viewcvs.cgi/typing/typer.ml

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

open Location
open Ast

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

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 loc' : loc;
  mutable fv : string SortedList.t option; 
  mutable descr': descr;
  mutable type_node: Types.node option;
  mutable pat_node: Patterns.node option
} 
and descr =
   [ `Alias of string * ti
   | `Type of Types.descr
   | `Or of ti * ti
   | `And of ti * ti
   | `Diff of ti * ti
   | `Times of ti * ti
   | `Arrow of ti * ti
   | `Record of Types.label * bool * ti
   | `Capture of Patterns.capture
   | `Constant of Patterns.capture * Types.const
   ]
    

module S = struct type t = string let compare = compare end
module StringMap = Map.Make(S)
module StringSet = Set.Make(S)

let mk' =
  let counter = ref 0 in
  fun loc ->
    incr counter;
    let rec x = { 
      id = !counter; 
      loc' = loc; 
      fv = None; 
      descr' = `Alias ("__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 memo = Hashtbl.create 51
  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 (StringSet.add v accu) r

  let rec propagate vars = function
    | Epsilon -> `Epsilon
    | Elem x -> `Elem (vars,x)
    | Seq (r1,r2) -> `Seq (propagate vars r1,propagate vars r2)
    | Alt (r1,r2) -> `Alt (propagate vars r1, propagate vars r2)
    | Star r -> `Star (propagate vars r)
    | WeakStar r -> `WeakStar (propagate vars r)
    | SeqCapture (v,x) -> propagate (StringSet.add v vars) x

  let cup r1 r2 = 
    match (r1,r2) with
      | (_, `Empty) -> r1
      | (`Empty, _) -> r2
      | (`Res t1, `Res t2) -> `Res (mk noloc (Or (t1,t2)))

  let rec compile fin e seq : [`Res of Ast.ppat | `Empty] = 
    if List.mem seq e then `Empty
    else 
      let e = seq :: e in
      match seq with
        | [] ->
            `Res fin
        | `Epsilon :: rest -> 
            compile fin e rest
        | `Elem (vars,x) :: rest -> 
            let capt = StringSet.fold
                         (fun v t -> mk noloc (And (t, (mk noloc (Capture v)))))
                         vars x in
            `Res (mk noloc (Prod (capt, guard_compile fin rest)))
        | `Seq (r1,r2) :: rest -> 
            compile fin e (r1 :: r2 :: rest)
        | `Alt (r1,r2) :: rest -> 
            cup (compile fin e (r1::rest)) (compile fin e (r2::rest))
        | `Star r :: rest -> cup (compile fin e (r::seq)) (compile fin e rest) 
        | `WeakStar r :: rest -> cup (compile fin e rest) (compile fin e (r::seq))

  and guard_compile fin seq =
    try Hashtbl.find memo seq 
    with
        Not_found ->
          let n = name () in
          let v = mk noloc (PatVar n) in
          Hashtbl.add memo seq v;
          let d = compile fin [] seq in
          (match d with
             | `Empty -> assert false
             | `Res d -> defs := (n,d) :: !defs);
          v


  let atom_nil = Types.mk_atom "nil"
  let constant_nil v t = 
    mk noloc (And (t, (mk noloc (Constant (v, Types.Atom atom_nil)))))

  let compile regexp queue : ppat =
    let vars = seq_vars StringSet.empty regexp in
    let fin = StringSet.fold constant_nil vars queue in
    let n = guard_compile fin [propagate StringSet.empty regexp] in
    Hashtbl.clear memo;
    let d = !defs in
    defs := [];
    mk noloc (Recurs (n,d))
end

let compile_regexp = Regexp.compile


let rec compile env { loc = loc; descr = d } : ti = 
  match (d : Ast.ppat') with
  | PatVar s -> 
      (try StringMap.find s env
       with Not_found -> 
         raise_loc loc (Pattern ("Undefined type variable " ^ s))
      )
  | Recurs (t, b) -> compile (compile_many env b) t
  | Regexp (r,q) -> compile env (Regexp.compile r q)
  | Internal t -> cons loc (`Type t)
  | Or (t1,t2) -> cons loc (`Or (compile env t1, compile env t2))
  | And (t1,t2) -> cons loc (`And (compile env t1, compile env t2))
  | Diff (t1,t2) -> cons loc (`Diff (compile env t1, compile env t2))
  | Prod (t1,t2) -> cons loc (`Times (compile env t1, compile env t2))
  | Arrow (t1,t2) -> cons loc (`Arrow (compile env t1, compile env t2))
  | Record (l,o,t) -> cons loc (`Record (l,o,compile env t))
  | Constant (x,v) -> cons loc (`Constant (x,v))
  | Capture x -> cons loc (`Capture 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) -> StringMap.add v x env) env b in
  List.iter (fun (v,t,x) -> x.descr' <- `Alias (v, compile env t)) b;
  env


