Source file constant_propagation.ml

(****************************************************************************)
(*     Sail                                                                 *)
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(*  are subject to the BSD two-clause licence below.                        *)
(*                                                                          *)
(*  The ASL derived parts of the ARMv8.3 specification in                   *)
(*  aarch64/no_vector and aarch64/full are copyright ARM Ltd.               *)
(*                                                                          *)
(*  Copyright (c) 2013-2021                                                 *)
(*    Kathyrn Gray                                                          *)
(*    Shaked Flur                                                           *)
(*    Stephen Kell                                                          *)
(*    Gabriel Kerneis                                                       *)
(*    Robert Norton-Wright                                                  *)
(*    Christopher Pulte                                                     *)
(*    Peter Sewell                                                          *)
(*    Alasdair Armstrong                                                    *)
(*    Brian Campbell                                                        *)
(*    Thomas Bauereiss                                                      *)
(*    Anthony Fox                                                           *)
(*    Jon French                                                            *)
(*    Dominic Mulligan                                                      *)
(*    Stephen Kell                                                          *)
(*    Mark Wassell                                                          *)
(*    Alastair Reid (Arm Ltd)                                               *)
(*                                                                          *)
(*  All rights reserved.                                                    *)
(*                                                                          *)
(*  This work was partially supported by EPSRC grant EP/K008528/1 <a        *)
(*  href="http://www.cl.cam.ac.uk/users/pes20/rems">REMS: Rigorous          *)
(*  Engineering for Mainstream Systems</a>, an ARM iCASE award, EPSRC IAA   *)
(*  KTF funding, and donations from Arm.  This project has received         *)
(*  funding from the European Research Council (ERC) under the European     *)
(*  Union’s Horizon 2020 research and innovation programme (grant           *)
(*  agreement No 789108, ELVER).                                            *)
(*                                                                          *)
(*  This software was developed by SRI International and the University of  *)
(*  Cambridge Computer Laboratory (Department of Computer Science and       *)
(*  Technology) under DARPA/AFRL contracts FA8650-18-C-7809 ("CIFV")        *)
(*  and FA8750-10-C-0237 ("CTSRD").                                         *)
(*                                                                          *)
(*  SPDX-License-Identifier: BSD-2-Clause                                   *)
(****************************************************************************)

open Ast
open Ast_compare
open Ast_util
open Ast_defs
open Spec_analysis
open Type_check

(* COULD DO: dead code is only eliminated at if expressions, but we could
   also cut out impossible case branches and code after assertions. *)

(* Constant propogation.
   Takes maps of immutable/mutable variables to subsitute.
   The substs argument also contains the current type-level kid refinements
   so that we can check for dead code.
   Extremely conservative about evaluation order of assignments in
   subexpressions, dropping assignments rather than committing to
   any particular order *)

let kbindings_from_list = List.fold_left (fun s (v, i) -> KBindings.add v i s) KBindings.empty
let bindings_from_list = List.fold_left (fun s (v, i) -> Bindings.add v i s) Bindings.empty

(* union was introduced in 4.03.0, a bit too recently *)
let bindings_union s1 s2 =
  Bindings.merge (fun _ x y -> match (x, y) with _, Some x -> Some x | Some x, _ -> Some x | _, _ -> None) s1 s2
let kbindings_union s1 s2 =
  KBindings.merge (fun _ x y -> match (x, y) with _, Some x -> Some x | Some x, _ -> Some x | _, _ -> None) s1 s2

let remove_bound (substs, ksubsts) pat =
  let bound = bindings_from_pat pat in
  (List.fold_left (fun sub v -> Bindings.remove v sub) substs bound, ksubsts)

let rec is_value (E_aux (e, (l, annot))) =
  let is_constructor id =
    match destruct_tannot annot with
    | None ->
        Reporting.print_err l "Monomorphisation" ("Missing type information for identifier " ^ string_of_id id);
        false (* Be conservative if we have no info *)
    | Some (env, _) -> (
        Env.is_union_constructor id env
        || match Env.lookup_id id env with Enum _ -> true | Unbound _ | Local _ | Register _ -> false
      )
  in
  match e with
  | E_id id -> is_constructor id
  | E_lit _ -> true
  | E_tuple es | E_vector es -> List.for_all is_value es
  | E_struct (_, fes) -> List.for_all (fun (FE_aux (FE_fexp (_, e), _)) -> is_value e) fes
  | E_app (id, es) -> is_constructor id && List.for_all is_value es
  (* We add casts to undefined to keep the type information in the AST *)
  | E_typ (typ, E_aux (E_undef, _)) -> true
  (* Also keep casts around, as type inference fails without (e.g., for records for vectors) *)
  | E_typ (_, e') -> is_value e'
  (* TODO: more? *)
  | _ -> false

let isubst_minus_set subst set = IdSet.fold Bindings.remove set subst

let threaded_map f state l =
  let l', state' =
    List.fold_left
      (fun (tl, state) element ->
        let el', state' = f state element in
        (el' :: tl, state')
      )
      ([], state) l
  in
  (List.rev l', state')

(* Attempt simple pattern matches *)
let lit_match = function
  | (L_bin [Non_empty (Bin_0, [])] | L_false), (L_bin [Non_empty (Bin_0, [])] | L_false) -> true
  | (L_bin [Non_empty (Bin_1, [])] | L_true), (L_bin [Non_empty (Bin_1, [])] | L_true) -> true
  | L_num i1, L_num i2 -> Big_int.equal i1 i2
  | l1, l2 -> l1 = l2

