Source file olf.ml

(*

   Copyright (c) 2001-2002,
    John Kodumal        <jkodumal@eecs.berkeley.edu>
   All rights reserved.

   Redistribution and use in source and binary forms, with or without
   modification, are permitted provided that the following conditions are
   met:

   1. Redistributions of source code must retain the above copyright
   notice, this list of conditions and the following disclaimer.

   2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.

   3. The names of the contributors may not be used to endorse or promote
   products derived from this software without specific prior written
   permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
   IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
   TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
   PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
   OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
   EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
   PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
   PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
   LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
   NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
   SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

 *)
open GoblintCil

(***********************************************************************)
(*                                                                     *)
(* Exceptions                                                          *)
(*                                                                     *)
(***********************************************************************)

exception Inconsistent (* raised if constraint system is inconsistent *)
exception WellFormed   (* raised if types are not well-formed *)
exception NoContents
exception ReachedTop   (* raised if top (from an undefined function)
                          flows to a c_absloc during the flow step *)
exception UnknownLocation

module U = Uref
module S = Setp
module H = Hashtbl
module Q = Queue

(** Generic bounds *)
type 'a bound = {info : 'a U.uref}

module Bound =
struct
  type 'a t = 'a bound
  let compare (x : 'a t) (y : 'a t) =
    Stdlib.compare (U.deref x.info) (U.deref y.info)
end

module B = S.Make (Bound)

type 'a boundset = 'a B.t

(** Abslocs, which identify elements in points-to sets *)
(* jk : I'd prefer to make this an 'a absloc and specialize it to
    varinfo for use with the Cil frontend, but for now, this will do *)
type absloc = int * string * Cil.varinfo option

module Absloc =
struct
  type t = absloc
  let compare (xid, _, _) (yid, _, _) = xid - yid
end

module C = Set.Make (Absloc)

(** Sets of abslocs. Set union is used when two c_abslocs containing
    absloc sets are unified *)
type abslocset = C.t

let d_absloc () (a: absloc) : Pretty.doc =
  let i,s,_ = a in
  Pretty.dprintf "<%d, %s>" i s

type c_abslocinfo = {
  mutable l_name: string;   (** name of the location *)
  loc : absloc;
  l_stamp : int;
  mutable l_top : bool;
  mutable aliases : abslocset;
  mutable lbounds : c_abslocinfo boundset;
  mutable ubounds : c_abslocinfo boundset;
  mutable flow_computed : bool
}
and c_absloc = c_abslocinfo U.uref

(** The type of lvalues. *)
type lvalue = {
  l: c_absloc;
  contents: tau
}
and vinfo = {
  v_stamp : int;
  v_name : string;
  mutable v_top : bool;
  mutable v_lbounds : tinfo boundset;
  mutable v_ubounds : tinfo boundset
}
and rinfo = {
  r_stamp : int;
  rl : c_absloc;
  points_to : tau
}
and finfo = {
  f_stamp : int;
  fl : c_absloc;
  ret : tau;
  mutable args : tau list
}
and pinfo = {
  p_stamp : int;
  ptr : tau;
  lam : tau
}
and tinfo =
    Var of vinfo
  | Ref of rinfo
  | Fun of finfo
  | Pair of pinfo
and tau = tinfo U.uref

type tconstraint =
    Unification of tau * tau
  | Leq of tau * tau

(** Association lists, used for printing recursive types. The first
    element is a type that has been visited. The second element is the
    string representation of that type (so far). If the string option is
    set, then this type occurs within itself, and is associated with the
    recursive var name stored in the option. When walking a type, add it
    to an association list.

    Example: suppose we have the constraint 'a = ref('a). The type is
    unified via cyclic unification, and would loop infinitely if we
    attempted to print it. What we want to do is print the type u
    rv. ref(rv). This is accomplished in the following manner:

    -- ref('a) is visited. It is not in the association list, so it is
    added and the string "ref(" is stored in the second element. We
    recurse to print the first argument of the constructor.

    -- In the recursive call, we see that 'a (or ref('a)) is already
    in the association list, so the type is recursive. We check the
    string option, which is None, meaning that this is the first
    recurrence of the type. We create a new recursive variable, rv and
    set the string option to 'rv. Next, we prepend u rv. to the string
    representation we have seen before, "ref(", and return "rv" as the
    string representation of this type.

