(***********************************************************************) (* *) (* Objective Caml *) (* *) (* Xavier Leroy and Jerome Vouillon, projet Cristal, INRIA Rocquencourt*) (* *) (* Copyright 1996 Institut National de Recherche en Informatique et *) (* en Automatique. Distributed only by permission. *) (* *) (***********************************************************************) (* $Id$ *) (* Operations on core types *) open Misc open Asttypes open Types open Btype (* Type manipulation after type inference ====================================== If one wants to manipulate a type after type inference (for instance, during code generation or in the debugger), one must first make sure that the type levels are correct, using the function [correct_levels]. Then, this type can be correctely manipulated by [apply], [expand_head] and [moregeneral]. *) (* General notes ============= - As much sharing as possible should be kept : it makes types smaller and better abbreviated. When necessary, some sharing can be lost. Types will still be printed correctly (+++ TO DO...), and abbreviations defined by a class do not depend on sharing thanks to constrained abbreviations. (Of course, even if some sharing is lost, typing will still be correct.) - All nodes of a type have a level : that way, one know whether a node need to be duplicated or not when instantiating a type. - Levels of a type are decreasing (generic level being considered as greatest). - The level of a type constructor is superior to the binding time of its path. - Recursive types without limitation should be handled (even if there is still an occur check). This avoid treating specially the case for objects, for instance. Furthermore, the occur check policy can then be easily changed. *) (* A faire ======= - Revoir affichage des types. - Etendre la portee d'un alias [... as 'a] a tout le type englobant. - #-type implementes comme de vraies abreviations. - Niveaux plus fins pour les identificateurs : Champ [global] renomme en [level]; Niveau -1 : global 0 : module toplevel 1 : module contenu dans module toplevel ... En fait, incrementer le niveau a chaque fois que l'on rentre dans un module. 3 4 6 \ / / 1 2 5 \|/ 0 [Subst] doit ecreter les niveaux (pour qu'un variable non generalisable dans un module de niveau 2 ne se retrouve pas generalisable lorsque l'on l'utilise au niveau 0). - Traitement de la trace de l'unification separe de la fonction [unify]. *) (**** Errors ****) exception Unify of (type_expr * type_expr) list exception Subtype of (type_expr * type_expr) list * (type_expr * type_expr) list exception Cannot_expand exception Cannot_apply exception Recursive_abbrev (**** Type level management ****) let current_level = ref 0 let nongen_level = ref 0 let global_level = ref 1 let saved_level = ref [] let saved_global_level = ref [] let init_def level = current_level := level; nongen_level := level let begin_def () = saved_level := (!current_level, !nongen_level) :: !saved_level; incr current_level; nongen_level := !current_level let begin_class_def () = saved_level := (!current_level, !nongen_level) :: !saved_level; incr current_level let raise_nongen_level () = saved_level := (!current_level, !nongen_level) :: !saved_level; nongen_level := !current_level let end_def () = let (cl, nl) = List.hd !saved_level in saved_level := List.tl !saved_level; current_level := cl; nongen_level := nl let reset_global_level () = global_level := !current_level + 1; saved_global_level := [] let increase_global_level () = saved_global_level := !global_level :: !saved_global_level; global_level := !current_level let restore_global_level () = match !saved_global_level with gl::rem -> global_level := gl; saved_global_level := rem | [] -> assert false (**** Some type creators ****) (* Re-export generic type creators *) let newty2 = Btype.newty2 let newty desc = newty2 !current_level desc let new_global_ty desc = newty2 !global_level desc let newvar () = newty2 !current_level Tvar let newvar2 level = newty2 level Tvar let newmarkedvar = Btype.newmarkedvar let new_global_var () = newty2 !global_level Tvar let newmarkedgenvar = Btype.newmarkedgenvar let newobj fields = newty (Tobject (fields, ref None)) let newconstr path tyl = newty (Tconstr (path, tyl, ref Mnil)) let none = newty (Ttuple []) (* Clearly ill-formed type *) (**** Representative of a type ****) (* Re-export repr *) let repr = repr (**** Type maps ****) module TypePairs = Hashtbl.Make (struct type t = type_expr * type_expr let equal (t1, t1') (t2, t2') = (t1 == t2) && (t1' == t2') let hash (t, t') = t.id + 93 * t'.id end) (**********************************************) (* Miscellaneous operations on object types *) (**********************************************) (**** Object field manipulation. ****) let object_fields ty = match (repr ty).desc with Tobject (fields, _) -> fields | _ -> assert false let flatten_fields ty = let rec flatten l ty = let ty = repr ty in match ty.desc with Tfield(s, k, ty1, ty2) -> flatten ((s, k, ty1)::l) ty2 | _ -> (l, ty) in let (l, r) = flatten [] ty in (Sort.list (fun (n, _, _) (n', _, _) -> n < n') l, r) let build_fields level = List.fold_right (fun (s, k, ty1) ty2 -> newty2 level (Tfield(s, k, ty1, ty2))) let associate_fields fields1 fields2 = let rec associate p s s' = function (l, []) -> (List.rev p, (List.rev s) @ l, List.rev s') | ([], l') -> (List.rev p, List.rev s, (List.rev s') @ l') | ((n, k, t)::r, (n', k', t')::r') when n = n' -> associate ((n, k, t, k', t')::p) s s' (r, r') | ((n, k, t)::r, ((n', k', t')::_ as l')) when n < n' -> associate p ((n, k, t)::s) s' (r, l') | (((n, k, t)::r as l), (n', k', t')::r') (* when n > n' *) -> associate p s ((n', k', t')::s') (l, r') in associate [] [] [] (fields1, fields2) (**** Check whether an object is open ****) (* +++ Il faudra penser a eventuellement expanser l'abreviation *) let rec opened_object ty = match (repr ty).desc with Tobject (t, _) -> opened_object t | Tfield(_, _, _, t) -> opened_object t | Tvar -> true | _ -> false (**** Close an object ****) let close_object ty = let rec close ty = let ty = repr ty in match ty.desc with Tvar -> ty.desc <- Tlink (newty2 ty.level Tnil) | Tfield(_, _, _, ty') -> close ty' | _ -> assert false in match (repr ty).desc with Tobject (ty, _) -> close ty | _ -> assert false (**** Row variable of an object type ****) let row_variable ty = let rec find ty = let ty = repr ty in match ty.desc with Tfield (_, _, _, ty) -> find ty | Tvar -> ty | _ -> assert false in match (repr ty).desc with Tobject (fi, _) -> find fi | _ -> assert false (**** Object name manipulation ****) (* +++ Bientot obsolete *) let set_object_name id rv params ty = match (repr ty).desc with Tobject (fi, nm) -> begin try nm := Some (Path.Pident id, rv::params) with Not_found -> () end | _ -> assert false let remove_object_name ty = match (repr ty).desc with Tobject (_, nm) -> nm := None | Tconstr (_, _, _) -> () | _ -> fatal_error "Ctype.remove_object_name" (**** Hiding of private methods ****) let hide_private_methods ty = let (fl, _) = flatten_fields (object_fields ty) in List.iter (function (_, k, _) -> let k = field_kind_repr k in match