octez-proto-libs 19.0 · OCaml Package

List

A replacement for Stdlib.List which:

replaces the exception-raising functions by exception-safe variants,
provides Lwt-, result- and Lwt-result-aware traversors.

List is intended to shadow both Stdlib.List and Lwt_list.

Basics

Checkout Lwtreslib for an introduction to the naming and semantic convention of Lwtreslib. In a nutshell:

Stdlib functions that raise exceptions are replaced by safe variants (typically returning option).
The _e suffix is for result-aware traversors ("e" stands for "error"), _s and _p are for Lwt-aware, and _es and _ep are for Lwt-result-aware.
_e, _s, and _es traversors are fail-early: they stop traversal as soon as a failure (Error or Fail) occurs; _p and _ep traversors are best-effort: they only resolve once all of the intermediate promises have, even if a failure occurs.

Double-traversal and combine

Note that double-list traversors (iter2, map2, etc., and also combine) take an additional when_different_lengths parameter. This is to control the error that is returned when the two lists passed as arguments have different lengths.

This mechanism is a replacement for Stdlib.List.iter2 (etc.) raising Invalid_argument.

Note that, as per the fail-early behaviour mentioned above, _e, _s, and _es traversors will have already processed the common-prefix before the error is returned.

Because the best-effort behaviour of _p and _ep is unsatisfying for this failure case, double parallel traversors are omitted from this library. (Specifically, it is not obvious whether nor how the when_different_lengths error should be composed with the other errors.)

To obtain a different behaviour for sequential traversors, or to process two lists in parallel, you can use combine or any of the alternatives that handles the error differently: combine_drop, combine_with_leftovers. Finally, the rev_combine is provided to allow to avoid multiple-reversing.

Special considerations

Because they traverse the list from right-to-left, the fold_right2 function and all its variants fail with when_different_lengths before any of the processing starts. Whilst this is still within the fail-early behaviour, it may be surprising enough that it requires mentioning here.

Because they may return early, for_all2 and exists2 and all their variants may return Ok _ even though the arguments have different lengths.

API

type 'a t = 'a list =

| []
| :: of 'a * 'a list

The list type

Constructors and some such

val nil : 'a list

nil is []

val nil_e : ('a list, 'trace) Pervasives.result

nil_e is Ok []

val nil_s : 'a list Lwt.t

nil_s is Lwt.return_nil

val nil_es : ('a list, 'trace) Pervasives.result Lwt.t

nil_es is Lwt.return (Ok [])

val cons : 'a -> 'a list -> 'a list

cons x xs is x :: xs

val is_empty : 'a list -> bool

is_empty xs is true iff xs is []

Safe wrappers

This part of the module simply shadows some functions from Stdlib.List with exceptionless variants. As per the design principles of Lwtreslib,

functions which may fail with Not_found or otherwise from unavailability of data return an option instead,
function which may fail with Invalid_argument _ or otherwise from malformedness of input receive an additional parameter to return as an Error instead,
functions which perform polymorphic comparison receive an additional parameter for monomorphic comparison instead.

val hd : 'a list -> 'a option

hd xs is the head (first element) of the list or None if the list is empty.

val tl : 'a list -> 'a list option

tl xs is the tail of the list (the whole list except the first element) or None if the list is empty.

val nth : 'a list -> int -> 'a option

nth xs n is the nth element of the list or None if the list has fewer than n elements.

For example, nth xs 0 = hd xs and nth ['x'; 'y'] 1 = Some 'y'.

val nth_opt : 'a list -> int -> 'a option

nth_opt is an alias for nth provided for compatibility with Stdlib.List.

val last : 'a -> 'a list -> 'a

last x xs is the last element of the list xs or x if xs is empty.

The primary intended use for last is after destructing a list: match l with | [] -> … | x :: xs -> last x xs but it can also be used for a default value: last default_value_if_empty xs.

val last_opt : 'a list -> 'a option

last_opt xs is the last element of the list xs or None if the list xs is empty.

val find : ('a -> bool) -> 'a list -> 'a option

find predicate xs is the first element x of the list xs such that predicate x is true or None if the list xs has no such element.

val find_opt : ('a -> bool) -> 'a list -> 'a option

find_opt is an alias for find provided for compatibility with Stdlib.List.

val find_map : ('a -> 'b option) -> 'a list -> 'b option

find_map f xs applies f to each of the elements of xs until it returns Some _ at which point it is returned. If no such elements are found then it returns None.

Note that it only applies f to a prefix of xs. It doesn't apply f to the elements of xs which are after the found element. Consequently, find_map f xs has better performance and a different semantic than calling map and find separately.

val mem : equal:('a -> 'a -> bool) -> 'a -> 'a list -> bool

mem ~equal a l is true iff there is an element e of l such that equal a e.

val assoc : equal:('a -> 'a -> bool) -> 'a -> ('a * 'b) list -> 'b option

assoc ~equal k kvs is Some v such that (k', v) is the first pair in the list such that equal k' k or None if the list contains no such pair.

val assoc_opt : equal:('a -> 'a -> bool) -> 'a -> ('a * 'b) list -> 'b option

assoc_opt is an alias for assoc provided for compatibility with Stdlib.List.

