viewcvs.cgi/typing/typer.ml

(* I. Transform the abstract syntax of types and patterns into
      the internal form *)

open Location
open Ast
open Ident

module S = struct type t = string let compare = compare end
module TypeEnv = Map.Make(S)
module Env = Map.Make(Ident.Id)
(*
module StringSet = Set.Make(S)
*)

exception NonExhaustive of Types.descr
exception MultipleLabel of Types.label
exception Constraint of Types.descr * Types.descr * string
exception ShouldHave of Types.descr * string
exception WrongLabel of Types.descr * Types.label
exception UnboundId of string

let raise_loc loc exn = raise (Location (loc,exn))

(* Internal representation as a graph (desugar recursive types and regexp),
   to compute freevars, etc... *)

type ti = {
  id : int; 
  mutable seen : bool;
  mutable loc' : loc;
  mutable fv : fv option; 
  mutable descr': descr;
  mutable type_node: Types.node option;
  mutable pat_node: Patterns.node option
} 
and descr =
  | IAlias of string * ti
  | IType of Types.descr
  | IOr of ti * ti
  | IAnd of ti * ti
  | IDiff of ti * ti
  | ITimes of ti * ti
  | IXml of ti * ti
  | IArrow of ti * ti
  | IOptional of ti
  | IRecord of bool * (Types.label * ti) list
  | ICapture of id
  | IConstant of id * Types.const
    

type glb = ti TypeEnv.t

let mk' =
  let counter = ref 0 in
  fun loc ->
    incr counter;
    let rec x = { 
      id = !counter; 
      seen = false;
      loc' = loc; 
      fv = None; 
      descr' = IAlias ("__dummy__", x);
      type_node = None; 
      pat_node = None 
    } in
    x

let cons loc d =
  let x = mk' loc in
  x.descr' <- d;
  x
    
(* Note:
   Compilation of Regexp is implemented as a ``rewriting'' of
   the parsed syntax, in order to be able to print its result
   (for debugging for instance)
   
   It would be possible (and a little more efficient) to produce
   directly ti nodes.
*)
    
module Regexp = struct
  let defs = ref []
  let name =
    let c = ref 0 in
    fun () ->
      incr c;
      "#" ^ (string_of_int !c)

  let rec seq_vars accu = function
    | Epsilon | Elem _ -> accu
    | Seq (r1,r2) | Alt (r1,r2) -> seq_vars (seq_vars accu r1) r2
    | Star r | WeakStar r -> seq_vars accu r
    | SeqCapture (v,r) -> seq_vars (IdSet.add v accu) r

  let uniq_id = let r = ref 0 in fun () -> incr r; !r

  type flat =  
    | REpsilon 
    | RElem of int * Ast.ppat  (* the int arg is used
                                            to stop generic comparison *)
    | RSeq of flat * flat
    | RAlt of flat * flat
    | RStar of flat
    | RWeakStar of flat

  let re_loc = ref noloc

  let rec propagate vars : regexp -> flat = function
    | Epsilon -> REpsilon
    | Elem x -> let p = vars x in RElem (uniq_id (),p)
    | Seq (r1,r2) -> RSeq (propagate vars r1,propagate vars r2)
    | Alt (r1,r2) -> RAlt (propagate vars r1, propagate vars r2)
    | Star r -> RStar (propagate vars r)
    | WeakStar r -> RWeakStar (propagate vars r)
    | SeqCapture (v,x) -> 
        let v= mk !re_loc (Capture v) in
        propagate (fun p -> mk !re_loc (And (vars p,v))) x

  let dummy_pat = mk noloc (PatVar "DUMMY")
  let cup r1 r2 =
    if r1 == dummy_pat then r2 else
      if r2 == dummy_pat then r1 else
        mk !re_loc (Or (r1,r2))