k with Fvar r -> r := Some Fabsent | _ -> ()) fl (*******************************) (* Operations on class types *) (*******************************) let rec signature_of_class_type = function Tcty_constr (_, _, cty) -> signature_of_class_type cty | Tcty_signature sign -> sign | Tcty_fun (ty, cty) -> signature_of_class_type cty let self_type cty = repr (signature_of_class_type cty).cty_self let rec class_type_arity = function Tcty_constr (_, _, cty) -> class_type_arity cty | Tcty_signature _ -> 0 | Tcty_fun (_, cty) -> 1 + class_type_arity cty (**************************************) (* Check genericity of type schemes *) (**************************************) exception Non_closed let rec closed_schema_rec ty = let ty = repr ty in if ty.level >= lowest_level then begin let level = ty.level in ty.level <- pivot_level - level; match ty.desc with Tvar when level <> generic_level -> raise Non_closed | Tobject(f, {contents = Some (_, p)}) -> closed_schema_rec f; List.iter closed_schema_rec p | Tobject(f, _) -> closed_schema_rec f | Tfield(_, kind, t1, t2) -> if field_kind_repr kind = Fpresent then closed_schema_rec t1; closed_schema_rec t2 | _ -> iter_type_expr closed_schema_rec ty end (* Return whether all variables of type [ty] are generic. *) let closed_schema ty = try closed_schema_rec ty; unmark_type ty; true with Non_closed -> unmark_type ty; false exception Non_closed of type_expr * bool let free_variables = ref [] let rec free_vars_rec real ty = let ty = repr ty in if ty.level >= lowest_level then begin ty.level <- pivot_level - ty.level; begin match ty.desc with Tvar -> free_variables := (ty, real) :: !free_variables | Tobject(ty, {contents = Some (_, p)}) -> free_vars_rec false ty; List.iter (free_vars_rec true) p | Tobject (ty, _) -> free_vars_rec false ty | Tfield (_, _, ty1, ty2) -> free_vars_rec true ty1; free_vars_rec false ty2 | _ -> iter_type_expr (free_vars_rec true) ty end; end let free_vars ty = free_variables := []; free_vars_rec true ty; let res = !free_variables in free_variables := []; res let rec closed_type ty = match free_vars ty with [] -> () | (v, real) :: _ -> raise (Non_closed (v, real)) let closed_parameterized_type params ty = List.iter mark_type params; try closed_type ty; List.iter unmark_type params; unmark_type ty; true with Non_closed _ -> List.iter unmark_type params; unmark_type ty; false let closed_type_decl decl = try List.iter mark_type decl.type_params; begin match decl.type_kind with Type_abstract -> () | Type_variant v -> List.iter (fun (_, tyl) -> List.iter closed_type tyl) v | Type_record r -> List.iter (fun (_, _, ty) -> closed_type ty) r end; begin match decl.type_manifest with None -> () | Some ty -> closed_type ty end; unmark_type_decl decl; None with Non_closed (ty, _) -> unmark_type_decl decl; Some ty type closed_class_failure = CC_Method of type_expr * bool * string * type_expr | CC_Value of type_expr * bool * string * type_expr exception Failure of closed_class_failure let closed_class params sign = let ty = object_fields (repr sign.cty_self) in let (fields, rest) = flatten_fields ty in List.iter mark_type params; mark_type rest; List.iter (fun (lab, _, ty) -> if lab = "*dummy method*" then mark_type ty) fields; try mark_type_node (repr sign.cty_self); List.iter (fun (lab, kind, ty) -> if field_kind_repr kind = Fpresent then try closed_type ty with Non_closed (ty0, real) -> raise (Failure (CC_Method (ty0, real, lab, ty)))) fields; mark_type_params (repr sign.cty_self); List.iter unmark_type params; unmark_class_signature sign; None with Failure reason -> mark_type_params (repr sign.cty_self); List.iter unmark_type params; unmark_class_signature sign; Some reason (**********************) (* Type duplication *) (**********************) (* Duplicate a type, preserving only type variables *) let duplicate_type ty = Subst.type_expr Subst.identity ty (* Same, for class types *) let duplicate_class_type ty = Subst.class_type Subst.identity ty (*****************************) (* Type level manipulation *) (*****************************) (* It would be a bit more efficient to remove abbreviation expansions rather than generalizing them: these expansions will usually not be used anymore. However, this is not possible in the general case, as [expand_abbrev] (via [subst]) requires these expansions to be preserved. Does it worth duplicating this code ? *) let rec iter_generalize tyl ty = let ty = repr ty in if (ty.level > !current_level) && (ty.level <> generic_level) then begin ty.level <- generic_level; begin match ty.desc with Tconstr (_, _, abbrev) -> generalize_expans tyl !abbrev | _ -> () end; iter_type_expr (iter_generalize tyl) ty end else tyl := ty :: !tyl and generalize_expans tyl = function Mnil -> () | Mcons(_, ty, ty', rem) -> iter_generalize tyl ty; iter_generalize tyl ty'; generalize_expans tyl rem | Mlink rem -> generalize_expans tyl !rem let rec generalize ty = iter_generalize (ref []) ty (* Efficient repeated generalisation of the same type *) let iterative_generalization min_level tyl = let tyl' = ref [] in List.iter (iter_generalize tyl') tyl; List.fold_right (fun ty l -> if ty.level <= min_level then l else ty::l) !tyl' [] let try_expand_head' = (* Forward declaration *) ref (fun env ty -> raise Cannot_expand) (* Lower the levels of a type (assume [level] is not [generic_level]). *) (* The level of a type constructor must be greater than its binding time. That way, a type constructor cannot escape the scope of its definition, as would be the case in let x = ref [] module M = struct type t let _ = (x : t list ref) end (without this constraint, the type system would actually be unsound.) *) let rec update_level env level ty = let ty = repr ty in if ty.level > level then begin begin match ty.desc with Tconstr(p, tl, abbrev) when level < Path.binding_time p -> (* Try first to replace an abbreviation by its expansion. *) begin try ty.desc <- Tlink (!try_expand_head' env ty); update_level env level ty with Cannot_expand -> (* +++ Levels should be restored... *) raise (Unify [(ty, newvar2 level)]) end | Tfield(_, k, _, _) -> begin match field_kind_repr k with Fvar _ (* {contents = None} *) -> raise (Unify [(ty, newvar2 level)]) | _ -> () end; ty.level <- level; iter_type_expr (update_level env level) ty | _ -> ty.level <- level; iter_type_expr (update_level env level) ty end end (* Function [update_level] will never try to expand an abbreviation in this case ([current_level] is greater than the binding time of any type constructor path). So, it can be called with the empty environnement. *) let make_nongen ty = try update_level Env.empty !nongen_level ty with Unify [_, ty'] -> raise (Unify [ty, ty']) (* Correct the levels of type [ty]. *) let correct_levels ty = duplicate_type ty (* Only generalize the type ty0 in ty *) let limited_generalize ty0 ty = let ty0 = repr ty0 in let graph = Hashtbl.create 17 in let idx = ref lowest_level in let roots = ref [] in let rec inverse pty ty = let ty = repr ty in if (ty.level > !current_level) || (ty.level = generic_level) then begin decr idx; Hashtbl.add graph !idx (ty, ref pty); if (ty.level = generic_level) || (ty == ty0) then roots := ty :: !roots; ty.level <- !idx; iter_type_expr (inverse [ty]) ty end else if ty.level < lowest_level then begin let (_, parents) = Hashtbl.find graph ty.level in parents := pty @ !parents end and generalize_parents ty = let idx = ty.level in if idx <> generic_level then begin ty.level <- generic_level; List.iter generalize_parents !