(* There's no undefined nexp, so replace undefined sizes with a plausible size.
   32 is used as a sensible default. *)

let fabricate_nexp_exist env l typ kids nc typ' =
  match (kids, nc, Env.expand_synonyms env typ') with
  | ( [kid],
      NC_aux (NC_set (Nexp_aux (Nexp_var kid', _), i :: _), _),
      Typ_aux (Typ_app (Id_aux (Id "atom", _), [A_aux (A_nexp (Nexp_aux (Nexp_var kid'', _)), _)]), _) )
    when Kid.compare kid kid' = 0 && Kid.compare kid kid'' = 0 ->
      Nexp_aux (Nexp_constant i, Unknown)
  | ( [kid],
      NC_aux (NC_true, _),
      Typ_aux (Typ_app (Id_aux (Id "atom", _), [A_aux (A_nexp (Nexp_aux (Nexp_var kid'', _)), _)]), _) )
    when Kid.compare kid kid'' = 0 ->
      nint 32
  | ( [kid],
      NC_aux (NC_set (Nexp_aux (Nexp_var kid', _), i :: _), _),
      Typ_aux
        ( Typ_app
            ( Id_aux (Id "range", _),
              [A_aux (A_nexp (Nexp_aux (Nexp_var kid'', _)), _); A_aux (A_nexp (Nexp_aux (Nexp_var kid''', _)), _)]
            ),
          _
        ) )
    when Kid.compare kid kid' = 0 && Kid.compare kid kid'' = 0 && Kid.compare kid kid''' = 0 ->
      Nexp_aux (Nexp_constant i, Unknown)
  | ( [kid],
      NC_aux (NC_true, _),
      Typ_aux
        ( Typ_app
            ( Id_aux (Id "range", _),
              [A_aux (A_nexp (Nexp_aux (Nexp_var kid'', _)), _); A_aux (A_nexp (Nexp_aux (Nexp_var kid''', _)), _)]
            ),
          _
        ) )
    when Kid.compare kid kid'' = 0 && Kid.compare kid kid''' = 0 ->
      nint 32
  | [], _, typ -> nint 32
  | kids, nc, typ ->
      raise
        (Reporting.err_general l
           ("Undefined value at unsupported type " ^ string_of_typ typ ^ " with "
           ^ Util.string_of_list ", " string_of_kid kids
           )
        )

let fabricate_nexp l tannot =
  match destruct_tannot tannot with
  | None -> nint 32
  | Some (env, typ) -> (
      match Type_check.destruct_exist (Type_check.Env.expand_synonyms env typ) with
      | None -> nint 32
      (* TODO: check this *)
      | Some (kopts, nc, typ') -> fabricate_nexp_exist env l typ (List.map kopt_kid kopts) nc typ'
    )

let atom_typ_kid kid = function
  | Typ_aux (Typ_app (Id_aux (Id "atom", _), [A_aux (A_nexp (Nexp_aux (Nexp_var kid', _)), _)]), _) ->
      Kid.compare kid kid' = 0
  | _ -> false

(* We reduce casts in a few cases, in particular to ensure that where the
   type checker has added a ({'n, true. atom('n)}) ex_int(...) cast we can
   fill in the 'n.  For undefined we fabricate a suitable value for 'n. *)

let reduce_cast typ exp l annot =
  let env = env_of_annot (l, annot) in
  let typ' = Env.base_typ_of env typ in
  match (exp, destruct_exist (Env.expand_synonyms env typ')) with
  | E_aux (E_lit (L_aux (L_num n, _)), _), Some ([kopt], nc, typ'') when atom_typ_kid (kopt_kid kopt) typ'' ->
      let nc_env = Env.add_typ_var l kopt env in
      let nc_env = Env.add_constraint (nc_eq (nvar (kopt_kid kopt)) (nconstant n)) nc_env in
      if prove __POS__ nc_env nc then exp
      else
        raise
          (Reporting.err_unreachable l __POS__
             ("Constant propagation error: literal " ^ Big_int.to_string n ^ " does not satisfy constraint "
            ^ string_of_n_constraint nc
             )
          )
  | E_aux (E_undef, _), Some ([kopt], nc, typ'') when atom_typ_kid (kopt_kid kopt) typ'' ->
      let nexp = fabricate_nexp_exist env Unknown typ [kopt_kid kopt] nc typ'' in
      let newtyp = subst_kids_typ (KBindings.singleton (kopt_kid kopt) nexp) typ'' in
      E_aux (E_typ (newtyp, exp), (Generated l, replace_typ newtyp annot))
  | E_aux (E_typ (_, (E_aux (E_undef, _) as exp)), _), Some ([kopt], nc, typ'') when atom_typ_kid (kopt_kid kopt) typ''
    ->
      let nexp = fabricate_nexp_exist env Unknown typ [kopt_kid kopt] nc typ'' in
      let newtyp = subst_kids_typ (KBindings.singleton (kopt_kid kopt) nexp) typ'' in
      E_aux (E_typ (newtyp, exp), (Generated l, replace_typ newtyp annot))
  | _ -> E_aux (E_typ (typ, exp), (l, annot))

(* Used for constant propagation in pattern matches *)
type 'a matchresult = DoesMatch of 'a | DoesNotMatch | GiveUp

(* Remove top-level casts from an expression.  Useful when we need to look at
   subexpressions to reduce something, but could break type-checking if we used
   it everywhere. *)
let rec drop_casts = function E_aux (E_typ (_, e), _) -> drop_casts e | exp -> exp

let construct_lit_vector args =
  let rec aux l = function
    | [] -> Some (L_aux (L_bin (non_empty_singleton (List.rev l)), Unknown))
    | E_aux (E_lit (L_aux (L_bin [Non_empty (b, [])], _)), _) :: t -> aux (b :: l) t
    | _ -> None
  in
  aux [] args