val assq : 'a -> ('a * 'b) list -> 'b option

assq k kvs is the same as assoc ~equal:Stdlib.( == ) k kvs: it uses the physical equality.

val assq_opt : 'a -> ('a * 'b) list -> 'b option

assq_opt is an alias for assq provided for compatibility with Stdlib.List.

val mem_assoc : equal:('a -> 'a -> bool) -> 'a -> ('a * 'b) list -> bool

mem_assoc ~equal k l is equivalent to Option.is_some @@ assoc ~equal k l.

val mem_assq : 'a -> ('a * 'b) list -> bool

mem_assq k l is mem_assoc ~equal:Stdlib.( == ) k l.

val remove_assoc : 
  equal:('a -> 'a -> bool) ->
  'a ->
  ('a * 'b) list ->
  ('a * 'b) list

remove_assoc ~equal k l is l without the first element (k', _) such that equal k k'.

val remove_assq : 'a -> ('a * 'b) list -> ('a * 'b) list

remove_assoq k l is remove_assoc ~equal:Stdlib.( == ) k l.

Initialisation

val init : 
  when_negative_length:'trace ->
  int ->
  (int -> 'a) ->
  ('a list, 'trace) Pervasives.result

init ~when_negative_length n f is a list of n elements f 0, f 1, etc.

If n is negative, it is Error when_negative_length instead.

Basic traversal

val length : 'a list -> int

length xs is the number of elements in xs.

length [] is 0, length ['x'] is 1, etc.

val rev : 'a list -> 'a list

rev xs is a list with the elements appearing in the reverse order as in xs.

rev ['x'; 'y'] is 'y'; 'x'

val concat : 'a list list -> 'a list

concat xs is a list containing the elements of the elements of xs.

concat [['x'; 'y']; ['a'; 'b']] is ['x'; 'y'; 'a'; 'b']

val append : 'a list -> 'a list -> 'a list

append xs ys is a list containing the elements of xs and the elements of ys, in this order.

concat ['x'; 'y'] ['a'; 'b'] is ['x'; 'y'; 'a'; 'b']

val rev_append : 'a list -> 'a list -> 'a list

rev_append xs ys is append (rev xs) ys but more efficient. In other words, rev_append xs ys is a list containing the elements of xs in reverse order followed by the elements of ys.

There are two main use-cases for rev_append. First, you should use rev_append when the order of elements is unimportant. In this case you simply replace append xs ys with rev_append xs ys.

Second, you can use rev_append on an already reversed list. You may obtain an already reversed list from any of the other rev_* functions of this module, or simply via your own traversal. In this case, you replace, say, append (map f xs) ys with rev_append (rev_map f xs) ys.

val flatten : 'a list list -> 'a list

flatten is an alias for concat.

Double-list traversals

These safe-wrappers take an explicit value to handle the case of lists of unequal length. This value is passed as a named parameter: when_different_lengths.

Note that the traversal function passed as argument (if any) is applied to the common prefix of the two lists, even if they are of different lengths. E.g., in map2 f ['x', 'y'] ['a'] the call f 'x' 'a' is made and all its side-effects are performed before the value Error when_different_lengths is returned

val combine : 
  when_different_lengths:'trace ->
  'a list ->
  'b list ->
  (('a * 'b) list, 'trace) Pervasives.result

combine ~when_different_lengths l1 l2 is either

Error when_different_lengths if List.length l1 <> List.length l2
a list of pairs of elements from l1 and l2

E.g., combine ~when_different_lengths [] [] is Ok []

E.g., combine ~when_different_lengths [1; 2] ['a'; 'b'] is Ok [(1,'a'); (2, 'b')]

E.g., combine ~when_different_lengths:"wrong" [1] [] is Error "wrong"

Note: combine ~when_different_lengths l1 l2 is equivalent to try Ok (Stdlib.List.combine l1 l2) with Invalid_argument _ -> when_different_lengths

The same equivalence almost holds for the other double traversors below. The notable difference is if the functions passed as argument to the traversors raise the Invalid_argument _ exception.

val rev_combine : 
  when_different_lengths:'trace ->
  'a list ->
  'b list ->
  (('a * 'b) list, 'trace) Pervasives.result

rev_combine ~when_different_lengths xs ys is rev (combine ~when_different_lengths xs ys) but more efficient.

val split : ('a * 'b) list -> 'a list * 'b list

split xs is (List.map fst xs, List.map snd xs) but more efficient.

val iter2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> unit) ->
  'a list ->
  'b list ->
  (unit, 'trace) Pervasives.result

iter2 ~when_different_lengths f xs ys is f x0 y0; f x1 y1; ….

Remember that, even if the lists are of different lengths, the function f is applied to the common prefix of xs and ys. This is true for other traversals, but especially relevant to iter which is commonly used for side-effects.

val map2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result

map2 ~when_different_lengths f xs ys is a list with elements f x0 y0, f x1 y1, etc.

Remember that, even if the lists are of different lengths, the function f is applied to the common prefix of xs and ys. Beware of side-effects and computational cost.

val rev_map2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result

rev_map2 ~when_different_lengths f xs ys is Result.map rev @@ map2 ~when_different_lengths f xs ys but more efficient.

