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open Recursive
open Printf



type label = int
type atom  = int

type const = Integer of int | Atom of atom | String of string

module I = struct
  type 'a t = {
    ints  : Intervals.t;
    atoms : atom Atoms.t;
    times : ('a * 'a) Boolean.t;
    arrow : ('a * 'a) Boolean.t;
    record: (label * bool * 'a) Boolean.t;
    strs  : Strings.t;
  }
		
  let empty = { 
    times = Boolean.empty; 
    arrow = Boolean.empty; 
    record= Boolean.empty;
    ints  = Intervals.empty;
    atoms = Atoms.empty;
    strs  = Strings.empty;
  }
  let any =  {
    times = Boolean.full; 
    arrow = Boolean.full; 
    record= Boolean.full; 
    ints  = Intervals.full;
    atoms = Atoms.full;
    strs  = Strings.any;
  }
	       
  let interval i j = { empty with ints = Intervals.atom (i,j) }
  let times x y = { empty with times = Boolean.atom (x,y) }
  let arrow x y = { empty with arrow = Boolean.atom (x,y) }
  let record label opt t = { empty with record = Boolean.atom (label,opt,t) }
  let atom a = { empty with atoms = Atoms.atom a }
  let string r = { empty with strs = Strings.Regexp.compile r }
  let constant = function
    | Integer i -> interval i i
    | Atom a -> atom a
    | String s -> string (Strings.Regexp.str s)

		   
  let any_record = { empty with record = any.record }

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  let cup x y = 
    if x = y then x else { 
      times = Boolean.cup x.times y.times;
      arrow = Boolean.cup x.arrow y.arrow;
      record= Boolean.cup x.record y.record;
      ints  = Intervals.cup x.ints  y.ints;
      atoms = Atoms.cup x.atoms y.atoms;
      strs  = Strings.cup x.strs y.strs;
    }
      
  let cap x y = 
    if x = y then x else {
      times = Boolean.cap x.times y.times;
      record= Boolean.cap x.record y.record;
      arrow = Boolean.cap x.arrow y.arrow;
      ints  = Intervals.cap x.ints  y.ints;
      atoms = Atoms.cap x.atoms y.atoms;
      strs  = Strings.cap x.strs y.strs;
    }
      
  let diff x y = 
    if x = y then empty else { 
      times = Boolean.diff x.times y.times;
      arrow = Boolean.diff x.arrow y.arrow;
      record= Boolean.diff x.record y.record;
      ints  = Intervals.diff x.ints  y.ints;
      atoms = Atoms.diff x.atoms y.atoms;
      strs  = Strings.diff x.strs y.strs;
    }

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  let neg x = diff any x
		   
  let equal e a b =
    if a.ints <> b.ints then raise NotEqual;
    if a.atoms <> b.atoms then raise NotEqual;
    if a.strs <> b.strs then raise NotEqual;
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.times b.times;
    Boolean.equal (fun (x1,x2) (y1,y2) -> e x1 y1; e x2 y2) a.arrow b.arrow;
    Boolean.equal (fun (l1,o1,x1) (l2,o2,x2) -> 
		     if (l1 <> l2) || (o1 <> o2) then raise NotEqual;
		     e x1 x2) a.record b.record
      
  let map f a =
    { times = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.times;
      arrow = Boolean.map (fun (x1,x2) -> (f x1, f x2)) a.arrow;
      record= Boolean.map (fun (l,o,x) -> (l,o, f x)) a.record;
      ints  = a.ints;
      atoms = a.atoms;
      strs  = a.strs;
    }
    
  let hash h a =
    Hashtbl.hash (map h a)
      
  let iter f a =
    ignore (map f a)
      
  let deep = 4
end

	     
module Algebra = Recursive.Make(I)
include I
include Algebra

let check d =
  Boolean.check d.times;
  Boolean.check d.arrow;
  Boolean.check d.record;
  ()

(*
let define n d = check d; define n d
*)

let cons d =
  let n = make () in
  define n d;
  internalize n


module Positive =
struct
  type rhs = [ `Type of descr | `Cup of v list | `Times of v * v ]
  and v = { mutable def : rhs; mutable node : node option }


  let rec make_descr seen v =
    if List.memq v seen then empty
    else
      let seen = v :: seen in
      match v.def with
	| `Type d -> d
	| `Cup vl -> 
	    List.fold_left (fun acc v -> cup acc (make_descr seen v)) empty vl
	| `Times (v1,v2) -> times (make_node v1) (make_node v2)

  and make_node v =
    match v.node with
      | Some n -> n
      | None ->
	  let n = make () in
	  v.node <- Some n;
	  let d = make_descr [] v in
	  define n d;
	  n

