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open! Base
module Location : sig
include Identifiable.S
end = struct
include String
end
module Uuid : sig
include Identifiable.S
end = struct
include String
end
let eval_fail loc fmt =
Printf.ksprintf (fun s -> failwith (Printf.sprintf !"%{Location}: %s" loc s)) fmt
;;
let equal_option equal a b =
match a, b with
| Some _, None | None, Some _ -> false
| None, None -> true
| Some x, Some y -> equal x y
;;
module Sorted_table : sig
type 'a t [@@deriving compare, sexp]
val create : Location.t -> eq:('a -> 'a -> bool) -> (string * 'a) list -> 'a t
val expose : 'a t -> (string * 'a) list
val map : 'a t -> f:('a -> 'b) -> 'b t
end = struct
type 'a t = { sorted : (string * 'a) list } [@@deriving compare, sexp]
let merge_check_adjacent_dups
: eq:('a -> 'a -> bool) -> (string * 'a) list
-> [ `Ok of (string * 'a) list | `Mismatch of string ]
=
fun ~eq ->
let rec loop acc ~last_key ~last_value = function
| [] -> `Ok (List.rev acc)
| (key, value) :: xs ->
if String.(last_key = key)
then
if eq last_value value then loop acc ~last_key ~last_value xs else `Mismatch key
else loop ((key, value) :: acc) ~last_key:key ~last_value:value xs
in
function
| [] -> `Ok []
| (key, value) :: xs -> loop [ key, value ] ~last_key:key ~last_value:value xs
;;
let create loc ~eq xs =
let sorted = List.sort ~compare:(fun (s1, _) (s2, _) -> String.compare s1 s2) xs in
match merge_check_adjacent_dups ~eq sorted with
| `Ok sorted -> { sorted }
| `Mismatch s ->
eval_fail loc "Different shapes for duplicated polymorphic constructor: `%s" s ()
;;
let expose t = t.sorted
let map t ~f = { sorted = List.map t.sorted ~f:(fun (k, v) -> k, f v) }
end
module Digest : sig
type t = Md5_lib.t [@@deriving compare, sexp]
val to_md5 : t -> Md5_lib.t
val of_md5 : Md5_lib.t -> t
val to_hex : t -> string
val constructor : string -> t list -> t
val list : t list -> t
val pair : t -> t -> t
val string : string -> t
val uuid : Uuid.t -> t
val int : int -> t
val option : t option -> t
end = struct
include Md5_lib
let to_md5 t = t
let of_md5 t = t
let sexp_of_t t = t |> to_hex |> sexp_of_string
let t_of_sexp s = s |> string_of_sexp |> of_hex_exn
let uuid u = string (Uuid.to_string u)
let int x = string (Int.to_string x)
let pair x y = string (to_binary x ^ to_binary y)
let list l = string (String.concat ~sep:"" (List.map ~f:to_binary l))
let constructor s l = string (s ^ to_binary (list l))
let option = function
| None -> constructor "none" []
| Some x -> constructor "some" [ x ]
;;
end
module Canonical_exp_constructor = struct
type 'a t =
| Annotate of Uuid.t * 'a
| Base of Uuid.t * 'a list
| Tuple of 'a list
| Record of (string * 'a) list
| Variant of (string * 'a list) list
| Poly_variant of 'a option Sorted_table.t
| Application of 'a * 'a list
| Rec_app of int * 'a list
| Var of int
[@@deriving sexp, compare]
let map x ~f =
match x with
| Annotate (u, x) -> Annotate (u, f x)
| Base (s, xs) -> Base (s, List.map ~f xs)
| Tuple xs -> Tuple (List.map ~f xs)
| Record l -> Record (List.map l ~f:(fun (s, x) -> s, f x))
| Variant l -> Variant (List.map l ~f:(fun (s, xs) -> s, List.map ~f xs))
| Poly_variant t -> Poly_variant (Sorted_table.map t ~f:(Option.map ~f))
| Application (x, l) -> Application (f x, List.map ~f l)
| Rec_app (t, l) -> Rec_app (t, List.map ~f l)
| Var v -> Var v
;;
let to_string t = Sexp.to_string (sexp_of_t (fun _ -> Atom "...") t)
end
module Create_digest : sig
val digest_layer : Digest.t Canonical_exp_constructor.t -> Digest.t
end = struct
let digest_layer = function
