Source file linkable_list.ml

(*Generated by Lem from linkable_list.lem.*)
open Lem_basic_classes
open Lem_function
open Lem_string
open Lem_string_extra
open Lem_tuple
open Lem_bool
open Lem_list
open Lem_list_extra
open Lem_set
open Lem_set_extra
(*import Map*)
open Lem_sorting
open Lem_num
open Lem_maybe
open Lem_assert_extra

open Byte_sequence
open Default_printing
open Error
open Missing_pervasives
open Show

open Elf_types_native_uint
open Elf_memory_image
open Elf_header
open Elf_file
open Memory_image
open Elf_memory_image
open Elf_section_header_table
open Elf_symbol_table
open String_table
open Input_list

open Elf_memory_image
open Elf_memory_image_of_elf64_file

type script = byte_sequence0 (* FIXME *)

type linkable_object = RelocELF of elf_memory_image    (* memory image without address assignments *)
                     | SharedELF of elf_memory_image   (* memory image with address assignments *)
                     | ScriptAST of script       (* FIXME: should be elaborated away *)
                     | ControlScriptDefs

(*val string_of_linkable_object : linkable_object -> string*)
let string_of_linkable_object l:string=  ((match l with
    RelocELF(_)    -> "a relocatable file (...)"
    | SharedELF(_) -> "a shared library (...)"
    | ScriptAST(_) -> "a linker script (...)"
    | ControlScriptDefs -> "the control script"
))

(* We keep the original input item around, hence the filename and byte sequence
 * and options. *)
type linkable_item = linkable_object * input_item * input_options

(*val short_string_of_linkable_item : linkable_item -> string*)
let short_string_of_linkable_item item:string=
     (let (obj, inp, opts) = item
    in
    short_string_of_input_item inp)

let instance_Show_Show_Linkable_list_linkable_object_dict:(linkable_object)show_class= ({

  show_method = string_of_linkable_object})

type linkable_list = linkable_item list

type symbol_resolution_oracle = linkable_list -> int -> string -> int list
type binding      = (Nat_big_num.num * symbol_reference * linkable_item) *  (Nat_big_num.num * symbol_definition * linkable_item)option
type binding_list = binding list
type binding_map  = (string, ( (Nat_big_num.num * binding)list)) Pmap.map


let image_of_linkable_item item:(Abis.any_abi_feature)annotated_memory_image=  ((match item with
    (RelocELF(image), _, _) -> image
    | (SharedELF(image), _, _) -> image
    | _ -> failwith "no image"
))

(*val linkable_item_of_input_item_and_options : forall 'abifeature. abi 'abifeature -> input_item -> input_options -> linkable_item*)
let linkable_item_of_input_item_and_options a it opts:linkable_object*(string*input_blob*(Command_line.input_unit*(origin_coord)list))*input_options=
     ((match ((match it with
        (fname1, Reloc(seq), origin) ->
            let _ = (prerr_endline ("Considering relocatable file " ^ fname1)) in bind (Elf_file.read_elf64_file seq) (fun e ->
            return (RelocELF(elf_memory_image_of_elf64_file a fname1 e), it, opts))
        | (fname1, Shared(seq), origin) ->
            (*let _ = Missing_pervasives.errln ("Skipping shared object " ^ fname) in *)
            fail "unsupported input item"
        | (fname1, Script(seq), origin) ->
            (*let _ = Missing_pervasives.errln ("Skipping linker script " ^ fname) in*)
            fail "unsupported input item"
        ))
    with
        Success(item) -> item
        | Fail(str) -> failwith (str ^ ": non-ELF or non-relocatable input file")
    ))

(*val string_of_linkable : linkable_item -> string*)
let string_of_linkable l:string=  ((match l with
    (_, item, _) -> string_of_triple 
  instance_Show_Show_string_dict instance_Show_Show_Input_list_input_blob_dict (instance_Show_Show_tup2_dict
   Command_line.instance_Show_Show_Command_line_input_unit_dict
   (instance_Show_Show_list_dict
      instance_Show_Show_Input_list_origin_coord_dict)) item
))