    -- The string so far is "u rv.ref(". The recursive call returns,
    and we complete the type by printing the result of the call, "rv",
    and ")"

    In a type where the recursive variable appears twice, e.g. 'a =
    pair('a,'a), the second time we hit 'a, the string option will be
    set, so we know to reuse the same recursive variable name.
*)
type association = tau * string ref * string option ref

(** The current state of the solver engine either adding more
    constraints, or finished adding constraints and querying graph *)
type state =
    AddingConstraints
  | FinishedConstraints

(***********************************************************************)
(*                                                                     *)
(* Global Variables                                                    *)
(*                                                                     *)
(***********************************************************************)

(** A count of the constraints introduced from the AST. Used for
    debugging. *)
let toplev_count = ref 0

let solver_state : state ref = ref AddingConstraints

(** Print the instantiations constraints. *)
let print_constraints : bool ref = ref false

(** If true, print all constraints (including induced) and show
    additional debug output. *)
let debug = ref false

(** Just debug all the constraints (including induced) *)
let debug_constraints = ref false

(** Compatibility with GOLF *)
let debug_aliases = ref false
let smart_aliases = ref false
let no_flow = ref false
let analyze_mono = ref false

(** If true, disable subtyping (unification at all levels) *)
let no_sub = ref false

(** A list of equality constraints. *)
let eq_worklist : tconstraint Q.t = Q.create ()

(** A list of leq constraints. *)
let leq_worklist : tconstraint Q.t = Q.create ()

(** A hashtable mapping pairs of tau's to their join node. *)
let join_cache : (int * int, tau) H.t = H.create 64

(** *)
let label_prefix = "l_"


(***********************************************************************)
(*                                                                     *)
(* Utility Functions                                                   *)
(*                                                                     *)
(***********************************************************************)

let starts_with s p =
  let n = String.length p in
    if String.length s < n then false
    else String.sub s 0 n = p


let die s =
  Printf.printf "*******\nAssertion failed: %s\n*******\n" s;
  assert false

let insist b s =
  if not b then die s else ()


let can_add_constraints () =
  !solver_state = AddingConstraints

let can_query_graph () =
  !solver_state = FinishedConstraints

let finished_constraints () =
  insist (!solver_state = AddingConstraints) "inconsistent states";
  solver_state := FinishedConstraints

let find = U.deref


(** Generate a unique integer. *)
let fresh_index : (unit -> int) =
  let counter = ref 0 in
    fun () ->
      incr counter;
      !counter

let fresh_stamp : (unit -> int) =
  let stamp = ref 0 in
    fun () ->
      incr stamp;
      !stamp

(** Return a unique integer representation of a tau *)
let get_stamp (t : tau) : int =
  match find t with
      Var v -> v.v_stamp
    | Ref r -> r.r_stamp
    | Pair p -> p.p_stamp
    | Fun f -> f.f_stamp

(** Consistency checks for inferred types *)
let  pair_or_var (t : tau) =
  match find t with
      Pair _ -> true
    | Var _ -> true
    | _ -> false

let ref_or_var (t : tau) =
   match find t with
       Ref _ -> true
     | Var _ -> true
     | _ -> false

let fun_or_var (t : tau) =
  match find t with
      Fun _ -> true
    | Var _ -> true
    |  _ -> false


(** Apply [f] structurally down [t]. Guaranteed to terminate, even if [t]
    is recursive *)
let iter_tau f t =
  let visited : (int, tau) H.t = H.create 4 in
  let rec iter_tau' t =
    if H.mem visited (get_stamp t) then () else
      begin
        f t;
        H.add visited (get_stamp t) t;
        match find t with
            Pair p ->
              iter_tau' p.ptr;
              iter_tau' p.lam
          | Fun f ->
              List.iter iter_tau' f.args;
              iter_tau' f.ret;
          | Ref r -> iter_tau' r.points_to
          | _ -> ()
      end
  in
    iter_tau' t

let equal_absloc = function
    (i, _, _), (i', _, _) -> i = i'