(* Add a cast to undefined so that it retains its type, otherwise it can't be
   substituted safely *)
let keep_undef_typ value =
  let e_aux (e, ann) =
    match e with
    | E_undef ->
        (* Add cast to undefined... *)
        E_aux (E_typ (typ_of_annot ann, E_aux (e, ann)), ann)
    | E_typ (typ, E_aux (E_typ (_, e), _)) ->
        (* ... unless there was a cast already *)
        E_aux (E_typ (typ, e), ann)
    | _ -> E_aux (e, ann)
  in
  let open Rewriter in
  fold_exp { id_exp_alg with e_aux } value

(* Check whether the current environment with the given kid assignments is
   inconsistent (and hence whether the code is dead) *)
let is_env_inconsistent env ksubsts =
  let env = KBindings.fold (fun k nexp env -> Env.add_constraint (nc_eq (nvar k) nexp) env) ksubsts env in
  prove __POS__ env nc_false

let rec typ_has_existential (Typ_aux (t, _)) =
  match t with
  | Typ_internal_unknown | Typ_id _ | Typ_var _ -> false
  | Typ_fn _ | Typ_bidir _ -> assert false
  | Typ_tuple typs -> List.exists typ_has_existential typs
  | Typ_app (_, args) -> List.exists typ_arg_has_existential args
  | Typ_exist _ -> true

and typ_arg_has_existential (A_aux (a, _)) =
  match a with A_nexp _ | A_bool _ -> false | A_typ typ -> typ_has_existential typ

module StringSet = Set.Make (String)
module StringMap = Map.Make (String)

let never_fold_ids ast =
  List.fold_left
    (fun ids def ->
      match def with
      | DEF_aux (DEF_val vs, def_annot) -> (
          let id = id_of_val_spec vs in
          match get_def_attribute "never_fold" def_annot with Some _ -> IdSet.add id ids | None -> ids
        )
      | _ -> ids
    )
    IdSet.empty ast.defs

(* This is set up so that a partially applied version can be used multiple
   times, reducing start up time. *)

let const_props target env ast =
  (* Constant-fold function applications with constant arguments *)
  let interpreter_istate =
    (* Do not interpret undefined_X functions *)
    let open Interpreter in
    let remove_primop id = StringMap.remove (string_of_id id) in
    let remove_never_fold = IdSet.fold remove_primop (never_fold_ids ast) in
    let lstate, gstate = Constant_fold.initial_state target ast env in
    (lstate, { gstate with primops = remove_never_fold gstate.primops })
  in
  let const_fold exp =
    try
      strip_exp exp
      |> infer_exp (env_of exp)
      |> Constant_fold.rewrite_exp_once target interpreter_istate
      |> keep_undef_typ
    with _ -> exp
  in

