path: root/compiler/InterpreterLoopsJoinCtxs.ml

open Types
open Values
open Contexts
open Utils
open TypesUtils
open ValuesUtils
open InterpreterUtils
open InterpreterBorrows
open InterpreterLoopsCore
open InterpreterLoopsMatchCtxs
open Errors

(** The local logger *)
let log = Logging.loops_join_ctxs_log

(** Utility.

    An environment augmented with information about its borrows/loans/abstractions
    for the purpose of merging abstractions together.
    We provide functions to update this information when merging two abstractions
    together. We use it in {!reduce_ctx} and {!collapse_ctx}.
*)
type ctx_with_info = { ctx : eval_ctx; info : abs_borrows_loans_maps }

let ctx_with_info_merge_into_first_abs (span : Meta.span) (abs_kind : abs_kind)
    (can_end : bool) (merge_funs : merge_duplicates_funcs option)
    (ctx : ctx_with_info) (abs_id0 : AbstractionId.id)
    (abs_id1 : AbstractionId.id) : ctx_with_info =
  (* Compute the new context and the new abstraction id *)
  let nctx, nabs_id =
    merge_into_first_abstraction span abs_kind can_end merge_funs ctx.ctx
      abs_id0 abs_id1
  in
  let nabs = ctx_lookup_abs nctx nabs_id in
  (* Update the information *)
  let {
    abs_to_borrows = nabs_to_borrows;
    abs_to_loans = nabs_to_loans;
    borrow_to_abs = borrow_to_nabs;
    loan_to_abs = loan_to_nabs;
    _;
  } =
    compute_abs_borrows_loans_maps span (fun _ -> true) [ EAbs nabs ]
  in
  let { abs_ids; abs_to_borrows; abs_to_loans; borrow_to_abs; loan_to_abs } =
    ctx.info
  in
  let abs_ids =
    List.filter_map
      (fun id ->
        if id = abs_id0 then Some nabs_id
        else if id = abs_id1 then None
        else Some id)
      abs_ids
  in
  (* Update the maps from makred borrows/loans to abstractions *)
  let update_to_abs abs_to to_nabs to_abs =
    (* Remove the old bindings *)
    let abs0_elems = AbstractionId.Map.find abs_id0 abs_to in
    let abs1_elems = AbstractionId.Map.find abs_id1 abs_to in
    let abs01_elems = MarkerBorrowId.Set.union abs0_elems abs1_elems in
    let to_abs =
      MarkerBorrowId.Map.filter
        (fun id _ -> not (MarkerBorrowId.Set.mem id abs01_elems))
        to_abs
    in
    (* Add the new ones *)
    let merge _ _ _ =
      (* We shouldn't have twice the same key *)
      craise __FILE__ __LINE__ span "Unreachable"
    in
    MarkerBorrowId.Map.union merge to_nabs to_abs
  in
  let borrow_to_abs =
    update_to_abs abs_to_borrows borrow_to_nabs borrow_to_abs
  in
  let loan_to_abs = update_to_abs abs_to_loans loan_to_nabs loan_to_abs in

  (* Update the maps from abstractions to marked borrows/loans *)
  let update_abs_to nabs_to abs_to =
    AbstractionId.Map.add_strict nabs_id
      (AbstractionId.Map.find nabs_id nabs_to)
      (AbstractionId.Map.remove abs_id0
         (AbstractionId.Map.remove abs_id1 abs_to))
  in
  let abs_to_borrows = update_abs_to nabs_to_borrows abs_to_borrows in
  let abs_to_loans = update_abs_to nabs_to_loans abs_to_loans in
  let info =
    { abs_ids; abs_to_borrows; abs_to_loans; borrow_to_abs; loan_to_abs }
  in
  { ctx = nctx; info }

exception AbsToMerge of abstraction_id * abstraction_id

(** Repeatedly iterate through the borrows/loans in an environment and merge the
    abstractions that have to be merged according to a user-provided policy. *)
let repeat_iter_borrows_merge (span : Meta.span) (old_ids : ids_sets)
    (abs_kind : abs_kind) (can_end : bool)
    (merge_funs : merge_duplicates_funcs option)
    (iter : ctx_with_info -> ('a -> unit) -> unit)
    (policy : ctx_with_info -> 'a -> (abstraction_id * abstraction_id) option)
    (ctx : eval_ctx) : eval_ctx =
  (* Compute the information *)
  let ctx =
    let is_fresh_abs_id (id : AbstractionId.id) : bool =
      not (AbstractionId.Set.mem id old_ids.aids)
    in
    let explore (abs : abs) = is_fresh_abs_id abs.abs_id in
    let info = compute_abs_borrows_loans_maps span explore ctx.env in
    { ctx; info }
  in
  (* Explore and merge *)
  let rec explore_merge (ctx : ctx_with_info) : eval_ctx =
    try
      iter ctx (fun x ->
          (* Check if we need to merge some abstractions *)
          match policy ctx x with
          | None -> (* No *) ()
          | Some (abs_id0, abs_id1) ->
              (* Yes: raise an exception *)
              raise (AbsToMerge (abs_id0, abs_id1)));
      (* No exception raise: return the current context *)
      ctx.ctx
    with AbsToMerge (abs_id0, abs_id1) ->
      (* Merge and recurse *)
      let ctx =
        ctx_with_info_merge_into_first_abs span abs_kind can_end merge_funs ctx
          abs_id0 abs_id1
      in
      explore_merge ctx
  in
  explore_merge ctx