let equal_c_absloc l l' =
  (find l).l_stamp = (find l').l_stamp

let equal_tau (t : tau) (t' : tau) =
  get_stamp t = get_stamp t'

let top_c_absloc l =
  (find l).l_top

let get_flow_computed l =
  (find l).flow_computed

let set_flow_computed l =
  (find l).flow_computed <- true

let rec top_tau (t : tau) =
  match find t with
      Pair p -> top_tau p.ptr || top_tau p.lam
    | Ref r -> top_c_absloc r.rl
    | Fun f -> top_c_absloc f.fl
    | Var v -> v.v_top

let get_c_absloc_stamp (l : c_absloc) : int =
  (find l).l_stamp

let set_top_c_absloc (l : c_absloc) (b: bool) : unit =
  (find l).l_top <- b

let get_aliases (l : c_absloc) =
  if top_c_absloc l then raise ReachedTop
  else (find l).aliases

(***********************************************************************)
(*                                                                     *)
(* Printing Functions                                                  *)
(*                                                                     *)
(***********************************************************************)

(** Convert a c_absloc to a string, short representation *)
let string_of_c_absloc (l : c_absloc) : string =
  "\"" ^
    (find l).l_name ^
    if top_c_absloc l then "(top)" else "" ^
      "\""

(** Return true if the element [e] is present in the association list,
    according to uref equality *)
let rec assoc_list_mem (e : tau) (l : association list) =
  match l with
      [] -> None
    | (h, s, so) :: t ->
        if U.equal (h, e) then Some (s, so)
        else assoc_list_mem e t

(** Given a tau, create a unique recursive variable name. This should
    always return the same name for a given tau *)
let fresh_recvar_name (t : tau) : string =
  match find t with
      Pair p -> "rvp" ^ string_of_int p.p_stamp
    | Ref r -> "rvr" ^ string_of_int r.r_stamp
    | Fun f -> "rvf" ^ string_of_int f.f_stamp
    | _ -> die "fresh_recvar_name"


(** Return a string representation of a tau, using association lists. *)
let string_of_tau (t : tau) : string =
  let tau_map : association list ref = ref [] in
  let rec string_of_tau' t =
    match assoc_list_mem t !tau_map with
        Some (s, so) -> (* recursive type. see if a var name has been set *)
          begin
            match !so with
                None ->
                  let rv = fresh_recvar_name t in
                    s := "u " ^ rv ^ "." ^ !s;
                    so := Some rv;
                    rv
              | Some rv -> rv
          end
      | None -> (* type's not recursive. Add it to the assoc list and cont. *)
          let s = ref ""
          and so : string option ref = ref None in
            tau_map := (t, s, so) :: !tau_map;
            begin
              match find t with
                  Var v -> s := v.v_name
                | Pair p ->
                    insist (ref_or_var p.ptr) "wellformed";
                    insist (fun_or_var p.lam) "wellformed";
                    s := "{";
                    s := !s ^ string_of_tau' p.ptr;
                    s := !s ^ ",";
                    s := !s ^ string_of_tau' p.lam;
                    s := !s ^ "}"
                | Ref r ->
                    insist (pair_or_var r.points_to) "wellformed";
                    s := "ref(|";
                    s := !s ^ string_of_c_absloc r.rl;
                    s := !s ^ "|,";
                    s := !s ^ string_of_tau' r.points_to;
                    s := !s ^ ")"
                | Fun f ->
                    let rec string_of_args = function
                        [] -> ()
                      | h :: [] ->
                          insist (pair_or_var h) "wellformed";
                          s := !s ^ string_of_tau' h
                      | h :: t ->
                          insist (pair_or_var h) "wellformed";
                          s := !s ^ string_of_tau' h ^ ",";
                          string_of_args t
                    in
                      insist (pair_or_var f.ret) "wellformed";
                      s := "fun(|";
                      s := !s ^ string_of_c_absloc f.fl;
                      s := !s ^ "|,";
                      s := !s ^ "<";
                      if List.length f.args > 0 then string_of_args f.args
                      else s := !s ^ "void";
                      s := !s ^ ">,";
                      s := !s ^ string_of_tau' f.ret;
                      s := !s ^ ")"
            end;
            tau_map := List.tl !tau_map;
            !s
  in
    string_of_tau' t