(*TODO: review this compilation schema to avoid explosion when
  coding (Optional x) by  (Or(Epsilon,x)); memoization ... *)

  module Memo = Map.Make(struct type t = flat list let compare = compare end)
  module Coind = Set.Make(struct type t = flat list let compare = compare end)
  let memo = ref Memo.empty


  let rec compile fin e seq : Ast.ppat = 
    if Coind.mem seq !e then dummy_pat
    else (
      e := Coind.add seq !e;
      match seq with
        | [] ->
            fin
        | REpsilon :: rest -> 
            compile fin e rest
        | RElem (_,p) :: rest -> 
            mk !re_loc (Prod (p, guard_compile fin rest))
        | RSeq (r1,r2) :: rest -> 
            compile fin e (r1 :: r2 :: rest)
        | RAlt (r1,r2) :: rest -> 
            cup (compile fin e (r1::rest)) (compile fin e (r2::rest))
        | RStar r :: rest -> 
            cup (compile fin e (r::seq)) (compile fin e rest) 
        | RWeakStar r :: rest -> 
            cup (compile fin e rest) (compile fin e (r::seq))
    )
  and guard_compile fin seq =
    try Memo.find seq !memo
    with
        Not_found ->
          let n = name () in
          let v = mk !re_loc (PatVar n) in
          memo := Memo.add seq v !memo;
          let d = compile fin (ref Coind.empty) seq in
          assert (d != dummy_pat);
          defs := (n,d) :: !defs;
          v

(*
  type trans = [ `Alt of gnode * gnode | `Elem of Ast.ppat * gnode | `Final ]
  and gnode = 
      {
        mutable seen  : bool;
        mutable compile : bool;
        name  : string;
        mutable trans : trans;
      }

  let new_node() = { seen = false; compile = false; 
                     name = name(); trans = `Final }
  let to_compile = ref []

  let rec compile after = function
    | `Epsilon -> after
    | `Elem (_,p) -> 
        if not after.compile then (after.compile <- true; 
                                   to_compile := after :: !to_compile);
        { new_node () with trans = `Elem (p, after)  }
    | `Seq(r1,r2) -> compile (compile after r2) r1
    | `Alt(r1,r2) ->
        let r1 = compile after r1 and r2 = compile after r2 in
        { new_node () with trans = `Alt (r1,r2) }
    | `Star r ->
        let n  = new_node() in
        n.trans <- `Alt (compile n r, after);
        n
    | `WeakStar r ->
        let n  = new_node() in
        n.trans <- `Alt (after, compile n r);
        n

  let seens = ref []    
  let rec collect_aux accu n =
    if n.seen then accu 
    else ( seens := n :: !seens;
           match n.trans with
             | `Alt (n1,n2) -> collect_aux (collect_aux accu n2) n1
             | _ -> n :: accu
         )

  let collect fin n =
    let l = collect_aux [] n in
    List.iter (fun n -> n.seen <- false) !seens;
    let l = List.map (fun n ->
                        match n.trans with
                          | `Final -> fin
                          | `Elem (p,a) -> 
                              mk !re_loc (Prod(p, mk !re_loc (PatVar a.name)))
                          | _ -> assert false
                     ) l in
    match l with
      | h::t ->
          List.fold_left (fun accu p -> mk !re_loc (Or (accu,p))) h t
      | _ -> assert false
*)    
        

  let constant_nil t v = 
    mk !re_loc 
      (And (t, (mk !re_loc (Constant (v, Types.Atom Sequence.nil_atom)))))

  let compile loc regexp queue : ppat =
    re_loc := loc;
    let vars = seq_vars IdSet.empty regexp in
    let fin = IdSet.fold constant_nil queue vars in
    let re = propagate (fun p -> p) regexp in
    let n = guard_compile fin [re] in
    memo := Memo.empty; 
    let d = !defs in
    defs := [];

(*
    let after = new_node() in
    let n = collect queue (compile after re) in
    let d = List.map (fun n -> (n.name, collect queue n)) !to_compile in
    to_compile := [];
*)

