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(* I. Transform the abstract syntax of types and patterns into
      the internal form *)
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open Location
open Ast
exception ParsingPattern of string

let raise_loc loc msg = raise (Location loc (ParsingPattern msg))

(* 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 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 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 "Undefined variable"
      )
  | 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.descr' <- `Alias (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 x ->
	if List.memq s seen then failwith "Unguarded recursion 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)
    | _ -> failwith "This is not a type"

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 x ->
	if List.memq s seen then failwith "Unguarded recursion 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)
    | `Times (s1,s2) -> Patterns.times (pat_node s1) (pat_node s2)
    | `Record (l,false,s) -> Patterns.record l (pat_node s)
    | `Capture x ->  Patterns.capture x
    | `Constant (x,c) -> Patterns.constant x c
    | _ -> failwith "This is not a pattern"

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 failwith "This is not a type"

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



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(* II. Build skeleton *)

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module Fv = StringSet

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let rec expr { loc = loc; descr = d } = 
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  let (fv,td) = 
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    match d with
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      | 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))
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      | Abstraction a ->
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	  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 (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))
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  in
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  fv,
  { Typed.exp_loc = loc;
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    Typed.exp_typ = Types.empty;
    Typed.exp_descr = td;
  }
	      
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  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_typ = Types.empty;
		   Typed.br_pat = pat p;
		   Typed.br_body = e }
	      ) b in
    (!fv,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 env (Types.descr t1) a.fun_body in
		   if not (Types.subtype t (Types.descr t2)) then
		     failwith "Constraint not satisfied"
		) 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 env t b
  | Map (e,b) -> assert false

and type_branches env targ branches =
  if Types.is_empty targ then Types.empty 
  else branches_aux env targ Types.empty branches
    
and branches_aux env targ tres = function
  | [] -> failwith "Non-exhaustive pattern matching"
  | 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 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
	  branches_aux env (Types.diff targ acc) (Types.cup t tres) rem 
	)