(snd (Hashtbl.find graph idx)) end in inverse [] ty; if ty0.level < lowest_level then iter_type_expr (inverse []) ty0; List.iter generalize_parents !roots; Hashtbl.iter (fun _ (ty, _) -> if ty.level <> generic_level then ty.level <- !current_level) graph (*******************) (* Instantiation *) (*******************) let rec find_repr p1 = function Mnil -> None | Mcons (p2, ty, _, _) when Path.same p1 p2 -> Some ty | Mcons (_, _, _, rem) -> find_repr p1 rem | Mlink {contents = rem} -> find_repr p1 rem (* Generic nodes are duplicated, while non-generic nodes are left as-is. During instantiation, the description of a generic node is first replaced by a link to a stub ([Tlink (newmarkedvar ())]). Once the copy is made, it replaces the stub. After instantiation, the description of generic node, which was stored by [save_desc], must be put back, using [cleanup_types]. Marked on the copy are removed by [unmark]. *) let abbreviations = ref (ref Mnil) (* Abbreviation memorized. *) let rec copy ty = let ty = repr ty in if ty.level <> generic_level then ty else begin let desc = ty.desc in save_desc ty desc; let t = newmarkedvar !current_level in (* Stub *) ty.desc <- Tlink t; t.desc <- begin match desc with Tvar -> Tvar | Tarrow (t1, t2) -> Tarrow (copy t1, copy t2) | Ttuple tl -> Ttuple (List.map copy tl) | Tconstr (p, tl, _) -> begin match find_repr p !(!abbreviations) with Some ty when repr ty != t -> (* XXX Commentaire... *) Tlink ty | _ -> (* One must allocate a new reference, so that abbrevia- tions belonging to different branches of a type are independent. Moreover, a reference containing a [Mcons] must be shared, so that the memorized expansion of an abbrevi- ation can be released by changing the content of just one reference. *) Tconstr (p, List.map copy tl, ref (match !(!abbreviations) with Mcons _ -> Mlink !abbreviations | abbrev -> abbrev)) end | Tobject (t1, {contents = name}) -> let name' = match name with None -> None | Some (p, tl) -> Some (p, List.map copy tl) in Tobject (copy t1, ref name') | Tfield (label, kind, t1, t2) -> begin match field_kind_repr kind with Fpresent -> Tfield (label, Fpresent, copy t1, copy t2) | Fvar _ (* {contents = None} *) -> Tfield (label, Fvar (ref None), copy t1, copy t2) | Fabsent -> assert false end | Tnil -> Tnil | Tlink t -> (* Actually unused *) Tlink (copy t) end; t end (**** Variants of instantiations ****) let instance sch = let ty = copy sch in cleanup_types (); unmark_type ty; ty let instance_list schl = let tyl = List.map copy schl in cleanup_types (); List.iter unmark_type tyl; tyl let instance_constructor cstr = let ty_res = copy cstr.cstr_res in let ty_args = List.map copy cstr.cstr_args in cleanup_types (); List.iter unmark_type ty_args; unmark_type ty_res; (ty_args, ty_res) let instance_label lbl = let ty_res = copy lbl.lbl_res in let ty_arg = copy lbl.lbl_arg in cleanup_types (); unmark_type ty_arg; unmark_type ty_res; (ty_arg, ty_res) let instance_parameterized_type sch_args sch = let ty_args = List.map copy sch_args in let ty = copy sch in cleanup_types (); List.iter unmark_type ty_args; unmark_type ty; (ty_args, ty) let instance_parameterized_type_2 sch_args sch_lst sch = let ty_args = List.map copy sch_args in let ty_lst = List.map copy sch_lst in let ty = copy sch in cleanup_types (); List.iter unmark_type ty_args; List.iter unmark_type ty_lst; unmark_type ty; (ty_args, ty_lst, ty) let instance_class params cty = let rec copy_class_type = function Tcty_constr (path, tyl, cty) -> Tcty_constr (path, List.map copy tyl, copy_class_type cty) | Tcty_signature sign -> Tcty_signature {cty_self = copy sign.cty_self; cty_vars = Vars.map (function (mut, ty) -> (mut, copy ty)) sign.cty_vars; cty_concr = sign.cty_concr} | Tcty_fun (ty, cty) -> Tcty_fun (copy ty, copy_class_type cty) in let params' = List.map copy params in let cty' = copy_class_type cty in cleanup_types (); let rec unmark_class_type = function Tcty_constr (path, tyl, cty) -> List.iter unmark_type tyl; unmark_class_type cty | Tcty_signature sign -> unmark_type sign.cty_self; Vars.iter (fun lab (mut, ty) -> unmark_type ty) sign.cty_vars; | Tcty_fun (ty, cty) -> unmark_type ty; unmark_class_type cty in List.iter unmark_type params'; unmark_class_type cty'; (params', cty') (**** Instantiation with parameter substitution ****) let unify' = (* Forward declaration *) ref (fun env ty1 ty2 -> raise (Unify [])) let rec subst env level abbrev ty params args body = let old_level = !current_level in current_level := level; try let body0 = newvar () in (* Stub *) begin match ty with None -> () | Some ({desc = Tconstr (path, _, _)} as ty) -> memorize_abbrev abbrev path ty body0 | _ -> assert false end; abbreviations := abbrev; let (params', body') = instance_parameterized_type params body in abbreviations := ref Mnil; !unify' env body0 body'; List.iter2 (!unify' env) params' args; current_level := old_level; body' with Unify _ as exn -> current_level := old_level; raise exn (* Only the shape of the type matters, not whether is is generic or not. [generic_level] might be somewhat slower, but it ensures invariants on types are enforced (decreasing levels.), and we don't care about efficiency here. *) let apply env params body args = try subst env generic_level (ref Mnil) None params args body with Unify _ -> raise Cannot_apply (****************************) (* Abbreviation expansion *) (****************************) (* Search whether the expansion has been memorized. *) let rec find_expans p1 = function Mnil -> None | Mcons (p2, _, ty, _) when Path.same p1 p2 -> Some ty | Mcons (_, _, _, rem) -> find_expans p1 rem | Mlink {contents = rem} -> find_expans p1 rem let previous_env = ref Env.empty (* Expand an abbreviation. The expansion is memorized. *) (* Assume the level is greater than the path binding time of the expanded abbreviation. *) (* An abbreviation expansion will fail in either of these cases: 1. The type constructor does not correspond to a manifest type. 2. The type constructor is defined in an external file, and this file is not in the path (missing -I options). 