(** Reduce an environment.

    We do this to simplify an environment, for the purpose of finding a loop
    fixed point.

    We do the following:
    - we look for all the *new* dummy values (we use sets of old ids to decide
      wether a value is new or not) and convert them into abstractions
    - whenever there is a new abstraction in the context, and some of its
      its borrows are associated to loans in another new abstraction, we
      merge them.
    In effect, this allows us to merge newly introduced abstractions/borrows
    with their parent abstractions.
    
    For instance, looking at the [list_nth_mut] example, when evaluating the
    first loop iteration, we start in the following environment:
    {[
      abs@0 { ML l0 }
      ls -> MB l0 (s2 : loops::List<T>)
      i -> s1 : u32
    ]}
    
    and get the following environment upon reaching the [Continue] statement:
    {[
      abs@0 { ML l0 }
      ls -> MB l4 (s@6 : loops::List<T>)
      i -> s@7 : u32
      _@1 -> MB l0 (loops::List::Cons (ML l1, ML l2))
      _@2 -> MB l2 (@Box (ML l4))                      // tail
      _@3 -> MB l1 (s@3 : T)                           // hd
    ]}
    
    In this new environment, the dummy variables [_@1], [_@2] and [_@3] are
    considered as new.
    
    We first convert the new dummy values to abstractions. It gives:
    {[
      abs@0 { ML l0 }
      ls -> MB l4 (s@6 : loops::List<T>)
      i -> s@7 : u32
      abs@1 { MB l0, ML l1, ML l2 }
      abs@2 { MB l2, ML l4 }
      abs@3 { MB l1 }
    ]}

    We finally merge the new abstractions together (abs@1 and abs@2 because
    of l2, and abs@1 and abs@3 because of l1). It gives:
    {[
      abs@0 { ML l0 }
      ls -> MB l4 (s@6 : loops::List<T>)
      i -> s@7 : u32
      abs@4 { MB l0, ML l4 }
    ]}

    - If [merge_funs] is [None], we check that there are no markers in the environments.
      This is the "reduce" operation.
    - If [merge_funs] is [Some _], when merging abstractions together, we merge the pairs
      of borrows and the pairs of loans with the same markers **if this marker is not**
      [PNone]. This is useful to reuse the reduce operation to implement the collapse.
      Note that we ignore borrows/loans with the [PNone] marker: the goal of the collapse
      operation is to *eliminate* markers, not to simplify the environment.

      For instance, when merging:
      {[
        abs@0 { ML l0, |MB l1| }
        abs@1 { MB l0, ︙MB l1︙ }
      ]}
      We get:
      {[
        abs@2 { MB l1 }
      ]}
 *)
let reduce_ctx_with_markers (merge_funs : merge_duplicates_funcs option)
    (span : Meta.span) (loop_id : LoopId.id) (old_ids : ids_sets)
    (ctx0 : eval_ctx) : eval_ctx =
  (* Debug *)
  log#ldebug
    (lazy
      ("reduce_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids ^ "\n\n- ctx0:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx0
      ^ "\n\n"));