(* How do we signal "multiple definitions"?
 * This is part of the policy baked into the particular oracle:
 * are multiple definitions okay, or do we fail?
 *
 * NOTE that multiple definitions *globally* is not the same as
 * multiple definitions as candidates for a given binding. We
 * can get the former even if we don't have the latter, in some
 * weird group/archive arrangements. The right place to detect
 * this condition is probably when generating the output symtab.
 *)

(*val add_definition_to_map : (natural * symbol_definition * linkable_item) -> Map.map string (list (natural * symbol_definition * linkable_item))
                    -> Map.map string (list (natural * symbol_definition * linkable_item))*)
let add_definition_to_map def_idx_and_def_and_linkable m:((string),((Nat_big_num.num*symbol_definition*(linkable_object*input_item*input_options))list))Pmap.map=
     (let (def_idx, def, def_linkable) = def_idx_and_def_and_linkable
    in
    (match Pmap.lookup def.def_symname m with
        Some curlist -> Pmap.add def.def_symname ((def_idx, def, def_linkable) :: curlist) m
        | None -> Pmap.add def.def_symname [(def_idx, def, def_linkable)] m
    ))

(*val all_definitions_by_name : linkable_list -> Map.map string (list (natural * symbol_definition * linkable_item))*)
let all_definitions_by_name linkables:((string),((Nat_big_num.num*symbol_definition*linkable_item)list))Pmap.map=
     (
    (* Now that linkables are ELF memory images, we can make the
     * list of definitions much more easily. *)let list_of_deflists = (Lem_list.mapi (fun (idx1 : int) -> (fun (item : linkable_item) ->
        let img2 = (image_of_linkable_item item)
        in
        let (all_def_tags, all_def_ranges)
         = (List.split (Multimap.lookupBy0 
  (Memory_image_orderings.instance_Basic_classes_Ord_Memory_image_range_tag_dict
     Abis.instance_Basic_classes_Ord_Abis_any_abi_feature_dict) (instance_Basic_classes_Ord_Maybe_maybe_dict
   (instance_Basic_classes_Ord_tup2_dict
      instance_Basic_classes_Ord_string_dict
      (instance_Basic_classes_Ord_tup2_dict
         instance_Basic_classes_Ord_Num_natural_dict
         instance_Basic_classes_Ord_Num_natural_dict))) instance_Basic_classes_SetType_var_dict (instance_Basic_classes_SetType_Maybe_maybe_dict
   (instance_Basic_classes_SetType_tup2_dict
      instance_Basic_classes_SetType_var_dict
      (instance_Basic_classes_SetType_tup2_dict
         instance_Basic_classes_SetType_Num_natural_dict
         instance_Basic_classes_SetType_Num_natural_dict)))  (Memory_image_orderings.tagEquiv
    Abis.instance_Abi_classes_AbiFeatureTagEquiv_Abis_any_abi_feature_dict) (SymbolDef(null_symbol_definition)) img2.by_tag))
        in
        let all_defs = (Lem_list.map (fun tag -> (match tag with
            SymbolDef(def) -> (def, item)
            | _ -> failwith "matched tag not a symbol definition"
        )) all_def_tags)
        in
        let x2 = ([]) in  List.fold_right
   (fun(def, def_linkable) x2 ->
    if true then (Nat_big_num.of_int idx1, def, def_linkable) :: x2 else x2)
   all_defs x2
    )) linkables)
    in
    List.fold_left (fun accum -> (fun deflist ->
        List.fold_left (fun m -> (fun (def_idx, def, def_linkable) -> add_definition_to_map (def_idx, def, def_linkable) m)) accum deflist
    )) (Pmap.empty compare) list_of_deflists)

type binding_oracle =
    linkable_list
    -> (string, ( (Nat_big_num.num * symbol_definition * linkable_item)list)) Pmap.map
    -> (Nat_big_num.num * symbol_reference * linkable_item)
    ->  (Nat_big_num.num * symbol_definition * linkable_item)option

