path: root/compiler/PureToExtract.ml

(** This module is used to extract the pure ASTs to various theorem provers.
    It defines utilities and helpers to make the work as easy as possible:
    we try to factorize as much as possible the different extractions to the
    backends we target.
 *)

open Pure
open TranslateCore
module C = Contexts
module RegionVarId = T.RegionVarId
module F = Format

(** The local logger *)
let log = L.pure_to_extract_log

type region_group_info = {
  id : RegionGroupId.id;
      (** The id of the region group.
          Note that a simple way of generating unique names for backward
          functions is to use the region group ids.
       *)
  region_names : string option list;
      (** The names of the region variables included in this group.
          Note that names are not always available...
       *)
}

module StringSet = Collections.MakeSet (Collections.OrderedString)
module StringMap = Collections.MakeMap (Collections.OrderedString)

type name = Names.name
type type_name = Names.type_name
type global_name = Names.global_name
type fun_name = Names.fun_name

(* TODO: this should a module we give to a functor! *)

(** A formatter's role is twofold:
    1. Come up with name suggestions.
    For instance, provided some information about a function (its basename,
    information about the region group, etc.) it should come up with an
    appropriate name for the forward/backward function.
    
    It can of course apply many transformations, like changing to camel case/
    snake case, adding prefixes/suffixes, etc.
    
    2. Format some specific terms, like constants.
 *)
type formatter = {
  bool_name : string;
  char_name : string;
  int_name : integer_type -> string;
  str_name : string;
  field_name : name -> FieldId.id -> string option -> string;
      (** Inputs:
          - type name
          - field id
          - field name
          
          Note that fields don't always have names, but we still need to
          generate some names if we want to extract the structures to records...
          We might want to extract such structures to tuples, later, but field
          access then causes trouble because not all provers accept syntax like
          [x.3] where [x] is a tuple.
       *)
  variant_name : name -> string -> string;
      (** Inputs:
          - type name
          - variant name
       *)
  struct_constructor : name -> string;
      (** Structure constructors are used when constructing structure values.
      
          For instance, in F*:
          {[
            type pair = { x : nat; y : nat }
            let p : pair = Mkpair 0 1
          ]}
          
          Inputs:
          - type name
       *)
  type_name : type_name -> string;
      (** Provided a basename, compute a type name. *)
  global_name : global_name -> string;
      (** Provided a basename, compute a global name. *)
  fun_name :
    A.fun_id ->
    fun_name ->
    int ->
    region_group_info option ->
    bool * int ->
    string;
      (** Inputs:
          - function id: this is especially useful to identify whether the
            function is an assumed function or a local function
          - function basename
          - number of region groups
          - region group information in case of a backward function
            ([None] if forward function)
          - pair:
            - do we generate the forward function (it may have been filtered)?
            - the number of extracted backward functions (not necessarily equal
              to the number of region groups, because we may have filtered
              some of them)
          TODO: use the fun id for the assumed functions.
       *)
  decreases_clause_name : A.FunDeclId.id -> fun_name -> string;
      (** Generates the name of the definition used to prove/reason about
          termination. The generated code uses this clause where needed,
          but its body must be defined by the user.
      
          Inputs:
          - function id: this is especially useful to identify whether the
            function is an assumed function or a local function
          - function basename
       *)
  var_basename : StringSet.t -> string option -> ty -> string;
      (** Generates a variable basename.
      
          Inputs:
          - the set of names used in the context so far
          - the basename we got from the symbolic execution, if we have one
          - the type of the variable (can be useful for heuristics, in order
            not to always use "x" for instance, whenever naming anonymous
            variables)

          Note that once the formatter generated a basename, we add an index
          if necessary to prevent name clashes: the burden of name clashes checks
          is thus on the caller's side.
       *)
  type_var_basename : StringSet.t -> string -> string;
      (** Generates a type variable basename. *)
  append_index : string -> int -> string;
      (** Appends an index to a name - we use this to generate unique
          names: when doing so, the role of the formatter is just to concatenate
          indices to names, the responsability of finding a proper index is
          delegated to helper functions.
       *)
  extract_primitive_value : F.formatter -> bool -> primitive_value -> unit;
      (** Format a constant value.
      