  let with_markers = merge_funs <> None in

  let abs_kind : abs_kind = Loop (loop_id, None, LoopSynthInput) in
  let can_end = true in
  let destructure_shared_values = true in
  let is_fresh_did (id : DummyVarId.id) : bool =
    not (DummyVarId.Set.mem id old_ids.dids)
  in
  (* Convert the dummy values to abstractions (note that when we convert
     values to abstractions, the resulting abstraction should be destructured) *)
  (* Note that we preserve the order of the dummy values: we replace them with
     abstractions in place - this makes matching easier *)
  let env =
    List.concat
      (List.map
         (fun ee ->
           match ee with
           | EAbs _ | EFrame | EBinding (BVar _, _) -> [ ee ]
           | EBinding (BDummy id, v) ->
               if is_fresh_did id then
                 let absl =
                   convert_value_to_abstractions span abs_kind can_end
                     destructure_shared_values ctx0 v
                 in
                 List.map (fun abs -> EAbs abs) absl
               else [ ee ])
         ctx0.env)
  in
  let ctx = { ctx0 with env } in
  log#ldebug
    (lazy
      ("reduce_ctx: after converting values to abstractions:\n"
     ^ show_ids_sets old_ids ^ "\n\n- ctx:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  log#ldebug
    (lazy
      ("reduce_ctx: after decomposing the shared values in the abstractions:\n"
     ^ show_ids_sets old_ids ^ "\n\n- ctx:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  (*
   * Merge all the mergeable abs.
   *)
  (* We iterate over the *new* abstractions, then over the loans in the abstractions.
     We do this because we want to control the order in which abstractions
     are merged (the ids are iterated in increasing order). Otherwise, we
     could simply iterate over all the borrows in [loan_to_abs]... *)
  let iterate ctx f =
    List.iter
      (fun abs_id0 ->
        let lids = AbstractionId.Map.find abs_id0 ctx.info.abs_to_loans in
        MarkerBorrowId.Set.iter (fun lid -> f (abs_id0, lid)) lids)
      ctx.info.abs_ids
  in
  (* Given a loan, check if there is a fresh abstraction with the corresponding borrow *)
  let merge_policy ctx (abs_id0, lid) =
    if not with_markers then
      sanity_check __FILE__ __LINE__ (fst lid = PNone) span;
    (* If we use markers: we are doing a collapse, which means we attempt
       to eliminate markers (and this is the only goal of the operation).
       We thus ignore the non-marked values (we merge non-marked values
       when doing a "real" reduce, to simplify the environment in order
       to converge to a fixed-point, for instance). *)
    if with_markers && fst lid = PNone then None
    else
      (* Find the borrow corresponding to the loan we want to eliminate *)
      match MarkerBorrowId.Map.find_opt lid ctx.info.borrow_to_abs with
      | None -> (* Nothing to to *) None
      | Some abs_ids1 -> (
          (* We need to merge *)
          match AbstractionId.Set.elements abs_ids1 with
          | [] -> None
          | abs_id1 :: _ ->
              log#ldebug
                (lazy
                  ("reduce_ctx: merging abstraction "
                  ^ AbstractionId.to_string abs_id1
                  ^ " into "
                  ^ AbstractionId.to_string abs_id0
                  ^ ":\n\n"
                  ^ eval_ctx_to_string ~span:(Some span) ctx.ctx));
              Some (abs_id0, abs_id1))
  in
  (* Iterate and merge *)
  let ctx =
    repeat_iter_borrows_merge span old_ids abs_kind can_end merge_funs iterate
      merge_policy ctx
  in

  log#ldebug
    (lazy
      ("reduce_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids
     ^ "\n\n- after reduce:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  (* Reorder the loans and borrows in the fresh abstractions - note that we may
     not have eliminated all the markers at this point. *)
  let ctx = reorder_loans_borrows_in_fresh_abs span true old_ids.aids ctx in

  log#ldebug
    (lazy
      ("reduce_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids
     ^ "\n\n- after reduce and reorder borrows/loans:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  (* Return the new context *)
  ctx

(** Reduce_ctx can only be called in a context with no markers *)
let reduce_ctx = reduce_ctx_with_markers None

(** Auxiliary function for collapse (see below).

   We traverse all abstractions, and merge abstractions when they contain the same element,
   but with dual markers (i.e., [PLeft] and [PRight]).

   For instance, if we have the abstractions

   {[
     abs@0 { | MB l0 _ |, ML l1 }
     abs@1 { ︙MB l0 _ ︙, ML l2 }
   ]}

   We merge abs@0 and abs@1 into a new abstraction abs@2. This allows us to
   eliminate the markers used for [MB l0]:
   {[
     abs@2 { MB l0 _, ML l1, ML l2 }
   ]}
*)
let collapse_ctx_collapse (span : Meta.span) (loop_id : LoopId.id)
    (merge_funs : merge_duplicates_funcs) (old_ids : ids_sets) (ctx : eval_ctx)
    : eval_ctx =
  (* Debug *)
  log#ldebug
    (lazy
      ("collapse_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids
     ^ "\n\n- initial ctx:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  let abs_kind : abs_kind = Loop (loop_id, None, LoopSynthInput) in
  let can_end = true in

  let invert_proj_marker = function
    | PNone -> craise __FILE__ __LINE__ span "Unreachable"
    | PLeft -> PRight
    | PRight -> PLeft
  in

  (* Merge all the mergeable abs where the same element in present in both abs,
     but with left and right markers respectively.
  *)
  (* The iter function: iterate over the abstractions, and inside an abstraction
     over the borrows then the loans *)
  let iter ctx f =
    List.iter
      (fun abs_id0 ->
        (* Small helper *)
        let iterate is_borrow =
          let m =
            if is_borrow then ctx.info.abs_to_borrows else ctx.info.abs_to_loans
          in
          let ids = AbstractionId.Map.find abs_id0 m in
          MarkerBorrowId.Set.iter (fun id -> f (abs_id0, is_borrow, id)) ids
        in
        (* Iterate over the borrows *)
        iterate true;
        (* Iterate over the loans *)
        iterate false)
      ctx.info.abs_ids
  in
  (* Small utility: check if we need to swap two region abstractions before
     merging them.