let rec comp_fv seen s =
  match s.fv with
    | Some l -> l
    | None ->
        let l = 
          match s.descr' with
            | `Alias (_,x) -> if List.memq s seen then [] else comp_fv (s :: seen) x
            | `Or (s1,s2) 
            | `And (s1,s2)
            | `Diff (s1,s2)
            | `Times (s1,s2)
            | `Arrow (s1,s2) -> SortedList.cup (comp_fv seen s1) (comp_fv seen s2)
            | `Record (l,opt,s) -> comp_fv seen s
            | `Type _ -> []
            | `Capture x
            | `Constant (x,_) -> [x]
        in
        if seen = [] then s.fv <- Some l;
        l


let fv = comp_fv []

let rec typ seen s : Types.descr =
  match s.descr' with
    | `Alias (v,x) ->
        if List.memq s seen then 
          raise_loc s.loc' 
            (Pattern 
               ("Unguarded recursion on variable " ^ v ^ " in this type"))
        else typ (s :: seen) x
    | `Type t -> t
    | `Or (s1,s2) -> Types.cup (typ seen s1) (typ seen s2)
    | `And (s1,s2) ->  Types.cap (typ seen s1) (typ seen s2)
    | `Diff (s1,s2) -> Types.diff (typ seen s1) (typ seen s2)
    | `Times (s1,s2) -> Types.times (typ_node s1) (typ_node s2)
    | `Arrow (s1,s2) -> Types.arrow (typ_node s1) (typ_node s2)
    | `Record (l,o,s) -> Types.record l o (typ_node s)
    | `Capture _ | `Constant _ -> 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 [] s in
        Types.define x t;
        x

let type_node s = Types.internalize (typ_node s)

let rec pat seen s : Patterns.descr =
  if fv s = [] then Patterns.constr (type_node s) else
  match s.descr' with
    | `Alias (v,x) ->
        if List.memq s seen then 
          raise_loc s.loc' 
            (Pattern 
               ("Unguarded recursion on variable " ^ v ^ " in this pattern"))
        else pat (s :: seen) x
    | `Or (s1,s2) -> Patterns.cup (pat seen s1) (pat seen s2)
    | `And (s1,s2) -> Patterns.cap (pat seen s1) (pat seen s2)
    | `Diff (s1,s2) when fv s2 = [] ->
        let s2 = Types.cons (Types.neg (Types.descr (type_node s2)))in
        Patterns.cap (pat seen s1) (Patterns.constr s2)
    | `Diff _ ->
        raise_loc s.loc' (Pattern "Difference not allowed in patterns")
    | `Times (s1,s2) -> Patterns.times (pat_node s1) (pat_node s2)
    | `Record (l,false,s) -> Patterns.record l (pat_node s)
    | `Record _ ->
        raise_loc s.loc' 
          (Pattern "Optional field not allowed in record patterns")
    | `Capture x ->  Patterns.capture x
    | `Constant (x,c) -> Patterns.constant x c
    | `Arrow _ ->
        raise_loc s.loc' (Pattern "Arrow not allowed in patterns")
    | `Type _ -> 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 [] s in
        Patterns.define x t;
        x

let global_types = ref StringMap.empty

let mk_typ e =
  if fv e = [] then type_node e 
  else raise_loc e.loc' (Pattern "Capture variables are not allowed in types")
    

let typ e =
  mk_typ (compile !global_types e)

let pat e =
  let e = compile !global_types e in
  pat_node e

let register_global_types b =
  let env = compile_many !global_types b in
  List.iter (fun (v,_) -> 
               let d = Types.descr (mk_typ (StringMap.find v env)) in
               Types.Print.register_global v d
            ) b;
  global_types := env