(*val resolve_one_reference_default : forall 'abifeature. abi 'abifeature -> binding_oracle*)
let resolve_one_reference_default a linkables defmap ref_idx_and_ref_and_linkable:(Nat_big_num.num*symbol_definition*(linkable_object*(string*input_blob*(Command_line.input_unit*(origin_coord)list))*input_options))option=
     (let (ref_idx, ref1, ref_linkable) = ref_idx_and_ref_and_linkable
    in
    (* Get the list of all definitions whose name matches.
     * Don't match empty names.
     * How should we handle common symbols here?
     * A common symbol is a potential definition, so it goes in the def list.
     *)
    let (defs_and_linkables_with_matching_name : (Nat_big_num.num * symbol_definition * linkable_item) list)
     = ((match Pmap.lookup ref1.ref_symname defmap with
        Some (l : ( (Nat_big_num.num * symbol_definition * linkable_item)list)) -> l
        | None -> []
    ))
    in
    (* Filter the list by eligibility rules.
     * Normally,
     *
     * - any .o file can supply any other .o file on the command line
     * - any .a file supplies only files appearing to its left
     *      i.e. "it is searched once for definitions"
     * - does a .o file supply a .a file? to both its right and left? Experimentally, YES.
     *
     * So the restrictions are
     * - archives may not supply weak references
     * - archives may only supply to the left, or to themselves, or to objects in the same group
     *)
    let (ref_obj, (ref_fname, ref_blob, (ref_u, ref_coords)), ref_options) = ref_linkable
    in
    let ref_is_weak = (Nat_big_num.equal (get_elf64_symbol_binding ref1.ref_syment) stb_weak)
    in
    let def_is_eligible = (fun (def_idx, def, def_linkable) ->
        let ref_is_unnamed = (ref1.ref_symname = "")
        in
        let ref_is_to_defined_or_common_symbol = ( not (Nat_big_num.equal (Uint32_wrapper.to_bigint ref1.ref_syment.elf64_st_shndx) stn_undef))
        in
        let def_sym_is_ref_sym = ( Nat_big_num.equal ref_idx def_idx && (Nat_big_num.equal ref1.ref_sym_scn def.def_sym_scn
            && Nat_big_num.equal ref1.ref_sym_idx def.def_sym_idx))
        in
        let (def_obj, (def_fname, def_blob, def_origin), def_options) = def_linkable
        in
        let (def_u, def_coords) = def_origin
        in
        let (def_in_group, def_in_archive) = ((match def_coords with
              InArchive(aid, aidx, _, _) :: InGroup(gid1, gidx) :: [_] -> (Some gid1, Some aid)
            | InArchive(aid, aidx, _, _) :: [_]                       -> (None, Some aid)
            | InGroup(gid1, gidx) :: [_]                              -> (Some gid1, None)
            | [_]                                                    -> (None, None)
            | _ -> failwith "internal error: didn't understand origin coordinates of definition"
        ))
        in
        let ref_is_leftmore = (Nat_big_num.less_equal ref_idx def_idx)
        in
        (* For simplicity we include the case of "same archive" in "in group with". *)
        let ref_is_in_group_with_def = ((match def_in_group with
              None -> false
            | Some def_gid ->
                (match ref_coords with
                  InArchive(_, _, _, _) :: InGroup(gid1, _) :: [_] -> Nat_big_num.equal gid1 def_gid
                | InGroup(gid1, _) :: [_]                       -> Nat_big_num.equal gid1 def_gid
                | _ -> false
                )
            ))
        in
        (* but maybe same archive? *)
        (* DEBUGGING: print some stuff out if we care about this symbol. *)let _ =
            (if (ref_fname = "backtrace.o") && (def.def_symname = "_Unwind_GetCFA") then
                (*Missing_pervasives.errln ("saw backtrace.o referencing _Unwind_GetCFA; coords are "
                    ^ "def: " ^ (show def_coords) ^ ", ref: " ^ (show ref_coords) ^ "; ref_is_in_group_with_def: "
                    ^ (show ref_is_in_group_with_def) ^ "; def_in_group: " ^ (show def_in_group))*)
              ()