Remember that, even if the lists are of different lengths, the function f is applied to the common prefix of xs and ys. Beware of side-effects and computational cost.

val fold_left2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> 'a) ->
  'a ->
  'b list ->
  'c list ->
  ('a, 'trace) Pervasives.result

fold_left2 ~when_different_lengths f init xs ys is … (f (f init x0 y0) x1 y1).

Remember that, even if the lists are of different lengths, the function f is applied to the common prefix of xs and ys. Beware of side-effects and computational cost.

val fold_right2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> 'c) ->
  'a list ->
  'b list ->
  'c ->
  ('c, 'trace) Pervasives.result

fold_right2 ~when_different_lengths f xs ys init is f x0 y0 (f x1 y1 (…)).

This function is not tail-recursive.

Note that unlike the left-to-right double-list traversors, fold_right2 only calls f if the lists are of the same length.

val for_all2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> bool) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result

for_all2 ~when_different_lengths f xs ys is f x0 y0 && f x1 y1 && ….

The function stops early if it encounters elements xn, yn such that f xn yn is false. (This is consistent with the short-circuit, lazy evaluation strategy of && in the description above.)

Also note that, if such an element is found in the common prefix of xs and ys, then the function returns Ok false even if xs and ys are of different lengths.

Examples:

for_all2 ~when_different_lengths (=) [] [] is Ok true

for_all2 ~when_different_lengths (=) ['x'] ['a'] is Ok false

for_all2 ~when_different_lengths (=) ['x'; 'y'] ['a'] is Ok false

for_all2 ~when_different_lengths (=) ['x'] ['x'] is Ok true

for_all2 ~when_different_lengths (=) ['x'; 'y'] ['x'] is Error when_different_lengths

for_all2 ~when_different_lengths (=) ['x'; 'y'] ['x'; 'b'] is Ok false

for_all2 ~when_different_lengths (=) ['x'; 'y'] ['x'; 'y'; 'c'] is Error when_different_lengths

Remember that, when it returns Error when_different_lengths, the function f has already been applied to the common prefix of xs and ys. Beware of side-effects and computational cost.

val exists2 : 
  when_different_lengths:'trace ->
  ('a -> 'b -> bool) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result

exists2 ~when_different_lengths f xs ys is f x0 y0 || f x1 y1 || ….

The function stops early if it encounters elements xn, yn such that f xn yn is true. (This is consistent with the short-circuit, lazy evaluation strategy of || in the description above.)

Also note that, if such an element is found in the common prefix of xs and ys, then the function returns Ok true even if xs and ys are of different lengths.

Examples:

exists2 ~when_different_lengths (=) [] [] is Ok false

exists2 ~when_different_lengths (=) ['x'] ['a'] is Ok false

exists2 ~when_different_lengths (=) ['x'; 'y'] ['a'] is Error when_different_lengths

exists2 ~when_different_lengths (=) ['x'] ['x'] is Ok true

exists2 ~when_different_lengths (=) ['x'; 'y'] ['x'] is Ok true

Remember that, when it returns Error when_different_lengths, the function f has already been applied to the common prefix of xs and ys. Beware of side-effects and computational cost.

Monad-aware variants

The functions below are strict extensions of the standard Stdlib.List module. It is for result-, lwt- and lwt-result-aware variants. The meaning of the suffix is as described above, in Lwtreslib, and in Sigs.Seq.

Initialisation variants

Note that for asynchronous variants (_s, _es, _p, and _ep), if the length parameter is negative, then the promise is returned already fulfilled with Error when_different_lengths.

val init_e : 
  when_negative_length:'trace ->
  int ->
  (int -> ('a, 'trace) Pervasives.result) ->
  ('a list, 'trace) Pervasives.result

init_e is a Result-aware variant of init.

val init_s : 
  when_negative_length:'trace ->
  int ->
  (int -> 'a Lwt.t) ->
  ('a list, 'trace) Pervasives.result Lwt.t

init_s is an Lwt-aware variant of init.

val init_es : 
  when_negative_length:'trace ->
  int ->
  (int -> ('a, 'trace) Pervasives.result Lwt.t) ->
  ('a list, 'trace) Pervasives.result Lwt.t

init_es is an Lwt-Result-aware variant of init.

val init_p : 
  when_negative_length:'trace ->
  int ->
  (int -> 'a Lwt.t) ->
  ('a list, 'trace) Pervasives.result Lwt.t

init_p is a variant of init_s where the promises are evaluated concurrently.

Query variants

val find_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a option, 'trace) Pervasives.result

find_e is a Result-aware variant of find.

val find_s : ('a -> bool Lwt.t) -> 'a list -> 'a option Lwt.t

find_s is an Lwt-aware variant of find.

val find_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a option, 'trace) Pervasives.result Lwt.t

find_es is an Lwt-Result-aware variant of find.

val find_map_e : 
  ('a -> ('b option, 'trace) Pervasives.result) ->
  'a list ->
  ('b option, 'trace) Pervasives.result

find_map_e is a Result-aware variant of find_map.

val find_map_s : ('a -> 'b option Lwt.t) -> 'a list -> 'b option Lwt.t

find_map_s is an Lwt-aware variant of find_map.

val find_map_es : 
  ('a -> ('b option, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b option, 'trace) Pervasives.result Lwt.t

find_map_es is an Lwt-Result-aware variant of find_map.