(* II. Build skeleton *)

module Fv = StringSet

let rec expr { loc = loc; descr = d } = 
  let (fv,td) = 
    match d with
      | DebugTyper t -> (Fv.empty, Typed.DebugTyper (typ t))
      | Var s -> (Fv.singleton s, Typed.Var s)
      | Apply (e1,e2) -> 
          let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
          (Fv.union fv1 fv2, Typed.Apply (e1,e2))
      | Abstraction a ->
          let iface = List.map (fun (t1,t2) -> (typ t1, typ 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 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.elements fv0
             }
          )
      | Cst c -> (Fv.empty, Typed.Cst c)
      | Pair (e1,e2) ->
          let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
          (Fv.union fv1 fv2, Typed.Pair (e1,e2))
      | Dot (e,l) ->
          let (fv,e) = expr e in
          (fv,  Typed.Dot (e,l))
      | RecordLitt r -> 
          (* XXX TODO: check that no label appears twice *)
          let fv = ref Fv.empty in
          let r = List.map 
                    (fun (l,e) -> 
                       let (fv2,e) = expr e in
                       fv := Fv.union !fv fv2;
                       (l,e)
                    ) r in
          (!fv, Typed.RecordLitt r)
      | Op (op,le) ->
          let (fvs,ltes) = List.split (List.map expr le) in
          let fv = List.fold_left Fv.union Fv.empty fvs in
          (fv, Typed.Op (op,ltes))
      | Match (e,b) -> 
          let (fv1,e) = expr e
          and (fv2,b) = branches b in
          (Fv.union fv1 fv2, Typed.Match (e, b))
      | Map (e,b) ->
          let (fv1,e) = expr e
          and (fv2,b) = branches b in
          (Fv.union fv1 fv2, Typed.Map (e, b))
  in
  fv,
  { Typed.exp_loc = loc;
    Typed.exp_typ = Types.empty;
    Typed.exp_descr = td;
  }
              
  and branches b = 
    let fv = ref Fv.empty in
    let accept = ref Types.empty in
    let b = List.map 
              (fun (p,e) ->
                 let (fv2,e) = expr e in
                 fv := Fv.union !fv fv2;
                 let p = pat p in
                 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 
     } 
    )

module Env = StringMap

open Typed


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
  | 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
  | Pair (e1,e2) -> 
      let rects = Types.Product.get constr in
      if Types.Product.is_empty rects then 
        raise_loc loc (ShouldHave (constr,"but it is a pair."));
      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 
        Types.times (Types.cons t1) (Types.cons t2)
      else
        constr
  | _ -> 
      let t : Types.descr = compute_type' loc env e in
      check loc t constr "";
      t

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

and compute_type' loc env = function
  | DebugTyper t -> Types.descr t
  | Var s -> Env.find s env
  | Apply (e1,e2) ->
      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
      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)
  | 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)))
  | RecordLitt r ->
      List.fold_left 
        (fun accu (l,e) ->
           let t = compute_type env e in
           let t = Types.record l false (Types.cons t) in
           Types.cap accu t
        ) Types.Record.any r
  | 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
  | _ -> 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_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 (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
    | _ -> 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 
               (t1,Types.Int.any,
                "The second argument must be an integer"));
  Types.Int.put
    (f (Types.Int.get t1) (Types.Int.get t2));
  