  fun ref_vars ->
    let constants =
      let add m = function
        | DEF_aux (DEF_let (P_aux ((P_id id | P_typ (_, P_aux (P_id id, _))), _), exp), _)
          when Constant_fold.is_constant exp ->
            Bindings.add id exp m
        | _ -> m
      in
      List.fold_left add Bindings.empty ast.defs
    in
    let replace_constant (E_aux (e, annot) as exp) =
      match e with
      | E_id id -> (
          match Bindings.find_opt id constants with Some e -> e | None -> exp
        )
      | _ -> exp
    in
    let rec const_prop_exp substs assigns (E_aux (e, (l, annot)) as exp) =
      (* Functions to treat lists and tuples of subexpressions as possibly
         non-deterministic: that is, we stop making any assumptions about
         variables that are assigned to in any of the subexpressions *)
      let non_det_exp_list es =
        let assigned_in = List.fold_left (fun vs exp -> IdSet.union vs (assigned_vars exp)) IdSet.empty es in
        let assigns = isubst_minus_set assigns assigned_in in
        let es' = List.map (fun e -> fst (const_prop_exp substs assigns e)) es in
        (es', assigns)
      in
      let non_det_exp_2 e1 e2 =
        let assigned_in_e12 = IdSet.union (assigned_vars e1) (assigned_vars e2) in
        let assigns = isubst_minus_set assigns assigned_in_e12 in
        let e1', _ = const_prop_exp substs assigns e1 in
        let e2', _ = const_prop_exp substs assigns e2 in
        (e1', e2', assigns)
      in
      let non_det_exp_3 e1 e2 e3 =
        let assigned_in_e12 = IdSet.union (assigned_vars e1) (assigned_vars e2) in
        let assigned_in_e123 = IdSet.union assigned_in_e12 (assigned_vars e3) in
        let assigns = isubst_minus_set assigns assigned_in_e123 in
        let e1', _ = const_prop_exp substs assigns e1 in
        let e2', _ = const_prop_exp substs assigns e2 in
        let e3', _ = const_prop_exp substs assigns e3 in
        (e1', e2', e3', assigns)
      in
      let rewrap e = E_aux (e, (l, annot)) in
      let re e assigns = (rewrap e, assigns) in
      match e with
      (* TODO: are there more circumstances in which we should get rid of these? *)
      | E_block [e] -> const_prop_exp substs assigns e
      | E_block es ->
          let es', assigns = threaded_map (const_prop_exp substs) assigns es in
          re (E_block es') assigns
      | E_id id ->
          let env = Type_check.env_of_annot (l, annot) in
          ( ( try
                match Env.lookup_id id env with
                | Local (Immutable, _) -> Bindings.find id (fst substs)
                | Local (Mutable, _) -> Bindings.find id assigns
                | _ -> exp
              with Not_found -> exp
            ),
            assigns
          )
      | E_undef | E_lit _ | E_sizeof _ | E_constraint _ | E_config _ -> (exp, assigns)
      | E_typ (t, e') ->
          let e'', assigns = const_prop_exp substs assigns e' in
          if is_value e'' then (reduce_cast t e'' l annot, assigns) else re (E_typ (t, e'')) assigns
      | E_app (id, es) ->
          let es', assigns = non_det_exp_list es in
          let env = Type_check.env_of_annot (l, annot) in
          (const_prop_try_fn env (id, es') (l, annot), assigns)
      | E_tuple es ->
          let es', assigns = non_det_exp_list es in
          re (E_tuple es') assigns
      | E_if (e1, e2, e3) -> (
          let e1', assigns = const_prop_exp substs assigns e1 in
          let e1_no_casts = drop_casts e1' in
          match e1_no_casts with
          | E_aux (E_lit (L_aux (((L_true | L_false) as lit), _)), _) -> (
              match lit with L_true -> const_prop_exp substs assigns e2 | _ -> const_prop_exp substs assigns e3
            )
          | _ ->
              (* If the guard is an equality check, propagate the value. *)
              let env1 = env_of e1_no_casts in
              let is_equal id =
                List.exists
                  (fun id' -> Id.compare id id' == 0)
                  (Env.get_overloads (Id_aux (Operator "==", Parse_ast.Unknown)) env1)
              in
              let substs_true =
                match e1_no_casts with
                | (E_aux (E_app (id, [E_aux (E_id var, _); vl]), _) | E_aux (E_app (id, [vl; E_aux (E_id var, _)]), _))
                  when is_equal id ->
                    if is_value vl then (
                      match Env.lookup_id var env1 with
                      | Local (Immutable, _) -> (Bindings.add var vl (fst substs), snd substs)
                      | _ -> substs
                    )
                    else substs
                | _ -> substs
              in
              (* Discard impossible branches *)
              if is_env_inconsistent (env_of e2) (snd substs) then const_prop_exp substs assigns e3
              else if is_env_inconsistent (env_of e3) (snd substs) then const_prop_exp substs_true assigns e2
              else (
                let e2', assigns2 = const_prop_exp substs_true assigns e2 in
                let e3', assigns3 = const_prop_exp substs assigns e3 in
                (* If one branch is a throw, use the assignments from the other *)
                let assigns =
                  match (e2', e3') with
                  | E_aux (E_throw _, _), _ -> assigns3
                  | _, E_aux (E_throw _, _) -> assigns2
                  | _, _ ->
                      let assigns = isubst_minus_set assigns (assigned_vars e2) in
                      let assigns = isubst_minus_set assigns (assigned_vars e3) in
                      assigns
                in
                re (E_if (e1', e2', e3')) assigns
              )
        )
      | E_for (id, e1, e2, e3, ord, e4) ->
          (* Treat e1, e2 and e3 (from, to and by) as a non-det tuple *)
          let e1', e2', e3', assigns = non_det_exp_3 e1 e2 e3 in
          let assigns = isubst_minus_set assigns (assigned_vars e4) in
          let e4', _ = const_prop_exp (Bindings.remove id (fst substs), snd substs) assigns e4 in
          re (E_for (id, e1', e2', e3', ord, e4')) assigns
      | E_loop (loop, m, e1, e2) ->
          let assigns = isubst_minus_set assigns (IdSet.union (assigned_vars e1) (assigned_vars e2)) in
          let m' =
            match m with
            | Measure_aux (Measure_none, _) -> m
            | Measure_aux (Measure_some exp, l) ->
                let exp', _ = const_prop_exp substs assigns exp in
                Measure_aux (Measure_some exp', l)
          in
          let e1', _ = const_prop_exp substs assigns e1 in
          let e2', _ = const_prop_exp substs assigns e2 in
          re (E_loop (loop, m', e1', e2')) assigns
      | E_vector es -> (
          let es', assigns = non_det_exp_list es in
          match construct_lit_vector es' with None -> re (E_vector es') assigns | Some lit -> re (E_lit lit) assigns
        )
      | E_vector_append (e1, e2) ->