    mk !re_loc (Recurs (n,d))
end

let compile_regexp = Regexp.compile noloc


let rec compile env { loc = loc; descr = d } : ti = 
  match (d : Ast.ppat') with
  | PatVar s -> 
      (try TypeEnv.find s env
       with Not_found -> 
         raise_loc_generic loc ("Undefined type variable " ^ s)
      )
  | Recurs (t, b) -> compile (compile_many env b) t
  | Regexp (r,q) -> compile env (Regexp.compile loc r q)
  | Internal t -> cons loc (IType t)
  | Or (t1,t2) -> cons loc (IOr (compile env t1, compile env t2))
  | And (t1,t2) -> cons loc (IAnd (compile env t1, compile env t2))
  | Diff (t1,t2) -> cons loc (IDiff (compile env t1, compile env t2))
  | Prod (t1,t2) -> cons loc (ITimes (compile env t1, compile env t2))
  | XmlT (t1,t2) -> cons loc (IXml (compile env t1, compile env t2))
  | Arrow (t1,t2) -> cons loc (IArrow (compile env t1, compile env t2))
  | Optional t -> cons loc (IOptional (compile env t))
  | Record (o,r) -> 
      cons loc (IRecord (o, List.map (fun (l,t) -> l,compile env t) r))
  | Constant (x,v) -> cons loc (IConstant (x,v))
  | Capture x -> cons loc (ICapture x)

and compile_many env b = 
  let b = List.map (fun (v,t) -> (v,t,mk' t.loc)) b in
  let env = 
    List.fold_left (fun env (v,t,x) -> TypeEnv.add v x env) env b in
  List.iter (fun (v,t,x) -> x.descr' <- IAlias (v, compile env t)) b;
  env

module IntSet = 
  Set.Make(struct type t = int let compare (x:int) y = compare x y end)

let comp_fv_seen = ref []
let comp_fv_res = ref IdSet.empty
let rec comp_fv s =
  match s.fv with
    | Some fv -> comp_fv_res := IdSet.cup fv !comp_fv_res
    | None ->
        (match s.descr' with
           | IAlias (_,x) -> 
               if x.seen then ()
               else ( 
                 x.seen <- true;
                 comp_fv_seen := x :: !comp_fv_seen; 
                 comp_fv x
               ) 
           | IOr (s1,s2) 
           | IAnd (s1,s2)
           | IDiff (s1,s2)
           | ITimes (s1,s2) | IXml (s1,s2)
           | IArrow (s1,s2) -> comp_fv s1; comp_fv s2
           | IOptional r -> comp_fv r
           | IRecord (_,r) -> List.iter (fun (l,s) -> comp_fv s) r
           | IType _ -> ()
           | ICapture x
           | IConstant (x,_) -> comp_fv_res := IdSet.add x !comp_fv_res
        )


let fv s =   
  match s.fv with
    | Some l -> l
    | None -> 
        comp_fv s;
        let l = !comp_fv_res in
        comp_fv_res := IdSet.empty;
        List.iter (fun n -> n.seen <- false) !comp_fv_seen;
        comp_fv_seen := [];
        s.fv <- Some l; 
        l

let rec typ seen s : Types.descr =
  match s.descr' with
    | IAlias (v,x) ->
        if IntSet.mem s.id seen then 
          raise_loc_generic s.loc' 
            ("Unguarded recursion on variable " ^ v ^ " in this type")
        else typ (IntSet.add s.id seen) x
    | IType t -> t
    | IOr (s1,s2) -> Types.cup (typ seen s1) (typ seen s2)
    | IAnd (s1,s2) ->  Types.cap (typ seen s1) (typ seen s2)
    | IDiff (s1,s2) -> Types.diff (typ seen s1) (typ seen s2)
    | ITimes (s1,s2) -> Types.times (typ_node s1) (typ_node s2)
    | IXml (s1,s2) ->   Types.xml (typ_node s1) (typ_node s2)
    | IArrow (s1,s2) -> Types.arrow (typ_node s1) (typ_node s2)
    | IOptional s -> Types.Record.or_absent (typ seen s)
    | IRecord (o,r) -> 
        Types.record' 
          (o,List.map (fun (l,s) -> (l,typ_node s)) r)
    | ICapture x | IConstant (x,_) -> assert false

and typ_node s : Types.node =
  match s.type_node with
    | Some x -> x
    | None ->
        let x = Types.make () in
        s.type_node <- Some x;
        let t = typ IntSet.empty s in
        Types.define x t;
        x

let type_node s = 
  let s = typ_node s in
  let s = Types.internalize s in
(*  Types.define s (Types.normalize (Types.descr s)); *)
  s