1	abate	5	(* I. Transform the abstract syntax of types and patterns into
2			the internal form *)
3
4			open Location
5			open Ast
6
7	abate	9	exception Pattern of string
8			exception NonExhaustive of Types.descr
9			exception Constraint of Types.descr * Types.descr * string
10	abate	19	exception ShouldHave of Types.descr * string
11	abate	26	exception WrongLabel of Types.descr * Types.label
12	abate	5
13	abate	9	let raise_loc loc exn = raise (Location (loc,exn))
14
15	abate	5	(* Internal representation as a graph (desugar recursive types and regexp),
16			to compute freevars, etc... *)
17
18	abate	9	type ti = {
19	abate	5	id : int;
20			mutable loc' : loc;
21			mutable fv : string SortedList.t option;
22			mutable descr': descr;
23			mutable type_node: Types.node option;
24			mutable pat_node: Patterns.node option
25			}
26			and descr =
27	abate	9	[ `Alias of string * ti
28	abate	5	\| `Type of Types.descr
29			\| `Or of ti * ti
30			\| `And of ti * ti
31			\| `Diff of ti * ti
32			\| `Times of ti * ti
33			\| `Arrow of ti * ti
34			\| `Record of Types.label * bool * ti
35			\| `Capture of Patterns.capture
36			\| `Constant of Patterns.capture * Types.const
37			]
38
39
40
41			module S = struct type t = string let compare = compare end
42			module StringMap = Map.Make(S)
43			module StringSet = Set.Make(S)
44
45			let mk' =
46			let counter = ref 0 in
47	abate	13	fun loc ->
48	abate	5	incr counter;
49	abate	9	let rec x = {
50			id = !counter;
51	abate	13	loc' = loc;
52	abate	9	fv = None;
53			descr' = `Alias ("__dummy__", x);
54			type_node = None;
55			pat_node = None
56			} in
57	abate	5	x
58
59			let cons loc d =
60	abate	13	let x = mk' loc in
61	abate	5	x.descr' <- d;
62			x
63
64			(* Note:
65			Compilation of Regexp is implemented as a ``rewriting'' of
66			the parsed syntax, in order to be able to print its result
67			(for debugging for instance)
68
69			It would be possible (and a little more efficient) to produce
70			directly ti nodes.
71			*)
72
73			module Regexp = struct
74			let memo = Hashtbl.create 51
75			let defs = ref []
76			let name =
77			let c = ref 0 in
78			fun () ->
79			incr c;
80			"#" ^ (string_of_int !c)
81
82			let rec seq_vars accu = function
83			\| Epsilon \| Elem _ -> accu
84			\| Seq (r1,r2) \| Alt (r1,r2) -> seq_vars (seq_vars accu r1) r2
85			\| Star r \| WeakStar r -> seq_vars accu r
86			\| SeqCapture (v,r) -> seq_vars (StringSet.add v accu) r
87
88			let rec propagate vars = function
89			\| Epsilon -> `Epsilon
90			\| Elem x -> `Elem (vars,x)
91			\| Seq (r1,r2) -> `Seq (propagate vars r1,propagate vars r2)
92			\| Alt (r1,r2) -> `Alt (propagate vars r1, propagate vars r2)
93			\| Star r -> `Star (propagate vars r)
94			\| WeakStar r -> `WeakStar (propagate vars r)
95			\| SeqCapture (v,x) -> propagate (StringSet.add v vars) x
96
97			let cup r1 r2 =
98			match (r1,r2) with
99			\| (_, `Empty) -> r1
100			\| (`Empty, _) -> r2
101			\| (`Res t1, `Res t2) -> `Res (mk noloc (Or (t1,t2)))
102
103			let rec compile fin e seq : [`Res of Ast.ppat \| `Empty] =
104			if List.mem seq e then `Empty
105			else
106			let e = seq :: e in
107			match seq with
108			\| [] ->
109			`Res fin
110			\| `Epsilon :: rest ->
111			compile fin e rest
112			\| `Elem (vars,x) :: rest ->
113			let capt = StringSet.fold
114			(fun v t -> mk noloc (And (t, (mk noloc (Capture v)))))
115			vars x in
116			`Res (mk noloc (Prod (capt, guard_compile fin rest)))
117			\| `Seq (r1,r2) :: rest ->
118			compile fin e (r1 :: r2 :: rest)
119			\| `Alt (r1,r2) :: rest ->
120			cup (compile fin e (r1::rest)) (compile fin e (r2::rest))