     We might have to swap the order to make sure that if there
     are loans in one abstraction and the corresponding borrows
     in the other they get properly merged (if we merge them in the wrong
     order, we might introduce borrowing cycles).

     Example:
     If we are merging abs0 and abs1 because of the marked value
     [MB l0]:
     {[
       abs0 { |MB l0|, MB l1 }
       abs1 { ︙MB l0︙, ML l1 }
     ]}
     we want to make sure that we swap them (abs1 goes to the
     left) to make sure [MB l1] and [ML l1] get properly eliminated.

     Remark: in case there is a borrowing cycle between the two abstractions
     (which shouldn't happen) then there isn't much we can do, and whatever
     the order in which we merge, we will preserve the cycle.
  *)
  let swap_abs info abs_id0 abs_id1 =
    let abs0_borrows =
      BorrowId.Set.of_list
        (List.map snd
           (MarkerBorrowId.Set.elements
              (AbstractionId.Map.find abs_id0 info.abs_to_borrows)))
    in
    let abs1_loans =
      BorrowId.Set.of_list
        (List.map snd
           (MarkerBorrowId.Set.elements
              (AbstractionId.Map.find abs_id1 info.abs_to_loans)))
    in
    not (BorrowId.Set.disjoint abs0_borrows abs1_loans)
  in
  (* Check if there is an abstraction with the same borrow/loan id and the dual
     marker, and merge them if it is the case. *)
  let merge_policy ctx (abs_id0, is_borrow, (pm, bid)) =
    if pm = PNone then None
    else
      (* Look for an element with the dual marker *)
      match
        MarkerBorrowId.Map.find_opt
          (invert_proj_marker pm, bid)
          (if is_borrow then ctx.info.borrow_to_abs else ctx.info.loan_to_abs)
      with
      | None -> (* Nothing to do *) None
      | Some abs_ids1 -> (
          (* We need to merge *)
          match AbstractionId.Set.elements abs_ids1 with
          | [] -> None
          | abs_id1 :: _ ->
              (* Check if we need to swap *)
              Some
                (if swap_abs ctx.info abs_id0 abs_id1 then (abs_id1, abs_id0)
                 else (abs_id0, abs_id1)))
  in
  (* Iterate and merge *)
  let ctx =
    repeat_iter_borrows_merge span old_ids abs_kind can_end (Some merge_funs)
      iter merge_policy ctx
  in

  log#ldebug
    (lazy
      ("collapse_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids
     ^ "\n\n- after collapse:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  (* Reorder the loans and borrows in the fresh abstractions - note that we may
     not have eliminated all the markers yet *)
  let ctx = reorder_loans_borrows_in_fresh_abs span true old_ids.aids ctx in

  log#ldebug
    (lazy
      ("collapse_ctx:\n\n- fixed_ids:\n" ^ show_ids_sets old_ids
     ^ "\n\n- after collapse and reorder borrows/loans:\n"
      ^ eval_ctx_to_string ~span:(Some span) ctx
      ^ "\n\n"));

  (* Return the new context *)
  ctx

(** Small utility: check whether an environment contains markers *)
let eval_ctx_has_markers (ctx : eval_ctx) : bool =
  let visitor =
    object
      inherit [_] iter_eval_ctx

      method! visit_proj_marker _ pm =
        match pm with PNone -> () | PLeft | PRight -> raise Found
    end
  in
  try
    visitor#visit_eval_ctx () ctx;
    false
  with Found -> true

(** Collapse two environments containing projection markers; this function is called after
    joining environments.

    The collapse is done in two steps.

    First, we reduce the environment, merging any two pair of fresh abstractions
    which contain a loan (in one) and its corresponding borrow (in the other).
    For instance, we merge abs@0 and abs@1 below:
    {[
      abs@0 { |ML l0|, ML l1 }
      abs@1 { |MB l0 _|, ML l2 }
                ~~>
      abs@2 { ML l1, ML l2 }
    ]}
    Note that we also merge abstractions when the loan/borrow don't have the same
    markers. For instance, below:
    {[
      abs@0 { ML l0, ML l1 } // ML l0 doesn't have markers
      abs@1 { |MB l0 _|, ML l2 }
                ~~>
      abs@2 { ︙ML l0︙, ML l1, ML l2 }
    ]}