            else ())
        in
        let ref_and_def_are_in_same_archive = ((match (def_coords, ref_coords) with
            (InArchive(x1, _, _, _) :: _, InArchive(x2, _, _, _) :: _) -> Nat_big_num.equal x1 x2
            | _ -> false
        ))
        in
        let def_is_in_archive = ((match def_in_archive with
            Some _ -> true
            | None -> false
        ))
        in
        if ref_is_to_defined_or_common_symbol then def_sym_is_ref_sym
        else
            if ref_is_unnamed then false
            else
                if def_is_in_archive
                then
                    (* Weak references *can* be resolved to archive members...
                     * if the reference itself is also in the archive. *)
                    ((not ref_is_weak) || ref_and_def_are_in_same_archive)
                    && (
                           ref_is_leftmore
                        || (ref_and_def_are_in_same_archive
                        || ref_is_in_group_with_def)
                    )
                else
                    true
    )
    in
    let eligible_defs = (List.filter def_is_eligible defs_and_linkables_with_matching_name)
    in
    let (maybe_target_def_idx, maybe_target_def, maybe_target_def_linkable) = ((match eligible_defs with
        [] -> (None, None, None)
        | [(def_idx, def, def_linkable)] -> (Some def_idx, Some def, Some def_linkable)
        | (d_idx, d, d_l) :: more_pairs ->
            (* Break ties by
             * - putting defs in relocs (or --defsym or linker script, a.k.a. command line) ahead of defs in archives;
             * - else whichever definition appeared first in the left-to-right order.
             *)
            let sorted = (insertSortBy (fun (d_idx1, d1, (_, (_, _, (_, d_l1_coords)), _)) -> (fun (d_idx2, d2, (_, (_, _, (_, d_l2_coords)), _)) ->
                (match (d_l1_coords, d_l2_coords) with
                      (InCommandLine(_) :: _, InCommandLine(_) :: _) -> Nat_big_num.less d_idx1 d_idx2
                    | (InCommandLine(_) :: _, _)                     -> (* command-line wins *) true
                    | (_,                     InCommandLine(_) :: _) -> (* command-line wins *) false
                    | (_, _) -> Nat_big_num.less d_idx1 d_idx2
                ))) eligible_defs)
            in
            (match sorted with
                (first_d_idx, first_d, first_d_l) :: _ -> (Some first_d_idx, Some first_d, Some first_d_l)
                | _ -> failwith "impossible: sorted list is shorter than original"
            )
    ))
    in
    let refstr = ("`"
                ^ (ref1.ref_symname ^ ("' (" ^
                ((if Nat_big_num.equal (Uint32_wrapper.to_bigint ref1.ref_syment.elf64_st_shndx) shn_undef then "UND" else "defined") ^
                (" symbol at index " ^ ((Nat_big_num.to_string ref1.ref_sym_idx) ^ (" in symtab "
                ^ ((Nat_big_num.to_string ref1.ref_sym_scn) ^ (" in " ^ (ref_fname
                ^ ")"))))))))))
    in
    (*let _ = Missing_pervasives.errs ("Bound a reference from " ^ refstr ^ " to ")
    in*)
    (match (maybe_target_def_idx, maybe_target_def, maybe_target_def_linkable) with
        (Some target_def_idx, Some target_def, Some target_def_linkable) ->
            (*let _ = Missing_pervasives.errln (" a definition in "^ (show (target_def_linkable)))
            in*)
            Some(target_def_idx, target_def, target_def_linkable)
    |  (None, None, None) ->
            (*let _ = Missing_pervasives.errln " no definition"
            in*)
            if ref_is_weak (* || a.symbol_is_generated_by_linker ref.ref_symname *) then None
            else (* failwith ("undefined symbol: " ^ refstr) *) None
            (* FIXME: do a check, *after* the linker script has been interpreted,
             * that all remaining undefined symbols are permitted by the ABI/policy. *)
    | _ -> failwith "impossible: non-matching maybes for target_def_idx and target_def"
    ))