(** Convert an lvalue to a string *)
let string_of_lvalue (lv : lvalue) : string =
  let contents = string_of_tau lv.contents
  and l = string_of_c_absloc lv.l
  in
    insist (pair_or_var lv.contents) "inconsistency at string_of_lvalue";
    (* do a consistency check *)
    Printf.sprintf "[%s]^(%s)" contents l

let print_constraint (c : tconstraint) =
  match c with
      Unification (t, t') ->
        let lhs = string_of_tau t in
        let rhs = string_of_tau t' in
          Printf.printf "%s == %s\n" lhs rhs
    | Leq (t, t') ->
        let lhs = string_of_tau t in
        let rhs = string_of_tau t' in
          Printf.printf "%s <= %s\n" lhs  rhs

(***********************************************************************)
(*                                                                     *)
(* Type Operations -- these do not create any constraints              *)
(*                                                                     *)
(***********************************************************************)

(** Create an lvalue with c_absloc [lbl] and tau contents [t]. *)
let make_lval (loc, t : c_absloc * tau) : lvalue =
  {l = loc; contents = t}

let make_c_absloc_int (is_top : bool) (name : string) (vio : Cil.varinfo option) : c_absloc =
  let my_absloc = (fresh_index (), name, vio) in
  let locc = C.add my_absloc C.empty
  in
    U.uref {
      l_name = name;
      l_top = is_top;
      l_stamp = fresh_stamp ();
      loc = my_absloc;
      aliases = locc;
      ubounds = B.empty;
      lbounds = B.empty;
      flow_computed = false
    }

(** Create a new c_absloc with name [name]. Also adds a fresh absloc
    with name [name] to this c_absloc's aliases set. *)
let make_c_absloc (is_top : bool) (name : string) (vio : Cil.varinfo option) =
  make_c_absloc_int is_top name vio

let fresh_c_absloc (is_top : bool) : c_absloc =
  let index = fresh_index () in
    make_c_absloc_int is_top (label_prefix ^ string_of_int index) None

(** Create a fresh bound (edge in the constraint graph). *)
let make_bound (a : c_absloc) : c_abslocinfo bound =
  {info = a}

let make_tau_bound (t : tau) : tinfo bound =
  {info = t}

(** Create a fresh named variable with name '[name]. *)
let make_var (is_top : bool) (name : string) : tau =
  U.uref (Var {v_name = ("'" ^ name);
               v_top = is_top;
               v_stamp = fresh_index ();
               v_lbounds = B.empty;
               v_ubounds = B.empty})

let fresh_var  (is_top : bool) : tau =
  make_var is_top ("fi" ^ string_of_int (fresh_index ()))

(** Create a fresh unnamed variable (name will be 'fi). *)
let fresh_var_i (is_top : bool) : tau =
  make_var is_top ("fi" ^ string_of_int (fresh_index ()))

(** Create a Fun constructor. *)
let make_fun (lbl, a, r : c_absloc * (tau list) * tau) : tau =
  U.uref (Fun {fl = lbl;
               f_stamp = fresh_index ();
               args = a;
               ret = r})

(** Create a Ref constructor. *)
let make_ref (lbl, pt : c_absloc * tau) : tau =
  U.uref (Ref {rl = lbl;
               r_stamp = fresh_index ();
               points_to = pt})

(** Create a Pair constructor. *)
let make_pair (p, f : tau * tau) : tau =
  U.uref (Pair {ptr = p;
                p_stamp = fresh_index ();
                lam = f})

(** Copy the toplevel constructor of [t], putting fresh variables in each
    argument of the constructor. *)
let copy_toplevel (t : tau) : tau =
  match find t with
      Pair _ -> make_pair (fresh_var_i false, fresh_var_i false)
    | Ref  _ -> make_ref (fresh_c_absloc false, fresh_var_i false)
    | Fun f ->
        make_fun (fresh_c_absloc false,
                  Util.list_map (fun _ -> fresh_var_i false) f.args,
                  fresh_var_i false)
    | _ -> die "copy_toplevel"

let pad_args (fi, tlr : finfo * tau list ref) : unit =
  let padding = List.length fi.args - List.length !tlr
  in
    if padding == 0 then ()
    else
      if padding > 0 then
        for _ = 1 to padding do
          tlr := !tlr @ [fresh_var false]
        done
      else
        for _ = 1 to -padding do
          fi.args <- fi.args @ [fresh_var false]
        done