121			\| `Star r :: rest -> cup (compile fin e (r::seq)) (compile fin e rest)
122			\| `WeakStar r :: rest -> cup (compile fin e rest) (compile fin e (r::seq))
123
124			and guard_compile fin seq =
125			try Hashtbl.find memo seq
126			with
127			Not_found ->
128			let n = name () in
129			let v = mk noloc (PatVar n) in
130			Hashtbl.add memo seq v;
131			let d = compile fin [] seq in
132			(match d with
133			\| `Empty -> assert false
134			\| `Res d -> defs := (n,d) :: !defs);
135			v
136
137
138			let atom_nil = Types.mk_atom "nil"
139			let constant_nil v t =
140			mk noloc (And (t, (mk noloc (Constant (v, Types.Atom atom_nil)))))
141
142			let compile regexp queue : ppat =
143			let vars = seq_vars StringSet.empty regexp in
144			let fin = StringSet.fold constant_nil vars queue in
145			let n = guard_compile fin [propagate StringSet.empty regexp] in
146			Hashtbl.clear memo;
147			let d = !defs in
148			defs := [];
149			mk noloc (Recurs (n,d))
150			end
151
152			let compile_regexp = Regexp.compile
153
154
155			let rec compile env { loc = loc; descr = d } : ti =
156			match (d : Ast.ppat') with
157			\| PatVar s ->
158			(try StringMap.find s env
159	abate	9	with Not_found ->
160			raise_loc loc (Pattern ("Undefined type variable " ^ s))
161	abate	5	)
162	abate	13	\| Recurs (t, b) -> compile (compile_many env b) t
163	abate	5	\| Regexp (r,q) -> compile env (Regexp.compile r q)
164			\| Internal t -> cons loc (`Type t)
165			\| Or (t1,t2) -> cons loc (`Or (compile env t1, compile env t2))
166			\| And (t1,t2) -> cons loc (`And (compile env t1, compile env t2))
167			\| Diff (t1,t2) -> cons loc (`Diff (compile env t1, compile env t2))
168			\| Prod (t1,t2) -> cons loc (`Times (compile env t1, compile env t2))
169			\| Arrow (t1,t2) -> cons loc (`Arrow (compile env t1, compile env t2))
170			\| Record (l,o,t) -> cons loc (`Record (l,o,compile env t))
171			\| Constant (x,v) -> cons loc (`Constant (x,v))
172			\| Capture x -> cons loc (`Capture x)
173
174	abate	13	and compile_many env b =
175			let b = List.map (fun (v,t) -> (v,t,mk' t.loc)) b in
176			let env =
177			List.fold_left (fun env (v,t,x) -> StringMap.add v x env) env b in
178			List.iter (fun (v,t,x) -> x.descr' <- `Alias (v, compile env t)) b;
179			env
180
181
182	abate	5	let rec comp_fv seen s =
183			match s.fv with
184			\| Some l -> l
185			\| None ->
186			let l =
187			match s.descr' with
188	abate	9	\| `Alias (_,x) -> if List.memq s seen then [] else comp_fv (s :: seen) x
189	abate	5	\| `Or (s1,s2)
190			\| `And (s1,s2)
191			\| `Diff (s1,s2)
192			\| `Times (s1,s2)
193			\| `Arrow (s1,s2) -> SortedList.cup (comp_fv seen s1) (comp_fv seen s2)
194			\| `Record (l,opt,s) -> comp_fv seen s
195			\| `Type _ -> []
196			\| `Capture x
197			\| `Constant (x,_) -> [x]
198			in
199			if seen = [] then s.fv <- Some l;
200			l
201
202
203			let fv = comp_fv []
204
205			let rec typ seen s : Types.descr =
206			match s.descr' with
207	abate	9	\| `Alias (v,x) ->
208			if List.memq s seen then
209			raise_loc s.loc'
210			(Pattern
211			("Unguarded recursion on variable " ^ v ^ " in this type"))
212	abate	5	else typ (s :: seen) x
213			\| `Type t -> t
214			\| `Or (s1,s2) -> Types.cup (typ seen s1) (typ seen s2)
215			\| `And (s1,s2) -> Types.cap (typ seen s1) (typ seen s2)
216			\| `Diff (s1,s2) -> Types.diff (typ seen s1) (typ seen s2)
217			\| `Times (s1,s2) -> Types.times (typ_node s1) (typ_node s2)
218			\| `Arrow (s1,s2) -> Types.arrow (typ_node s1) (typ_node s2)
219			\| `Record (l,o,s) -> Types.record l o (typ_node s)