(*val resolve_all :
    linkable_list
    -> Map.map string (list (natural * symbol_definition * linkable_item))                (* all definitions *)
    -> binding_oracle
    -> list (natural * symbol_reference * linkable_item)
    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))*)
let resolve_all linkables all_defs oracle refs:((Nat_big_num.num*symbol_reference*(linkable_object*input_item*input_options))*(Nat_big_num.num*symbol_definition*linkable_item)option)list=
     (Lem_list.map (fun (ref_idx, ref1, ref_linkable) -> ((ref_idx, ref1, ref_linkable), (oracle linkables all_defs (ref_idx, ref1, ref_linkable)))) refs)

(* To accumulate which inputs are needed, we work with a list of undefineds, starting with those
 * in the  forced-output objects. We then iteratively build a list of all needed symbol definitions,
 * pulling in the objects that contain them, until we reach a fixed point. *)
(*val resolve_undefs_in_one_object :
    linkable_list
    -> Map.map string (list (natural * symbol_definition * linkable_item))                (* all definitions *)
    -> binding_oracle
    -> natural
    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))*)
let resolve_undefs_in_one_object linkables all_defs oracle idx1:((Nat_big_num.num*symbol_reference*linkable_item)*(Nat_big_num.num*symbol_definition*linkable_item)option)list=
     (
    (* Get this object's list of references *)let item = ((match Lem_list.list_index linkables (Nat_big_num.to_int idx1) with
        Some it -> it
        | None -> failwith "impossible: linkable not in list of linkables"
    ))
    in
    let img2 = (image_of_linkable_item item)
    in
    let (all_ref_tags, all_ref_ranges)
     = (List.split (Multimap.lookupBy0 
  (Memory_image_orderings.instance_Basic_classes_Ord_Memory_image_range_tag_dict
     Abis.instance_Basic_classes_Ord_Abis_any_abi_feature_dict) (instance_Basic_classes_Ord_Maybe_maybe_dict
   (instance_Basic_classes_Ord_tup2_dict
      instance_Basic_classes_Ord_string_dict
      (instance_Basic_classes_Ord_tup2_dict
         instance_Basic_classes_Ord_Num_natural_dict
         instance_Basic_classes_Ord_Num_natural_dict))) instance_Basic_classes_SetType_var_dict (instance_Basic_classes_SetType_Maybe_maybe_dict
   (instance_Basic_classes_SetType_tup2_dict
      instance_Basic_classes_SetType_var_dict
      (instance_Basic_classes_SetType_tup2_dict
         instance_Basic_classes_SetType_Num_natural_dict
         instance_Basic_classes_SetType_Num_natural_dict)))  (Memory_image_orderings.tagEquiv
    Abis.instance_Abi_classes_AbiFeatureTagEquiv_Abis_any_abi_feature_dict) (SymbolRef(null_symbol_reference_and_reloc_site)) img2.by_tag))
    in
    (* By using SymbolRef, we are extracting and binding each relocation site individually.
     * since there might be more than one relocation site referencing the same symbol name,
     * in a given object.
     *
     * We are also binding SymbolRefs that have no relocation, which occur when there's
     * an UND symbol which is not actually used by a relocation site, but is nevertheless
     * in need of being resolved.
     *
     * We don't (for the moment) want to make different decisions for different reloc sites
     * in the same object referencing the same symbol. So we dedup from a list to a set.
     *)
    let all_refs = (Pset.from_list compare (Lem_list.map (fun tag -> (match tag with
        SymbolRef(r) -> r.ref
        | _ -> failwith "matched tag not a relocation site"
    )) all_ref_tags))
    in
    let ref_triples = (let x2 =(Pset.from_list (tripleCompare Nat_big_num.compare compare (tripleCompare compare (tripleCompare compare compare (pairCompare compare (lexicographic_compare compare))) compare)) 
  []) in  Pset.fold
   (fun ref1 x2 -> if true then Pset.add (idx1, ref1, item) x2 else x2)
   all_refs x2)
    in
    (*let _ = Missing_pervasives.errln ("object " ^ (show item) ^ " has " ^
        (show (Set.size ref_triples)) ^ " reloc references (symname, sym_scn, sym_idx, st_shndx) (" ^
        (show (List.map (fun x -> ("\"" ^ x.ref_symname ^ "\"", x.ref_sym_scn, x.ref_sym_idx, natural_of_elf64_half x.ref_syment.elf64_st_shndx)) (Set_extra.toList all_refs))) ^ ")")
    in*)
    let und_ref_triples = (let x2 =(Pset.from_list (tripleCompare Nat_big_num.compare compare (tripleCompare compare (tripleCompare compare compare (pairCompare compare (lexicographic_compare compare))) compare)) 
  []) in  Pset.fold
   (fun(idx1, ref1, ref_item) x2 ->
    if Nat_big_num.equal
         (Uint32_wrapper.to_bigint ref1.ref_syment.elf64_st_shndx) shn_undef then
      Pset.add (idx1, ref1, ref_item) x2 else x2) ref_triples x2)
    in
    (*let _ = Missing_pervasives.errln ("... of which " ^
        (show (Set.size und_ref_triples)) ^ " are to undefined symbols: (symname, sym_scn, sym_idx, st_shndx) (" ^
        (show (List.map (fun (idx, x, _) -> ("\"" ^ x.ref_symname ^ "\"", x.ref_sym_scn, x.ref_sym_idx, natural_of_elf64_half x.ref_syment.elf64_st_shndx)) (Set_extra.toList und_ref_triples))) ^ ")")
    in*)
    resolve_all linkables all_defs oracle (Pset.elements ref_triples))

