
opam install sequence
manually (need OCaml >= 4.02.0):
make all install
If you have qtest installed, you can build and run tests with
$ ./configure --enable-tests $ make test
If you have benchmarks installed, you can build and run benchmarks with
$ make benchs $ ./benchs.native
To see how to use the library, check the
tests.ml has a few examples of how to convert basic data structures into
sequences, and conversely.
Conversion between n container types
would take n² functions. In practice, for a given collection
we can at best hope for
With sequence, if the source structure provides a
iter function (or a
to_seq wrapper), it becomes:
# let q = Queue.create();; # Sequence.( 1 -- 10 |> to_queue q);; - : unit = () # Sequence.of_queue q |> Sequence.to_list ;; - : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] # let s = Stack.create();; # Sequence.(of_queue q |> to_stack s);; - : unit = () # Sequence.of_stack s |> Sequence.to_list ;; - : int list = [10; 9; 8; 7; 6; 5; 4; 3; 2; 1]
Note how the list of elements is reversed when we transfer them from the queue to the stack.
Another example is extracting the list of values of a hashtable (in an undefined order that depends on the underlying hash function):
# let h = Hashtbl.create 16;; # for i = 0 to 10 do Hashtbl.add h i (string_of_int i) done;; - : unit = () # Hashtbl.length h;; - : int = 11 (* now to get the values *) # Sequence.of_hashtbl h |> Sequence.map snd |> Sequence.to_list;; - : string list = ["6"; "2"; "8"; "7"; "3"; "5"; "4"; "9"; "0"; "10"; "1"]
for loop is a bit limited, and lacks compositionality.
Instead, it can be more convenient and readable to
Sequence.(--) : int → int → int Sequence.t.
# Sequence.(1 -- 10_000_000 |> fold (+) 0);; - : int = 50000005000000 # let p x = x mod 5 = 0 in Sequence.(1 -- 5_000 |> filter p |> map (fun x -> x * x) |> fold (+) 0 );; - : int = 8345837500
|with flambda under sufficiently strong optimization flags, such compositions of operators should be compiled to an actual loop with no overhead!|
Iterating on sub-trees
A small λ-calculus AST, and some operations on it.
# type term = | Var of string | App of term * term | Lambda of term ;; # let rec subterms : term -> term Sequence.t = fun t -> let open Sequence.Infix in Sequence.cons t (match t with | Var _ -> Sequence.empty | Lambda u -> subterms u | App (a,b) -> Sequence.append (subterms a) (subterms b)) ;; (* Now we can define many other functions easily! *) # let vars t = Sequence.filter_map (function Var s -> Some s | _ -> None) (subterms t) ;; val vars : term -> string sequence = <fun > # let size t = Sequence.length (subterms t) ;; val size : term -> int = <fun > # let vars_list l = Sequence.(of_list l |> flat_map vars);; val vars_list : term list -> string sequence = <fun >
Makes it easy to write backtracking code (a non-deterministic
function returning several
will just return a
Here, we generate all permutations of a list by
enumerating the ways we can insert an element in a list.
# open Sequence.Infix;; # module S = Sequence ;; # let rec insert x l = match l with |  -> S.return [x] | y :: tl -> S.append S.(insert x tl >|= fun tl' -> y :: tl') (S.return (x :: l)) ;; # let rec permute l = match l with |  -> S.return  | x :: tl -> permute tl >>= insert x ;; # permute [1;2;3;4] |> S.take 2 |> S.to_list ;; - : int list list = [[4; 3; 2; 1]; [4; 3; 1; 2]]
examples/sexpr.mli exposes the interface of the S-expression
example library. It requires OCaml>=4.0 to compile, because of the GADT
structure used in the monadic parser combinators part of
Be careful that this is quite obscure.
Genis an external iterator. It means that the code which consumes some iterator of type
'a Gen.tis the one which decides when to go to the next element. This gives a lot of flexibility, for example when iterating on several iterators at the same time:
let zip (g1: 'a Gen.t) (g2:'b Gen.t) : ('a * 'b) Gen.t = let x1 = ref (g1 ()) in let x2 = ref (g2 ()) in fun () -> match !x1, !x2 with | None, _ | _, None -> None | Some x, Some y -> (* fetch next elements from g1 and g2 *) x1 := g1 (); x2 := g2 (); Some (x,y)
Sequenceis an internal iterator. When one wishes to iterate over an
'a Sequence.t, one has to give a callback
f : 'a → unitthat is called in succession over every element of the sequence. Control is not handed back to the caller before the whole iteration is over. This makes
zipimpossible to implement. However, the type
'a Sequence.tis general enough that it can be extracted from any classic
iterfunction, including from data structures such as
Hashtbl.t; one cannot obtain a
'a Gen.tfrom these without having access to the internal data structure.
'a Gen.t is more expressive than
'a Sequence.t, but it also
requires more knowledge of the underlying source of items.
For some operations such as
flat_map, Sequence is also extremely
efficient and will, if flambda permits, be totally removed at
compile time (e.g.
Sequence.(--) becomes a for loop, and
becomes a if test).
For more details, you can read http://gallium.inria.fr/blog/generators-iterators-control-and-continuations/ .
Sequence is available under the BSD license.