val filter : ('a -> bool) -> 'a list -> 'a list

filter f xs is the list of all the elements xn of xs such that f xn is true.

filter (fun x -> x > 10) [0; 2; 19; 22; -1; 3; 11] is [19; 22; 11]

val filteri : (int -> 'a -> bool) -> 'a list -> 'a list

filteri is similar to filter but the predicate also receives the element's index as an argument.

val find_all : ('a -> bool) -> 'a list -> 'a list

find_all is an alias for filter.

val rev_filter : ('a -> bool) -> 'a list -> 'a list

rev_filter f l is rev (filter f l) but more efficient.

val rev_filteri : (int -> 'a -> bool) -> 'a list -> 'a list

rev_filteri f l is rev (filteri f l) but more efficient.

val rev_filter_some : 'a option list -> 'a list

rev_filter_some xs is rev @@ filter_some xs but more efficient.

val filter_some : 'a option list -> 'a list

filter_some extracts all the payloads of the Some variants. The order is preserved.

filter_some [None; Some 'a'; None; None; Some 'z'; Some 'u'] is ['a'; 'z'; 'u'].

val rev_filter_ok : ('a, 'b) Pervasives.result list -> 'a list

rev_filter_ok rs is rev @@ filter_ok rs but more efficient.

val filter_ok : ('a, 'b) Pervasives.result list -> 'a list

filter_ok extracts all the payloads of the Ok variants. The order is preserved.

filter_ok [Error 3; Ok 'a'; Error 3; Error 5; Ok 'z'; Ok 'u'] is ['a'; 'z'; 'u'].

val rev_filter_error : ('a, 'b) Pervasives.result list -> 'b list

rev_filter_error rs is rev @@ filter_error rs but more efficient.

val filter_error : ('a, 'b) Pervasives.result list -> 'b list

filter_error extracts all the payloads of the Error variants. The order is preserved.

filter_ok [Error 3; Ok 'a'; Error 3; Error 5; Ok 'z'; Ok 'u'] is [3; 3; 5].

val rev_filter_left : ('a, 'b) Either.t list -> 'a list

rev_filter_left es is rev @@ filter_left es but more efficient.

val filter_left : ('a, 'b) Either.t list -> 'a list

filter_left extracts all the payloads of the Left variants. The order is preserved.

filter_left [Right 3; Left 'a'; Right 3; Right 5; Left 'z'; Left 'u'] is ['a'; 'z'; 'u'].

val rev_filter_right : ('a, 'b) Either.t list -> 'b list

rev_filter_right es is rev @@ filter_right es but more efficient.

val filter_right : ('a, 'b) Either.t list -> 'b list

filter_right extracts all the payloads of the Right variants. The order is preserved.

filter_right [Right 3; Left 'a'; Right 3; Right 5; Left 'z'; Left 'u'] is [3; 3; 5].

val rev_filter_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list, 'trace) Pervasives.result

rev_filter_e is a Result-aware variant of rev_filter.

val filter_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list, 'trace) Pervasives.result

filter_e is a Result-aware variant of filter.

val rev_filter_s : ('a -> bool Lwt.t) -> 'a list -> 'a list Lwt.t

rev_filter_s is an Lwt-aware variant of rev_filter.

val filter_s : ('a -> bool Lwt.t) -> 'a list -> 'a list Lwt.t

filter_s is an Lwt-aware variant of filter.

val rev_filter_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list, 'trace) Pervasives.result Lwt.t

rev_filter_es is an Lwt-Result-aware variant of rev_filter.

val filter_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list, 'trace) Pervasives.result Lwt.t

filter_es is an Lwt-Result-aware variant of filter.

val rev_filteri_e : 
  (int -> 'a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list, 'trace) Pervasives.result

rev_filteri_e is a Result-aware variant of rev_filteri.

val filteri_e : 
  (int -> 'a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list, 'trace) Pervasives.result

filteri_e is a Result-aware variant of filteri.

val rev_filteri_s : (int -> 'a -> bool Lwt.t) -> 'a list -> 'a list Lwt.t

rev_filteri_s is an Lwt-aware variant of rev_filteri.

val filteri_s : (int -> 'a -> bool Lwt.t) -> 'a list -> 'a list Lwt.t

filteri_s is an Lwt-aware variant of filteri.

val rev_filteri_es : 
  (int -> 'a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list, 'trace) Pervasives.result Lwt.t

rev_filteri_es is an Lwt-Result-aware variant of rev_filteri.

val filteri_es : 
  (int -> 'a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list, 'trace) Pervasives.result Lwt.t

filteri_es is an Lwt-Result-aware variant of filteri.

val rev_partition : ('a -> bool) -> 'a list -> 'a list * 'a list

rev_partition f xs is let rt, rf = partition f xs in (rev rt, rev rf) but more efficient.

val partition : ('a -> bool) -> 'a list -> 'a list * 'a list

partition f xs is a couple of lists (ts, fs) where ts contains all the elements of xs such that f x is true and fs contains all the elements of xs such that f x is false.