          Inputs:
          - formatter
          - [inside]: if [true], the value should be wrapped in parentheses
            if it is made of an application (ex.: [U32 3])
          - the constant value
       *)
  extract_unop :
    (bool -> texpression -> unit) ->
    F.formatter ->
    bool ->
    unop ->
    texpression ->
    unit;
      (** Format a unary operation
      
          Inputs:
          - a formatter for expressions (called on the argument of the unop)
          - extraction context (see below)
          - formatter
          - expression formatter
          - [inside]
          - unop
          - argument
       *)
  extract_binop :
    (bool -> texpression -> unit) ->
    F.formatter ->
    bool ->
    E.binop ->
    integer_type ->
    texpression ->
    texpression ->
    unit;
      (** Format a binary operation
      
          Inputs:
          - a formatter for expressions (called on the arguments of the binop)
          - extraction context (see below)
          - formatter
          - expression formatter
          - [inside]
          - binop
          - argument 0
          - argument 1
       *)
}

(** We use identifiers to look for name clashes *)
type id =
  | GlobalId of A.GlobalDeclId.id
  | FunId of A.fun_id * RegionGroupId.id option
  | DecreasesClauseId of A.fun_id
      (** The definition which provides the decreases/termination clause.
          We insert calls to this clause to prove/reason about termination:
          the body of those clauses must be defined by the user, in the
          proper files.
       *)
  | TypeId of type_id
  | StructId of type_id
      (** We use this when we manipulate the names of the structure
          constructors.
          
          For instance, in F*:
          {[
            type pair = { x: nat; y : nat }
            let p : pair = Mkpair 0 1
          ]}
       *)
  | VariantId of type_id * VariantId.id
      (** If often happens that variant names must be unique (it is the case in
          F* ) which is why we register them here.
       *)
  | FieldId of type_id * FieldId.id
      (** If often happens that in the case of structures, the field names
          must be unique (it is the case in F* ) which is why we register
          them here.
       *)
  | TypeVarId of TypeVarId.id
  | VarId of VarId.id
  | UnknownId
      (** Used for stored various strings like keywords, definitions which
          should always be in context, etc. and which can't be linked to one
          of the above.
       *)
[@@deriving show, ord]

module IdOrderedType = struct
  type t = id

  let compare = compare_id
  let to_string = show_id
  let pp_t = pp_id
  let show_t = show_id
end

module IdMap = Collections.MakeMap (IdOrderedType)

(** The names map stores the mappings from names to identifiers and vice-versa.

    We use it for lookups (during the translation) and to check for name clashes.
    
    [id_to_string] is for debugging.
  *)
type names_map = {
  id_to_name : string IdMap.t;
  name_to_id : id StringMap.t;
      (** The name to id map is used to look for name clashes, and generate nice
          debugging messages: if there is a name clash, it is useful to know
          precisely which identifiers are mapped to the same name...
       *)
  names_set : StringSet.t;
}

let names_map_add (id_to_string : id -> string) (id : id) (name : string)
    (nm : names_map) : names_map =
  (* Check if there is a clash *)
  (match StringMap.find_opt name nm.name_to_id with
  | None -> () (* Ok *)
  | Some clash ->
      (* There is a clash: print a nice debugging message for the user *)
      let id1 = "\n- " ^ id_to_string clash in
      let id2 = "\n- " ^ id_to_string id in
      let err =
        "Name clash detected: the following identifiers are bound to the same \
         name \"" ^ name ^ "\":" ^ id1 ^ id2
      in
      log#serror err;
      failwith err);
  (* Sanity check *)
  assert (not (StringSet.mem name nm.names_set));
  (* Insert *)
  let id_to_name = IdMap.add id name nm.id_to_name in
  let name_to_id = StringMap.add name id nm.name_to_id in
  let names_set = StringSet.add name nm.names_set in
  { id_to_name; name_to_id; names_set }

let names_map_add_assumed_type (id_to_string : id -> string) (id : assumed_ty)
    (name : string) (nm : names_map) : names_map =
  names_map_add id_to_string (TypeId (Assumed id)) name nm

let names_map_add_assumed_struct (id_to_string : id -> string) (id : assumed_ty)
    (name : string) (nm : names_map) : names_map =
  names_map_add id_to_string (StructId (Assumed id)) name nm

let names_map_add_assumed_variant (id_to_string : id -> string)
    (id : assumed_ty) (variant_id : VariantId.id) (name : string)
    (nm : names_map) : names_map =
  names_map_add id_to_string (VariantId (Assumed id, variant_id)) name nm

let names_map_add_assumed_function (id_to_string : id -> string)
    (fid : A.assumed_fun_id) (rg_id : RegionGroupId.id option) (name : string)
    (nm : names_map) : names_map =
  names_map_add id_to_string (FunId (A.Assumed fid, rg_id)) name nm

(** Make a (variable) basename unique (by adding an index).