let rec pat seen s : Patterns.descr =
  if IdSet.is_empty (fv s) 
  then Patterns.constr (Types.descr (type_node s)) 
  else
    try pat_aux seen s
    with Patterns.Error e -> raise_loc_generic s.loc' e
      | Location (loc,exn) when loc = noloc -> raise (Location (s.loc', exn))


and pat_aux seen s = match s.descr' with
  | IAlias (v,x) ->
      if IntSet.mem s.id seen 
      then raise 
        (Patterns.Error
           ("Unguarded recursion on variable " ^ v ^ " in this pattern"));
      pat (IntSet.add s.id seen) x
  | IOr (s1,s2) -> Patterns.cup (pat seen s1) (pat seen s2)
  | IAnd (s1,s2) -> Patterns.cap (pat seen s1) (pat seen s2)
  | IDiff (s1,s2) when IdSet.is_empty (fv s2) ->
      let s2 = Types.neg (Types.descr (type_node s2)) in
      Patterns.cap (pat seen s1) (Patterns.constr s2)
  | IDiff _ ->
      raise (Patterns.Error "Difference not allowed in patterns")
  | ITimes (s1,s2) -> Patterns.times (pat_node s1) (pat_node s2)
  | IXml (s1,s2) -> Patterns.xml (pat_node s1) (pat_node s2)
  | IOptional _ -> 
      raise 
      (Patterns.Error 
         "Optional field not allowed in record patterns")
  | IRecord (o,r) ->
      let pats = ref [] in
      let aux (l,s) = 
        if IdSet.is_empty (fv s) then (l,type_node s)
        else
          ( 
            pats := Patterns.record l (pat_node s) :: !pats;
            (l,Types.any_node)
          ) in
      let constr = Types.record' (o,List.map aux r) in
      List.fold_left Patterns.cap (Patterns.constr constr) !pats
(* TODO: can avoid constr when o=true, and all fields have fv *)
  | ICapture x ->  Patterns.capture x
  | IConstant (x,c) -> Patterns.constant x c
  | IArrow _ ->
      raise (Patterns.Error "Arrow not allowed in patterns")
  | IType _ -> assert false

and pat_node s : Patterns.node =
  match s.pat_node with
    | Some x -> x
    | None ->
        let x = Patterns.make (fv s) in
        s.pat_node <- Some x;
        let t = pat IntSet.empty s in
        Patterns.define x t;
        x

let mk_typ e =
  if IdSet.is_empty (fv e) then type_node e
  else raise_loc_generic e.loc' "Capture variables are not allowed in types"
    

let typ glb e =
  mk_typ (compile glb e)

let pat glb e =
  pat_node (compile glb e)

let register_global_types glb b =
  let env' = compile_many glb b in
  List.fold_left 
    (fun glb (v,{ loc = loc }) -> 
       let t = TypeEnv.find v env' in
       let d = Types.descr (mk_typ t) in
       (*              let d = Types.normalize d in*)
       Types.Print.register_global v d;
       if TypeEnv.mem v glb
       then raise_loc_generic loc ("Multiple definition for type " ^ v);
       TypeEnv.add v t glb
    ) glb b


(* II. Build skeleton *)

module Fv = IdSet

(* IDEA: introduce a node Loc in the AST to override nolocs
   in sub-expressions *)
   