| Canonical_exp_constructor.Annotate (u, x) ->
Digest.constructor "annotate" [ Digest.uuid u; x ]
| Base (u, l) -> Digest.constructor "base" [ Digest.uuid u; Digest.list l ]
| Tuple l -> Digest.constructor "tuple" [ Digest.list l ]
| Record l ->
Digest.constructor
"record"
[ Digest.list (List.map l ~f:(fun (s, t) -> Digest.pair (Digest.string s) t)) ]
| Variant l ->
Digest.constructor
"variant"
[ Digest.list
(List.map l ~f:(fun (s, l) -> Digest.pair (Digest.string s) (Digest.list l)))
]
| Poly_variant table ->
Digest.constructor
"poly_variant"
[ Digest.list
(List.map (Sorted_table.expose table) ~f:(fun (x, y) ->
Digest.pair (Digest.string x) (Digest.option y)))
]
| Application (x, l) -> Digest.constructor "application" [ x; Digest.list l ]
| Rec_app (n, l) -> Digest.constructor "rec_app" [ Digest.int n; Digest.list l ]
| Var n -> Digest.constructor "var" [ Digest.int n ]
;;
end
module Visibility = struct
type visible = Visible
type opaque = Opaque
let _ = Visible
let _ = Opaque
end
module type Canonical = sig
type t
val to_digest : t -> Digest.t
module Exp1 : sig
type _ t
val var : int -> _ t
val recurse : int -> _ t list -> _ t
val apply : 'a t -> 'a t list -> _ t
val opaque : _ t -> Visibility.opaque t
val get_poly_variant
: Visibility.visible t
-> (Visibility.opaque t option Sorted_table.t, string) Result.t
end
module Def : sig
type t = Visibility.visible Exp1.t
end
module Create : sig
val annotate : Uuid.t -> _ Exp1.t -> _ Exp1.t
val basetype : Uuid.t -> _ Exp1.t list -> _ Exp1.t
val tuple : _ Exp1.t list -> _ Exp1.t
val poly_variant : Location.t -> (string * _ Exp1.t option) list -> _ Exp1.t
val define : Visibility.visible Exp1.t -> Def.t
val record : (string * _ Exp1.t) list -> _ Exp1.t
val variant : (string * _ Exp1.t list) list -> _ Exp1.t
val create : _ Exp1.t -> t
end
end
module Canonical_digest : Canonical = struct
type t = Canonical of Digest.t
let to_digest (Canonical x) = x
module CD = Create_digest
module Exp1 = struct
type opaque = Digest.t
type 'a t =
| Poly_variant of opaque option Sorted_table.t
| Non_poly_variant of (string * opaque)
| Opaque : opaque -> Visibility.opaque t
let to_digest (type a) (x : a t) =
match x with
| Opaque x -> x
| Non_poly_variant (_, x) -> x
| Poly_variant x -> CD.digest_layer (Poly_variant x)
;;
let equal (type a) (x : a t) (y : a t) =
Digest.compare (to_digest x) (to_digest y) = 0
;;
let opaque x = Opaque (to_digest x)
let create x =
let x = Canonical_exp_constructor.map ~f:to_digest x in
let desc = Canonical_exp_constructor.to_string x in
match x with
| Canonical_exp_constructor.Poly_variant l -> Poly_variant l
| Base _ -> Non_poly_variant (desc, CD.digest_layer x)
| Annotate _ ->
Non_poly_variant (desc, CD.digest_layer x)
| Application _ ->
Non_poly_variant (desc, CD.digest_layer x)
| Rec_app _ ->
Non_poly_variant (desc, CD.digest_layer x)
| Var _ | Tuple _ | Record _ | Variant _ ->
Non_poly_variant (desc, CD.digest_layer x)
;;
let var x = create (Var x)
let apply def l = create (Application (def, l))
let recurse tid l = create (Rec_app (tid, l))
let get_poly_variant (x : Visibility.visible t) =
match x with
| Non_poly_variant (desc, _) -> Error desc
| Poly_variant l -> Ok (Sorted_table.map ~f:(Option.map ~f:(fun x -> Opaque x)) l)
;;
end
module Def = struct
type t = Visibility.visible Exp1.t
end
module Create = struct
let annotate u x = Exp1.create (Annotate (u, x))
let basetype u l = Exp1.create (Base (u, l))
let tuple l = Exp1.create (Tuple l)
let poly_variant loc l =
Exp1.create (Poly_variant (Sorted_table.create loc ~eq:(equal_option Exp1.equal) l))