    We do this in an inefficient manner (by testing all indices starting from
    0) but it shouldn't be a bottleneck.
    
    Also note that at some point, we thought about trying to reuse names of
    variables which are not used anymore, like here:
    {[
      let x = ... in
      ...
      let x0 = ... in // We could use the name "x" if [x] is not used below
      ...
    ]}
    
    However it is a good idea to keep things as they are for F*: as F* is
    designed for extrinsic proofs, a proof about a function follows this
    function's structure. The consequence is that we often end up
    copy-pasting function bodies. As in the proofs (in assertions and
    when calling lemmas) we often need to talk about the "past" (i.e.,
    previous values), it is very useful to generate code where all variable
    names are assigned at most once.
    
    [append]: function to append an index to a string
 *)
let basename_to_unique (names_set : StringSet.t)
    (append : string -> int -> string) (basename : string) : string =
  let rec gen (i : int) : string =
    let s = append basename i in
    if StringSet.mem s names_set then gen (i + 1) else s
  in
  if StringSet.mem basename names_set then gen 0 else basename

(** Extraction context.

    Note that the extraction context contains information coming from the
    LLBC AST (not only the pure AST). This is useful for naming, for instance:
    we use the region information to generate the names of the backward
    functions, etc.
 *)
type extraction_ctx = {
  trans_ctx : trans_ctx;
  names_map : names_map;
  fmt : formatter;
  indent_incr : int;
      (** The indent increment we insert whenever we need to indent more *)
}

(** Debugging function *)
let id_to_string (id : id) (ctx : extraction_ctx) : string =
  let global_decls = ctx.trans_ctx.global_context.global_decls in
  let fun_decls = ctx.trans_ctx.fun_context.fun_decls in
  let type_decls = ctx.trans_ctx.type_context.type_decls in
  (* TODO: factorize the pretty-printing with what is in PrintPure *)
  let get_type_name (id : type_id) : string =
    match id with
    | AdtId id ->
        let def = TypeDeclId.Map.find id type_decls in
        Print.name_to_string def.name
    | Assumed aty -> show_assumed_ty aty
    | Tuple -> failwith "Unreachable"
  in
  match id with
  | GlobalId gid ->
      let name = (A.GlobalDeclId.Map.find gid global_decls).name in
      "global name: " ^ Print.global_name_to_string name
  | FunId (fid, rg_id) ->
      let fun_name =
        match fid with
        | A.Regular fid ->
            Print.fun_name_to_string (A.FunDeclId.Map.find fid fun_decls).name
        | A.Assumed aid -> A.show_assumed_fun_id aid
      in
      let fun_kind =
        match rg_id with
        | None -> "forward"
        | Some rg_id -> "backward " ^ RegionGroupId.to_string rg_id
      in
      "fun name (" ^ fun_kind ^ "): " ^ fun_name
  | DecreasesClauseId fid ->
      let fun_name =
        match fid with
        | A.Regular fid ->
            Print.fun_name_to_string (A.FunDeclId.Map.find fid fun_decls).name
        | A.Assumed aid -> A.show_assumed_fun_id aid
      in
      "decreases clause for function: " ^ fun_name
  | TypeId id -> "type name: " ^ get_type_name id
  | StructId id -> "struct constructor of: " ^ get_type_name id
  | VariantId (id, variant_id) ->
      let variant_name =
        match id with
        | Tuple -> failwith "Unreachable"
        | Assumed State -> failwith "Unreachable"
        | Assumed Result ->
            if variant_id = result_return_id then "@result::Return"
            else if variant_id = result_fail_id then "@result::Fail"
            else failwith "Unreachable"
        | Assumed Option ->
            if variant_id = option_some_id then "@option::Some"
            else if variant_id = option_none_id then "@option::None"
            else failwith "Unreachable"
        | Assumed Vec -> failwith "Unreachable"
        | AdtId id -> (
            let def = TypeDeclId.Map.find id type_decls in
            match def.kind with
            | Struct _ | Opaque -> failwith "Unreachable"
            | Enum variants ->
                let variant = VariantId.nth variants variant_id in
                Print.name_to_string def.name ^ "::" ^ variant.variant_name)
      in
      "variant name: " ^ variant_name
  | FieldId (id, field_id) ->
      let field_name =
        match id with
        | Tuple -> failwith "Unreachable"
        | Assumed (State | Result | Option) -> failwith "Unreachable"
        | Assumed Vec ->
            (* We can't directly have access to the fields of a vector *)
            failwith "Unreachable"
        | AdtId id -> (
            let def = TypeDeclId.Map.find id type_decls in
            match def.kind with
            | Enum _ | Opaque -> failwith "Unreachable"
            | Struct fields ->
                let field = FieldId.nth fields field_id in
                let field_name =
                  match field.field_name with
                  | None -> FieldId.to_string field_id
                  | Some name -> name
                in
                Print.name_to_string def.name ^ "." ^ field_name)
      in
      "field name: " ^ field_name
  | UnknownId -> "keyword"
  | TypeVarId _ | VarId _ ->
      (* We should never get there: we add indices to make sure variable
       * names are unique *)
      failwith "Unreachable"