let rec expr loc' glb { loc = loc; descr = d } = 
  let loc =  if loc = noloc then loc' else loc in
  let (fv,td) = 
    match d with
      | Forget (e,t) ->
          let (fv,e) = expr loc glb e and t = typ glb t in
          (fv, Typed.Forget (e,t))
      | Var s -> (Fv.singleton s, Typed.Var s)
      | Apply (e1,e2) -> 
          let (fv1,e1) = expr loc glb e1 and (fv2,e2) = expr loc glb e2 in
          (Fv.cup fv1 fv2, Typed.Apply (e1,e2))
      | Abstraction a ->
          let iface = List.map (fun (t1,t2) -> (typ glb t1, typ glb t2)) 
                        a.fun_iface in
          let t = List.fold_left 
                    (fun accu (t1,t2) -> Types.cap accu (Types.arrow t1 t2)) 
                    Types.any iface in
          let iface = List.map 
                        (fun (t1,t2) -> (Types.descr t1, Types.descr t2)) 
                        iface in
          let (fv0,body) = branches loc glb a.fun_body in
          let fv = match a.fun_name with
            | None -> fv0
            | Some f -> Fv.remove f fv0 in
          (fv,
           Typed.Abstraction 
             { Typed.fun_name = a.fun_name;
               Typed.fun_iface = iface;
               Typed.fun_body = body;
               Typed.fun_typ = t;
               Typed.fun_fv = fv
             }
          )
      | Cst c -> (Fv.empty, Typed.Cst c)
      | Pair (e1,e2) ->
          let (fv1,e1) = expr loc glb e1 and (fv2,e2) = expr loc glb e2 in
          (Fv.cup fv1 fv2, Typed.Pair (e1,e2))
      | Xml (e1,e2) ->
          let (fv1,e1) = expr loc glb e1 and (fv2,e2) = expr loc glb e2 in
          (Fv.cup fv1 fv2, Typed.Xml (e1,e2))
      | Dot (e,l) ->
          let (fv,e) = expr loc glb e in
          (fv,  Typed.Dot (e,l))
      | RecordLitt r -> 
          let fv = ref Fv.empty in
          let r  = List.sort (fun (l1,_) (l2,_) -> compare l1 l2) r in
          let r = List.map 
                    (fun (l,e) -> 
                       let (fv2,e) = expr loc glb e 
                       in fv := Fv.cup !fv fv2; (l,e))
                    r in
          let rec check = function
            | (l1,_) :: (l2,_) :: _ when l1 = l2 -> 
                raise_loc loc (MultipleLabel l1)
            | _ :: rem -> check rem
            | _ -> () in
          check r;
          (!fv, Typed.RecordLitt r)
      | Op (op,le) ->
          let (fvs,ltes) = List.split (List.map (expr loc glb) le) in
          let fv = List.fold_left Fv.cup Fv.empty fvs in
          (fv, Typed.Op (op,ltes))
      | Match (e,b) -> 
          let (fv1,e) = expr loc glb e
          and (fv2,b) = branches loc glb b in
          (Fv.cup fv1 fv2, Typed.Match (e, b))
      | Map (e,b) ->
          let (fv1,e) = expr loc glb e
          and (fv2,b) = branches loc glb b in
          (Fv.cup fv1 fv2, Typed.Map (e, b))
      | Try (e,b) ->
          let (fv1,e) = expr loc glb e
          and (fv2,b) = branches loc glb b in
          (Fv.cup fv1 fv2, Typed.Try (e, b))
  in
  fv,
  { Typed.exp_loc = loc;
    Typed.exp_typ = Types.empty;
    Typed.exp_descr = td;
  }
              
  and branches loc glb b = 
    let fv = ref Fv.empty in
    let accept = ref Types.empty in
    let b = List.map 
              (fun (p,e) ->
                 let (fv2,e) = expr loc glb e in
                 let p = pat glb p in
                 let fv2 = Fv.diff fv2 (Patterns.fv p) in
                 fv := Fv.cup !fv fv2;
                 accept := Types.cup !accept (Types.descr (Patterns.accept p));
                 { Typed.br_used = false;
                   Typed.br_pat = p;
                   Typed.br_body = e }
              ) b in
    (!fv, 
     { 
       Typed.br_typ = Types.empty; 
       Typed.br_branches = b; 
       Typed.br_accept = !accept;
       Typed.br_compiled = None;
     } 
    )

let expr = expr noloc

let let_decl glb p e =
  let (_,e) = expr glb e in
  { Typed.let_pat = pat glb p;
    Typed.let_body = e;
    Typed.let_compiled = None }

(* III. Type-checks *)

type env = Types.descr Env.t

open Typed

let warning loc msg =
  Format.fprintf !Location.warning_ppf "Warning %a:@\n%a%s@\n" 
    Location.print_loc loc
    Location.html_hilight loc
    msg

let check loc t s msg =
  if not (Types.subtype t s) then raise_loc loc (Constraint (t, s, msg))

let rec type_check env e constr precise = 
(*  Format.fprintf Format.std_formatter "constr=%a precise=%b@\n"
    Types.Print.print_descr constr precise; 
*)
  let d = type_check' e.exp_loc env e.exp_descr constr precise in
  e.exp_typ <- Types.cup e.exp_typ d;
  d

