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 () ->
    incr counter;
    let rec x = { 
      id = !counter; 
      loc' = noloc; 
      fv = None; 
      descr' = `Alias ("__dummy__", x);  
      type_node = None; 
      pat_node = None 
    } in
    x

let cons loc d =
  let x = mk' () in
  x.loc' <- loc;
  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) ->
      let b = List.map (fun (v,t) -> (v,t,mk' ())) 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.loc' <- t.loc; x.descr' <- `Alias (v, compile env t)) 
        b;
      compile env 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)

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

let pat e =
  let e = compile StringMap.empty e in
  pat_node e


(* 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
      Types.apply t1 t2
  | 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 () ->
46	incr counter;
47	let rec x = {
48	id = !counter;
49	loc' = noloc;
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' () in
59	x.loc' <- loc;
60	x.descr' <- d;
61	x
62
63	(* Note:
64	Compilation of Regexp is implemented as a ``rewriting'' of
65	the parsed syntax, in order to be able to print its result
66	(for debugging for instance)
67
68	It would be possible (and a little more efficient) to produce
69	directly ti nodes.
70	*)
71
72	module Regexp = struct
73	let memo = Hashtbl.create 51
74	let defs = ref []
75	let name =
76	let c = ref 0 in
77	fun () ->
78	incr c;
79	"#" ^ (string_of_int !c)
80
81	let rec seq_vars accu = function
82	\| Epsilon \| Elem _ -> accu
83	\| Seq (r1,r2) \| Alt (r1,r2) -> seq_vars (seq_vars accu r1) r2
84	\| Star r \| WeakStar r -> seq_vars accu r
85	\| SeqCapture (v,r) -> seq_vars (StringSet.add v accu) r
86
87	let rec propagate vars = function
88	\| Epsilon -> `Epsilon
89	\| Elem x -> `Elem (vars,x)
90	\| Seq (r1,r2) -> `Seq (propagate vars r1,propagate vars r2)
91	\| Alt (r1,r2) -> `Alt (propagate vars r1, propagate vars r2)
92	\| Star r -> `Star (propagate vars r)
93	\| WeakStar r -> `WeakStar (propagate vars r)
94	\| SeqCapture (v,x) -> propagate (StringSet.add v vars) x
95
96	let cup r1 r2 =
97	match (r1,r2) with
98	\| (_, `Empty) -> r1
99	\| (`Empty, _) -> r2
100	\| (`Res t1, `Res t2) -> `Res (mk noloc (Or (t1,t2)))
101
102	let rec compile fin e seq : [`Res of Ast.ppat \| `Empty] =
103	if List.mem seq e then `Empty
104	else
105	let e = seq :: e in
106	match seq with
107	\| [] ->
108	`Res fin
109	\| `Epsilon :: rest ->
110	compile fin e rest
111	\| `Elem (vars,x) :: rest ->
112	let capt = StringSet.fold
113	(fun v t -> mk noloc (And (t, (mk noloc (Capture v)))))
114	vars x in
115	`Res (mk noloc (Prod (capt, guard_compile fin rest)))
116	\| `Seq (r1,r2) :: rest ->
117	compile fin e (r1 :: r2 :: rest)
118	\| `Alt (r1,r2) :: rest ->
119	cup (compile fin e (r1::rest)) (compile fin e (r2::rest))
120	\| `Star r :: rest -> cup (compile fin e (r::seq)) (compile fin e rest)
121	\| `WeakStar r :: rest -> cup (compile fin e rest) (compile fin e (r::seq))
122
123	and guard_compile fin seq =
124	try Hashtbl.find memo seq
125	with
126	Not_found ->
127	let n = name () in
128	let v = mk noloc (PatVar n) in
129	Hashtbl.add memo seq v;