;;
let define x = x
let record l = Exp1.create (Record l)
let variant l = Exp1.create (Variant l)
let create e = Canonical (Exp1.to_digest e)
end
end
module Canonical_full = struct
module CD = Create_digest
module Exp1 = struct
type t0 = Exp of t0 Canonical_exp_constructor.t [@@deriving compare, sexp]
let equal_t0 x y = compare_t0 x y = 0
type 'a t = t0 [@@deriving compare, sexp]
let var x = Exp (Canonical_exp_constructor.Var x)
let apply d xs = Exp (Canonical_exp_constructor.Application (d, xs))
let recurse r xs = Exp (Canonical_exp_constructor.Rec_app (r, xs))
let poly_variant loc xs =
Exp
(Canonical_exp_constructor.Poly_variant
(Sorted_table.create loc ~eq:(equal_option equal_t0) xs))
;;
let get_poly_variant = function
| Exp (Poly_variant tab) -> Ok tab
| Exp cc -> Error (Canonical_exp_constructor.to_string cc)
;;
let opaque t = t
let rec to_digest = function
| Exp e -> CD.digest_layer (Canonical_exp_constructor.map ~f:to_digest e)
;;
end
module Def = struct
type t = Exp1.t0 [@@deriving compare, sexp]
end
type t = Exp1.t0 [@@deriving compare, sexp]
let to_digest e = Exp1.to_digest e
module Create = struct
let annotate u x = Exp1.Exp (Annotate (u, x))
let basetype u xs = Exp1.Exp (Base (u, xs))
let tuple xs = Exp1.Exp (Tuple xs)
let poly_variant loc xs = Exp1.poly_variant loc xs
let var n = Exp1.Exp (Var n)
let recurse r xs = Exp1.recurse r xs
let apply d xs = Exp1.apply d xs
let define x = x
let record xs = Exp1.Exp (Record xs)
let variant xs = Exp1.Exp (Variant xs)
let create exp = exp
end
let to_string_hum t = Sexp.to_string_hum (sexp_of_t t)
end
module Tid : sig
include Identifiable.S
end = struct
include String
end
module Vid : sig
include Identifiable.S
end = struct
include String
end
module Gid : sig
type t [@@deriving compare, equal, sexp]
val create : unit -> t
end = struct
type t = int [@@deriving compare, equal, sexp]
let r = ref 0
let create () =
let u = !r in
r := 1 + u;
u
;;
end
module Expression = struct
type 't poly_constr =
[ `Constr of string * 't option
| `Inherit of Location.t * 't
]
[@@deriving compare, equal, sexp]
module Group : sig
type 'a t [@@deriving compare, equal, sexp]
val create : Location.t -> (Tid.t * Vid.t list * 'a) list -> 'a t
val id : 'a t -> Gid.t
val lookup : 'a t -> Tid.t -> Vid.t list * 'a
end = struct
type 'a t =
{ gid : Gid.t
; loc : Location.t
; members : (Tid.t * (Vid.t list * 'a)) list
}
[@@deriving compare, equal, sexp]
let create loc trips =
let gid = Gid.create () in
let members = List.map trips ~f:(fun (x, vs, t) -> x, (vs, t)) in
{ gid; loc; members }
;;
let id g = g.gid
let lookup g tid =
match List.Assoc.find g.members ~equal:Tid.( = ) tid with
| Some scheme -> scheme
| None ->
eval_fail
g.loc
!"impossible: lookup_group, unbound type-identifier: %{Tid}"
tid
()
;;
end
module Stable = struct
module V1 = struct
type t =
| Annotate of Uuid.t * t
| Base of Uuid.t * t list
| Record of (string * t) list
| Variant of (string * t list) list
| Tuple of t list
| Poly_variant of (Location.t * t poly_constr list)
| Var of (Location.t * Vid.t)
| Rec_app of Tid.t * t list
| Top_app of t Group.t * Tid.t * t list
[@@deriving equal, sexp, variants]
end
end
include Stable.V1
type group = t Group.t
let group = Group.create
type poly_variant_row = t poly_constr
let constr s t = `Constr (s, t)
let inherit_ loc t = `Inherit (loc, t)
let var loc t = Var (loc, t)
let poly_variant loc xs = Poly_variant (loc, xs)
let basetype = base
let is_cyclic_0 ~(via_VR : bool) : group -> Tid.t -> bool =
fun group tid ->
let set = ref [] in