    Second, we merge abstractions containing the same element with left and right markers
    respectively. For instance:
    {[
      abs@0 { | MB l0 _ |, ML l1 }
      abs@1 { ︙MB l0 _ ︙, ML l2 }
                ~~>
      abs@2 { MB l0 _, ML l1, ML l2 }
    ]}

    At the end of the second step, all markers should have been removed from the resulting
    environment.
*)
let collapse_ctx (span : Meta.span) (loop_id : LoopId.id)
    (merge_funs : merge_duplicates_funcs) (old_ids : ids_sets) (ctx0 : eval_ctx)
    : eval_ctx =
  let ctx =
    reduce_ctx_with_markers (Some merge_funs) span loop_id old_ids ctx0
  in
  let ctx = collapse_ctx_collapse span loop_id merge_funs old_ids ctx in
  (* Sanity check: there are no markers remaining *)
  sanity_check __FILE__ __LINE__ (not (eval_ctx_has_markers ctx)) span;
  ctx

let mk_collapse_ctx_merge_duplicate_funs (span : Meta.span)
    (loop_id : LoopId.id) (ctx : eval_ctx) : merge_duplicates_funcs =
  (* Rem.: the merge functions raise exceptions (that we catch). *)
  let module S : MatchJoinState = struct
    let span = span
    let loop_id = loop_id
    let nabs = ref []
  end in
  let module JM = MakeJoinMatcher (S) in
  let module M = MakeMatcher (JM) in
  (* Functions to match avalues (see {!merge_duplicates_funcs}).

     Those functions are used to merge borrows/loans with the *same ids*.

     They will always be called on destructured avalues (whose children are
     [AIgnored] - we enforce that through sanity checks). We rely on the join
     matcher [JM] to match the concrete values (for shared loans for instance).
     Note that the join matcher doesn't implement match functions for avalues
     (see the comments in {!MakeJoinMatcher}.
  *)
  let merge_amut_borrows id ty0 _pm0 child0 _ty1 _pm1 child1 =
    (* Sanity checks *)
    sanity_check __FILE__ __LINE__ (is_aignored child0.value) span;
    sanity_check __FILE__ __LINE__ (is_aignored child1.value) span;

    (* We need to pick a type for the avalue. The types on the left and on the
       right may use different regions: it doesn't really matter (here, we pick
       the one from the left), because we will merge those regions together
       anyway (see the comments for {!merge_into_first_abstraction}).
    *)
    let ty = ty0 in
    let child = child0 in
    let value = ABorrow (AMutBorrow (PNone, id, child)) in
    { value; ty }
  in

  let merge_ashared_borrows id ty0 _pm0 ty1 _pm1 =
    (* Sanity checks *)
    let _ =
      let _, ty0, _ = ty_as_ref ty0 in
      let _, ty1, _ = ty_as_ref ty1 in
      sanity_check __FILE__ __LINE__
        (not (ty_has_borrows ctx.type_ctx.type_infos ty0))
        span;
      sanity_check __FILE__ __LINE__
        (not (ty_has_borrows ctx.type_ctx.type_infos ty1))
        span
    in

    (* Same remarks as for [merge_amut_borrows] *)
    let ty = ty0 in
    let value = ABorrow (ASharedBorrow (PNone, id)) in
    { value; ty }
  in

  let merge_amut_loans id ty0 _pm0 child0 _ty1 _pm1 child1 =
    (* Sanity checks *)
    sanity_check __FILE__ __LINE__ (is_aignored child0.value) span;
    sanity_check __FILE__ __LINE__ (is_aignored child1.value) span;

    (* Same remarks as for [merge_amut_borrows] *)
    let ty = ty0 in
    let child = child0 in
    let value = ALoan (AMutLoan (PNone, id, child)) in
    { value; ty }
  in
  let merge_ashared_loans ids ty0 _pm0 (sv0 : typed_value) child0 _ty1 _pm1
      (sv1 : typed_value) child1 =
    (* Sanity checks *)
    sanity_check __FILE__ __LINE__ (is_aignored child0.value) span;
    sanity_check __FILE__ __LINE__ (is_aignored child1.value) span;
    (* Same remarks as for [merge_amut_borrows].

       This time we need to also merge the shared values. We rely on the
       join matcher [JM] to do so.
    *)
    sanity_check __FILE__ __LINE__
      (not (value_has_loans_or_borrows ctx sv0.value))
      span;
    sanity_check __FILE__ __LINE__
      (not (value_has_loans_or_borrows ctx sv1.value))
      span;

    let ty = ty0 in
    let child = child0 in
    let sv = M.match_typed_values ctx ctx sv0 sv1 in
    let value = ALoan (ASharedLoan (PNone, ids, sv, child)) in
    { value; ty }
  in
  {
    merge_amut_borrows;
    merge_ashared_borrows;
    merge_amut_loans;
    merge_ashared_loans;
  }

let merge_into_first_abstraction (span : Meta.span) (loop_id : LoopId.id)
    (abs_kind : abs_kind) (can_end : bool) (ctx : eval_ctx)
    (aid0 : AbstractionId.id) (aid1 : AbstractionId.id) :
    eval_ctx * AbstractionId.id =
  let merge_funs = mk_collapse_ctx_merge_duplicate_funs span loop_id ctx in
  merge_into_first_abstraction span abs_kind can_end (Some merge_funs) ctx aid0
    aid1

(** Collapse an environment, merging the duplicated borrows/loans.