130	let d = compile fin [] seq in
131	(match d with
132	\| `Empty -> assert false
133	\| `Res d -> defs := (n,d) :: !defs);
134	v
135
136
137	let atom_nil = Types.mk_atom "nil"
138	let constant_nil v t =
139	mk noloc (And (t, (mk noloc (Constant (v, Types.Atom atom_nil)))))
140
141	let compile regexp queue : ppat =
142	let vars = seq_vars StringSet.empty regexp in
143	let fin = StringSet.fold constant_nil vars queue in
144	let n = guard_compile fin [propagate StringSet.empty regexp] in
145	Hashtbl.clear memo;
146	let d = !defs in
147	defs := [];
148	mk noloc (Recurs (n,d))
149	end
150
151	let compile_regexp = Regexp.compile
152
153
154	let rec compile env { loc = loc; descr = d } : ti =
155	match (d : Ast.ppat') with
156	\| PatVar s ->
157	(try StringMap.find s env
158	with Not_found ->
159	raise_loc loc (Pattern ("Undefined type variable " ^ s))
160	)
161	\| Recurs (t, b) ->
162	let b = List.map (fun (v,t) -> (v,t,mk' ())) b in
163	let env =
164	List.fold_left (fun env (v,t,x) -> StringMap.add v x env) env b in
165	List.iter
166	(fun (v,t,x) -> x.loc' <- t.loc; x.descr' <- `Alias (v, compile env t))
167	b;
168	compile env t
169	\| Regexp (r,q) -> compile env (Regexp.compile r q)
170	\| Internal t -> cons loc (`Type t)
171	\| Or (t1,t2) -> cons loc (`Or (compile env t1, compile env t2))
172	\| And (t1,t2) -> cons loc (`And (compile env t1, compile env t2))
173	\| Diff (t1,t2) -> cons loc (`Diff (compile env t1, compile env t2))
174	\| Prod (t1,t2) -> cons loc (`Times (compile env t1, compile env t2))
175	\| Arrow (t1,t2) -> cons loc (`Arrow (compile env t1, compile env t2))
176	\| Record (l,o,t) -> cons loc (`Record (l,o,compile env t))
177	\| Constant (x,v) -> cons loc (`Constant (x,v))
178	\| Capture x -> cons loc (`Capture x)
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 typ e =
270	let e = compile StringMap.empty e in
271	if fv e = [] then type_node e
272	else (raise_loc e.loc'
273	(Pattern "Capture variables are not allowed in types"))
274
275	let pat e =
276	let e = compile StringMap.empty e in
277	pat_node e
278
279
280
281	(* II. Build skeleton *)
282
283	module Fv = StringSet
284
285	let rec expr { loc = loc; descr = d } =
286	let (fv,td) =
287	match d with
288	\| Var s -> (Fv.singleton s, Typed.Var s)
289	\| Apply (e1,e2) ->
290	let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
291	(Fv.union fv1 fv2, Typed.Apply (e1,e2))
292	\| Abstraction a ->
293	let iface = List.map (fun (t1,t2) -> (typ t1, typ t2)) a.fun_iface in
294	let t = List.fold_left
295	(fun accu (t1,t2) -> Types.cap accu (Types.arrow t1 t2))
296	Types.any iface in
297	let iface = List.map
298	(fun (t1,t2) -> (Types.descr t1, Types.descr t2))
299	iface in
300	let (fv0,body) = branches a.fun_body in
301	let fv = match a.fun_name with
302	\| None -> fv0
303	\| Some f -> Fv.remove f fv0 in
304	(fv,
305	Typed.Abstraction
306	{ Typed.fun_name = a.fun_name;
307	Typed.fun_iface = iface;
308	Typed.fun_body = body;
309	Typed.fun_typ = t;
310	Typed.fun_fv = Fv.elements fv0
311	}
312	)
313	\| Cst c -> (Fv.empty, Typed.Cst c)
314	\| Pair (e1,e2) ->
315	let (fv1,e1) = expr e1 and (fv2,e2) = expr e2 in
316	(Fv.union fv1 fv2, Typed.Pair (e1,e2))
