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diff --git a/src/SymbolicToPure.ml b/src/SymbolicToPure.ml
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+open Errors
+module Id = Identifiers
+module T = Types
+module V = Values
+module E = Expressions
+module A = CfimAst
+module S = SymbolicAst
+
+type name =
+  | FunName of A.FunDefId.id * V.BackwardFunctionId.id option
+  | TypeName of T.TypeDefId.id
+[@@deriving show, ord]
+
+let name_to_string (n : name) : string = show_name n
+
+module NameOrderedType = struct
+  type t = name
+
+  let compare = compare_name
+
+  let to_string = name_to_string
+
+  let pp_t = pp_name
+
+  let show_t = show_name
+end
+
+module NameMap = Collections.MakeMapInj (NameOrderedType) (Id.NameOrderedType)
+(** Notice that we use the *injective* map to map identifiers to names.
+
+    Of course, even if those names (which are string lists) don't collide,
+    when converting them to strings we can still introduce collisions: we
+    check that later.
+    
+    Note that we use injective maps for sanity: though we write the name
+    generation with collision in mind, it is always good to have such checks.
+ *)
+
+let fun_to_name (fdef : A.fun_def) (bid : V.BackwardFunctionId.id option) :
+    Id.name =
+  let sg = fdef.signature in
+  (* General function to generate a suffix for a region group
+   * (i.e., an abstraction)*)
+  let rg_to_string (rg : T.region_var_group) : string =
+    (* We are just a little bit smart:
+       - if there is exactly one region id in the region group and this region
+         has a name, we use this name
+       - otherwise, we use the region number (note that region names shouldn't
+         start with numbers)
+    *)
+    match rg.T.regions with
+    | [ rid ] -> (
+        let rvar = T.RegionVarId.nth sg.region_params rid in
+        match rvar.name with
+        | None -> T.RegionGroupId.to_string rg.T.id
+        | Some name -> name)
+    | _ -> T.RegionGroupId.to_string rg.T.id
+  in
+  (* There are several cases:
+     - this is a forward function: we add "_fwd"
+     - this is a backward function:
+       - this function has one backward function: we add "_back"
+       - this function has several backward function: we add "_back" and an
+         additional suffix to identify the precise backward function
+  *)
+  let suffix =
+    match bid with
+    | None -> "_fwd"
+    | Some bid -> (
+        match sg.regions_hierarchy with
+        | [] ->
+            failwith "Unreachable"
+            (* we can't get there if we ask for a back function *)
+        | [ _ ] ->
+            (* Exactly one backward function *)
+            "_back"
+        | _ ->
+            (* Several backward functions - note that **we use the backward function id
+             * as if it were a region group id** (there is a direct mapping between the
+             * two - TODO: merge them) *)
+            let rg = V.BackwardFunctionId.nth sg.regions_hierarchy bid in
+            "_back" ^ rg_to_string rg)
+  in
+  (* Final name *)
+  let rec add_to_last (n : Id.name) : Id.name =
+    match n with
+    | [] -> failwith "Unreachable"
+    | [ x ] -> [ x ^ suffix ]
+    | x :: n -> x :: add_to_last n
+  in
+  add_to_last fdef.name