    This function simply calls {!collapse_ctx} with the proper merging functions.

    We do this because when we join environments, we may introduce duplicated
    loans and borrows. See the explanations for {!join_ctxs}.
 *)
let collapse_ctx_with_merge (span : Meta.span) (loop_id : LoopId.id)
    (old_ids : ids_sets) (ctx : eval_ctx) : eval_ctx =
  let merge_funs = mk_collapse_ctx_merge_duplicate_funs span loop_id ctx in
  try collapse_ctx span loop_id merge_funs old_ids ctx
  with ValueMatchFailure _ -> craise __FILE__ __LINE__ span "Unexpected"

let join_ctxs (span : Meta.span) (loop_id : LoopId.id) (fixed_ids : ids_sets)
    (ctx0 : eval_ctx) (ctx1 : eval_ctx) : ctx_or_update =
  (* Debug *)
  log#ldebug
    (lazy
      ("join_ctxs:\n\n- fixed_ids:\n" ^ show_ids_sets fixed_ids
     ^ "\n\n- ctx0:\n"
      ^ eval_ctx_to_string_no_filter ~span:(Some span) ctx0
      ^ "\n\n- ctx1:\n"
      ^ eval_ctx_to_string_no_filter ~span:(Some span) ctx1
      ^ "\n\n"));

  let env0 = List.rev ctx0.env in
  let env1 = List.rev ctx1.env in
  let nabs = ref [] in

  (* Explore the environments. *)
  let join_suffixes (env0 : env) (env1 : env) : env =
    (* Debug *)
    log#ldebug
      (lazy
        ("join_suffixes:\n\n- fixed_ids:\n" ^ show_ids_sets fixed_ids
       ^ "\n\n- ctx0:\n"
        ^ eval_ctx_to_string_no_filter ~span:(Some span)
            { ctx0 with env = List.rev env0 }
        ^ "\n\n- ctx1:\n"
        ^ eval_ctx_to_string_no_filter ~span:(Some span)
            { ctx1 with env = List.rev env1 }
        ^ "\n\n"));

    (* Sanity check: there are no values/abstractions which should be in the prefix *)
    let check_valid (ee : env_elem) : unit =
      match ee with
      | EBinding (BVar _, _) ->
          (* Variables are necessarily in the prefix *)
          craise __FILE__ __LINE__ span "Unreachable"
      | EBinding (BDummy did, _) ->
          sanity_check __FILE__ __LINE__
            (not (DummyVarId.Set.mem did fixed_ids.dids))
            span
      | EAbs abs ->
          sanity_check __FILE__ __LINE__
            (not (AbstractionId.Set.mem abs.abs_id fixed_ids.aids))
            span
      | EFrame ->
          (* This should have been eliminated *)
          craise __FILE__ __LINE__ span "Unreachable"
    in

    (* Add projection marker to all abstractions in the left and right environments *)
    let add_marker (pm : proj_marker) (ee : env_elem) : env_elem =
      match ee with
      | EAbs abs -> EAbs (abs_add_marker span ctx0 pm abs)
      | x -> x
    in

    let env0 = List.map (add_marker PLeft) env0 in
    let env1 = List.map (add_marker PRight) env1 in

    List.iter check_valid env0;
    List.iter check_valid env1;
    (* Concatenate the suffixes and append the abstractions introduced while
       joining the prefixes *)
    let absl = List.map (fun abs -> EAbs abs) (List.rev !nabs) in
    List.concat [ env0; env1; absl ]
  in

  let module S : MatchJoinState = struct
    let span = span
    let loop_id = loop_id
    let nabs = nabs
  end in
  let module JM = MakeJoinMatcher (S) in
  let module M = MakeMatcher (JM) in
  (* Rem.: this function raises exceptions *)
  let rec join_prefixes (env0 : env) (env1 : env) : env =
    match (env0, env1) with
    | ( (EBinding (BDummy b0, v0) as var0) :: env0',
        (EBinding (BDummy b1, v1) as var1) :: env1' ) ->
        (* Debug *)
        log#ldebug
          (lazy
            ("join_prefixes: BDummys:\n\n- fixed_ids:\n" ^ "\n"
           ^ show_ids_sets fixed_ids ^ "\n\n- value0:\n"
            ^ env_elem_to_string span ctx0 var0
            ^ "\n\n- value1:\n"
            ^ env_elem_to_string span ctx1 var1
            ^ "\n\n"));