317	\| RecordLitt r ->
318	(* XXX TODO: check that no label appears twice *)
319	let fv = ref Fv.empty in
320	let r = List.map
321	(fun (l,e) ->
322	let (fv2,e) = expr e in
323	fv := Fv.union !fv fv2;
324	(l,e)
325	) r in
326	(!fv, Typed.RecordLitt r)
327	\| Op (o,e) ->
328	let (fv,e) = expr e in (fv, Typed.Op (o,e))
329	\| Match (e,b) ->
330	let (fv1,e) = expr e
331	and (fv2,b) = branches b in
332	(Fv.union fv1 fv2, Typed.Match (e, b))
333	\| Map (e,b) ->
334	let (fv1,e) = expr e
335	and (fv2,b) = branches b in
336	(Fv.union fv1 fv2, Typed.Map (e, b))
337	in
338	fv,
339	{ Typed.exp_loc = loc;
340	Typed.exp_typ = Types.empty;
341	Typed.exp_descr = td;
342	}
343
344	and branches b =
345	let fv = ref Fv.empty in
346	let b = List.map
347	(fun (p,e) ->
348	let (fv2,e) = expr e in
349	fv := Fv.union !fv fv2;
350	{ Typed.br_used = false;
351	Typed.br_pat = pat p;
352	Typed.br_body = e }
353	) b in
354	(!fv, { Typed.br_typ = Types.empty; Typed.br_branches = b } )
355
356	module Env = StringMap
357
358	open Typed
359
360	let rec compute_type env e =
361	let d = compute_type' e.exp_loc env e.exp_descr in
362	e.exp_typ <- Types.cup e.exp_typ d;
363	d
364
365	and compute_type' loc env = function
366	\| Var s -> Env.find s env
367	\| Apply (e1,e2) ->
368	let t1 = compute_type env e1 and t2 = compute_type env e2 in
369	Types.apply t1 t2
370	\| Abstraction a ->
371	let env = match a.fun_name with
372	\| None -> env
373	\| Some f -> Env.add f a.fun_typ env in
374	List.iter (fun (t1,t2) ->
375	let t = type_branches loc env t1 a.fun_body in
376	if not (Types.subtype t t2) then
377	raise_loc loc (Constraint (t,t2,"Constraint not satisfied in interface"))
378	) a.fun_iface;
379	a.fun_typ
380	\| Cst c -> Types.constant c
381	\| Pair (e1,e2) ->
382	let t1 = compute_type env e1 and t2 = compute_type env e2 in
383	let t1 = Types.cons t1 and t2 = Types.cons t2 in
384	Types.times t1 t2
385	\| RecordLitt r ->
386	List.fold_left
387	(fun accu (l,e) ->
388	let t = compute_type env e in
389	let t = Types.record l false (Types.cons t) in
390	Types.cap accu t
391	) Types.Record.any r
392	\| Op (op,e) -> assert false
393	\| Match (e,b) ->
394	let t = compute_type env e in
395	type_branches loc env t b
396	\| Map (e,b) -> assert false
397
398	and type_branches loc env targ brs =
399	if Types.is_empty targ then Types.empty
400	else (
401	brs.br_typ <- Types.cup brs.br_typ targ;
402	branches_aux loc env targ Types.empty brs.br_branches
403	)
404
405	and branches_aux loc env targ tres = function
406	\| [] -> raise_loc loc (NonExhaustive targ)
407	\| b :: rem ->
408	let p = b.br_pat in
409	let acc = Types.descr (Patterns.accept p) in
410
411	let targ' = Types.cap targ acc in
412	if Types.is_empty targ'
413	then branches_aux loc env targ tres rem
414	else
415	( b.br_used <- true;
416	let res = Patterns.filter targ' p in
417	let env' = List.fold_left
418	(fun env (x,t) -> Env.add x (Types.descr t) env)
419	env res in
420	let t = compute_type env' b.br_body in
421	let tres = Types.cup t tres in
422	let targ'' = Types.diff targ acc in
423	if (Types.non_empty targ'') then
424	branches_aux loc env targ'' (Types.cup t tres) rem
425	else
426	tres
427	)