and type_check' loc env e constr precise = match e with
  | Forget (e,t) ->
      let t = Types.descr t in
      ignore (type_check env e t false);
      t
  | Abstraction a ->
      let t =
        try Types.Arrow.check_strenghten a.fun_typ constr 
        with Not_found -> 
          raise_loc loc 
          (ShouldHave
             (constr, "but the interface of the abstraction is not compatible"))
      in
      let env = match a.fun_name with
        | None -> env
        | Some f -> Env.add f a.fun_typ env in
      List.iter 
        (fun (t1,t2) ->
           ignore (type_check_branches loc env t1 a.fun_body t2 false)
        ) a.fun_iface;
      t

  | Match (e,b) ->
      let t = type_check env e b.br_accept true in
      type_check_branches loc env t b constr precise

  | Try (e,b) ->
      let te = type_check env e constr precise in
      let tb = type_check_branches loc env Types.any b constr precise in
      Types.cup te tb

  | Pair (e1,e2) ->
      type_check_pair loc env e1 e2 constr precise
  | Xml (e1,e2) ->
      type_check_pair ~kind:`XML loc env e1 e2 constr precise

(*
  | RecordLitt r ->
      let rconstr = Types.Record.get constr in
      if Types.Record.is_empty rconstr then
        raise_loc loc (ShouldHave (constr,"but it is a record."));

(* Completely buggy !  Need to check at the end that all required labels 
   are present ...A better to do it without precise = true ? *)
      let precise = true in

      let (rconstr,res) = 
        List.fold_left 
          (fun (rconstr,res) (l,e) ->
             let rconstr = Types.Record.restrict_label_present rconstr l in
             let pi = Types.Record.project_field rconstr l in
             if Types.Record.is_empty rconstr then
               raise_loc loc 
                 (ShouldHave (constr,(Printf.sprintf 
                                        "Field %s is not allowed here."
                                        (Types.LabelPool.value l)
                                     )
                             ));
             let t = type_check env e pi true in
             let rconstr = Types.Record.restrict_field rconstr l t in
             
             let res = 
               if precise 
               then Types.cap res (Types.record l false (Types.cons t))
               else res in
             (rconstr,res)
          ) (rconstr, if precise then Types.Record.any else constr) r
      in
(*      check loc res constr ""; *)
      res
*)

  | Map (e,b) ->
      let t = type_check env e (Sequence.star b.br_accept) true in

      let constr' = Sequence.approx (Types.cap Sequence.any constr) in
      let exact = Types.subtype (Sequence.star constr') constr in
      (* Note: 
         - could be more precise by integrating the decomposition
         of constr inside Sequence.map.
      *)
      let res = 
        Sequence.map 
          (fun t -> 
             type_check_branches loc env t b constr' (precise || (not exact)))
          t in
      if not exact then check loc res constr "";
      if precise then res else constr
  | Op ("@", [e1;e2]) ->
      let constr' = Sequence.star 
                      (Sequence.approx (Types.cap Sequence.any constr)) in
      let exact = Types.subtype constr' constr in
      if exact then
        let t1 = type_check env e1 constr' precise
        and t2 = type_check env e2 constr' precise in
        if precise then Sequence.concat t1 t2 else constr
      else
        (* Note:
           the knownledge of t1 may makes it useless to
           check t2 with 'precise' ... *)
        let t1 = type_check env e1 constr' true
        and t2 = type_check env e2 constr' true in
        let res = Sequence.concat t1 t2 in
        check loc res constr "";
        if precise then res else constr
  | Apply (e1,e2) ->
(*
      let constr' = Sequence.star 
                      (Sequence.approx (Types.cap Sequence.any constr)) in
      let t1 = type_check env e1 (Types.cup Types.Arrow.any constr') true in
      let t1_fun = Types.Arrow.get t1 in

      let has_fun = not (Types.Arrow.is_empty t1_fun)
      and has_seq = not (Types.subtype t1 Types.Arrow.any) in

