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include Stdlib.List
include Module_types
type 'a t = 'a list
let return (a:'a): 'a t = [a]
let rec (>>=) (l:'a t) (f:'a -> 'b t): 'b t =
match l with
| [] ->
[]
| hd :: tl ->
f hd @ (tl >>= f)
let (>=>) (f:'a -> 'b t) (g:'b -> 'c t) (a:'a): 'c t =
f a >>= g
let (<*>) (flst: ('a -> 'b) t) (lst:'a t): 'b t =
flst >>= fun f -> map f lst
let join = concat
let find (p:'a -> bool) (l:'a t): 'a option =
try
Some (find p l)
with Not_found ->
None
let nth (i: int) (lst: 'a t): 'a option =
nth_opt lst i
let nth_strict (i: int) (lst: 'a t): 'a =
match nth i lst with
| None ->
assert false
| Some e ->
e
let split_head_tail (lst: 'a t): 'a * 'a t =
assert (lst <> []);
match lst with
| [] ->
assert false
| hd :: tl ->
hd, tl
let head_strict (lst: 'a t): 'a =
assert (lst <> []);
fst (split_head_tail lst)
let tail_strict (lst: 'a t): 'a t =
assert (lst <> []);
snd (split_head_tail lst)
let map_and_filter (f:'a -> 'b option) (l:'a list): 'b list =
let rec map = function
| [] ->
[]
| hd :: tl ->
match f hd with
| None ->
map tl
| Some b ->
b :: map tl
in
map l
let split_at (p:'a -> bool) (l: 'a t): 'a t * 'a t =
let rec split prefix rest =
match rest with
| [] ->
rev prefix, rest
| hd :: tl ->
if p hd then
rev prefix, rest
else
split (hd :: prefix) tl
in
split [] l
let transpose (row_list: 'a list list): 'a list list =
assert (row_list <> []);
let first_column row_list =
fold_right
(fun row (column, row_list)->
match row with
| [] ->
assert false
| el :: rest_row ->
el :: column,
rest_row :: row_list
)
row_list
([], [])
in
let rec get_columns columns row_list =
match row_list with
| [] ->
assert false
| [] :: _ ->
columns
| (_ :: _) :: _ ->
let column, row_list = first_column row_list in
get_columns (column :: columns) row_list
in
rev (get_columns [] row_list)
module Monadic (M: MONAD) =
struct
let foldi_left (f:int -> 'a -> 'b -> 'b M.t) (l:'a t) (start:'b)
: 'b M.t =
let rec foldi i l start =
match l with
| [] ->
M.return start
| hd :: tl ->
M.(f i hd start >>= foldi (i+1) tl)
in
foldi 0 l start
let fold_left (f:'a -> 'b -> 'b M.t) (l:'a t) (start:'b): 'b M.t =
foldi_left (fun _ -> f) l start
let fold_right (f:'a -> 'b -> 'b M.t) (l:'a t) (start:'b): 'b M.t =
fold_left f (rev l) start
end
let%test _ =
transpose [ [1] ] = [ [1] ]
let%test _ =
transpose
[ [1;2;3] ] = [ [1]; [2]; [3] ]
let%test _ =
transpose
[ [1;2;3]; [4;5;6] ] = [ [1;4]; [2;5]; [3;6] ]