(***********************************************************************)
(*                                                                     *)
(* Constraint Generation/ Resolution                                   *)
(*                                                                     *)
(***********************************************************************)

let set_top (b : bool) (t : tau) : unit =
  let set_top_down t =
    match find t with
        Var v -> v.v_top <- b
      | Ref r -> set_top_c_absloc r.rl b
      | Fun f -> set_top_c_absloc f.fl b
      | Pair p -> ()
  in
    iter_tau set_top_down t

let rec unify_int (t, t' : tau * tau) : unit =
  if equal_tau t t' then ()
  else
    let ti, ti' = find t, find t' in
      U.unify combine (t, t');
      match ti, ti' with
          Var v, Var v' ->
            set_top (v.v_top || v'.v_top) t';
            merge_v_lbounds (v, v');
            merge_v_ubounds (v, v')
        | Var v, _ ->
            set_top (v.v_top || top_tau t') t';
            notify_vlbounds t v;
            notify_vubounds t v
        | _, Var v ->
            set_top (v.v_top || top_tau t) t;
            notify_vlbounds t' v;
            notify_vubounds t' v
        | Ref r, Ref r' -> unify_ref (r, r')
        | Fun f, Fun f' -> unify_fun (f, f')
        | Pair p, Pair p' -> unify_pair (p, p')
        | _ -> raise Inconsistent
and notify_vlbounds (t : tau) (vi : vinfo) : unit =
  let notify bounds =
    List.iter
      (fun b ->
         add_constraint (Unification (b.info, copy_toplevel t));
         add_constraint (Leq (b.info, t)))
      bounds
  in
    notify (B.elements vi.v_lbounds)
and notify_vubounds (t : tau) (vi : vinfo) : unit =
  let notify bounds =
    List.iter
      (fun b ->
         add_constraint (Unification (b.info, copy_toplevel t));
         add_constraint (Leq (t, b.info)))
      bounds
  in
    notify (B.elements vi.v_ubounds)
and unify_ref (ri, ri' : rinfo * rinfo) : unit =
  unify_c_abslocs (ri.rl, ri'.rl);
  add_constraint (Unification (ri.points_to, ri'.points_to))
and unify_fun (fi, fi' : finfo * finfo) : unit =
  let rec union_args  = function
      _, [] -> false
    | [], _ -> true
    | h :: t, h' :: t' ->
        add_constraint (Unification (h, h'));
        union_args(t, t')
  in
    unify_c_abslocs (fi.fl, fi'.fl);
    add_constraint (Unification (fi.ret, fi'.ret));
    if union_args (fi.args, fi'.args) then fi.args <- fi'.args
and unify_pair (pi, pi' : pinfo * pinfo) : unit =
  add_constraint (Unification (pi.ptr, pi'.ptr));
  add_constraint (Unification (pi.lam, pi'.lam))
and unify_c_abslocs (l, l' : c_absloc * c_absloc) : unit =
  let pick_name (li, li' : c_abslocinfo * c_abslocinfo) =
    if starts_with li.l_name label_prefix then li.l_name <- li'.l_name
    else () in
  let combine_c_absloc (li, li' : c_abslocinfo * c_abslocinfo) : c_abslocinfo =
    pick_name (li, li');
    li.l_top <- li.l_top || li'.l_top;
    li.aliases <- C.union li.aliases li'.aliases;
    li.ubounds <- B.union li.ubounds li'.ubounds;
    li.lbounds <- B.union li.lbounds li'.lbounds;
    li
  in
    if !debug_constraints then
      Printf.printf
        "%s == %s\n"
        (string_of_c_absloc l)
        (string_of_c_absloc l');
    U.unify combine_c_absloc (l, l')
and merge_v_lbounds (vi, vi' : vinfo * vinfo) : unit =
  vi'.v_lbounds <- B.union vi.v_lbounds vi'.v_lbounds;
and merge_v_ubounds (vi, vi' : vinfo * vinfo) : unit =
  vi'.v_ubounds <- B.union vi.v_ubounds vi'.v_ubounds