          let e1', e2', assigns = non_det_exp_2 e1 e2 in
          re (E_vector_append (e1', e2')) assigns
      | E_list es ->
          let es', assigns = non_det_exp_list es in
          re (E_list es') assigns
      | E_cons (e1, e2) ->
          let e1', e2', assigns = non_det_exp_2 e1 e2 in
          re (E_cons (e1', e2')) assigns
      | E_struct (struct_name, fes) ->
          let assigned_in_fes = assigned_vars_in_fexps fes in
          let assigns = isubst_minus_set assigns assigned_in_fes in
          re (E_struct (struct_name, const_prop_fexps substs assigns fes)) assigns
      | E_struct_update (e, fes) -> (
          let assigned_in = IdSet.union (assigned_vars_in_fexps fes) (assigned_vars e) in
          let assigns = isubst_minus_set assigns assigned_in in
          let e', _ = const_prop_exp substs assigns e in
          let fes' = const_prop_fexps substs assigns fes in
          match unaux_exp (fst (uncast_exp e')) with
          | E_struct (struct_name, fes0) ->
              let apply_fexp (FE_aux (FE_fexp (id, e), _)) (FE_aux (FE_fexp (id', e'), ann)) =
                if Id.compare id id' = 0 then FE_aux (FE_fexp (id', e), ann) else FE_aux (FE_fexp (id', e'), ann)
              in
              let update_fields fexp = List.map (apply_fexp fexp) in
              let fes0' = List.fold_right update_fields fes' fes0 in
              re (E_struct (struct_name, fes0')) assigns
          | _ -> re (E_struct_update (e', fes')) assigns
        )
      | E_field (e, id) -> (
          let e', assigns = const_prop_exp substs assigns e in
          let is_field (FE_aux (FE_fexp (id', _), _)) = Id.compare id id' = 0 in
          match unaux_exp e' with
          | E_struct (_, fes0) when List.exists is_field fes0 ->
              let (FE_aux (FE_fexp (_, e), _)) = List.find is_field fes0 in
              re (unaux_exp e) assigns
          | _ -> re (E_field (e', id)) assigns
        )
      | E_match (e, cases) -> (
          let e', assigns = const_prop_exp substs assigns e in
          match can_match l e' cases substs assigns with
          | None ->
              let assigned_in =
                List.fold_left (fun vs pe -> IdSet.union vs (assigned_vars_in_pexp pe)) IdSet.empty cases
              in
              let assigns' = isubst_minus_set assigns assigned_in in
              re (E_match (e', List.map (const_prop_pexp substs assigns) cases)) assigns'
          | Some ((E_aux (_, (_, annot')) as exp), newbindings, kbindings) ->
              let exp = nexp_subst_exp (kbindings_from_list kbindings) exp in
              let newbindings_env = bindings_from_list newbindings in
              let substs' = (bindings_union (fst substs) newbindings_env, snd substs) in
              const_prop_exp substs' assigns exp
        )
      | E_let (p, e, e2) -> (
          let e', assigns = const_prop_exp substs assigns e in
          let substs' = remove_bound substs p in
          let plain () =
            let e2', assigns = const_prop_exp substs' assigns e2 in
            re (E_let (p, e', e2')) assigns
          in
          match can_match l e' [Pat_aux (Pat_exp (p, e2), (Unknown, empty_tannot))] substs assigns with
          | None -> plain ()
          | Some (e'', bindings, kbindings) ->
              let val_bindings, exp_bindings = List.partition (fun (_, e) -> is_value e) bindings in
              let e'' = nexp_subst_exp (kbindings_from_list kbindings) e'' in
              let val_bindings = bindings_from_list val_bindings in
              let substs'' = (bindings_union (fst substs') val_bindings, snd substs') in
              let tail_exp, tail_assigns = const_prop_exp substs'' assigns e'' in
              ( List.fold_left
                  (fun (E_aux (_, t_annot) as t_exp) (id, bind_exp) ->
                    let p_tannot = mk_tannot (env_of_annot (l, annot)) (typ_of bind_exp) in
                    E_aux (E_let (P_aux (P_id id, (Generated l, p_tannot)), bind_exp, t_exp), t_annot)
                  )
                  tail_exp exp_bindings,
                tail_assigns
              )
        )
      (* TODO maybe - tuple assignments *)
      | E_assign (le, e) ->
          let env = Type_check.env_of_annot (l, annot) in
          let assigned_in = IdSet.union (assigned_vars_in_lexp le) (assigned_vars e) in
          let assigns = isubst_minus_set assigns assigned_in in
          let le', idopt = const_prop_lexp substs assigns le in
          let e', _ = const_prop_exp substs assigns e in
          let assigns =
            match idopt with
            | Some id -> (
                match Env.lookup_id id env with
                | Local (Mutable, _) | Unbound _ ->
                    if is_value e' && not (IdSet.mem id ref_vars) then Bindings.add id (keep_undef_typ e') assigns
                    else Bindings.remove id assigns
                | _ -> assigns
              )
            | None -> assigns
          in
          re (E_assign (le', e')) assigns
      | E_var (le, e, e2) ->
          let env = Type_check.env_of_annot (l, annot) in
          let assigned_in = IdSet.union (assigned_vars_in_lexp le) (assigned_vars e) in
          let assigns = isubst_minus_set assigns assigned_in in
          let le', idopt = const_prop_lexp substs assigns le in
          let e', _ = const_prop_exp substs assigns e in
          let assigns =
            match idopt with
            | Some id -> (
                match Env.lookup_id id env with
                | Local (Mutable, _) | Unbound _ ->
                    if is_value e' && not (IdSet.mem id ref_vars) then Bindings.add id (keep_undef_typ e') assigns
                    else Bindings.remove id assigns
                | _ -> assigns
              )
            | None -> assigns
          in
          let e2', _ = const_prop_exp substs assigns e2 in
          re (E_var (le', e', e2')) assigns
      | E_exit e ->
          let e', _ = const_prop_exp substs assigns e in
          re (E_exit e') Bindings.empty
      | E_ref id -> re (E_ref id) Bindings.empty
      | E_throw e ->
          let e', _ = const_prop_exp substs assigns e in
          re (E_throw e') Bindings.empty
      | E_try (e, cases) ->
          (* TODO: try and preserve *any* assignment info; note the special case in E_if if
             one of the branches throws. *)
          let e', _ = const_prop_exp substs assigns e in
          re (E_match (e', List.map (const_prop_pexp substs Bindings.empty) cases)) Bindings.empty
      | E_return e ->
          let e', _ = const_prop_exp substs assigns e in
          re (E_return e') Bindings.empty
      | E_assert (e1, e2) ->
          let e1', e2', assigns = non_det_exp_2 e1 e2 in
          re (E_assert (e1', e2')) assigns
      | E_internal_assume (nc, e) ->
          let e', _ = const_prop_exp substs assigns e in
          re (E_internal_assume (nc, e')) assigns