      let constr' =
        Types.cap 
          (if has_fun then Types.Arrow.domain t1_fun else Types.any)
          (if has_seq then constr' else Types.any)
      in
      let need_arg = has_fun && Types.Arrow.need_arg t1_fun in
      let precise  = need_arg || has_seq in
      let t2 = type_check env e2 constr' precise in
      let res = Types.cup 
                  (if has_fun then 
                     if need_arg then Types.Arrow.apply t1_fun t2
                     else Types.Arrow.apply_noarg t1_fun
                   else Types.empty)
                  (if has_seq then Sequence.concat t1 t2
                   else Types.empty)
      in
      check loc res constr "";
      res
*)
      let t1 = type_check env e1 Types.Arrow.any true in
      let t1 = Types.Arrow.get t1 in
      let dom = Types.Arrow.domain t1 in
      let res =
        if Types.Arrow.need_arg t1 then
          let t2 = type_check env e2 dom true in
          Types.Arrow.apply t1 t2
        else
          (ignore (type_check env e2 dom false); Types.Arrow.apply_noarg t1)
      in
      check loc res constr "";
      res
  | Op ("flatten", [e]) ->
      let constr' = Sequence.star 
                      (Sequence.approx (Types.cap Sequence.any constr)) in
      let sconstr' = Sequence.star constr' in
      let exact = Types.subtype constr' constr in
      if exact then
        let t = type_check env e sconstr' precise in
        if precise then Sequence.flatten t else constr
      else
        let t = type_check env e sconstr' true in
        let res = Sequence.flatten t in
        check loc res constr "";
        if precise then res else constr
  | _ -> 
      let t : Types.descr = compute_type' loc env e in
      check loc t constr "";
      t

and type_check_pair ?(kind=`Normal) loc env e1 e2 constr precise =
  let rects = Types.Product.get ~kind constr in
  if Types.Product.is_empty rects then 
    (match kind with
      | `Normal -> raise_loc loc (ShouldHave (constr,"but it is a pair."))
      | `XML -> raise_loc loc (ShouldHave (constr,"but it is an XML element.")));
  let pi1 = Types.Product.pi1 rects in
  
  let t1 = type_check env e1 (Types.Product.pi1 rects) 
             (precise || (Types.Product.need_second rects))in
  let rects = Types.Product.restrict_1 rects t1 in
  let t2 = type_check env e2 (Types.Product.pi2 rects) precise in
  if precise then 
    match kind with
      | `Normal -> Types.times (Types.cons t1) (Types.cons t2)
      | `XML -> Types.xml (Types.cons t1) (Types.cons t2)
  else
    constr


and compute_type env e =
  type_check env e Types.any true

and compute_type' loc env = function
  | Var s -> 
      (try Env.find s env 
       with Not_found -> raise_loc loc (UnboundId (Id.value s))
      )
  | Cst c -> Types.constant c
  | Dot (e,l) ->
      let t = type_check env e Types.Record.any true in
         (try (Types.Record.project t l) 
          with Not_found -> raise_loc loc (WrongLabel(t,l)))
  | Op (op, el) ->
      let args = List.map (fun e -> (e.exp_loc, compute_type env e)) el in
      type_op loc op args
  | Map (e,b) ->
      let t = compute_type env e in
      Sequence.map (fun t -> type_check_branches loc env t b Types.any true) t

(* We keep these cases here to allow comparison and benchmarking ...
   Just comment the corresponding cases in type_check' to
   activate these ones.
*)
  | Pair (e1,e2) -> 
      let t1 = compute_type env e1 
      and t2 = compute_type env e2 in
      Types.times (Types.cons t1) (Types.cons t2)
  | RecordLitt r ->
      let r = 
        List.map
          (fun (l,e) -> (l,Types.cons (compute_type env e)))
          r in
      Types.record' (false,r)
  | _ -> assert false

and type_check_branches loc env targ brs constr precise =
  if Types.is_empty targ then Types.empty 
  else (
    brs.br_typ <- Types.cup brs.br_typ targ;
    branches_aux loc env targ 
      (if precise then Types.empty else constr) 
      constr precise brs.br_branches
  )
    
and branches_aux loc env targ tres constr precise = function
  | [] -> raise_loc loc (NonExhaustive targ)
  | b :: rem ->
      let p = b.br_pat in
      let acc = Types.descr (Patterns.accept p) in