(*val accumulate_bindings_bf : forall 'abifeature.
    abi 'abifeature
    -> linkable_list
    -> Map.map string (list (natural * symbol_definition * linkable_item))                (* all definitions *)
    -> set natural                                        (* inputs fully-bound so far *)
    -> list natural                                       (* ordered list of inputs to bind next *)
    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))  (* bindings made so far *)
    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))*)  (* all accumulated bindings bindings *)
let rec accumulate_bindings_bf a linkables all_defs fully_bound to_bind bindings_accum:((Nat_big_num.num*symbol_reference*linkable_item)*(Nat_big_num.num*symbol_definition*linkable_item)option)list=
     (
    (* This is like foldl, except that each stage
     * can add stuff to the work list *)(match to_bind with
        [] -> bindings_accum (* termination *)
        | l_idx :: more_idx ->
            (* Get the new bindings for this object *)
            let new_bindings = (resolve_undefs_in_one_object
                linkables
                all_defs
                (resolve_one_reference_default a)
                l_idx)
            in
            let new_fully_bound = (Pset.add l_idx fully_bound)
            in
            (* Which of the new bindings are to objects
             * not yet fully bound or not yet in the to-bind list? *)
            let new_bindings_def_idx = (list_concat_map (fun (ref1, maybe_def_and_idx_and_linkable) ->
                (match maybe_def_and_idx_and_linkable with
                    Some (def_idx, def, def_linkable) -> [def_idx]
                    | None -> []
                )
            ) new_bindings)
            in
            let new_bindings_def_idx_set = (Pset.from_list Nat_big_num.compare new_bindings_def_idx)
            in
            let included_linkables_idx =  (Pset.(union) fully_bound ((Pset.from_list Nat_big_num.compare to_bind)))
            in
            let new_l_idx = (Pset.diff new_bindings_def_idx_set included_linkables_idx)
            in
            let new_l_idx_list = (Pset.elements new_l_idx)
            in
            (*let _ = Missing_pervasives.errln (
                if List.null new_l_idx_list
                then
                    "Fully bound references in  " ^ (show (List.index linkables (natFromNatural l_idx)))
                        ^ " using only already-included linkables ("
                        ^ (show (List.map (fun i -> List.index linkables (natFromNatural i)) (Set_extra.toList included_linkables_idx)))
                else
                    "Including additional linkables "
                    ^ (show (List.mapMaybe (fun i -> List.index linkables (natFromNatural i)) new_l_idx_list))
                    )
            in*)
            accumulate_bindings_bf
                a
                linkables
                all_defs
                new_fully_bound
                ( List.rev_append (List.rev more_idx) new_l_idx_list)
                ( List.rev_append (List.rev bindings_accum) new_bindings)
    ))

(* We need a generalised kind of depth-first search in which there are multiple start points.
 * Also, we always work one object at a time, not one edge at a time; when we pull in an object,
 * we resolve *all* the references therein.
 *)
(*val accumulate_bindings_objectwise_df : forall 'abifeature.
    abi 'abifeature
    -> linkable_list
    -> Map.map string (list (natural * symbol_definition * linkable_item))                (* all definitions *)