      | E_internal_plet _ | E_internal_return _ | E_internal_value _ ->
          raise
            (Reporting.err_unreachable l __POS__
               ("Unexpected expression encountered in monomorphisation: " ^ string_of_exp exp)
            )
    and const_prop_fexps substs assigns fes = List.map (const_prop_fexp substs assigns) fes
    and const_prop_fexp substs assigns (FE_aux (FE_fexp (id, e), annot)) =
      FE_aux (FE_fexp (id, fst (const_prop_exp substs assigns e)), annot)
    and const_prop_pexp substs assigns = function
      | Pat_aux (Pat_exp (p, e), l) -> Pat_aux (Pat_exp (p, fst (const_prop_exp (remove_bound substs p) assigns e)), l)
      | Pat_aux (Pat_when (p, e1, e2), l) ->
          let substs' = remove_bound substs p in
          let e1', assigns = const_prop_exp substs' assigns e1 in
          Pat_aux (Pat_when (p, e1', fst (const_prop_exp substs' assigns e2)), l)
    and const_prop_lexp substs assigns (LE_aux (e, annot) as le) =
      let re e = (LE_aux (e, annot), None) in
      match e with
      | LE_id id (* shouldn't end up substituting here *) | LE_typ (_, id) -> (le, Some id)
      | LE_tuple les -> re (LE_tuple (List.map (fun le -> fst (const_prop_lexp substs assigns le)) les))
      | LE_vector (le, e) ->
          re (LE_vector (fst (const_prop_lexp substs assigns le), fst (const_prop_exp substs assigns e)))
      | LE_vector_range (le, e1, e2) ->
          re
            (LE_vector_range
               ( fst (const_prop_lexp substs assigns le),
                 fst (const_prop_exp substs assigns e1),
                 fst (const_prop_exp substs assigns e2)
               )
            )
      | LE_vector_concat les -> re (LE_vector_concat (List.map (fun le -> fst (const_prop_lexp substs assigns le)) les))
      | LE_field (le, id) -> re (LE_field (fst (const_prop_lexp substs assigns le), id))
      | LE_deref e -> re (LE_deref (fst (const_prop_exp substs assigns e)))
    (* Try to evaluate function calls with constant arguments via
       (interpreter-based) constant folding.
       Boolean connectives are special-cased to support short-circuiting when one
       argument has a suitable value (even if the other one is not constant).
       Moreover, calls to a __size function (in particular generated by sizeof
       rewriting) with a known-constant return type are replaced by that constant;
       e.g., (length(op : bits(32)) : int(32)) becomes 32 even if op is not constant.
    *)
    and const_prop_try_fn env (id, args) (l, annot) =
      let exp_orig = E_aux (E_app (id, args), (l, annot)) in
      let args = List.map replace_constant args in
      let exp = E_aux (E_app (id, args), (l, annot)) in
      let rec is_overload_of f =
        Env.get_overloads f env |> List.exists (fun id' -> Id.compare id id' = 0 || is_overload_of id')
      in
      match (string_of_id id, args) with
      | ( "and_bool",
          ( [(E_aux (E_lit (L_aux (L_false, _)), _) as e_false); _]
          | [E_aux (E_typ (_, (E_aux (E_lit (L_aux (L_false, _)), _) as e_false)), _); _]
          | [_; (E_aux (E_lit (L_aux (L_false, _)), _) as e_false)]
          | [_; E_aux (E_typ (_, (E_aux (E_lit (L_aux (L_false, _)), _) as e_false)), _)] ) ) ->
          e_false
      | ( "or_bool",
          ( [(E_aux (E_lit (L_aux (L_true, _)), _) as e_true); _]
          | [E_aux (E_typ (_, (E_aux (E_lit (L_aux (L_true, _)), _) as e_true)), _); _]
          | [_; (E_aux (E_lit (L_aux (L_true, _)), _) as e_true)]
          | [_; E_aux (E_typ (_, (E_aux (E_lit (L_aux (L_true, _)), _) as e_true)), _)] ) ) ->
          e_true
      | (_, [E_aux (E_vector [], _); e'] | _, [e'; E_aux (E_vector [], _)]) when is_overload_of (mk_id "append") -> e'
      | _, _ when List.for_all Constant_fold.is_constant args -> const_fold exp
      | _, [arg] when is_overload_of (mk_id "__size") -> (
          match destruct_atom_nexp env (typ_of exp) with
          | Some (Nexp_aux (Nexp_constant i, _)) -> E_aux (E_lit (mk_lit (L_num i)), (l, annot))
          | _ -> exp_orig
        )
      | _ -> exp_orig
    and can_match_with_env l env (E_aux (e, (_l, annot)) as exp0) cases (substs, ksubsts) assigns =
      let rec check_exp_pat (E_aux (e, (l, annot)) as exp) (P_aux (p, (l', p_annot)) as pat) =
        match (e, p) with
        | _, P_wild -> DoesMatch ([], [])
        | _, P_typ (typ, p') -> (
            match (typ_has_existential typ, check_exp_pat exp p') with
            | false, DoesMatch ([(id, v)], ns) -> DoesMatch ([(id, E_aux (E_typ (typ, v), (l', p_annot)))], ns)
            | _, m -> m
          )
        | _, P_id id' when pat_id_is_variable env id' ->
            let exp_typ = typ_of exp in
            let pat_typ = typ_of_pat pat in
            let goals = KidSet.diff (tyvars_of_typ pat_typ) (tyvars_of_typ exp_typ) in
            let unifiers = try Type_check.unify l env goals pat_typ exp_typ with _ -> KBindings.empty in
            let is_nexp (k, a) = match a with A_aux (A_nexp n, _) -> Some (k, n) | _ -> None in
            let kbindings = List.filter_map is_nexp (KBindings.bindings unifiers) in
            DoesMatch ([(id', exp)], kbindings)
        | E_tuple es, P_tuple ps ->
            let check = function
              | DoesNotMatch -> fun _ -> DoesNotMatch
              | GiveUp -> fun _ -> GiveUp
              | DoesMatch (s, ns) -> (
                  fun (e, p) ->
                    match check_exp_pat e p with DoesMatch (s', ns') -> DoesMatch (s @ s', ns @ ns') | x -> x
                )
            in
            List.fold_left check (DoesMatch ([], [])) (List.combine es ps)
        | E_id id, _ -> (
            match Env.lookup_id id env with
            | Enum _ -> (
                match p with
                | P_id id' | P_app (id', []) -> if Id.compare id id' = 0 then DoesMatch ([], []) else DoesNotMatch
                | _ ->
                    Reporting.print_err l' "Monomorphisation"
                      ("Unexpected kind of pattern for enumeration: " ^ string_of_pat pat);
                    GiveUp
              )
            | _ -> GiveUp
          )
        | E_undef, P_var (P_aux (P_id id, p_id_annot), TP_aux (TP_var kid, _)) ->
            (* For undefined we fix the type-level size (because there's no good
               way to construct an undefined size), but leave the term as undefined
               to make the meaning clear. *)
            let nexp = fabricate_nexp l annot in
            let typ = subst_kids_typ (KBindings.singleton kid nexp) (typ_of_annot p_id_annot) in
            DoesMatch ([(id, E_aux (E_typ (typ, E_aux (e, (l, empty_tannot))), (l, empty_tannot)))], [(kid, nexp)])
        | E_lit (L_aux (lit_e, lit_l)), P_lit (L_aux (lit_p, _)) ->
            if lit_match (lit_e, lit_p) then DoesMatch ([], []) else DoesNotMatch
        | E_lit (L_aux (lit_e, lit_l)), P_var (P_aux (P_id id, p_id_annot), TP_aux (TP_var kid, _)) -> (