The function f is applied once to each element of xs.

val rev_partition_map : 
  ('a -> ('b, 'c) Either.t) ->
  'a list ->
  'b list * 'c list

rev_partition_map f xs is let rt, rf = partition_map f xs in (rev rt, rev rf) but more efficient.

val partition_map : ('a -> ('b, 'c) Either.t) -> 'a list -> 'b list * 'c list

partition_map f xs applies f to each of the element of xs and returns a couple of lists (ls, rs) where ls contains all the l such that f x is Left l and rs contains all the r such that f x is Right r.

val rev_partition_result : ('a, 'b) Pervasives.result list -> 'a list * 'b list

rev_partition_result rs is partition_result @@ rev rs but more efficient.

val partition_result : ('a, 'b) Pervasives.result list -> 'a list * 'b list

partition_result rs is a tuple of lists (os, es) where os contains all the payloads of Ok variants of rs and es contains all the payloads of Error variants of rs.

partition_result rs is (filter_ok rs, filter_error rs) but more efficient.

val rev_partition_either : ('a, 'b) Either.t list -> 'a list * 'b list

rev_partition_either rs is partition_either @@ rev rs but more efficient.

val partition_either : ('a, 'b) Either.t list -> 'a list * 'b list

partition_either es is a tuple of lists (ls, rs) where ls contains all the payloads of Left variants of ls and rs contains all the payloads of Right variants of es.

partition_either es is (filter_left es, filter_right es) but more efficient.

val rev_partition_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list * 'a list, 'trace) Pervasives.result

rev_partition_e is a Result-aware variant of rev_partition.

val partition_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  ('a list * 'a list, 'trace) Pervasives.result

partition_e is a Result-aware variant of partition.

val rev_partition_s : 
  ('a -> bool Lwt.t) ->
  'a list ->
  ('a list * 'a list) Lwt.t

rev_partition_s is an Lwt-aware variant of rev_partition.

val partition_s : ('a -> bool Lwt.t) -> 'a list -> ('a list * 'a list) Lwt.t

partition_s is an Lwt-aware variant of partition.

val rev_partition_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list * 'a list, 'trace) Pervasives.result Lwt.t

rev_partition_es is an Lwt-Result-aware variant of rev_partition.

val partition_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list * 'a list, 'trace) Pervasives.result Lwt.t

partition_es is an Lwt-Result-aware variant of partition.

val partition_p : ('a -> bool Lwt.t) -> 'a list -> ('a list * 'a list) Lwt.t

partition_p is a variant of partition_s where the promises are evaluated concurrently.

val rev_partition_map_e : 
  ('a -> (('b, 'c) Either.t, 'trace) Pervasives.result) ->
  'a list ->
  ('b list * 'c list, 'trace) Pervasives.result

rev_partition_map_e is a Result-aware variant of rev_partition_map.

val partition_map_e : 
  ('a -> (('b, 'c) Either.t, 'trace) Pervasives.result) ->
  'a list ->
  ('b list * 'c list, 'trace) Pervasives.result

partition_map_e is a Result-aware variant of partition_map.

val rev_partition_map_s : 
  ('a -> ('b, 'c) Either.t Lwt.t) ->
  'a list ->
  ('b list * 'c list) Lwt.t

rev_partition_map_s is an Lwt-aware variant of rev_partition_map.

val partition_map_s : 
  ('a -> ('b, 'c) Either.t Lwt.t) ->
  'a list ->
  ('b list * 'c list) Lwt.t

partition_map_s is an Lwt-aware variant of partition_map.

val rev_partition_map_es : 
  ('a -> (('b, 'c) Either.t, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list * 'c list, 'trace) Pervasives.result Lwt.t

rev_partition_map_es is an Lwt-Result-aware variant of rev_partition_map.

val partition_map_es : 
  ('a -> (('b, 'c) Either.t, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list * 'c list, 'trace) Pervasives.result Lwt.t

partition_map_es is an Lwt-Result-aware variant of partition_map.

Traversal variants

val iter : ('a -> unit) -> 'a list -> unit

iter f xs is f x0; f x1; ….

val iter_e : 
  ('a -> (unit, 'trace) Pervasives.result) ->
  'a list ->
  (unit, 'trace) Pervasives.result

iter_e is a Result-aware variant of iter.

val iter_s : ('a -> unit Lwt.t) -> 'a list -> unit Lwt.t

iter_s is an Lwt-aware variant of iter.

val iter_es : 
  ('a -> (unit, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  (unit, 'trace) Pervasives.result Lwt.t

iter_es is an Lwt-Result-aware variant of iter.

val iter_p : ('a -> unit Lwt.t) -> 'a list -> unit Lwt.t

iter_p is a variant of iter_s where the promises are evaluated concurrently.

val iteri : (int -> 'a -> unit) -> 'a list -> unit

iteri f xs is f 0 x0; f 1 x1; ….

val iteri_e : 
  (int -> 'a -> (unit, 'trace) Pervasives.result) ->
  'a list ->
  (unit, 'trace) Pervasives.result

iteri_e is a Result-aware variant of iteri.

val iteri_s : (int -> 'a -> unit Lwt.t) -> 'a list -> unit Lwt.t

iteri_s is an Lwt-aware variant of iteri.

val iteri_es : 
  (int -> 'a -> (unit, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  (unit, 'trace) Pervasives.result Lwt.t

iteri_es is an Lwt-Result-aware variant of iteri.

val iteri_p : (int -> 'a -> unit Lwt.t) -> 'a list -> unit Lwt.t

iteri_p is a variant of iteri_s where the promises are evaluated concurrently.

