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

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,_) -> ignore (mk_typ (StringMap.find v env))) b;
  global_types := env


(* II. Build skeleton *)

module Fv = StringSet

let rec expr { loc = loc; descr = d } = 
  let (fv,td) = 
    match d with
      | 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))
      | 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 (o,e) -> 
          let (fv,e) = expr e in (fv, Typed.Op (o,e))
      | 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 b = List.map 
              (fun (p,e) ->
                 let (fv2,e) = expr e in
                 fv := Fv.union !fv fv2;
                 { Typed.br_used = false;
                   Typed.br_pat = pat p;
                   Typed.br_body = e }
              ) b in
    (!fv, { Typed.br_typ = Types.empty; Typed.br_branches = b } )

module Env = StringMap

open Typed

let rec compute_type env e = 
  let d = compute_type' e.exp_loc env e.exp_descr in
  e.exp_typ <- Types.cup e.exp_typ d;
  d

and compute_type' loc env = function
  | Var s -> Env.find s env
  | Apply (e1,e2) ->
      let t1 = compute_type env e1 and t2 = compute_type env e2 in
      if Types.is_empty t2 
      then Types.empty
      else 
        if Types.subtype t1 Types.Arrow.any 
        then
          let t1 = Types.Arrow.get t1 in
          let dom = Types.Arrow.domain t1 in
          if Types.subtype t2 dom
          then Types.Arrow.apply t1 t2
          else
            raise_loc loc 
              (Constraint 
                 (t2,dom,"The argument is not in the domain of the function"))
        else
          raise_loc loc
            (Constraint
               (t1,Types.Arrow.any,"The expression in function position is not necessarily a function"))
  | Abstraction a ->
      let env = match a.fun_name with
        | None -> env
        | Some f -> Env.add f a.fun_typ env in
      List.iter (fun (t1,t2) ->
                   let t = type_branches loc env t1 a.fun_body in
                   if not (Types.subtype t t2) then
                     raise_loc loc (Constraint (t,t2,"Constraint not satisfied in interface"))
                ) a.fun_iface;
      a.fun_typ
  | Cst c -> Types.constant c
  | Pair (e1,e2) -> 
      let t1 = compute_type env e1 and t2 = compute_type env e2 in
      let t1 = Types.cons t1 and t2 = Types.cons t2 in
      Types.times t1 t2
  | 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,e) -> assert false
  | Match (e,b) ->
      let t = compute_type env e in
      type_branches loc env t b
  | Map (e,b) -> assert false

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