3. The type constructor is not in the "local" environment. This can happens when a non-generic type variable has been instantiated afterwards to the not yet defined type constructor. (Actually, this cannot happen at the moment due to the strong constraints between type levels and constructor binding time.) 4. The expansion requires the expansion of another abbreviation, and this other expansion fails. *) let expand_abbrev env ty = (* If the environnement has changed, memorized expansions might not be correct anymore, and so we flush the cache. This is safe but quite pessimistic: it would be enough to flush the cache when a type or module definition is overriden in the environnement. *) if env != !previous_env then begin cleanup_abbrev (); previous_env := env end; match ty with {desc = Tconstr (path, args, abbrev); level = level} -> begin match find_expans path !abbrev with Some ty -> if level <> generic_level then begin try update_level env level ty with Unify _ -> (* XXX This should not happen. However, levels are not correctly restored after a typing error *) () end; ty | None -> let (params, body) = try Env.find_type_expansion path env with Not_found -> raise Cannot_expand in (* begin try *) subst env level abbrev (Some ty) params args body (* with Unify _ -> raise Cannot_expand end *) end | _ -> assert false (* Fully expand the head of a type. Raise an exception if the type cannot be expanded. *) let rec try_expand_head env ty = let ty = repr ty in match ty.desc with Tconstr _ -> let ty' = expand_abbrev env ty in begin try try_expand_head env ty' with Cannot_expand -> repr ty' end | _ -> raise Cannot_expand let _ = try_expand_head' := try_expand_head (* Fully expand the head of a type. *) let rec expand_head env ty = try try_expand_head env ty with Cannot_expand -> repr ty (* Recursively expand the head of a type. Also expand #-types. *) let rec full_expand env ty = let ty = repr (expand_head env ty) in match ty.desc with Tobject (fi, {contents = Some (_, v::_)}) when (repr v).desc = Tvar -> newty2 ty.level (Tobject (fi, ref None)) | _ -> ty (* Check whether the abbreviation expands to a well-defined type. During the typing of a class, abbreviations for correspondings types expand to non-generic types. *) let generic_abbrev env path = try let (_, body) = Env.find_type_expansion path env in (repr body).level = generic_level with Not_found -> false (*****************) (* Occur check *) (*****************) exception Occur (* The marks are already used by [expand_abbrev]... *) let visited = ref [] let rec non_recursive_abbrev env ty = let ty = repr ty in if ty == none then raise Recursive_abbrev; if not (List.memq ty !visited) then begin let level = ty.level in visited := ty :: !visited; match ty.desc with Tconstr(p, args, abbrev) -> begin try non_recursive_abbrev env (try_expand_head env ty) with Cannot_expand -> iter_type_expr (non_recursive_abbrev env) ty end | Tobject (_, _) -> () | _ -> iter_type_expr (non_recursive_abbrev env) ty end let correct_abbrev env ident params ty = visited := []; non_recursive_abbrev env (subst env generic_level (ref (Mcons (Path.Pident ident, none, none, Mnil))) None [] [] ty); visited := [] let rec occur_rec env visited ty0 ty = if ty == ty0 then raise Occur; match ty.desc with Tconstr(p, tl, abbrev) -> begin try if List.memq ty visited then raise Occur; iter_type_expr (occur_rec env (ty::visited) ty0) ty with Occur -> try let ty' = try_expand_head env ty in if List.memq ty' visited then raise Occur; occur_rec env (ty'::visited) ty0 ty' with Cannot_expand -> raise Occur end | Tobject (_, _) -> () | _ -> iter_type_expr (occur_rec env visited ty0) ty let occur env ty0 ty = try occur_rec env [] ty0 ty with Occur -> raise (Unify []) (*****************) (* Unification *) (*****************) (**** Transform error trace ****) (* +++ Move it to some other place ? *) let expand_trace env trace = List.fold_right (fun (t1, t2) rem -> (repr t1, full_expand env t1)::(repr t2, full_expand env t2)::rem) trace [] (**** Unification ****) (* Return whether [t0] occurs in [ty]. Objects are also traversed. *) let deep_occur t0 ty = let rec occur_rec ty = let ty = repr ty in if ty.level >= lowest_level then begin if ty == t0 then raise Occur; ty.level <- pivot_level - ty.level; iter_type_expr occur_rec ty end in try occur_rec ty; unmark_type ty; false with Occur -> unmark_type ty; true (* 1. When unifying two non-abbreviated types, one type is made a link to the other. When unifying an abbreviated type with a non-abbreviated type, the non-abbreviated type is made a link to the other one. When unifying to abbreviated types, these two types are kept distincts, but they are made to (temporally) expand to the same type. 2. Abbreviations with at least one parameter are systematically expanded. The overhead does not seem to high, and that way abbreviations where some parameters does not appear in the expansion, such as ['a t = int], are correctly handled. In particular, for this example, unifying ['a t] with ['b t] keeps ['a] and ['b] distincts. (Is it really important ?) 3. Unifying an abbreviation ['a t = 'a] with ['a] should not yield ['a t as 'a]. Indeed, the type variable would otherwise be lost. This problem occurs for abbreviations expanding to a type variable, but also to many other constrained abbreviations (for instance, [(< x : 'a > -> unit) t = ]). The solution is that, if an abbreviation is unified with some subpart of its parameters, then the parameter actually does not get abbreviated. It would be possible to check whether some information is indeed lost, but it probably does not worth it. *) let rec unify env t1 t2 = (* First step: special cases (optimizations) *) if t1 == t2 then () else let t1 = repr t1 in let t2 = repr t2 in if t1 == t2 then () else try match (t1.desc, t2.desc) with (Tvar, Tconstr _) when deep_occur t1 t2 -> unify2 env t1 t2 | (Tconstr _, Tvar) when deep_occur t2 t1 -> unify2 env t1 t2 | (Tvar, _) -> occur env t1 t2; update_level env t1.level t2; t1.desc <- Tlink t2 | (_, Tvar) -> occur env t2 t1; update_level env t2.level t1; t2.desc <- Tlink t1 | (Tconstr (p1, [], _), Tconstr (p2, [], _)) when Path.same p1 p2 -> update_level env t1.level t2; t1.desc <- Tlink t2 | _ -> unify2 env t1 t2 with Unify trace -> raise (Unify ((t1, t2)::trace)) and unify2 env t1 t2 = (* Second step: expansion of abbreviations *) let t1' = expand_head env t1 in let t2' = expand_head env t2 in (* Expansion may have changed the representative of the types... *) let t1' = repr t1' and t2' = repr t2' in if t1' == t2' then () else let t1 = repr t1 and t2 = repr t2 in if (t1 == t1') || (t2 != t2') then unify3 env t1 t1' t2 t2' else try unify3 env t2 t2' t1 t1' with Unify trace -> raise (Unify (List.map (fun (x, y) -> (y, x)) trace)) and unify3 env t1 t1' t2 t2' = (* Third step: truly unification *) (* Assumes either [t1 == t1'] or [t2 != t2'] *) let d1 = t1'.desc and d2 = t2'.desc in let create_recursion = (t2 != t2') && (deep_occur t1' t2) in occur env t1' t2; update_level env t1'.level t2; t1'.desc <- Tlink t2; try begin match (d1, d2) with (Tvar, _) -> () | (_, Tvar) -> occur env t2' (newty d1); if t1 == t1' then begin (* The variable must be instantiated... *) let ty = newty2 t1'.level d1 in update_level env t2'.level ty; t2'.desc <- Tlink ty end else begin t1'.desc <- d1; update_level env t2'.level t1; t2'.desc <- Tlink t1 end | (Tarrow (t1, u1), Tarrow (t2, u2)) -> unify env t1 t2; unify env u1 u2 | (Ttuple tl1, Ttuple tl2) -> unify_list env tl1 tl2 | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _)) when Path.same p1 p2 -> unify_list env tl1 tl2 | (Tobject (fi1, nm1), Tobject (fi2, _)) -> unify_fields env fi1 fi2; (* Type [t2'] may have been instantiated by [unify_fields] *) (* XXX One should do some kind of unification... *) begin match (repr t2').desc with Tobject (_, {contents = Some (_, va::_)}) when (repr va).desc = Tvar -> () | Tobject (_, nm2) -> nm2 := !nm1 | _ -> () end | (Tfield _, Tfield _) -> (* Actually unused *) unify_fields env t1' t2' | (Tnil, Tnil) -> () | (_, _) -> raise (Unify []) end; (* XXX Commentaires + changer "create_recursion" *) if create_recursion then begin match t2.desc with Tconstr (p, tl, abbrev) -> forget_abbrev abbrev p; let t2'' = expand_head env t2 in if not (closed_parameterized_type tl t2'') then (repr t2).desc <- Tlink (repr t2') | _ -> assert false end (* (* Can only be done afterwards, once the row variable has (possibly) been instantiated. *) if t1 != t1' (* && t2 != t2' *) then begin match (t1.desc, t2.desc) with (Tconstr (p, ty::_, _), _) when ((repr ty).desc <> Tvar) && weak_abbrev p && not (deep_occur t1 t2) -> update_level env t1.level t2; t1.desc <- Tlink t2 | (_, Tconstr (p, ty::_, _)) when ((repr ty).desc <> Tvar) && weak_abbrev p && not (deep_occur t2 t1) -> update_level env t2.level t1; t2.desc <- Tlink t1; t1'.desc <- Tlink t2' | _ -> () end *) with Unify trace -> t1'.desc <- d1; raise (Unify trace) and unify_list env tl1 tl2 = if List.length tl1 <> List.length tl2 then raise (Unify []); List.iter2 (unify env) tl1 tl2 and unify_fields env ty1 ty2 = (* Optimization *) let (fields1, rest1) = flatten_fields ty1 and (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in let va = newvar () in unify env (build_fields (repr ty1).level miss1 va) rest2; unify env rest1 (build_fields (repr ty2).level miss2 va); List.iter (fun (n, k1, t1, k2, t2) -> unify_kind k1 k2; try unify env t1 t2 with Unify trace -> raise (Unify ((newty (Tfield(n, k1, t1, va)), newty (Tfield(n, k2, t2, va)))::trace))) pairs and unify_kind k1 k2 = let k1 = field_kind_repr k1 in let k2 = field_kind_repr k2 in match k1, k2 with (Fvar r, (Fvar _ | Fpresent)) -> r := Some k2 | (Fpresent, Fvar r) -> r := Some k1 | (Fpresent, Fpresent) -> () | _ -> assert false let unify env ty1 ty2 = try unify env ty1 ty2 with Unify trace -> raise (Unify (expand_trace env trace)) let _ = unify' := unify (**** Special cases of unification ****) (* Unify [t] and ['a -> 'b]. Return ['a] and ['b]. *) let rec filter_arrow env t = let t = expand_head env t in match t.desc with Tvar -> let t1 = newvar () and t2 = newvar () in let t' = newty (Tarrow (t1, t2)) in update_level env t.level t'; t.desc <- Tlink t'; (t1, t2) | Tarrow(t1, t2) -> (t1, t2) | _ -> raise (Unify []) (* Used by [filter_method]. *) let rec filter_method_field env name priv ty = let ty = repr ty in match ty.desc with Tvar -> let level = ty.level in let ty1 = newvar2 level and ty2 = newvar2 level in let ty' = newty2 level (Tfield (name, begin match priv with Private -> Fvar (ref None) | Public -> Fpresent end, ty1, ty2)) in ty.desc <- Tlink ty'; ty1 | Tfield(n, kind, ty1, ty2) -> let kind = field_kind_repr kind in if (n = name) && (kind <> Fabsent) then begin if priv = Public then unify_kind kind Fpresent; ty1 end else filter_method_field env name priv ty2 | _ -> raise (Unify []) (* Unify [ty] and [< name : 'a; .. >]. Return ['a]. *) let rec filter_method env name priv ty = let ty = expand_head env ty in match ty.desc with Tvar -> let ty1 = newvar () in let ty' = newobj ty1 in update_level env ty.level ty'; ty.desc <- Tlink ty'; filter_method_field env name priv ty1 | Tobject(f, _) -> filter_method_field env name priv f | _ -> raise (Unify []) let check_filter_method env name priv ty = let _ = filter_method env name priv ty in () let filter_self_method env lab priv meths ty = let ty' = filter_method env lab priv ty in try Meths.find lab !meths with Not_found -> let pair = (Ident.create lab, ty') in meths := Meths.add lab pair !meths; pair (***********************************) (* Matching between type schemes *) (***********************************) (* Update the level of [ty]. First check that the levels of variables from the subject are not lowered. *) let moregen_occur env level ty = let rec occur ty = let ty = repr ty in if ty.level > level then begin if ty.desc = Tvar then raise Occur; ty.level <- pivot_level - ty.level; iter_type_expr occur ty end in begin try occur ty; unmark_type ty with Occur -> unmark_type ty; raise (Unify []) end; update_level env level ty let rec moregen inst_nongen type_pairs env t1 t2 = if t1 == t2 then () else let t1 = repr t1 in let t2 = repr t2 in if t1 == t2 then () else try match (t1.desc, t2.desc) with (Tvar, _) when if inst_nongen then t1.level <> generic_level - 1 else t1.level = generic_level -> moregen_occur env t1.level t2; t1.desc <- Tlink t2 | (Tconstr (p1, [], _), Tconstr (p2, [], _)) when Path.same p1 p2 -> () | _ -> let t1' = expand_head env t1 in let t2' = expand_head env t2 in (* Expansion may have changed the representative of the types... *) let t1' = repr t1' and t2' = repr t2' in if t1' == t2' then () else begin try TypePairs.find type_pairs (t1', t2') with Not_found -> TypePairs.add type_pairs (t1', t2') (); match (t1'.desc, t2'.desc) with (Tvar, _) when if inst_nongen then t1'.level <> generic_level - 1 else t1'.level = generic_level -> moregen_occur env t1'.level t2; t1'.desc <- Tlink t2 | (Tarrow (t1, u1), Tarrow (t2, u2)) -> moregen inst_nongen type_pairs env t1 t2; moregen inst_nongen type_pairs env u1 u2 | (Ttuple tl1, Ttuple tl2) -> moregen_list inst_nongen type_pairs env tl1 tl2 | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _)) when Path.same p1 p2 -> moregen_list inst_nongen type_pairs env tl1 tl2 | (Tobject (fi1, nm1), Tobject (fi2, nm2)) -> moregen_fields inst_nongen type_pairs env fi1 fi2 | (Tfield _, Tfield _) -> (* Actually unused *) moregen_fields inst_nongen type_pairs env t1' t2' | (Tfield (_, kind, _, t1''), _) when field_kind_repr kind = Fabsent -> moregen inst_nongen type_pairs env t1'' t2' | (_, Tfield (_, kind, _, t2'')) when field_kind_repr kind = Fabsent -> moregen inst_nongen type_pairs env t1' t2'' | (Tnil, Tnil) -> () | (_, _) -> raise (Unify []) end with Unify trace -> raise (Unify ((t1, t2)::trace)) and moregen_list inst_nongen type_pairs env tl1 tl2 = if List.length tl1 <> List.length tl2 then raise (Unify []); List.iter2 (moregen inst_nongen type_pairs env) tl1 tl2 and moregen_fields inst_nongen type_pairs env ty1 ty2 = let (fields1, rest1) = flatten_fields ty1 and (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in if miss1 <> [] then raise (Unify []); moregen inst_nongen type_pairs env rest1 (build_fields (repr ty2).level miss2 rest2); List.iter (fun (n, k1, t1, k2, t2) -> moregen_kind k1 k2; try moregen inst_nongen type_pairs env t1 t2 with Unify trace -> raise (Unify ((newty (Tfield(n, k1, t1, rest2)), newty (Tfield(n, k2, t2, rest2)))::trace))) pairs and moregen_kind k1 k2 = let k1 = field_kind_repr k1 in let k2 = field_kind_repr k2 in match k1, k2 with (Fvar r, (Fvar _ | Fpresent)) -> r := Some k2 | (Fpresent, Fpresent) -> () | _ -> raise (Unify []) (* Non-generic variable can be instanciated only if [inst_nongen] is true. So, [inst_nongen] should be set to false if the subject might contain non-generic variables (and we do not want them to be instanciated). Usually, the subject is given by the user, and the pattern is unimportant. So, no need to propagate abbreviations. *) let moregeneral env