val map : ('a -> 'b) -> 'a list -> 'b list

map f xs is the list [f x0; f x1; …].

val map_e : 
  ('a -> ('b, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

map_e is a Result-aware variant of map.

val map_s : ('a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

map_s is an Lwt-aware variant of map.

val map_es : 
  ('a -> ('b, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

map_es is an Lwt-Result-aware variant of map.

val map_p : ('a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

map_p is a variant of map_s where the promises are evaluated concurrently.

val mapi : (int -> 'a -> 'b) -> 'a list -> 'b list

mapi f xs is the list [f 0 x0; f 1 x1; …].

val mapi_e : 
  (int -> 'a -> ('b, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

mapi_e is a Result-aware variant of mapi.

val mapi_s : (int -> 'a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

mapi_s is an Lwt-aware variant of mapi.

val mapi_es : 
  (int -> 'a -> ('b, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

mapi_es is an Lwt-Result-aware variant of mapi.

val mapi_p : (int -> 'a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

mapi_p is a variant of mapi_s where the promises are evaluated concurrently.

val rev_map : ('a -> 'b) -> 'a list -> 'b list

rev_map f xs is rev @@ map f xs but more efficient.

val rev_mapi : (int -> 'a -> 'b) -> 'a list -> 'b list

rev_mapi f xs is rev @@ mapi f xs but more efficient.

val rev_map_e : 
  ('a -> ('b, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

rev_map_e is a Result-aware variant of rev_map.

val rev_map_s : ('a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

rev_map_s is an Lwt-aware variant of rev_map.

val rev_map_es : 
  ('a -> ('b, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

rev_map_es is an Lwt-Result-aware variant of rev_map.

val rev_map_p : ('a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

rev_map_p is a variant of rev_map_s where the promises are evaluated concurrently.

val rev_mapi_e : 
  (int -> 'a -> ('b, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

rev_mapi_e is a Result-aware variant of rev_mapi.

val rev_mapi_s : (int -> 'a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

rev_mapi_s is an Lwt-aware variant of rev_mapi.

val rev_mapi_es : 
  (int -> 'a -> ('b, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

rev_mapi_es is an Lwt-Result-aware variant of rev_mapi.

val rev_mapi_p : (int -> 'a -> 'b Lwt.t) -> 'a list -> 'b list Lwt.t

rev_mapi_p is a variant of rev_mapi_s where the promises are evaluated concurrently.

val rev_filter_map : ('a -> 'b option) -> 'a list -> 'b list

rev_filter_map f xs is rev @@ filter_map f xs but more efficient.

val rev_filter_map_e : 
  ('a -> ('b option, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

rev_filter_map_e is a Result-aware variant of rev_filter_map.

val filter_map_e : 
  ('a -> ('b option, 'trace) Pervasives.result) ->
  'a list ->
  ('b list, 'trace) Pervasives.result

filter_map_e is a Result-aware variant of filter_map.

val rev_filter_map_s : ('a -> 'b option Lwt.t) -> 'a list -> 'b list Lwt.t

rev_filter_map_s is an Lwt-aware variant of rev_filter_map.

val filter_map : ('a -> 'b option) -> 'a list -> 'b list

filter_map f xs is filter_some @@ map f xs but more efficient.

val filter_map_s : ('a -> 'b option Lwt.t) -> 'a list -> 'b list Lwt.t

filter_map_s is an Lwt-aware variant of filter_map.

val rev_filter_map_es : 
  ('a -> ('b option, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

rev_filter_map_es is an Lwt-Result-aware variant of rev_filter_map.

val filter_map_es : 
  ('a -> ('b option, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'trace) Pervasives.result Lwt.t

filter_map_es is an Lwt-Result-aware variant of filter_map.

val filter_map_p : ('a -> 'b option Lwt.t) -> 'a list -> 'b list Lwt.t

filter_map_p is a variant of filter_map_s where the promises are evaluated concurrently.

val concat_map : ('a -> 'b list) -> 'a list -> 'b list

concat_map f xs is concat (map f xs) but more efficient.

val concat_map_s : ('a -> 'b list Lwt.t) -> 'a list -> 'b list Lwt.t

concat_map_s is an Lwt-aware variant of concat_map.

val concat_map_e : 
  ('a -> ('b list, 'error) Pervasives.result) ->
  'a list ->
  ('b list, 'error) Pervasives.result

concat_map_e is a Result-aware variant of concat_map.

val concat_map_es : 
  ('a -> ('b list, 'error) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error) Pervasives.result Lwt.t

concat_map_es is an Lwt-Result-aware variant of concat_map.

val concat_map_p : ('a -> 'b list Lwt.t) -> 'a list -> 'b list Lwt.t

concat_map_p is a variant of concat_map_s where the promises are evaluated concurrently.

val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a

val fold_left_e : 
  ('a -> 'b -> ('a, 'trace) Pervasives.result) ->
  'a ->
  'b list ->
  ('a, 'trace) Pervasives.result

fold_left_e is a Result-aware variant of fold_left.

val fold_left_s : ('a -> 'b -> 'a Lwt.t) -> 'a -> 'b list -> 'a Lwt.t

fold_left_s is an Lwt-aware variant of fold_left.