220	abate	9	\| `Capture _ \| `Constant _ -> assert false
221	abate	5
222			and typ_node s : Types.node =
223			match s.type_node with
224			\| Some x -> x
225			\| None ->
226			let x = Types.make () in
227			s.type_node <- Some x;
228			let t = typ [] s in
229			Types.define x t;
230			x
231
232			let type_node s = Types.internalize (typ_node s)
233
234			let rec pat seen s : Patterns.descr =
235			if fv s = [] then Patterns.constr (type_node s) else
236			match s.descr' with
237	abate	9	\| `Alias (v,x) ->
238			if List.memq s seen then
239			raise_loc s.loc'
240			(Pattern
241			("Unguarded recursion on variable " ^ v ^ " in this pattern"))
242	abate	5	else pat (s :: seen) x
243			\| `Or (s1,s2) -> Patterns.cup (pat seen s1) (pat seen s2)
244			\| `And (s1,s2) -> Patterns.cap (pat seen s1) (pat seen s2)
245			\| `Diff (s1,s2) when fv s2 = [] ->
246			let s2 = Types.cons (Types.neg (Types.descr (type_node s2)))in
247			Patterns.cap (pat seen s1) (Patterns.constr s2)
248	abate	9	\| `Diff _ ->
249			raise_loc s.loc' (Pattern "Difference not allowed in patterns")
250	abate	5	\| `Times (s1,s2) -> Patterns.times (pat_node s1) (pat_node s2)
251			\| `Record (l,false,s) -> Patterns.record l (pat_node s)
252	abate	9	\| `Record _ ->
253			raise_loc s.loc'
254			(Pattern "Optional field not allowed in record patterns")
255	abate	5	\| `Capture x -> Patterns.capture x
256			\| `Constant (x,c) -> Patterns.constant x c
257	abate	9	\| `Arrow _ ->
258			raise_loc s.loc' (Pattern "Arrow not allowed in patterns")
259			\| `Type _ -> assert false
260	abate	5
261			and pat_node s : Patterns.node =
262			match s.pat_node with
263			\| Some x -> x
264			\| None ->
265			let x = Patterns.make (fv s) in
266			s.pat_node <- Some x;
267			let t = pat [] s in
268			Patterns.define x t;
269			x
270
271	abate	13	let global_types = ref StringMap.empty
272
273			let mk_typ e =
274	abate	9	if fv e = [] then type_node e
275	abate	13	else raise_loc e.loc' (Pattern "Capture variables are not allowed in types")
276
277	abate	5
278	abate	13	let typ e =
279			mk_typ (compile !global_types e)
280
281	abate	5	let pat e =
282	abate	13	let e = compile !global_types e in
283	abate	5	pat_node e
284
285	abate	13	let register_global_types b =
286			let env = compile_many !global_types b in
287	abate	15	List.iter (fun (v,_) ->
288			let d = Types.descr (mk_typ (StringMap.find v env)) in
289			Types.Print.register_global v d
290			) b;
291	abate	13	global_types := env
292	abate	5
293
294			(* II. Build skeleton *)
295
296	abate	6	module Fv = StringSet
297
298	abate	5	let rec expr { loc = loc; descr = d } =
299	abate	6	let (fv,td) =
300	abate	5	match d with
301	abate	18	\| DebugTyper t -> (Fv.empty, Typed.DebugTyper (typ t))
302	abate	6	\| Var s -> (Fv.singleton s, Typed.Var s)
303			\| Apply (e1,e2) ->
304			let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
305			(Fv.union fv1 fv2, Typed.Apply (e1,e2))
306	abate	5	\| Abstraction a ->
307	abate	6	let iface = List.map (fun (t1,t2) -> (typ t1, typ t2)) a.fun_iface in
308			let t = List.fold_left
309			(fun accu (t1,t2) -> Types.cap accu (Types.arrow t1 t2))
310			Types.any iface in
311	abate	9	let iface = List.map
312			(fun (t1,t2) -> (Types.descr t1, Types.descr t2))
313			iface in
314	abate	6	let (fv0,body) = branches a.fun_body in
315			let fv = match a.fun_name with
316			\| None -> fv0
317			\| Some f -> Fv.remove f fv0 in
318			(fv,
319			Typed.Abstraction
320			{ Typed.fun_name = a.fun_name;
321			Typed.fun_iface = iface;
322			Typed.fun_body = body;
323			Typed.fun_typ = t;
324			Typed.fun_fv = Fv.elements fv0