let visited tid = List.mem !set tid ~equal:Tid.equal in
let add tid = set := tid :: !set in
let rec trav = function
| Annotate (_, t) -> trav t
| Base (_, ts) | Tuple ts | Top_app (_, _, ts) -> List.iter ts ~f:trav
| Poly_variant (_, cs) ->
List.iter cs ~f:(function
| `Constr (_, None) -> ()
| `Constr (_, Some t) -> trav t
| `Inherit (_loc, t) -> trav t)
| Record xs -> if via_VR then List.iter xs ~f:(fun (_, t) -> trav t) else ()
| Variant xs ->
if via_VR then List.iter xs ~f:(fun (_, ts) -> List.iter ~f:trav ts) else ()
| Var _ -> ()
| Rec_app (tid, ts) ->
if visited tid
then ()
else (
add tid;
trav_tid tid);
List.iter ts ~f:trav
and trav_tid tid =
let _, body = Group.lookup group tid in
trav body
in
trav_tid tid;
let res = visited tid in
res
;;
let is_cyclic = is_cyclic_0 ~via_VR:true
let is_cyclic_with_no_intervening_VR = is_cyclic_0 ~via_VR:false
end
include Expression
module Evaluation (Canonical : Canonical) = struct
module Venv : sig
type t
val lookup : t -> Vid.t -> Visibility.visible Canonical.Exp1.t option
val create : (Vid.t * Visibility.visible Canonical.Exp1.t) list -> t
end = struct
type t = Visibility.visible Canonical.Exp1.t Map.M(Vid).t
let create =
List.fold
~init:(Map.empty (module Vid))
~f:(fun t (k, v) -> Map.set ~key:k ~data:v t)
;;
let lookup t k = Map.find t k
end
module Applicand = struct
type t =
| Recursion_level of int
| Definition of Canonical.Def.t
end
module Tenv : sig
type key = Gid.t * Tid.t
type t
val find : t -> key -> [ `Recursion_level of int ] option
val empty : t
val extend : t -> key -> [ `Recursion_level of int ] -> t
end = struct
module Key = struct
module T = struct
type t = Gid.t * Tid.t [@@deriving compare, sexp_of]
end
include T
include Comparator.Make (T)
end
type key = Key.t
type t = [ `Recursion_level of int ] Map.M(Key).t
let find t k = Map.find t k
let empty = Map.empty (module Key)
let extend t k v = Map.set ~key:k ~data:v t
end
module Defining : sig
type 'a t
val return : 'a -> 'a t
val bind : 'a t -> ('a -> 'b t) -> 'b t
val look_env : Tenv.key -> Applicand.t option t
val extend_new_tid : Tenv.key -> Canonical.Def.t t -> Applicand.t t
val exec : 'a t -> 'a
end = struct
type 'a t = depth:int -> Tenv.t -> 'a
let return x ~depth:_ _tenv = x
let bind t f ~depth tenv =
let x = t ~depth tenv in
(f x) ~depth tenv
;;
let look_env key ~depth:_ tenv =
let result = Tenv.find tenv key in
Option.map ~f:(fun (`Recursion_level x) -> Applicand.Recursion_level x) result
;;
let extend_new_tid key def_t ~depth tenv =
Applicand.Definition
(let value = `Recursion_level depth in
let tenv = Tenv.extend tenv key value in
def_t ~depth:(depth + 1) tenv)
;;
let exec t = t ~depth:0 Tenv.empty
end
type 'a defining = 'a Defining.t
let ( >>= ) = Defining.bind
let return = Defining.return
let sequence_defining : 'a list -> f:('a -> 'b defining) -> 'b list defining =
fun xs ~f ->
let rec loop acc_ys = function
| [] -> return (List.rev acc_ys)
| x :: xs -> f x >>= fun y -> loop (y :: acc_ys) xs
in
loop [] xs
;;
let rec eval : group -> Venv.t -> t -> Visibility.visible Canonical.Exp1.t defining =
fun group venv t ->
match t with
| Record binds ->
sequence_defining binds ~f:(fun (s, x) ->
eval group venv x >>= fun y -> return (s, y))
>>= fun binds -> return (Canonical.Create.record binds)
| Variant alts ->
sequence_defining alts ~f:(fun (s, xs) ->
eval_list group venv xs >>= fun ys -> return (s, ys))
>>= fun alts -> return (Canonical.Create.variant alts)
| Var (loc, vid) ->
(match Venv.lookup venv vid with
| Some x -> return x
| None -> eval_fail loc !"Free type variable: '%{Vid}" vid ())