val fold_left_es : 
  ('a -> 'b -> ('a, 'trace) Pervasives.result Lwt.t) ->
  'a ->
  'b list ->
  ('a, 'trace) Pervasives.result Lwt.t

fold_left_es is an Lwt-Result-aware variant of fold_left.

val fold_left_map : ('a -> 'b -> 'a * 'c) -> 'a -> 'b list -> 'a * 'c list

fold_left_map f a xs is a combination of fold_left and map that maps over all elements of xs and threads an accumulator with initial value a through calls to f.

val fold_left_map_e : 
  ('a -> 'b -> ('a * 'c, 'trace) Pervasives.result) ->
  'a ->
  'b list ->
  ('a * 'c list, 'trace) Pervasives.result

fold_left_map_e f a xs is a combination of fold_left_e and map_e that maps over all elements of xs and threads an accumulator with initial value a through calls to f. The list is traversed from left to right and the first encountered error is returned.

val fold_left_map_s : 
  ('a -> 'b -> ('a * 'c) Lwt.t) ->
  'a ->
  'b list ->
  ('a * 'c list) Lwt.t

fold_left_map_s f a xs is a combination of fold_left_s and map_s that maps over all elements of xs and threads an accumulator with initial value a through calls to f.

val fold_left_map_es : 
  ('a -> 'b -> ('a * 'c, 'trace) Pervasives.result Lwt.t) ->
  'a ->
  'b list ->
  ('a * 'c list, 'trace) Pervasives.result Lwt.t

fold_left_map_es f a xs is a combination of fold_left_es and map_es that maps over all elements of xs and threads an accumulator with initial value a through calls to f. The list is traversed from left to right and the first encountered error is returned.

val fold_left_i : (int -> 'a -> 'b -> 'a) -> 'a -> 'b list -> 'a

val fold_left_i_e : 
  (int -> 'a -> 'b -> ('a, 'trace) Pervasives.result) ->
  'a ->
  'b list ->
  ('a, 'trace) Pervasives.result

val fold_left_i_s : (int -> 'a -> 'b -> 'a Lwt.t) -> 'a -> 'b list -> 'a Lwt.t

val fold_left_i_es : 
  (int -> 'a -> 'b -> ('a, 'trace) Pervasives.result Lwt.t) ->
  'a ->
  'b list ->
  ('a, 'trace) Pervasives.result Lwt.t

val fold_right : ('a -> 'b -> 'b) -> 'a list -> 'b -> 'b

This function is not tail-recursive

val fold_right_e : 
  ('a -> 'b -> ('b, 'trace) Pervasives.result) ->
  'a list ->
  'b ->
  ('b, 'trace) Pervasives.result

This function is not tail-recursive

val fold_right_s : ('a -> 'b -> 'b Lwt.t) -> 'a list -> 'b -> 'b Lwt.t

This function is not tail-recursive

val fold_right_es : 
  ('a -> 'b -> ('b, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b ->
  ('b, 'trace) Pervasives.result Lwt.t

This function is not tail-recursive

Double-traversal variants

As mentioned above, there are no _p and _ep double-traversors. Use combine (and variants) to circumvent this.

val iter2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (unit, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  (unit, 'trace) Pervasives.result

val iter2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> unit Lwt.t) ->
  'a list ->
  'b list ->
  (unit, 'trace) Pervasives.result Lwt.t

val iter2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (unit, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  (unit, 'trace) Pervasives.result Lwt.t

val map2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> ('c, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result

val map2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c Lwt.t) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result Lwt.t

val map2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> ('c, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result Lwt.t

val rev_map2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> ('c, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result

val rev_map2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c Lwt.t) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result Lwt.t

val rev_map2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> ('c, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  ('c list, 'trace) Pervasives.result Lwt.t

val fold_left2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> ('a, 'trace) Pervasives.result) ->
  'a ->
  'b list ->
  'c list ->
  ('a, 'trace) Pervasives.result

val fold_left2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> 'a Lwt.t) ->
  'a ->
  'b list ->
  'c list ->
  ('a, 'trace) Pervasives.result Lwt.t

val fold_left2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> ('a, 'trace) Pervasives.result Lwt.t) ->
  'a ->
  'b list ->
  'c list ->
  ('a, 'trace) Pervasives.result Lwt.t

val fold_right2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> ('c, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  'c ->
  ('c, 'trace) Pervasives.result

This function is not tail-recursive

val fold_right2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> 'c Lwt.t) ->
  'a list ->
  'b list ->
  'c ->
  ('c, 'trace) Pervasives.result Lwt.t

This function is not tail-recursive

val fold_right2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> 'c -> ('c, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  'c ->
  ('c, 'trace) Pervasives.result Lwt.t

This function is not tail-recursive

Scanning variants

val for_all : ('a -> bool) -> 'a list -> bool

val for_all_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  (bool, 'trace) Pervasives.result

val for_all_s : ('a -> bool Lwt.t) -> 'a list -> bool Lwt.t

val for_all_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  (bool, 'trace) Pervasives.result Lwt.t

val for_all_p : ('a -> bool Lwt.t) -> 'a list -> bool Lwt.t

val exists : ('a -> bool) -> 'a list -> bool

val exists_e : 
  ('a -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  (bool, 'trace) Pervasives.result

val exists_s : ('a -> bool Lwt.t) -> 'a list -> bool Lwt.t

val exists_es : 
  ('a -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  (bool, 'trace) Pervasives.result Lwt.t

val exists_p : ('a -> bool Lwt.t) -> 'a list -> bool Lwt.t

Double-scanning variants

As mentioned above, there are no _p and _ep double-scanners. Use combine (and variants) to circumvent this.