325			}
326			)
327			\| Cst c -> (Fv.empty, Typed.Cst c)
328			\| Pair (e1,e2) ->
329			let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
330			(Fv.union fv1 fv2, Typed.Pair (e1,e2))
331	abate	26	\| Dot (e,l) ->
332			let (fv,e) = expr e in
333	abate	27	(fv, Typed.Dot (e,l))
334	abate	6	\| RecordLitt r ->
335			(* XXX TODO: check that no label appears twice *)
336			let fv = ref Fv.empty in
337			let r = List.map
338			(fun (l,e) ->
339			let (fv2,e) = expr e in
340			fv := Fv.union !fv fv2;
341			(l,e)
342			) r in
343			(!fv, Typed.RecordLitt r)
344	abate	16	\| Op (op,le) ->
345			let (fvs,ltes) = List.split (List.map expr le) in
346			let fv = List.fold_left Fv.union Fv.empty fvs in
347			(fv, Typed.Op (op,ltes))
348	abate	6	\| Match (e,b) ->
349			let (fv1,e) = expr e
350			and (fv2,b) = branches b in
351			(Fv.union fv1 fv2, Typed.Match (e, b))
352			\| Map (e,b) ->
353			let (fv1,e) = expr e
354			and (fv2,b) = branches b in
355			(Fv.union fv1 fv2, Typed.Map (e, b))
356	abate	5	in
357	abate	6	fv,
358			{ Typed.exp_loc = loc;
359	abate	5	Typed.exp_typ = Types.empty;
360			Typed.exp_descr = td;
361			}
362
363	abate	6	and branches b =
364			let fv = ref Fv.empty in
365	abate	19	let accept = ref Types.empty in
366	abate	6	let b = List.map
367			(fun (p,e) ->
368			let (fv2,e) = expr e in
369			fv := Fv.union !fv fv2;
370	abate	19	let p = pat p in
371			accept := Types.cup !accept (Types.descr (Patterns.accept p));
372	abate	6	{ Typed.br_used = false;
373	abate	19	Typed.br_pat = p;
374	abate	6	Typed.br_body = e }
375			) b in
376	abate	19	(!fv,
377			{
378			Typed.br_typ = Types.empty;
379			Typed.br_branches = b;
380			Typed.br_accept = !accept
381			}
382			)
383	abate	5
384	abate	6	module Env = StringMap
385
386			open Typed
387
388	abate	17
389			let check loc t s msg =
390			if not (Types.subtype t s) then raise_loc loc (Constraint (t, s, msg))
391
392	abate	19	let rec type_check env e constr precise =
393			(* Format.fprintf Format.std_formatter "constr=%a precise=%b@\n"
394			Types.Print.print_descr constr precise; *)
395			let d = type_check' e.exp_loc env e.exp_descr constr precise in
396	abate	6	e.exp_typ <- Types.cup e.exp_typ d;
397			d
398
399	abate	19	and type_check' loc env e constr precise = match e with
400			\| Abstraction a ->
401			let t =
402			try Types.Arrow.check_strenghten a.fun_typ constr
403			with Not_found ->
404			raise_loc loc
405			(ShouldHave
406			(constr, "but the interface of the abstraction is not compatible"))
407			in
408			let env = match a.fun_name with
409			\| None -> env
410			\| Some f -> Env.add f a.fun_typ env in
411			List.iter
412			(fun (t1,t2) ->
413			ignore (type_check_branches loc env t1 a.fun_body t2 false)
414			) a.fun_iface;
415			t
416			\| Match (e,b) ->
417			let t = type_check env e b.br_accept true in
418			type_check_branches loc env t b constr precise
419			\| Pair (e1,e2) ->
420			let rects = Types.Product.get constr in
421			if Types.Product.is_empty rects then
422			raise_loc loc (ShouldHave (constr,"but it is a pair."));
423			let pi1 = Types.Product.pi1 rects in
424
425			let t1 = type_check env e1 (Types.Product.pi1 rects)
426			(precise \|\| (Types.Product.need_second rects))in
427			let rects = Types.Product.restrict_1 rects t1 in
428			let t2 = type_check env e2 (Types.Product.pi2 rects) precise in
429			if precise then
430			Types.times (Types.cons t1) (Types.cons t2)
431			else
432			constr
433			\| _ ->
434			let t : Types.descr = compute_type' loc env e in
435			check loc t constr "";
436			t
437
438			and compute_type env e =