let ctx_add (id : id) (name : string) (ctx : extraction_ctx) : extraction_ctx =
  (* The id_to_string function to print nice debugging messages if there are
   * collisions *)
  let id_to_string (id : id) : string = id_to_string id ctx in
  let names_map = names_map_add id_to_string id name ctx.names_map in
  { ctx with names_map }

let ctx_get (id : id) (ctx : extraction_ctx) : string =
  match IdMap.find_opt id ctx.names_map.id_to_name with
  | Some s -> s
  | None ->
      log#serror ("Could not find: " ^ id_to_string id ctx);
      raise Not_found

let ctx_get_global (id : A.GlobalDeclId.id) (ctx : extraction_ctx) : string =
  ctx_get (GlobalId id) ctx

let ctx_get_function (id : A.fun_id) (rg : RegionGroupId.id option)
    (ctx : extraction_ctx) : string =
  ctx_get (FunId (id, rg)) ctx

let ctx_get_local_function (id : A.FunDeclId.id) (rg : RegionGroupId.id option)
    (ctx : extraction_ctx) : string =
  ctx_get_function (A.Regular id) rg ctx

let ctx_get_type (id : type_id) (ctx : extraction_ctx) : string =
  assert (id <> Tuple);
  ctx_get (TypeId id) ctx

let ctx_get_local_type (id : TypeDeclId.id) (ctx : extraction_ctx) : string =
  ctx_get_type (AdtId id) ctx

let ctx_get_assumed_type (id : assumed_ty) (ctx : extraction_ctx) : string =
  ctx_get_type (Assumed id) ctx

let ctx_get_var (id : VarId.id) (ctx : extraction_ctx) : string =
  ctx_get (VarId id) ctx

let ctx_get_type_var (id : TypeVarId.id) (ctx : extraction_ctx) : string =
  ctx_get (TypeVarId id) ctx

let ctx_get_field (type_id : type_id) (field_id : FieldId.id)
    (ctx : extraction_ctx) : string =
  ctx_get (FieldId (type_id, field_id)) ctx

let ctx_get_struct (def_id : type_id) (ctx : extraction_ctx) : string =
  ctx_get (StructId def_id) ctx

let ctx_get_variant (def_id : type_id) (variant_id : VariantId.id)
    (ctx : extraction_ctx) : string =
  ctx_get (VariantId (def_id, variant_id)) ctx

let ctx_get_decreases_clause (def_id : A.FunDeclId.id) (ctx : extraction_ctx) :
    string =
  ctx_get (DecreasesClauseId (A.Regular def_id)) ctx

(** Generate a unique type variable name and add it to the context *)
let ctx_add_type_var (basename : string) (id : TypeVarId.id)
    (ctx : extraction_ctx) : extraction_ctx * string =
  let name = ctx.fmt.type_var_basename ctx.names_map.names_set basename in
  let name =
    basename_to_unique ctx.names_map.names_set ctx.fmt.append_index name
  in
  let ctx = ctx_add (TypeVarId id) name ctx in
  (ctx, name)

(** See {!ctx_add_type_var} *)
let ctx_add_type_vars (vars : (string * TypeVarId.id) list)
    (ctx : extraction_ctx) : extraction_ctx * string list =
  List.fold_left_map
    (fun ctx (name, id) -> ctx_add_type_var name id ctx)
    ctx vars