            match lit_e with
            | L_num i -> DoesMatch ([(id, E_aux (e, (l, annot)))], [(kid, Nexp_aux (Nexp_constant i, Unknown))])
            (* For undefined we fix the type-level size (because there's no good
               way to construct an undefined size), but leave the term as undefined
               to make the meaning clear. *)
            | _ ->
                Reporting.print_err lit_l "Monomorphisation"
                  ("Unexpected kind of literal for var match: " ^ string_of_lit (L_aux (lit_e, lit_l)));
                GiveUp
          )
        | E_lit (L_aux ((L_bin _ | L_hex _), _) as lit), P_vector _ ->
            let mk_bitlit lit = E_aux (E_lit lit, (Generated l, mk_tannot env bit_typ)) in
            let lits' = List.map mk_bitlit (vector_string_to_bit_list lit) in
            check_exp_pat (E_aux (E_vector lits', (l, annot))) pat
        | E_lit _, _ ->
            Reporting.print_err l' "Monomorphisation" ("Unexpected kind of pattern for literal: " ^ string_of_pat pat);
            GiveUp
        | E_vector es, P_vector ps when List.for_all (function E_aux (E_lit _, _) -> true | _ -> false) es -> (
            let matches =
              List.map2
                (fun e p ->
                  let p = match p with P_aux (P_typ (_, p'), _) -> p' | _ -> p in
                  match (e, p) with
                  | E_aux (E_lit (L_aux (lit, _)), _), P_aux (P_lit (L_aux (lit', _)), _) ->
                      if lit_match (lit, lit') then DoesMatch ([], []) else DoesNotMatch
                  | E_aux (E_lit l, _), P_aux (P_id var, _) when pat_id_is_variable env var -> DoesMatch ([(var, e)], [])
                  | _, P_aux (P_wild, _) -> DoesMatch ([], [])
                  | _ -> GiveUp
                )
                es ps
            in
            let final =
              List.fold_left
                (fun acc m ->
                  match (acc, m) with
                  | _, GiveUp -> GiveUp
                  | GiveUp, _ -> GiveUp
                  | DoesMatch (sub, ksub), DoesMatch (sub', ksub') -> DoesMatch (sub @ sub', ksub @ ksub')
                  | _ -> DoesNotMatch
                )
                (DoesMatch ([], []))
                matches
            in
            match final with
            | GiveUp ->
                Reporting.print_err l "Monomorphisation"
                  ("Unexpected kind of pattern for vector literal: " ^ string_of_pat pat);
                GiveUp
            | _ -> final
          )
        | E_vector _, P_lit (L_aux ((L_bin _ | L_hex _), _) as lit) ->
            let mk_bitlit lit = P_aux (P_lit lit, (Generated l, mk_tannot env bit_typ)) in
            let lits' = List.map mk_bitlit (vector_string_to_bit_list lit) in
            check_exp_pat exp (P_aux (P_vector lits', (l, annot)))
        | E_vector _, _ ->
            Reporting.print_err l "Monomorphisation"
              ("Unexpected kind of pattern for vector literal: " ^ string_of_pat pat);
            GiveUp
        | E_typ (undef_typ, E_aux (E_undef, _)), P_lit (L_aux (lit_p, _)) -> DoesNotMatch
        | E_typ (undef_typ, (E_aux (E_undef, _) as e_undef)), P_var (P_aux (P_id id, p_id_annot), TP_aux (TP_var kid, _))
          ->
            (* For undefined we fix the type-level size (because there's no good
               way to construct an undefined size), but leave the term as undefined
               to make the meaning clear. *)
            let nexp = fabricate_nexp l annot in
            let kids = equal_kids (env_of_annot p_id_annot) kid in
            let ksubst = KidSet.fold (fun k b -> KBindings.add k nexp b) kids KBindings.empty in
            let typ = subst_kids_typ ksubst (typ_of_annot p_id_annot) in
            DoesMatch ([(id, E_aux (E_typ (typ, e_undef), (l, empty_tannot)))], KBindings.bindings ksubst)
        | E_typ (undef_typ, E_aux (E_undef, _)), _ ->
            Reporting.print_err l' "Monomorphisation" ("Unexpected kind of pattern for literal: " ^ string_of_pat pat);
            GiveUp
        | E_typ (_, exp'), _ -> check_exp_pat exp' pat
        | E_struct _, _ -> DoesNotMatch
        | _ -> GiveUp
      in
      let check_pat = check_exp_pat exp0 in
      let add_ksubst_synonyms env' ksubst =
        (* The type checker sometimes automatically generates kid synonyms, e.g.
           in let 'datasize = ... in ... it binds both 'datasize and '_datasize.
           If we subsitute one, we also want to substitute the other.
           In order to find synonyms, we consult the environment after the
           bind (see findpat_generic below). *)
        let get_synonyms (kid, nexp) =
          let rec synonyms_of_nc nc =
            match unaux_constraint nc with
            | NC_equal (A_aux (A_nexp (Nexp_aux (Nexp_var kid1, _)), _), A_aux (A_nexp (Nexp_aux (Nexp_var kid2, _)), _))
              when Kid.compare kid kid1 = 0 ->
                [(kid2, nexp)]
            | NC_and _ -> List.concat_map synonyms_of_nc (constraint_conj nc)
            | _ -> []
          in
          List.concat_map synonyms_of_nc (Env.get_constraints env')
        in
        ksubst @ List.concat_map get_synonyms ksubst
      in
      let rec findpat_generic description assigns = function
        | [] ->
            Reporting.print_err l "Monomorphisation" ("Failed to find a case for " ^ description);
            None
        | Pat_aux (Pat_when (p, guard, exp), _) :: tl -> (
            match check_pat p with
            | DoesNotMatch -> findpat_generic description assigns tl
            | DoesMatch (vsubst, ksubst) -> (
                let guard = nexp_subst_exp (kbindings_from_list ksubst) guard in
                let substs =
                  ( bindings_union substs (bindings_from_list vsubst),
                    kbindings_union ksubsts (kbindings_from_list ksubst)
                  )
                in
                let E_aux (guard, _), assigns = const_prop_exp substs assigns guard in
                match guard with
                | E_lit (L_aux (L_true, _)) ->
                    let ksubst = add_ksubst_synonyms (env_of exp) ksubst in
                    Some (exp, vsubst, ksubst)
                | E_lit (L_aux (L_false, _)) -> findpat_generic description assigns tl
                | _ -> None
              )
            | GiveUp -> None
          )
        | Pat_aux (Pat_exp (p, exp), _) :: tl -> (
            match check_pat p with
            | DoesNotMatch -> findpat_generic description assigns tl
            | DoesMatch (subst, ksubst) ->
                let ksubst = add_ksubst_synonyms (env_of exp) ksubst in
                Some (exp, subst, ksubst)
            | GiveUp -> None
          )
      in
      findpat_generic (string_of_exp exp0) assigns cases
    and can_match l exp =
      let env = Type_check.env_of exp in
      can_match_with_env l env exp
    in