439			type_check env e Types.any true
440
441	abate	6	and compute_type' loc env = function
442	abate	18	\| DebugTyper t -> Types.descr t
443	abate	6	\| Var s -> Env.find s env
444			\| Apply (e1,e2) ->
445	abate	19	let t1 = type_check env e1 Types.Arrow.any true in
446			let t1 = Types.Arrow.get t1 in
447			let dom = Types.Arrow.domain t1 in
448			if Types.Arrow.need_arg t1 then
449			let t2 = type_check env e2 dom true in
450			Types.Arrow.apply t1 t2
451			else
452			(ignore (type_check env e2 dom false); Types.Arrow.apply_noarg t1)
453	abate	6	\| Cst c -> Types.constant c
454	abate	26	\| Dot (e,l) ->
455			let t = type_check env e Types.Record.any true in
456			(try (Types.Record.project t l)
457			with Not_found -> raise_loc loc (WrongLabel(t,l)))
458	abate	6	\| RecordLitt r ->
459			List.fold_left
460			(fun accu (l,e) ->
461			let t = compute_type env e in
462			let t = Types.record l false (Types.cons t) in
463			Types.cap accu t
464			) Types.Record.any r
465	abate	16	\| Op (op, el) ->
466			let args = List.map (fun e -> (e.exp_loc, compute_type env e)) el in
467			type_op loc op args
468	abate	17	\| Map (e,b) ->
469			let t = compute_type env e in
470	abate	19	Sequence.map (fun t -> type_check_branches loc env t b Types.any true) t
471			\| _ -> assert false
472	abate	6
473	abate	19	and type_check_branches loc env targ brs constr precise =
474	abate	6	if Types.is_empty targ then Types.empty
475	abate	9	else (
476			brs.br_typ <- Types.cup brs.br_typ targ;
477	abate	19	branches_aux loc env targ
478			(if precise then Types.empty else constr)
479			constr precise brs.br_branches
480	abate	9	)
481	abate	6
482	abate	19	and branches_aux loc env targ tres constr precise = function
483	abate	9	\| [] -> raise_loc loc (NonExhaustive targ)
484	abate	6	\| b :: rem ->
485			let p = b.br_pat in
486			let acc = Types.descr (Patterns.accept p) in
487
488			let targ' = Types.cap targ acc in
489			if Types.is_empty targ'
490	abate	19	then branches_aux loc env targ tres constr precise rem
491	abate	6	else
492			( b.br_used <- true;
493			let res = Patterns.filter targ' p in
494			let env' = List.fold_left
495			(fun env (x,t) -> Env.add x (Types.descr t) env)
496			env res in
497	abate	19	let t = type_check env' b.br_body constr precise in
498			let tres = if precise then Types.cup t tres else tres in
499	abate	9	let targ'' = Types.diff targ acc in
500			if (Types.non_empty targ'') then
501	abate	19	branches_aux loc env targ'' tres constr precise rem
502	abate	9	else
503			tres
504	abate	6	)
505	abate	16
506			and type_op loc op args =
507			match (op,args) with
508			\| ("+", [loc1,t1; loc2,t2]) ->
509			type_int_binop Intervals.add loc1 t1 loc2 t2
510			\| ("*", [loc1,t1; loc2,t2]) ->
511			type_int_binop (fun i1 i2 -> Intervals.any) loc1 t1 loc2 t2
512	abate	17	\| ("@", [loc1,t1; loc2,t2]) ->
513			check loc1 t1 Sequence.any
514			"The first argument of @ must be a sequence";
515			Sequence.concat t1 t2
516			\| ("flatten", [loc1,t1]) ->
517			check loc1 t1 Sequence.seqseq
518			"The argument of flatten must be a sequence of sequences";
519			Sequence.flatten t1
520	abate	16	\| _ -> assert false
521
522			and type_int_binop f loc1 t1 loc2 t2 =
523			if not (Types.Int.is_int t1) then
524			raise_loc loc1
525			(Constraint
526			(t1,Types.Int.any,
527			"The first argument must be an integer"));
528			if not (Types.Int.is_int t2) then
529			raise_loc loc2
530			(Constraint
531			(t1,Types.Int.any,
532			"The second argument must be an integer"));
533			Types.Int.put
534			(f (Types.Int.get t1) (Types.Int.get t2));
535
536