(** Generate a unique variable name and add it to the context *)
let ctx_add_var (basename : string) (id : VarId.id) (ctx : extraction_ctx) :
    extraction_ctx * string =
  let name =
    basename_to_unique ctx.names_map.names_set ctx.fmt.append_index basename
  in
  let ctx = ctx_add (VarId id) name ctx in
  (ctx, name)

(** See {!ctx_add_var} *)
let ctx_add_vars (vars : var list) (ctx : extraction_ctx) :
    extraction_ctx * string list =
  List.fold_left_map
    (fun ctx (v : var) ->
      let name = ctx.fmt.var_basename ctx.names_map.names_set v.basename v.ty in
      ctx_add_var name v.id ctx)
    ctx vars

let ctx_add_type_params (vars : type_var list) (ctx : extraction_ctx) :
    extraction_ctx * string list =
  List.fold_left_map
    (fun ctx (var : type_var) -> ctx_add_type_var var.name var.index ctx)
    ctx vars

let ctx_add_type_decl_struct (def : type_decl) (ctx : extraction_ctx) :
    extraction_ctx * string =
  let cons_name = ctx.fmt.struct_constructor def.name in
  let ctx = ctx_add (StructId (AdtId def.def_id)) cons_name ctx in
  (ctx, cons_name)

let ctx_add_type_decl (def : type_decl) (ctx : extraction_ctx) : extraction_ctx
    =
  let def_name = ctx.fmt.type_name def.name in
  let ctx = ctx_add (TypeId (AdtId def.def_id)) def_name ctx in
  ctx

let ctx_add_field (def : type_decl) (field_id : FieldId.id) (field : field)
    (ctx : extraction_ctx) : extraction_ctx * string =
  let name = ctx.fmt.field_name def.name field_id field.field_name in
  let ctx = ctx_add (FieldId (AdtId def.def_id, field_id)) name ctx in
  (ctx, name)

let ctx_add_fields (def : type_decl) (fields : (FieldId.id * field) list)
    (ctx : extraction_ctx) : extraction_ctx * string list =
  List.fold_left_map
    (fun ctx (vid, v) -> ctx_add_field def vid v ctx)
    ctx fields

let ctx_add_variant (def : type_decl) (variant_id : VariantId.id)
    (variant : variant) (ctx : extraction_ctx) : extraction_ctx * string =
  let name = ctx.fmt.variant_name def.name variant.variant_name in
  let ctx = ctx_add (VariantId (AdtId def.def_id, variant_id)) name ctx in
  (ctx, name)

let ctx_add_variants (def : type_decl)
    (variants : (VariantId.id * variant) list) (ctx : extraction_ctx) :
    extraction_ctx * string list =
  List.fold_left_map
    (fun ctx (vid, v) -> ctx_add_variant def vid v ctx)
    ctx variants

let ctx_add_struct (def : type_decl) (ctx : extraction_ctx) :
    extraction_ctx * string =
  let name = ctx.fmt.struct_constructor def.name in
  let ctx = ctx_add (StructId (AdtId def.def_id)) name ctx in
  (ctx, name)

let ctx_add_decrases_clause (def : fun_decl) (ctx : extraction_ctx) :
    extraction_ctx =
  let name = ctx.fmt.decreases_clause_name def.def_id def.basename in
  ctx_add (DecreasesClauseId (A.Regular def.def_id)) name ctx

let ctx_add_global_decl_and_body (def : A.global_decl) (ctx : extraction_ctx) :
    extraction_ctx =
  let name = ctx.fmt.global_name def.name in
  let decl = GlobalId def.def_id in
  let body = FunId (Regular def.body_id, None) in
  let ctx = ctx_add decl (name ^ "_c") ctx in
  let ctx = ctx_add body (name ^ "_body") ctx in
  ctx

