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module type Array = sig
type index
type 'a t
val empty : 'a t
val singleton : 'a -> 'a t
val extend : 'a t -> index -> (index -> 'a) -> 'a t
val retract : 'a t -> index -> 'a t
val contains : 'a t -> index -> bool
val last : 'a t -> index option
val set : 'a t -> index -> 'a -> unit
val get : 'a t -> index -> 'a
end
module type S_no_zero = sig
type t
val one : t
val maximum : t
val succ : t -> t
val pred : t -> t option
val compare : t -> t -> int
val equal : t -> t -> bool
val less_than : t -> t -> bool
val less_than_or_equal : t -> t -> bool
val max : t -> t -> t
val plus : t -> t -> t
val pp : Format.formatter -> t -> unit
module Map : Map.S with type key = t
module Set : Set.S with type elt = t
module Tbl : Hashtbl.S with type key = t
module Array : Array with type index = t
end
module type S = sig
include S_no_zero
val zero : t
end
module IntOps = struct
type t = int
let compare (x : t) (y : t) =
compare x y
let equal (x : t) (y : t) =
x = y
let less_than (x : t) (y : t) =
x < y
let less_than_or_equal (x : t) (y : t) =
x <= y
let max (x : t) (y : t) =
if x >= y then x
else y
let hash = Hashtbl.hash
let pp ppf x = Format.pp_print_int ppf x
end
module IntMap = Map.Make(IntOps)
module IntSet = Set.Make(IntOps)
module IntTbl = Hashtbl.Make(IntOps)
module Array_zero_indexed = struct
type index = int
type 'a t = 'a array
let empty = [| |]
let singleton x = [| x |]
let extend t idx init =
let len = idx + 1 in
let old_len = Array.length t in
if old_len > idx then
failwith "Natural.Array.extend: array already contains index";
if old_len = 0 then begin
Array.init len init
end else begin
let extended = Array.make len (t.(0)) in
Array.blit t 0 extended 0 old_len;
for i = old_len to idx do
Array.unsafe_set extended i (init i)
done;
extended
end
let retract t idx =
let old_len = Array.length t in
if old_len <= idx then
failwith "Natural.Array.retract: array already doesn't contain index";
Array.sub t 0 idx
let contains t idx =
let len = Array.length t in
idx < len
let last t =
let len = Array.length t in
if len = 0 then None
else Some (len - 1)
let set t idx data =
t.(idx) <- data
let get t idx =
t.(idx)
end
module Array_one_indexed = struct
type index = int
type 'a t = 'a array
let empty = [| |]
let singleton x = [| x |]
let extend t idx init =
let old_len = Array.length t in
if old_len >= idx then
failwith "Natural.Array.extend: array already contains index";
if old_len = 0 then begin
let initial = init 1 in
let res = Array.make idx initial in
for i = 1 to (idx - 1) do
Array.unsafe_set res i (init (i + 1))
done;
res
end else begin
let extended = Array.make idx (t.(0)) in
Array.blit t 0 extended 0 old_len;
for i = old_len to (idx - 1) do
Array.unsafe_set extended i (init (i + 1))
done;
extended
end
let retract t idx =
let old_len = Array.length t in
if old_len < idx then
failwith "Natural.Array.retract: array already doesn't contain index";
Array.sub t 0 (idx - 1)
let contains t idx =
let len = Array.length t in
idx <= len
let last t =
let len = Array.length t in
if len = 0 then None
else Some len
let set t idx data =
t.(idx - 1) <- data
let get t idx =
t.(idx - 1)
end
module Nat = struct
include IntOps
let zero = 0
let one = 1
let maximum = max_int
let succ t =
if t = maximum then t
else t + 1
let pred t =
if t = 0 then None
else Some (t - 1)
let plus t1 t2 =
let res = t1 + t2 in
if res < 0 then maximum
else res
module Map = IntMap
module Set = IntSet
module Tbl = IntTbl
module Array = Array_zero_indexed
end
module Nat_no_zero = struct
include IntOps
let one = 1
let maximum = max_int
let succ t =
if t = maximum then t
else t + 1
let pred t =
if t = 1 then None
else Some (t - 1)
let plus t1 t2 =
let res = t1 + t2 in
if res < 0 then maximum
else res
module Map = IntMap
module Set = IntSet
module Tbl = IntTbl
module Array = Array_one_indexed
end
module Make () = Nat
module Make_no_zero () = Nat_no_zero