(** Pick the representative info for two tinfo's. This function
    prefers the first argument when both arguments are the same
    structure, but when one type is a structure and the other is a
    var, it picks the structure.  All other actions (e.g., updating
    the info) is done in unify_int *)
and combine (ti, ti' : tinfo * tinfo) : tinfo =
  match ti, ti' with
      Var _, _ -> ti'
    | _, _ -> ti
and leq_int (t, t') : unit =
  if equal_tau t t' then ()
  else
    let ti, ti' = find t, find t' in
      match ti, ti' with
          Var v, Var v' ->
            v.v_ubounds <- B.add (make_tau_bound t') v.v_ubounds;
            v'.v_lbounds <- B.add (make_tau_bound t) v'.v_lbounds
        | Var v, _ ->
            add_constraint (Unification (t, copy_toplevel t'));
            add_constraint (Leq (t, t'))
        | _, Var v ->
            add_constraint (Unification (t', copy_toplevel t));
            add_constraint (Leq (t, t'))
        | Ref r, Ref r' -> leq_ref (r, r')
        | Fun f, Fun f' ->
            (* TODO: check, why not do subtyping here? *)
            add_constraint (Unification (t, t'))
        | Pair pr, Pair pr' ->
            add_constraint (Leq (pr.ptr, pr'.ptr));
            add_constraint (Leq (pr.lam, pr'.lam))
        | _ -> raise Inconsistent
and leq_ref (ri, ri') : unit =
  leq_c_absloc (ri.rl, ri'.rl);
  add_constraint (Unification (ri.points_to, ri'.points_to))
and leq_c_absloc (l, l') : unit =
  let li, li' = find l, find l' in
    if !debug_constraints then
      Printf.printf
        "%s <= %s\n"
        (string_of_c_absloc l)
        (string_of_c_absloc l');
    if U.equal (l, l') then ()
    else
      begin
        li.ubounds <- B.add (make_bound l') li.ubounds;
        li'.lbounds <- B.add (make_bound l) li'.lbounds
      end
and add_constraint_int (c : tconstraint) (toplev : bool) =
  if !debug_constraints && toplev then
    begin
      Printf.printf "%d:>" !toplev_count;
      print_constraint c;
      incr toplev_count
    end
  else
    if !debug_constraints then print_constraint c else ();
  insist (can_add_constraints ())
    "can't add constraints after compute_results is called";
  begin
    match c with
        Unification _ -> Q.add c eq_worklist
      | Leq _ -> Q.add c leq_worklist
  end;
  solve_constraints () (* solve online *)
and add_constraint (c : tconstraint) =
  add_constraint_int c false
and add_toplev_constraint (c : tconstraint) =
  if !print_constraints && not !debug_constraints then
    begin
      Printf.printf "%d:>" !toplev_count;
      incr toplev_count;
      print_constraint c
    end
  else ();
  add_constraint_int c true
and fetch_constraint () : tconstraint option =
  try Some (Q.take eq_worklist)
  with Q.Empty ->
    begin
      try Some (Q.take leq_worklist)
      with Q.Empty -> None
    end

(** The main solver loop. *)
and solve_constraints () : unit =
  match fetch_constraint () with
      None -> ()
    | Some c ->
        begin
          match c with
              Unification (t, t') -> unify_int (t, t')
            | Leq (t, t') ->
                if !no_sub then unify_int (t, t')
                else leq_int (t, t')
        end;
        solve_constraints ()

(***********************************************************************)
(*                                                                     *)
(* Interface Functions                                                 *)
(*                                                                     *)
(***********************************************************************)

(** Return the contents of the lvalue. *)
let rvalue (lv : lvalue) : tau =
  lv.contents