inst_nongen pat_sch subj_sch = let old_level = !current_level in current_level := generic_level - 1; (* Generic variables are first duplicated with [instance]. So, their levels are lowered to [generic_level - 1]. The subject is then copied with [duplicate_type]. That way, its levels won't be changed. *) let subj = duplicate_type (instance subj_sch) in current_level := generic_level; (* Duplicate generic variables *) let patt = instance pat_sch in let res = try moregen inst_nongen (TypePairs.create 13) env patt subj; true with Unify _ -> false in current_level := old_level; res (*********************************************) (* Equivalence between parameterized types *) (*********************************************) let rec eqtype rename type_pairs subst env t1 t2 = if t1 == t2 then () else let t1 = repr t1 in let t2 = repr t2 in if t1 == t2 then () else try match (t1.desc, t2.desc) with (Tvar, Tvar) when rename -> begin try if List.assq t1 !subst != t2 then raise (Unify []) with Not_found -> subst := (t1, t2) :: !subst end | (Tconstr (p1, [], _), Tconstr (p2, [], _)) when Path.same p1 p2 -> () | _ -> let t1' = expand_head env t1 in let t2' = expand_head env t2 in (* Expansion may have changed the representative of the types... *) let t1' = repr t1' and t2' = repr t2' in if t1' == t2' then () else begin try TypePairs.find type_pairs (t1', t2') with Not_found -> TypePairs.add type_pairs (t1', t2') (); match (t1'.desc, t2'.desc) with (Tvar, Tvar) when rename -> begin try if List.assq t1' !subst == t2' then raise (Unify []) with Not_found -> subst := (t1', t2') :: !subst end | (Tarrow (t1, u1), Tarrow (t2, u2)) -> eqtype rename type_pairs subst env t1 t2; eqtype rename type_pairs subst env u1 u2; | (Ttuple tl1, Ttuple tl2) -> eqtype_list rename type_pairs subst env tl1 tl2 | (Tconstr (p1, tl1, _), Tconstr (p2, tl2, _)) when Path.same p1 p2 -> eqtype_list rename type_pairs subst env tl1 tl2 | (Tobject (fi1, nm1), Tobject (fi2, nm2)) -> eqtype_fields rename type_pairs subst env fi1 fi2 | (Tfield _, Tfield _) -> (* Actually unused *) eqtype_fields rename type_pairs subst env t1' t2' | (Tfield (_, kind, _, t1''), _) when field_kind_repr kind = Fabsent -> eqtype rename type_pairs subst env t1'' t2' | (_, Tfield (_, kind, _, t2'')) when field_kind_repr kind = Fabsent -> eqtype rename type_pairs subst env t1' t2'' | (Tnil, Tnil) -> () | (_, _) -> raise (Unify []) end with Unify trace -> raise (Unify ((t1, t2)::trace)) and eqtype_list rename type_pairs subst env tl1 tl2 = if List.length tl1 <> List.length tl2 then raise (Unify []); List.iter2 (eqtype rename type_pairs subst env) tl1 tl2 and eqtype_fields rename type_pairs subst env ty1 ty2 = let (fields1, rest1) = flatten_fields ty1 and (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in eqtype rename type_pairs subst env rest1 rest2; if (miss1 <> []) || (miss2 <> []) then raise (Unify []); List.iter (function (n, k1, t1, k2, t2) -> eqtype_kind k1 k2; try eqtype rename type_pairs subst env t1 t2 with Unify trace -> raise (Unify ((newty (Tfield(n, k1, t1, rest2)), newty (Tfield(n, k2, t2, rest2)))::trace))) pairs and eqtype_kind k1 k2 = let k1 = field_kind_repr k1 in let k2 = field_kind_repr k2 in match k1, k2 with (Fvar _, Fvar _) | (Fpresent, Fpresent) -> () | _ -> raise (Unify []) (* Two modes: with or without renaming of variables *) let equal env rename tyl1 tyl2 = try eqtype_list rename (TypePairs.create 11) (ref []) env tyl1 tyl2; true with Unify _ -> false (*************************) (* Class type matching *) (*************************) type class_match_failure = CM_Virtual_class | CM_Parameter_arity_mismatch of int * int | CM_Type_parameter_mismatch of (type_expr * type_expr) list | CM_Class_type_mismatch of class_type * class_type | CM_Parameter_mismatch of (type_expr * type_expr) list | CM_Val_type_mismatch of string * (type_expr * type_expr) list | CM_Meth_type_mismatch of string * (type_expr * type_expr) list | CM_Non_mutable_value of string | CM_Missing_value of string | CM_Missing_method of string | CM_Hide_public of string | CM_Hide_virtual of string | CM_Public_method of string | CM_Private_method of string | CM_Virtual_method of string exception Failure of class_match_failure list let rec moregen_clty trace type_pairs env cty1 cty2 = try match cty1, cty2 with Tcty_constr (_, _, cty1), _ -> moregen_clty true type_pairs env cty1 cty2 | _, Tcty_constr (_, _, cty2) -> moregen_clty true type_pairs env cty1 cty2 | Tcty_fun (ty1, cty1'), Tcty_fun (ty2, cty2') -> begin try moregen true type_pairs env ty1 ty2 with Unify trace -> raise (Failure [CM_Parameter_mismatch (expand_trace env trace)]) end; moregen_clty false type_pairs env cty1' cty2' | Tcty_signature sign1, Tcty_signature sign2 -> let ty1 = object_fields (repr sign1.cty_self) in let ty2 = object_fields (repr sign2.cty_self) in let (fields1, rest1) = flatten_fields ty1 and (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in List.iter (fun (lab, k1, t1, k2, t2) -> begin try moregen true type_pairs env t1 t2 with Unify trace -> raise (Failure [CM_Meth_type_mismatch (lab, expand_trace env trace)]) end) pairs; Vars.iter (fun lab (mut, ty) -> let (mut', ty') = Vars.find lab sign1.cty_vars in try moregen true type_pairs env ty ty' with Unify trace -> raise (Failure [CM_Val_type_mismatch (lab, expand_trace env trace)])) sign2.cty_vars | _ -> raise (Failure []) with Failure error when trace -> raise (Failure (CM_Class_type_mismatch (cty1, cty2)::error)) let match_class_types env pat_sch subj_sch = let type_pairs = TypePairs.create 53 in let old_level = !current_level in current_level := generic_level - 1; (* Generic variables are first duplicated with [instance]. So, their levels are lowered to [generic_level - 1]. The subject is then copied with [duplicate_type]. That way, its levels won't be changed. *) let (_, subj_inst) = instance_class [] subj_sch in let subj = duplicate_class_type subj_inst in current_level := generic_level; (* Duplicate generic variables *) let (_, patt) = instance_class [] pat_sch in let res = let sign1 = signature_of_class_type patt in let sign2 = signature_of_class_type subj in let t1 = repr sign1.cty_self in let t2 = repr sign2.cty_self in TypePairs.add type_pairs (t1, t2) (); let (fields1, rest1) = flatten_fields (object_fields t1) and (fields2, rest2) = flatten_fields (object_fields t2) in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in let error = List.fold_right (fun (lab, k, _) err -> let err = let k = field_kind_repr k in begin match k with Fvar r -> r := Some Fabsent; err | _ -> CM_Hide_public lab::err end in if Concr.mem lab sign1.cty_concr then err else CM_Hide_virtual lab::err) miss1 [] in let missing_method = List.map (fun (m, _, _) -> m) miss2 in let error = (List.map (fun m -> CM_Missing_method m) missing_method) @ error in (* Always succeeds *) moregen true type_pairs env rest1 rest2; let error = List.fold_right (fun (lab, k1, t1, k2, t2) err -> try moregen_kind k1 k2; err with Unify _ -> CM_Public_method lab::err) pairs error in let error = Vars.fold (fun lab (mut, ty) err -> try let (mut', ty') = Vars.find lab sign1.cty_vars in if mut = Mutable && mut' <> Mutable then