let ctx_add_fun_decl (trans_group : bool * pure_fun_translation)
    (def : fun_decl) (ctx : extraction_ctx) : extraction_ctx =
  (* Sanity check: the function should not be a global body - those are handled
   * separately *)
  assert (not def.is_global_decl_body);
  (* Lookup the LLBC def to compute the region group information *)
  let def_id = def.def_id in
  let llbc_def =
    A.FunDeclId.Map.find def_id ctx.trans_ctx.fun_context.fun_decls
  in
  let sg = llbc_def.signature in
  let num_rgs = List.length sg.regions_hierarchy in
  let keep_fwd, (_, backs) = trans_group in
  let num_backs = List.length backs in
  let rg_info =
    match def.back_id with
    | None -> None
    | Some rg_id ->
        let rg = T.RegionGroupId.nth sg.regions_hierarchy rg_id in
        let regions =
          List.map
            (fun rid -> T.RegionVarId.nth sg.region_params rid)
            rg.regions
        in
        let region_names =
          List.map (fun (r : T.region_var) -> r.name) regions
        in
        Some { id = rg_id; region_names }
  in
  let def_id = A.Regular def_id in
  let name =
    ctx.fmt.fun_name def_id def.basename num_rgs rg_info (keep_fwd, num_backs)
  in
  ctx_add (FunId (def_id, def.back_id)) name ctx

type names_map_init = {
  keywords : string list;
  assumed_adts : (assumed_ty * string) list;
  assumed_structs : (assumed_ty * string) list;
  assumed_variants : (assumed_ty * VariantId.id * string) list;
  assumed_functions : (A.assumed_fun_id * RegionGroupId.id option * string) list;
}

(** Initialize a names map with a proper set of keywords/names coming from the
    target language/prover. *)
let initialize_names_map (init : names_map_init) : names_map =
  let name_to_id =
    StringMap.of_list (List.map (fun x -> (x, UnknownId)) init.keywords)
  in
  let names_set = StringSet.of_list init.keywords in
  (* We fist initialize [id_to_name] as empty, because the id of a keyword is [UnknownId].
   * Also note that we don't need this mapping for keywords: we insert keywords only
   * to check collisions. *)
  let id_to_name = IdMap.empty in
  let nm = { id_to_name; name_to_id; names_set } in
  (* For debugging - we are creating bindings for assumed types and functions, so
   * it is ok if we simply use the "show" function (those aren't simply identified
   * by numbers) *)
  let id_to_string = show_id in
  (* Then we add:
   * - the assumed types
   * - the assumed struct constructors
   * - the assumed variants
   * - the assumed functions
   *)
  let nm =
    List.fold_left
      (fun nm (type_id, name) ->
        names_map_add_assumed_type id_to_string type_id name nm)
      nm init.assumed_adts
  in
  let nm =
    List.fold_left
      (fun nm (type_id, name) ->
        names_map_add_assumed_struct id_to_string type_id name nm)
      nm init.assumed_structs
  in
  let nm =
    List.fold_left
      (fun nm (type_id, variant_id, name) ->
        names_map_add_assumed_variant id_to_string type_id variant_id name nm)
      nm init.assumed_variants
  in
  let nm =
    List.fold_left
      (fun nm (fun_id, rg_id, name) ->
        names_map_add_assumed_function id_to_string fun_id rg_id name nm)
      nm init.assumed_functions
  in
  (* Return *)
  nm

let compute_type_decl_name (fmt : formatter) (def : type_decl) : string =
  fmt.type_name def.name

(** A helper function: generates a function suffix from a region group
    information.
    TODO: move all those helpers.
*)
let default_fun_suffix (num_region_groups : int) (rg : region_group_info option)
    ((keep_fwd, num_backs) : bool * int) : string =
  (* There are several cases:
     - [rg] is [Some]: this is a forward function:
       - we add "_fwd"
     - [rg] is [None]: this is a backward function:
       - this function has one extracted backward function:
         - if the forward function has been filtered, we add "_fwd_back":
           the forward function is useless, so the unique backward function
           takes its place, in a way
         - otherwise we add "_back"
       - this function has several backward functions: we add "_back" and an
         additional suffix to identify the precise backward function
     Note that we always add a suffix (in case there are no region groups,
     we could not add the "_fwd" suffix) to prevent name clashes between
     definitions (in particular between type and function definitions).
  *)
  match rg with
  | None -> "_fwd"
  | Some rg ->
      assert (num_region_groups > 0 && num_backs > 0);
      if num_backs = 1 then
        (* Exactly one backward function *)
        if not keep_fwd then "_fwd_back" else "_back"
      else if
        (* Several region groups/backward functions:
           - if all the regions in the group have names, we use those names
           - otherwise we use an index
        *)
        List.for_all Option.is_some rg.region_names
      then
        (* Concatenate the region names *)
        "_back" ^ String.concat "" (List.map Option.get rg.region_names)
      else (* Use the region index *)
        "_back" ^ RegionGroupId.to_string rg.id