(** Dereference the rvalue. If it does not have enough structure to
    support the operation, then the correct structure is added via new
    unification constraints. *)
let rec deref (t : tau) : lvalue =
  match find t with
      Pair p ->
        begin
          match find p.ptr with
            | Var _ ->
                let is_top = top_tau p.ptr in
                let points_to = fresh_var is_top in
                let l = fresh_c_absloc is_top in
                let r = make_ref (l, points_to)
                in
                  add_toplev_constraint (Unification (p.ptr, r));
                  make_lval (l, points_to)
            | Ref r -> make_lval (r.rl, r.points_to)
            | _ -> raise WellFormed
        end
    | Var v ->
        let is_top = top_tau t in
          add_toplev_constraint
            (Unification (t, make_pair (fresh_var is_top, fresh_var is_top)));
          deref t
    | _ -> raise WellFormed


(** Form the union of [t] and [t'], if it doesn't exist already. *)
let join (t : tau) (t' : tau) : tau =
  let s, s' = get_stamp t, get_stamp t' in
    try H.find join_cache (s, s')
    with Not_found ->
      let t'' = fresh_var false in
        add_toplev_constraint (Leq (t, t''));
        add_toplev_constraint (Leq (t', t''));
        H.add join_cache (s, s') t'';
        t''

(** Form the union of a list [tl], expected to be the initializers of some
  structure or array type. *)
let join_inits (tl : tau list) : tau =
  let t' = fresh_var false in
    List.iter (function t -> add_toplev_constraint (Leq (t, t'))) tl;
    t'

(** Take the address of an lvalue. Does not add constraints. *)
let address (lv  : lvalue) : tau =
  make_pair (make_ref (lv.l, lv.contents), fresh_var false )

(** No instantiation in this analysis *)
let instantiate (lv : lvalue) (i : int) : lvalue =
  lv

(** Constraint generated from assigning [t] to [lv]. *)
let assign (lv : lvalue) (t : tau) : unit =
  add_toplev_constraint (Leq (t, lv.contents))

let assign_ret (i : int) (lv : lvalue) (t : tau) : unit =
  add_toplev_constraint (Leq (t, lv.contents))

(** Project out the first (ref) component or a pair. If the argument
    [t] has no discovered structure, raise NoContents. *)
let proj_ref (t : tau) : tau =
  match find t with
      Pair p -> p.ptr
    | Var v -> raise NoContents
    | _ ->  raise WellFormed

(* Project out the second (fun) component of a pair. If the argument
   [t] has no discovered structure, create it on the fly by adding
   constraints. *)
let proj_fun (t : tau) : tau =
  match find t with
      Pair p -> p.lam
    | Var v ->
        let p, f = fresh_var false, fresh_var false in
          add_toplev_constraint (Unification (t, make_pair (p, f)));
          f
    | _ -> raise WellFormed

let get_finfo (t : tau) : finfo =
  match find t with
      Fun f -> f
    | _ -> raise WellFormed

(** Function type [t] is applied to the arguments [actuals]. Unifies
    the actuals with the formals of [t]. If no functions have been
    discovered for [t] yet, create a fresh one and unify it with
    t. The result is the return value of the function plus the index
    of this application site.

    For this analysis, the application site is always 0 *)
let apply (t : tau) (al : tau list) : (tau * int) =
  let f = proj_fun t in
  let actuals = ref al in
  let fi, ret =
    match find f with
        Fun fi -> fi, fi.ret
      | Var v ->
          let new_l, new_ret, new_args =
            fresh_c_absloc false,
            fresh_var false,
            Util.list_map (function _ -> fresh_var false) !actuals
          in
          let new_fun = make_fun (new_l, new_args, new_ret) in
            add_toplev_constraint (Unification (new_fun, f));
            (get_finfo new_fun, new_ret)
      | _ -> raise WellFormed
  in
    pad_args (fi, actuals);
    List.iter2
      (fun actual -> fun formal ->
         add_toplev_constraint (Leq (actual, formal)))
      !actuals fi.args;
    (ret, 0)

let make_undefined_lvalue () =
  make_lval (make_c_absloc false "undefined" None,
             make_var true "undefined")

let make_undefined_rvalue () =
  make_var true "undefined"

let assign_undefined (lv : lvalue) : unit =
  assign lv (make_undefined_rvalue ())

let apply_undefined (al : tau list) : (tau * int) =
    List.iter
      (fun actual ->  assign (make_undefined_lvalue ()) actual)
      al;
   (fresh_var true, 0)