      let targ' = Types.cap targ acc in
      if Types.is_empty targ' 
      then branches_aux loc env targ tres constr precise rem
      else 
        ( b.br_used <- true;
          let res = Patterns.filter targ' p in
          let env' = List.fold_left 
                       (fun env (x,t) -> Env.add x (Types.descr t) env) 
                       env res in
          let t = type_check env' b.br_body constr precise in
          let tres = if precise then Types.cup t tres else tres in
          let targ'' = Types.diff targ acc in
          if (Types.non_empty targ'') then 
            branches_aux loc env targ'' tres constr precise rem 
          else
            tres
        )

and type_let_decl env l =
  let acc = Types.descr (Patterns.accept l.let_pat) in
  let t = type_check env l.let_body acc true in
  let res = Patterns.filter t l.let_pat in
  List.map (fun (x,t) -> (x, Types.descr t)) res

and type_rec_funs env l =
  let types = 
    List.fold_left
      (fun accu -> function  {let_body={exp_descr=Abstraction a}} as l ->
         let t = a.fun_typ in
         let acc = Types.descr (Patterns.accept l.let_pat) in
         if not (Types.subtype t acc) then
           raise_loc l.let_body.exp_loc (NonExhaustive (Types.diff t acc));
         let res = Patterns.filter t l.let_pat in
         List.fold_left (fun accu (x,t) -> (x, Types.descr t)::accu) accu res
         | _ -> assert false) [] l
  in
  let env' = List.fold_left (fun env (x,t) -> Env.add x t env) env types in
  List.iter 
    (function  { let_body = { exp_descr = Abstraction a } } as l ->
       ignore (type_check env' l.let_body Types.any false)
       | _ -> assert false) l;
  types


and type_op loc op args =
  match (op,args) with
    | "+", [loc1,t1; loc2,t2] ->
        type_int_binop Intervals.add loc1 t1 loc2 t2
    | "-", [loc1,t1; loc2,t2] ->
        type_int_binop Intervals.sub loc1 t1 loc2 t2
    | ("*" | "/" | "mod"), [loc1,t1; loc2,t2] ->
        type_int_binop (fun i1 i2 -> Intervals.any) loc1 t1 loc2 t2
    | "@", [loc1,t1; loc2,t2] ->
        check loc1 t1 Sequence.any
          "The first argument of @ must be a sequence";
        Sequence.concat t1 t2
    | "flatten", [loc1,t1] ->
        check loc1 t1 Sequence.seqseq 
          "The argument of flatten must be a sequence of sequences";
        Sequence.flatten t1
    | "load_xml", [loc1,t1] ->
        check loc1 t1 Sequence.string
          "The argument of load_xml must be a string (filename)";
        Types.any
    | "load_html", [loc1,t1] ->
        check loc1 t1 Sequence.string
          "The argument of load_html must be a string (filename)";
        Types.any
    | "raise", [loc1,t1] ->
        Types.empty
    | "print_xml", [loc1,t1] ->
        Sequence.string
    | "print", [loc1,t1] ->
        check loc1 t1 Sequence.string
          "The argument of print must be a string";
        Sequence.nil_type
    | "dump_to_file", [loc1,t1; loc2,t2] ->
        check loc1 t1 Sequence.string
          "The argument of dump_to_file must be a string (filename)";
        check loc2 t2 Sequence.string
          "The argument of dump_to_file must be a string (value to dump)";
        Sequence.nil_type
    | "int_of", [loc1,t1] ->
        check loc1 t1 Sequence.string
          "The argument of int_of must be a string";
        if not (Types.subtype t1 Builtin.intstr) then
          warning loc "This application of int_of may fail";
        Types.interval Intervals.any
    | "string_of", [loc1,t1] ->
        Sequence.string
    | _ -> assert false

and type_int_binop f loc1 t1 loc2 t2 =
  if not (Types.Int.is_int t1) then
    raise_loc loc1 
      (Constraint 
         (t1,Types.Int.any,
          "The first argument must be an integer"));
  if not (Types.Int.is_int t2) then
    raise_loc loc2
      (Constraint 
               (t2,Types.Int.any,
                "The second argument must be an integer"));
  Types.Int.put
    (f (Types.Int.get t1) (Types.Int.get t2));
  