val for_all2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result

val for_all2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> bool Lwt.t) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result Lwt.t

val for_all2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result Lwt.t

val exists2_e : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (bool, 'trace) Pervasives.result) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result

val exists2_s : 
  when_different_lengths:'trace ->
  ('a -> 'b -> bool Lwt.t) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result Lwt.t

val exists2_es : 
  when_different_lengths:'trace ->
  ('a -> 'b -> (bool, 'trace) Pervasives.result Lwt.t) ->
  'a list ->
  'b list ->
  (bool, 'trace) Pervasives.result Lwt.t

Combine variants

These are primarily intended to be used for preprocessing before applying a traversor to the resulting list of pairs. They give alternatives to the when_different_lengths mechanism of the immediate double-traversors above.

In case the semantic of, say, map2_es was unsatisfying, one can use map_es on a combine-preprocessed pair of lists. The different variants of combine give different approaches to different-length handling.

val combine_drop : 'a list -> 'b list -> ('a * 'b) list

combine_drop ll lr is a list l of pairs of elements taken from the common-length prefix of ll and lr. The suffix of whichever list is longer (if any) is dropped.

More formally nth l n is:

None if n >= min (length ll) (length lr)
Some (Option.get @@ nth ll n, Option.get @@ nth lr n) otherwise

val combine_with_leftovers : 
  'a list ->
  'b list ->
  ('a * 'b) list * ('a list, 'b list) Either.t option

combine_with_leftovers ll lr is a tuple (combined, leftover) where combined is combine_drop ll lr and leftover is either Either.Left lsuffix or Either.Right rsuffix depending on which of ll or lr is longer. leftover is None if the two lists have the same length.

Product

val product : 'a list -> 'b list -> ('a * 'b) list

product xs ys is the cartesian product of xs and ys.

In other words product xs ys is a list containing all the pairs (x, y) where x is an element of xs and y is an element of ys.

The order of the elements in the returned list is unspecified.

Comparison and equality

The comparison and equality functions are those of the OCaml Stdlib.

val compare : ('a -> 'a -> int) -> 'a list -> 'a list -> int

val compare_lengths : 'a list -> 'b list -> int

val compare_length_with : 'a list -> int -> int

val equal : ('a -> 'a -> bool) -> 'a list -> 'a list -> bool

Sorting

The sorting functions are those of the OCaml Stdlib.

val sort : ('a -> 'a -> int) -> 'a list -> 'a list

val stable_sort : ('a -> 'a -> int) -> 'a list -> 'a list

val fast_sort : ('a -> 'a -> int) -> 'a list -> 'a list

val sort_uniq : ('a -> 'a -> int) -> 'a list -> 'a list

Conversion

The conversion functions are those of the OCaml Stdlib.

val to_seq : 'a list -> 'a Seq.t

val of_seq : 'a Seq.t -> 'a list

val init_ep : 
  when_negative_length:'error ->
  int ->
  (int -> ('a, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  ('a list, 'error Error_monad.trace) Pervasives.result Lwt.t

val filter_ep : 
  ('a -> (bool, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list, 'error Error_monad.trace) Pervasives.result Lwt.t

val partition_ep : 
  ('a -> (bool, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('a list * 'a list, 'error Error_monad.trace) Pervasives.result Lwt.t

val partition_map_ep : 
  ('a -> (('b, 'c) Either.t, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list * 'c list, 'error Error_monad.trace) Pervasives.result Lwt.t

val iter_ep : 
  ('a -> (unit, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  (unit, 'error Error_monad.trace) Pervasives.result Lwt.t

val iteri_ep : 
  (int -> 'a -> (unit, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  (unit, 'error Error_monad.trace) Pervasives.result Lwt.t

val map_ep : 
  ('a -> ('b, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val mapi_ep : 
  (int -> 'a -> ('b, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val rev_map_ep : 
  ('a -> ('b, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val rev_mapi_ep : 
  (int -> 'a -> ('b, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val filter_map_ep : 
  ('a -> ('b option, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val concat_map_ep : 
  ('a -> ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  ('b list, 'error Error_monad.trace) Pervasives.result Lwt.t

val for_all_ep : 
  ('a -> (bool, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  (bool, 'error Error_monad.trace) Pervasives.result Lwt.t

val exists_ep : 
  ('a -> (bool, 'error Error_monad.trace) Pervasives.result Lwt.t) ->
  'a list ->
  (bool, 'error Error_monad.trace) Pervasives.result Lwt.t

package octez-proto-libs

List

Basics

Double-traversal and combine

Special considerations

API

Constructors and some such

Safe wrappers

Initialisation

Basic traversal

Double-list traversals

Monad-aware variants

Initialisation variants

Query variants

Traversal variants

Double-traversal variants

Scanning variants

Double-scanning variants

Combine variants

Product

Comparison and equality

Sorting

Conversion