        (* Two cases: the dummy value is an old value, in which case the bindings
           must be the same and we must join their values. Otherwise, it means we
           are not in the prefix anymore *)
        if DummyVarId.Set.mem b0 fixed_ids.dids then (
          (* Still in the prefix: match the values *)
          sanity_check __FILE__ __LINE__ (b0 = b1) span;
          let b = b0 in
          let v = M.match_typed_values ctx0 ctx1 v0 v1 in
          let var = EBinding (BDummy b, v) in
          (* Continue *)
          var :: join_prefixes env0' env1')
        else (* Not in the prefix anymore *)
          join_suffixes env0 env1
    | ( (EBinding (BVar b0, v0) as var0) :: env0',
        (EBinding (BVar b1, v1) as var1) :: env1' ) ->
        (* Debug *)
        log#ldebug
          (lazy
            ("join_prefixes: BVars:\n\n- fixed_ids:\n" ^ "\n"
           ^ show_ids_sets fixed_ids ^ "\n\n- value0:\n"
            ^ env_elem_to_string span ctx0 var0
            ^ "\n\n- value1:\n"
            ^ env_elem_to_string span ctx1 var1
            ^ "\n\n"));

        (* Variable bindings *must* be in the prefix and consequently their
           ids must be the same *)
        sanity_check __FILE__ __LINE__ (b0 = b1) span;
        (* Match the values *)
        let b = b0 in
        let v = M.match_typed_values ctx0 ctx1 v0 v1 in
        let var = EBinding (BVar b, v) in
        (* Continue *)
        var :: join_prefixes env0' env1'
    | (EAbs abs0 as abs) :: env0', EAbs abs1 :: env1' ->
        (* Debug *)
        log#ldebug
          (lazy
            ("join_prefixes: Abs:\n\n- fixed_ids:\n" ^ "\n"
           ^ show_ids_sets fixed_ids ^ "\n\n- abs0:\n"
            ^ abs_to_string span ctx0 abs0
            ^ "\n\n- abs1:\n"
            ^ abs_to_string span ctx1 abs1
            ^ "\n\n"));

        (* Same as for the dummy values: there are two cases *)
        if AbstractionId.Set.mem abs0.abs_id fixed_ids.aids then (
          (* Still in the prefix: the abstractions must be the same *)
          sanity_check __FILE__ __LINE__ (abs0 = abs1) span;
          (* Continue *)
          abs :: join_prefixes env0' env1')
        else (* Not in the prefix anymore *)
          join_suffixes env0 env1
    | _ ->
        (* The elements don't match: we are not in the prefix anymore *)
        join_suffixes env0 env1
  in

  try
    (* Remove the frame delimiter (the first element of an environment is a frame delimiter) *)
    let env0, env1 =
      match (env0, env1) with
      | EFrame :: env0, EFrame :: env1 -> (env0, env1)
      | _ -> craise __FILE__ __LINE__ span "Unreachable"
    in

    log#ldebug
      (lazy
        ("- env0:\n" ^ show_env env0 ^ "\n\n- env1:\n" ^ show_env env1 ^ "\n\n"));

    let env = List.rev (EFrame :: join_prefixes env0 env1) in

    (* Construct the joined context - of course, the type, fun, etc. contexts
     * should be the same in the two contexts *)
    let {
      type_ctx;
      fun_ctx;
      global_ctx;
      trait_decls_ctx;
      trait_impls_ctx;
      region_groups;
      type_vars;
      const_generic_vars;
      const_generic_vars_map;
      norm_trait_types;
      env = _;
      ended_regions = ended_regions0;
    } =
      ctx0
    in
    let {
      type_ctx = _;
      fun_ctx = _;
      global_ctx = _;
      trait_decls_ctx = _;
      trait_impls_ctx = _;
      region_groups = _;
      type_vars = _;
      const_generic_vars = _;
      const_generic_vars_map = _;
      norm_trait_types = _;
      env = _;
      ended_regions = ended_regions1;
    } =
      ctx1
    in
    let ended_regions = RegionId.Set.union ended_regions0 ended_regions1 in
    Ok
      {
        type_ctx;
        fun_ctx;
        global_ctx;
        trait_decls_ctx;
        trait_impls_ctx;
        region_groups;
        type_vars;
        const_generic_vars;
        const_generic_vars_map;
        norm_trait_types;
        env;
        ended_regions;
      }
  with ValueMatchFailure e -> Error e

(** Destructure all the new abstractions *)
let destructure_new_abs (span : Meta.span) (loop_id : LoopId.id)
    (old_abs_ids : AbstractionId.Set.t) (ctx : eval_ctx) : eval_ctx =
  let abs_kind : abs_kind = Loop (loop_id, None, LoopSynthInput) in
  let can_end = true in
  let destructure_shared_values = true in
  let is_fresh_abs_id (id : AbstractionId.id) : bool =
    not (AbstractionId.Set.mem id old_abs_ids)
  in
  let env =
    env_map_abs
      (fun abs ->
        if is_fresh_abs_id abs.abs_id then
          let abs =
            destructure_abs span abs_kind can_end destructure_shared_values ctx
              abs
          in
          abs
        else abs)
      ctx.env
  in
  { ctx with env }

(** Refresh the ids of the fresh abstractions.