    (const_prop_exp, const_prop_pexp)

let const_prop target env d =
  let f = const_props target env d in
  fun r -> fst (f r)

let referenced_vars exp =
  let open Rewriter in
  fst
    (fold_exp { (compute_exp_alg IdSet.empty IdSet.union) with e_ref = (fun id -> (IdSet.singleton id, E_ref id)) } exp)

(* This is intended to remove impossible cases when a type-level constant has
   been used to fix a property of the architecture.  In particular, the current
   version of the RISC-V model uses constructs like

   match (width, sizeof(xlen)) {
     (BYTE, _)    => ...
     ...
     (DOUBLE, 64) => ...
   };

   and the type checker will replace the sizeof with the literal 32 or 64.  This
   pass will then remove the DOUBLE case.

   It would be nice to have the full constant propagation above do this kind of
   thing too...
*)

let remove_impossible_int_cases _ =
  let must_keep_case exp (Pat_aux ((Pat_exp (p, _) | Pat_when (p, _, _)), _)) =
    let rec aux (E_aux (exp, _)) (P_aux (p, _)) =
      match (exp, p) with
      | E_tuple exps, P_tuple ps -> List.for_all2 aux exps ps
      | E_lit (L_aux (lit, _)), P_lit (L_aux (lit', _)) -> lit_match (lit, lit')
      | _ -> true
    in
    aux exp p
  in
  let e_case (exp, cases) = E_match (exp, List.filter (must_keep_case exp) cases) in
  let e_if (cond, e_then, e_else) =
    match destruct_atom_bool (env_of cond) (typ_of cond) with
    | Some nc ->
        if prove __POS__ (env_of cond) nc then unaux_exp e_then
        else if prove __POS__ (env_of cond) (nc_not nc) then unaux_exp e_else
        else E_if (cond, e_then, e_else)
    | _ -> E_if (cond, e_then, e_else)
  in
  let open Rewriter in
  let rewrite_exp _ = fold_exp { id_exp_alg with e_case; e_if } in
  rewrite_ast_base { rewriters_base with rewrite_exp }