| Annotate (s, t) ->
eval group venv t >>= fun v -> return (Canonical.Create.annotate s v)
| Base (s, ts) ->
eval_list group venv ts >>= fun vs -> return (Canonical.Create.basetype s vs)
| Tuple ts -> eval_list group venv ts >>= fun vs -> return (Canonical.Create.tuple vs)
| Top_app (in_group, tid, args) ->
eval_list group venv args
>>= fun args ->
eval_app in_group tid args
| Rec_app (tid, args) ->
eval_list group venv args >>= fun args -> eval_app group tid args
| Poly_variant (loc, cs) ->
sequence_defining ~f:(eval_poly_constr group venv) cs
>>= fun xss -> return (Canonical.Create.poly_variant loc (List.concat xss))
and eval_list : group -> Venv.t -> t list -> _ Canonical.Exp1.t list defining =
fun group venv ts -> sequence_defining ts ~f:(eval group venv)
and eval_poly_constr
: group -> Venv.t -> t poly_constr
-> (string * Visibility.opaque Canonical.Exp1.t option) list defining
=
fun group venv c ->
match c with
| `Constr (s, None) -> return [ s, None ]
| `Constr (s, Some t) ->
eval group venv t >>= fun v -> return [ s, Some (Canonical.Exp1.opaque v) ]
| `Inherit (loc, t) ->
eval group venv t
>>= fun v ->
(match Canonical.Exp1.get_poly_variant v with
| Ok tab -> return (Sorted_table.expose tab)
| Error desc ->
eval_fail
loc
"The shape for an inherited type is not described as a polymorphic-variant: %s"
desc
())
and eval_definition : group -> Vid.t list -> t -> Canonical.Def.t defining =
fun group formals body ->
let venv = Venv.create (List.mapi formals ~f:(fun i x -> x, Canonical.Exp1.var i)) in
eval group venv body >>= fun v -> return (Canonical.Create.define v)
and eval_app : group -> Tid.t -> _ Canonical.Exp1.t list -> _ Canonical.Exp1.t defining =
fun group tid args ->
let gid = Group.id group in
let formals, body = Group.lookup group tid in
let record_or_normal_variant =
match body with
| Record _ | Variant _ -> true
| Tuple _ | Annotate _ | Base _ | Poly_variant _ | Var _ | Rec_app _ | Top_app _ ->
false
in
let cyclic = is_cyclic group tid in
let cyclic_no_VR = is_cyclic_with_no_intervening_VR group tid in
if (record_or_normal_variant && cyclic) || cyclic_no_VR
then
Defining.look_env (gid, tid)
>>= (function
| Some recurse -> return recurse
| None ->
Defining.extend_new_tid (gid, tid) (eval_definition group formals body))
>>= function
| Recursion_level r -> return (Canonical.Exp1.recurse r args)
| Definition def -> return (Canonical.Exp1.apply def args)
else (
let venv =
match List.zip formals args with
| Ok x -> Venv.create x
| Unequal_lengths -> failwith "apply, incorrect type application arity"
in
eval group venv body)
;;
let eval : t -> Canonical.t =
fun t ->
let group = group (Location.of_string "top-level") [] in
let venv = Venv.create [] in
let v = Defining.exec (eval group venv t) in
Canonical.Create.create v
;;
end
module Canonical = struct
include Canonical_full
module Exp = struct
type t = Visibility.visible Exp1.t
end
end
include Evaluation (Canonical_full)
module Canonical_selected = Canonical_digest
module Evaluation_to_digest = Evaluation (Canonical_selected)
let eval_to_digest exp = Canonical_selected.to_digest (Evaluation_to_digest.eval exp)
let eval_to_digest_string exp = Digest.to_hex (eval_to_digest exp)
module For_typerep = struct
exception Not_a_tuple of t [@@deriving sexp_of]
let deconstruct_tuple_exn t =
match t with
| Tuple ts -> ts
| _ -> raise (Not_a_tuple t)
;;
end
module Expert = struct
module Sorted_table = Sorted_table
module Canonical_exp_constructor = Canonical_exp_constructor
module Canonical = Canonical
end