    We do this because {!prepare_ashared_loans} introduces some non-fixed
    abstractions in contexts which are later joined: we have to make sure two
    contexts we join don't have non-fixed abstractions with the same ids.
  *)
let refresh_abs (old_abs : AbstractionId.Set.t) (ctx : eval_ctx) : eval_ctx =
  let ids, _ = compute_ctx_ids ctx in
  let abs_to_refresh = AbstractionId.Set.diff ids.aids old_abs in
  let aids_subst =
    List.map
      (fun id -> (id, fresh_abstraction_id ()))
      (AbstractionId.Set.elements abs_to_refresh)
  in
  let aids_subst = AbstractionId.Map.of_list aids_subst in
  let subst id =
    match AbstractionId.Map.find_opt id aids_subst with
    | None -> id
    | Some id -> id
  in
  let env =
    Substitute.env_subst_ids
      (fun x -> x)
      (fun x -> x)
      (fun x -> x)
      (fun x -> x)
      (fun x -> x)
      subst ctx.env
  in
  { ctx with env }

let loop_join_origin_with_continue_ctxs (config : config) (span : Meta.span)
    (loop_id : LoopId.id) (fixed_ids : ids_sets) (old_ctx : eval_ctx)
    (ctxl : eval_ctx list) : (eval_ctx * eval_ctx list) * eval_ctx =
  (* # Join with the new contexts, one by one

     For every context, we repeteadly attempt to join it with the current
     result of the join: if we fail (because we need to end loans for instance),
     we update the context and retry.
     Rem.: we should never have to end loans in the aggregated context, only
     in the one we are trying to add to the join.
  *)
  let joined_ctx = ref old_ctx in
  let rec join_one_aux (ctx : eval_ctx) : eval_ctx =
    match join_ctxs span loop_id fixed_ids !joined_ctx ctx with
    | Ok nctx ->
        joined_ctx := nctx;
        ctx
    | Error err ->
        let ctx =
          match err with
          | LoanInRight bid ->
              InterpreterBorrows.end_borrow_no_synth config span bid ctx
          | LoansInRight bids ->
              InterpreterBorrows.end_borrows_no_synth config span bids ctx
          | AbsInRight _ | AbsInLeft _ | LoanInLeft _ | LoansInLeft _ ->
              craise __FILE__ __LINE__ span "Unexpected"
        in
        join_one_aux ctx
  in
  let join_one (ctx : eval_ctx) : eval_ctx =
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: initial ctx:\n"
        ^ eval_ctx_to_string ~span:(Some span) ctx));

    (* Destructure the abstractions introduced in the new context *)
    let ctx = destructure_new_abs span loop_id fixed_ids.aids ctx in
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: after destructure:\n"
        ^ eval_ctx_to_string ~span:(Some span) ctx));

    (* Reduce the context we want to add to the join *)
    let ctx = reduce_ctx span loop_id fixed_ids ctx in
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: after reduce:\n"
        ^ eval_ctx_to_string ~span:(Some span) ctx));

    (* Refresh the fresh abstractions *)
    let ctx = refresh_abs fixed_ids.aids ctx in

    (* Join the two contexts  *)
    let ctx1 = join_one_aux ctx in
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: after join:\n"
        ^ eval_ctx_to_string ~span:(Some span) ctx1));

    (* Collapse to eliminate the markers *)
    joined_ctx := collapse_ctx_with_merge span loop_id fixed_ids !joined_ctx;
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: after join-collapse:\n"
        ^ eval_ctx_to_string ~span:(Some span) !joined_ctx));

    (* Reduce again to reach a fixed point *)
    joined_ctx := reduce_ctx span loop_id fixed_ids !joined_ctx;
    log#ldebug
      (lazy
        ("loop_join_origin_with_continue_ctxs:join_one: after last reduce:\n"
        ^ eval_ctx_to_string ~span:(Some span) !joined_ctx));

    (* Sanity check *)
    if !Config.sanity_checks then Invariants.check_invariants span !joined_ctx;
    (* Return *)
    ctx1
  in

  let ctxl = List.map join_one ctxl in

  (* # Return *)
  ((old_ctx, ctxl), !joined_ctx)