(** Create a new function type with name [name], list of formal
    arguments [formals], and return value [ret]. Adds no constraints. *)
let make_function (name : string) (formals : lvalue list) (ret : tau) : tau =
  let f = make_fun (make_c_absloc false name None,
                    Util.list_map (fun x -> rvalue x) formals,
                    ret)
  in
    make_pair (fresh_var false, f)

(** Create an lvalue. *)
let make_lvalue (b : bool ) (name : string) (vio : Cil.varinfo option) =
  make_lval (make_c_absloc false name vio,
             make_var false name)

(** Create a fresh named variable. *)
let make_fresh (name : string) : tau =
  make_var false name

(** The default type for abslocs. *)
let bottom () : tau =
  make_var false "bottom"

(** Unify the result of a function with its return value. *)
let return (t : tau) (t' : tau) =
  add_toplev_constraint (Leq (t', t))

(***********************************************************************)
(*                                                                     *)
(* Query/Extract Solutions                                             *)
(*                                                                     *)
(***********************************************************************)

module IntHash = Hashtbl.Make (struct
                                 type t = int
                                 let equal x y = x = y
                                 let hash x = x
                               end)


(** this is a quadratic flow step. keep it for debugging the fast
    version above. *)
let collect_ptset_slow (l : c_absloc) : abslocset =
  let onpath : unit IntHash.t = IntHash.create 101 in
  let rec flow_step (l : c_absloc) : abslocset =
    if top_c_absloc l then raise ReachedTop
    else
      let stamp = get_c_absloc_stamp l in
        if IntHash.mem onpath stamp then C.empty
        else
          let li = find l in
            IntHash.add onpath stamp ();
            B.iter
              (fun lb -> li.aliases <- C.union li.aliases (flow_step lb.info))
              li.lbounds;
            li.aliases
  in
    insist (can_query_graph ()) "collect_ptset_slow can't query graph";
    if get_flow_computed l then get_aliases l
    else
      begin
        set_flow_computed l;
        flow_step l
      end

let collect_ptset =
  collect_ptset_slow
  (* if !debug_flow_step then collect_ptset_slow
     else collect_ptset_fast *)

let may_alias (t1 : tau) (t2 : tau) : bool =
  let get_l (t : tau) : c_absloc =
    match find (proj_ref t) with
        Ref r -> r.rl
      | Var v -> raise NoContents
      | _ ->  raise WellFormed
  in
    try
      let l1 = get_l t1
      and l2 = get_l t2 in
        equal_c_absloc l1 l2 ||
          not (C.is_empty (C.inter (collect_ptset l1) (collect_ptset l2)))
    with
        NoContents -> false
      | ReachedTop -> raise UnknownLocation

let points_to_aux (t : tau) : absloc list =
  try
    match find (proj_ref t) with
        Var v -> []
      | Ref r -> C.elements (collect_ptset r.rl)
      | _ -> raise WellFormed
  with
      NoContents -> []
    | ReachedTop -> raise UnknownLocation

let points_to (lv : lvalue) : Cil.varinfo list =
  let rec get_vinfos l : Cil.varinfo list =
    match l with
        [] -> []
      | (_, _, Some h) :: t -> h :: get_vinfos t
      | (_, _, None) :: t -> get_vinfos t
  in
    get_vinfos (points_to_aux lv.contents)

let epoints_to (t : tau) : Cil.varinfo list =
  let rec get_vinfos l : Cil.varinfo list = match l with
      [] -> []
    | (_, _, Some h) :: t -> h :: get_vinfos t
    | (_, _, None) :: t -> get_vinfos t
  in
    get_vinfos (points_to_aux t)

let points_to_names (lv : lvalue) : string list =
  Util.list_map (fun v -> v.vname) (points_to lv)

let absloc_points_to (lv : lvalue) : absloc list =
  points_to_aux lv.contents

let absloc_epoints_to (t : tau) : absloc list =
  points_to_aux t

let absloc_of_lvalue (lv : lvalue) : absloc =
  (find lv.l).loc

let absloc_eq = equal_absloc