CM_Non_mutable_value lab::err else err with Not_found -> CM_Missing_value lab::err) sign2.cty_vars error in let error = List.fold_right (fun e l -> if List.mem e missing_method then l else CM_Virtual_method e::l) (Concr.elements (Concr.diff sign2.cty_concr sign1.cty_concr)) error in match error with [] -> begin try moregen_clty true type_pairs env patt subj; [] with Failure r -> r end | error -> CM_Class_type_mismatch (patt, subj)::error in current_level := old_level; res let rec equal_clty trace type_pairs subst env cty1 cty2 = try match cty1, cty2 with Tcty_constr (_, _, cty1), Tcty_constr (_, _, cty2) -> equal_clty true type_pairs subst env cty1 cty2 | Tcty_constr (_, _, cty1), _ -> equal_clty true type_pairs subst env cty1 cty2 | _, Tcty_constr (_, _, cty2) -> equal_clty true type_pairs subst env cty1 cty2 | Tcty_fun (ty1, cty1'), Tcty_fun (ty2, cty2') -> begin try eqtype true type_pairs subst env ty1 ty2 with Unify trace -> raise (Failure [CM_Parameter_mismatch (expand_trace env trace)]) end; equal_clty false type_pairs subst env cty1' cty2' | Tcty_signature sign1, Tcty_signature sign2 -> let ty1 = object_fields (repr sign1.cty_self) in let ty2 = object_fields (repr sign2.cty_self) in let (fields1, rest1) = flatten_fields ty1 and (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in List.iter (fun (lab, k1, t1, k2, t2) -> begin try eqtype true type_pairs subst env t1 t2 with Unify trace -> raise (Failure [CM_Meth_type_mismatch (lab, expand_trace env trace)]) end) pairs; Vars.iter (fun lab (mut, ty) -> let (mut', ty') = Vars.find lab sign1.cty_vars in try eqtype true type_pairs subst env ty ty' with Unify trace -> raise (Failure [CM_Val_type_mismatch (lab, expand_trace env trace)])) sign2.cty_vars | _ -> if not trace then raise (Failure [CM_Class_type_mismatch (cty1, cty2)]) with Failure error when trace -> raise (Failure (CM_Class_type_mismatch (cty1, cty2)::error)) (* XXX On pourrait autoriser l'instantiation du type des parametres... *) (* XXX Correct ? (variables de type dans parametres et corps de classe *) let match_class_declarations env patt_params patt_type subj_params subj_type = let type_pairs = TypePairs.create 53 in let subst = ref [] in let sign1 = signature_of_class_type patt_type in let sign2 = signature_of_class_type subj_type in let t1 = repr sign1.cty_self in let t2 = repr sign2.cty_self in TypePairs.add type_pairs (t1, t2) (); let (fields1, rest1) = flatten_fields (object_fields t1) and (fields2, rest2) = flatten_fields (object_fields t2) in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in let error = List.fold_right (fun (lab, k, _) err -> let err = let k = field_kind_repr k in begin match k with Fvar r -> err | _ -> CM_Hide_public lab::err end in if Concr.mem lab sign1.cty_concr then err else CM_Hide_virtual lab::err) miss1 [] in let missing_method = List.map (fun (m, _, _) -> m) miss2 in let error = (List.map (fun m -> CM_Missing_method m) missing_method) @ error in (* Always succeeds *) eqtype true type_pairs subst env rest1 rest2; let error = List.fold_right (fun (lab, k1, t1, k2, t2) err -> let k1 = field_kind_repr k1 in let k2 = field_kind_repr k2 in match k1, k2 with (Fvar _, Fvar _) | (Fpresent, Fpresent) -> err | (Fvar _, Fpresent) -> CM_Private_method lab::err | (Fpresent, Fvar _) -> CM_Public_method lab::err | _ -> assert false) pairs error in let error = Vars.fold (fun lab (mut, ty) err -> try let (mut', ty') = Vars.find lab sign1.cty_vars in if mut = Mutable && mut' <> Mutable then CM_Non_mutable_value lab::err else err with Not_found -> CM_Missing_value lab::err) sign2.cty_vars error in let error = List.fold_right (fun e l -> if List.mem e missing_method then l else CM_Virtual_method e::l) (Concr.elements (Concr.diff sign2.cty_concr sign1.cty_concr)) error in match error with [] -> begin try let lp = List.length patt_params in let ls = List.length subj_params in if lp <> ls then raise (Failure [CM_Parameter_arity_mismatch (lp, ls)]); List.iter2 (fun p s -> try eqtype true type_pairs subst env p s with Unify trace -> raise (Failure [CM_Type_parameter_mismatch (expand_trace env trace)])) patt_params subj_params; equal_clty false type_pairs subst env patt_type subj_type; [] with Failure r -> r end | error -> error (***************) (* Subtyping *) (***************) (**** Build a subtype of a given type. ****) let subtypes = ref [] let rec build_subtype env t = let t = repr t in match t.desc with Tlink t' -> (* Redundant ! *) build_subtype env t' | Tvar -> (t, false) | Tarrow(t1, t2) -> let (t1', c1) = (t1, false) in let (t2', c2) = build_subtype env t2 in if c1 or c2 then (newty (Tarrow(t1', t2')), true) else (t, false) | Ttuple tlist -> let (tlist', clist) = List.split (List.map (build_subtype env) tlist) in if List.exists (function c -> c) clist then (newty (Ttuple tlist'), true) else (t, false) | Tconstr(p, tl, abbrev) when generic_abbrev env p -> let t' = expand_abbrev env t in let (t'', c) = build_subtype env t' in if c then (t'', true) else (t, false) | Tconstr(p, tl, abbrev) -> (t, false) | Tobject (t1, _) when opened_object t1 -> (t, false) | Tobject (t1, _) -> (begin try List.assq t !subtypes with Not_found -> let t' = newvar () in subtypes := (t, t')::!subtypes; let (t1', _) = build_subtype env t1 in t'.desc <- Tobject (t1', ref None); t' end, true) | Tfield(s, _, t1, t2) (* Always present *) -> let (t1', _) = build_subtype env t1 in let (t2', _) = build_subtype env t2 in (newty (Tfield(s, Fpresent, t1', t2')), true) | Tnil -> let v = newvar () in (v, true) let enlarge_type env ty = subtypes := []; let (ty', _) = build_subtype env ty in subtypes := []; ty' (**** Check whether a type is a subtype of another type. ****) (* During the traversal, a trace of visited types is maintained. It is printed in case of error. Constraints (pairs of types that must be equals) are accumulated rather than being enforced straight. Indeed, the result would otherwise depend on the order in which these constraints are enforced. A function enforcing these constraints is returned. That way, type variables can be bound to their actual values before this function is called (see Typecore). Only well-defined abbreviations are expanded (hence the tests [generic_abbrev ...]). *) let subtypes = TypePairs.create 17 let subtype_error env trace = raise (Subtype (expand_trace env (List.rev trace), [])) let rec subtype_rec env trace t1 t2 cstrs = let t1 = repr t1 in let t2 = repr t2 in if t1 == t2 then [] else begin try TypePairs.find subtypes (t1, t2); cstrs with Not_found -> TypePairs.add subtypes (t1, t2) (); match (t1.desc, t2.desc) with (Tvar, _) | (_, Tvar) -> (trace, t1, t2)::cstrs | (Tarrow(t1, u1), Tarrow(t2, u2)) -> let cstrs = subtype_rec env ((t2, t1)::trace) t2 t1 cstrs in subtype_rec env ((u1, u2)::trace) u1 u2 cstrs | (Ttuple tl1, Ttuple tl2) -> subtype_list env trace tl1 tl2 cstrs | (Tconstr(p1, [], _), Tconstr(p2, [], _)) when Path.same p1 p2 -> cstrs | (Tconstr(p1, tl1, abbrev1), _) when generic_abbrev env p1 -> subtype_rec env trace (expand_abbrev env t1) t2 cstrs | (_, Tconstr(p2, tl2, abbrev2)) when generic_abbrev env p2 -> subtype_rec env trace t1 (expand_abbrev env t2) cstrs | (Tobject (f1, _), Tobject (f2, _)) when opened_object f1 & opened_object f2 -> (* Same row variable implies same object. *) (trace, t1, t2)::cstrs | (Tobject (f1, _), Tobject (f2, _)) -> subtype_fields env trace f1 f2 cstrs | (_, _) -> (trace, t1, t2)::cstrs end and subtype_list env trace tl1 tl2 cstrs = if List.length tl1 <> List.length tl2 then subtype_error env trace; List.fold_left2 (fun cstrs t1 t2 -> subtype_rec env ((t1, t2)::trace) t1 t2 cstrs) cstrs tl1 tl2 and subtype_fields env trace ty1 ty2 cstrs = let (fields1, rest1) = flatten_fields ty1 in let (fields2, rest2) = flatten_fields ty2 in let (pairs, miss1, miss2) = associate_fields fields1 fields2 in [(trace, rest1, build_fields (repr ty2).level miss2 (newvar ()))] @ begin match rest2.desc with Tnil -> [] | _ -> [(trace, build_fields (repr ty1).level miss1 rest1, rest2)] end @ (List.fold_left (fun cstrs (_, k1, t1, k2, t2) -> (* Theses fields are always present *) subtype_rec env ((t1, t2)::trace) t1 t2 cstrs) cstrs pairs) let subtype env ty1 ty2 = TypePairs.clear subtypes; (* Build constraint set. *) let cstrs = subtype_rec env [(ty1, ty2)] ty1 ty2 [] in (* Enforce constraints. *) function () -> List.iter (function (trace0, t1, t2) -> try unify env t1 t2 with Unify trace -> raise (Subtype (expand_trace env (List.rev trace0), List.tl (List.tl trace)))) (List.rev cstrs); TypePairs.clear subtypes (*******************) (* Miscellaneous *) (*******************) let unalias ty = let ty = repr ty in match ty.desc with Tvar -> ty | _ -> newty2 ty.level ty.desc let unroll_abbrev id tl ty = let ty = repr ty in if (ty.desc = Tvar) || (List.exists (deep_occur ty) tl) then ty else let ty' = newty2 ty.level ty.desc in ty.desc <- Tlink (newty2 ty.level (Tconstr (Path.Pident id, tl, ref Mnil))); ty' (* Return the arity (as for curried functions) of the given type. *) let rec arity ty = match (repr ty).desc with Tarrow(t1, t2) -> 1 + arity t2 | _ -> 0 (* Check whether an abbreviation expands to itself. *) let rec cyclic_abbrev env id ty = let ty = repr ty in match ty.desc with Tconstr (Path.Pident id', _, _) when Ident.same id id' -> true | Tconstr (p, tl, abbrev) -> begin try cyclic_abbrev env id (try_expand_head env ty) with Cannot_expand -> false end | _ -> false (*************************) (* Remove dependencies *) (*************************) (* Variables are left unchanged. Other type nodes are duplicated, with levels set to generic level. During copying, the description of a (non-variable) node is first replaced by a link to a marked stub ([Tlink (newmarkedgenvar ())]). The mark allows to differentiate the original type from the copy. Once the copy is made, it replaces the stub. After copying, the description of node, which was stored by [save_desc], must be put back, using [cleanup_types], and the marks on the copy must be removed. *) let rec nondep_type_rec env id ty = let ty = repr ty in if (ty.desc = Tvar) || (ty.level < lowest_level) then ty else begin let desc = ty.desc in save_desc ty desc; let ty' = newmarkedgenvar () in (* Stub *) ty.desc <- Tlink ty'; ty'.desc <- begin match desc with Tvar -> fatal_error "Ctype.nondep_type_rec" | Tarrow(t1, t2) -> Tarrow(nondep_type_rec env id t1, nondep_type_rec env id t2) | Ttuple tl -> Ttuple(List.map (nondep_type_rec env id) tl) | Tconstr(p, tl, abbrev) -> if Path.isfree id p then begin try Tlink (nondep_type_rec env id (expand_abbrev env (newty2 ty.level desc))) (* The [Tlink] is important. The expanded type may be a variable, or may not be completely copied yet (recursive type), so one cannot just take its description. *) with Cannot_expand -> raise Not_found end else Tconstr(p, List.map (nondep_type_rec env id) tl, ref Mnil) | Tobject (t1, name) -> Tobject (nondep_type_rec env id t1, ref (match !name with None -> None | Some (p, tl) -> if Path.isfree id p then None else Some (p, List.map (nondep_type_rec env id) tl))) | Tfield(label, kind, t1, t2) -> begin match field_kind_repr kind with Fpresent -> Tfield(label, Fpresent, nondep_type_rec env id t1, nondep_type_rec env id t2) | Fvar _ (* {contents = None} *) as k -> Tfield(label, k, nondep_type_rec env id t1, nondep_type_rec env id t2) | Fabsent -> assert false end | Tnil -> Tnil | Tlink ty -> (* Actually unused *) Tlink(nondep_type_rec env id ty) end; ty' end let nondep_type env id ty = try let ty' = nondep_type_rec env id ty in cleanup_types (); unmark_type ty'; ty' with Not_found -> cleanup_types (); raise Not_found (* Preserve sharing inside type declarations. *) let nondep_type_decl env mid id is_covariant decl = try let params = List.map (nondep_type_rec env mid) decl.type_params in let decl = { type_params = params; type_arity = decl.type_arity; type_kind = begin try match decl.type_kind with Type_abstract -> Type_abstract | Type_variant cstrs -> Type_variant(List.map (fun (c, tl) -> (c, List.map (nondep_type_rec env mid) tl)) cstrs) | Type_record lbls -> Type_record(List.map (fun (c, mut, t) -> (c, mut, nondep_type_rec env mid t)) lbls) with Not_found when is_covariant -> Type_abstract end; type_manifest = begin try match decl.type_manifest with None -> None | Some ty -> Some (unroll_abbrev id params (nondep_type_rec env mid ty)) with Not_found when is_covariant -> None end } in cleanup_types (); List.iter unmark_type decl.type_params; begin match decl.type_kind with Type_abstract -> () | Type_variant cstrs -> List.iter (fun (c, tl) -> List.iter unmark_type tl) cstrs | Type_record lbls -> List.iter (fun (c, mut, t) -> unmark_type t) lbls end; begin match decl.type_manifest with None -> () | Some ty -> unmark_type ty end; decl with Not_found -> cleanup_types (); raise Not_found (* Preserve sharing inside class types. *) let nondep_class_signature env id sign = { cty_self = nondep_type_rec env id sign.cty_self; cty_vars = Vars.map (function (m, t) -> (m, nondep_type_rec env id t)) sign.cty_vars; cty_concr = sign.cty_concr } let rec nondep_class_type env id = function Tcty_constr (p, _, cty) when Path.isfree id p -> nondep_class_type env id cty | Tcty_constr (p, tyl, cty) -> Tcty_constr (p, List.map (nondep_type_rec env id) tyl, nondep_class_type env id cty) | Tcty_signature sign -> Tcty_signature (nondep_class_signature env id sign) | Tcty_fun (ty, cty) -> Tcty_fun (nondep_type_rec env id ty, nondep_class_type env id cty) let nondep_class_declaration env id decl = assert (not (Path.isfree id decl.cty_path)); let decl = { cty_params = List.map (nondep_type_rec env id) decl.cty_params; cty_type = nondep_class_type env id decl.cty_type; cty_path = decl.cty_path; cty_new = begin match decl.cty_new with None -> None | Some ty -> Some (nondep_type_rec env id ty) end } in cleanup_types (); List.iter unmark_type decl.cty_params; unmark_class_type decl.cty_type; begin match decl.cty_new with None -> () | Some ty -> unmark_type ty end; decl let nondep_cltype_declaration env id decl = assert (not (Path.isfree id decl.clty_path)); let decl = { clty_params = List.map (nondep_type_rec env id) decl.clty_params; clty_type = nondep_class_type env id decl.clty_type; clty_path = decl.clty_path } in cleanup_types (); List.iter unmark_type decl.clty_params; unmark_class_type decl.clty_type; decl