    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))  (* bindings made so far *)
    -> set natural                                        (* inputs fully-bound so far -- these are "black" *)
    -> list natural                                       (* inputs scheduled for binding -- these include
                                                             any "grey" (in-progress) nodes *and*
                                                             any nodes that we have committed to exploring
                                                             (the "start nodes").
                                                             Because we're depth-first, we prepend our adjacent
                                                             nodes to this list, making them grey, then we
                                                             recurse by taking from the head. We must always
                                                             filter out the prepended nodes from the existing list,
                                                             to ensure we don't recurse infinitely. *)
    -> list ((natural * symbol_reference * linkable_item) * maybe (natural * symbol_definition * linkable_item))*)  (* all accumulated bindings bindings *)
let rec accumulate_bindings_objectwise_df a linkables all_defs bindings_accum blacks greys:((Nat_big_num.num*symbol_reference*linkable_item)*(Nat_big_num.num*symbol_definition*linkable_item)option)list=
     ((match greys with
        [] -> bindings_accum (* termination *)
        | l_idx :: more_idx ->
            (* Get the new bindings for this object *)
            let new_bindings = (resolve_undefs_in_one_object
                linkables
                all_defs
                (resolve_one_reference_default a)
                l_idx)
            in
            (* We pull in the whole object at a time ("objectwise"), so by definition,
             * we have created bindings for everything in this object; it's now black. *)
            let new_fully_bound = (Pset.add l_idx blacks)
            in
            (* Which of the new bindings are to objects
             * not yet fully bound or not yet in the to-bind list? *)
            let new_bindings_def_idx = (list_concat_map (fun (ref1, maybe_def_and_idx_and_linkable) ->
                (match maybe_def_and_idx_and_linkable with
                    Some (def_idx, def, def_linkable) -> [def_idx]
                    | None -> []
                )
            ) new_bindings)
            in
            let new_bindings_def_idx_set = (Pset.from_list Nat_big_num.compare new_bindings_def_idx)
            in
            (* this is the "black or grey" set. *)
            let included_linkables_idx =  (Pset.(union) blacks ((Pset.from_list Nat_big_num.compare greys)))
            in
            (* these are the white ones that we're adjacent to *)
            let new_l_idx = (Pset.diff new_bindings_def_idx_set included_linkables_idx)
            in
            let new_l_idx_list = (Pset.elements new_l_idx)
            in
            (* What is the new grey-alike list? (This is the list we tail-recurse down.)
             * It's
             * - the existing grey-alike list
             * - with any new (were-white) objects prepended
             * - ... and filtered to *remove* these from the existing list (avoid duplication).
             *)
            let new_grey_list =  (List.rev_append (List.rev new_l_idx_list) (List.filter (fun x -> not ( Pset.mem x new_l_idx)) more_idx))
            in
            (* whether or not we've not uncovered any new white nodes, we tail-recurse  *)
            (*let _ = (if List.null new_l_idx_list then
                Missing_pervasives.errln ("Fully bound references in  " ^ (show (List.index linkables (natFromNatural l_idx)))
                    ^ " using only already-included linkables ("
                    ^ (show (List.map (fun i -> List.index linkables (natFromNatural i)) (Set_extra.toList included_linkables_idx)))
                ) else Missing_pervasives.errln ("Including additional linkables "
            ^ (show (List.mapMaybe (fun i -> List.index linkables (natFromNatural i)) new_l_idx_list))))
            in*)
            accumulate_bindings_objectwise_df
                a
                linkables
                all_defs
                ( List.rev_append (List.rev bindings_accum) new_bindings)
                (new_fully_bound : Nat_big_num.num Pset.set)
                (new_grey_list : Nat_big_num.num list)
   ))

(* Rather than recursively expanding the link by searching for definitions of undefs,
 * the GNU linker works by recursing/looping along the list of *linkables*, testing whether
 * any of the defs satisfies a currently-undef'd thing. On adding a new undef'd thing,
 * we re-search only from the current archive, not from the beginning (i.e. the
 * "def_is_leftmore or def_in_same_archive" logic).
 *
 * Why is this not the same as depth-first? One example is if we pull in a new object
 * which happens to have two undefs: one satisfied by the *first* element in the current archive,
 * and one satisfied by the last.
 *
 * In the GNU algorithm, we'll pull in the first archive element immediately afterwards, because
 * we'll re-traverse the archive and find it's needed.
 *
 * In the depth-first algorithm, it depends entirely on the ordering of the new bindings, i.e.
 * the symtab ordering of the two undefs. If the later-in-archive def was bound *first*, we'll
 * recurse down *that* object's dependencies first.
 *
 * So if we sort the new grey list
 * so that bindings formed in order of *current archive def pos*,
 * will we get the same behaviour?
 * We can't really do this, because we have no "current archive".
 *
 * Need to rewrite the algorithm to fold along the list of linkables.
 *)