  let forward () = { def = `Cup []; node = None }
  let def v d = v.def <- d
  let cons d = let v = forward () in def v d; v
  let ty d = cons (`Type d)
  let cup vl = cons (`Cup vl)
  let times d1 d2 = cons (`Times (d1,d2))
  let define v1 v2 = def v1 (`Cup [v2]) 

  let solve v = internalize (make_node v)
end


let get_record r =
  let add = SortedMap.add (fun (o1,t1) (o2,t2) -> (o1&&o2, cap t1 t2)) in
  let line (p,n) =
    let accu = List.fold_left 
		 (fun accu (l,o,t) -> add l (o,descr t) accu) [] p in
    List.fold_left 
      (fun accu (l,o,t) -> add l (not o,neg (descr t)) accu) accu n in
  List.map line r
    

let counter_label = ref 0
let label_table = Hashtbl.create 63
let label_names = Hashtbl.create 63

let label s =
  try Hashtbl.find label_table s
  with Not_found ->
    incr counter_label;
    Hashtbl.add label_table s !counter_label;
    Hashtbl.add label_names !counter_label s;
    !counter_label

let label_name l =
  Hashtbl.find label_names l

let mk_atom = label

let atom_name = label_name

(* Subtyping algorithm *)

let diff_t d t = diff d (descr t)
let cap_t d t = cap d (descr t)
let cap_product l = 
  List.fold_left 
    (fun (d1,d2) (t1,t2) -> (cap_t d1 t1, cap_t d2 t2))
    (any,any)
    l


module Assumptions = Set.Make(struct type t = descr let compare = compare end)

let memo = ref Assumptions.empty
let cache_false = ref Assumptions.empty

exception NotEmpty

let rec empty_rec d =
  if Assumptions.mem d !cache_false then false 
  else if Assumptions.mem d !memo then true
  else if not (Intervals.is_empty d.ints) then false
  else if not (Atoms.is_empty d.atoms) then false
  else if not (Strings.is_empty d.strs) then false
  else (
    let backup = !memo in
    memo := Assumptions.add d backup;
    if 
      (empty_rec_times d.times) &&
      (empty_rec_arrow d.arrow) &&
      (empty_rec_record d.record) 
    then true
    else (
      memo := backup;
      cache_false := Assumptions.add d !cache_false;
      false
    )
  )

and empty_rec_times c =
  List.for_all empty_rec_times_aux c

and empty_rec_times_aux (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
        let accu1' = diff_t accu1 t1 in
        if not (empty_rec accu1') then aux accu1' accu2 right;
        let accu2' = diff_t accu2 t2 in
        if not (empty_rec accu2') then aux accu1 accu2' right
    | [] -> raise NotEmpty
  in
  let (accu1,accu2) = cap_product left in
  (empty_rec accu1) || (empty_rec accu2) ||
  (try aux accu1 accu2 right; true with NotEmpty -> false)

and empty_rec_arrow c =
  List.for_all empty_rec_arrow_aux c

and empty_rec_arrow_aux (left,right) =
  let single_right (s1,s2) =
    let rec aux accu1 accu2 = function
      | (t1,t2)::left ->
          let accu1' = diff_t accu1 t1 in
          if not (empty_rec accu1') then aux accu1 accu2 left;
          let accu2' = cap_t accu2 t2 in
          if not (empty_rec accu2') then aux accu1 accu2 left
      | [] -> raise NotEmpty
    in
    let accu1 = descr s1 in
    (empty_rec accu1) ||
    (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)
  in
  List.exists single_right right

and empty_rec_record c =
  let aux = List.exists (fun (_,(opt,t)) -> (not opt) && (empty_rec t)) in
  List.for_all aux (get_record c)

let is_empty d =
  let r = empty_rec d in
  memo := Assumptions.empty;
  cache_false := Assumptions.empty;
  r

let non_empty d = 
  not (is_empty d)

let subtype d1 d2 =
  is_empty (diff d1 d2)

(* Sample value *)
module Sample =
struct

let rec find f = function
  | [] -> raise Not_found
  | x::r -> try f x with Not_found -> find f r

type t =
  | Int of int
  | Atom of atom
  | String of string
  | Pair of t * t
  | Record of (label * t) list
  | Fun of (node * node) list

let rec gen_atom i l =
  if SortedList.mem l i then gen_atom (succ i) l  else i

let rec sample_rec memo d =
  if (Assumptions.mem d memo) || (is_empty d) then raise Not_found 
  else 
    try Int (Intervals.sample d.ints) with Not_found ->
    try Atom (Atoms.sample (gen_atom 0) d.atoms) with Not_found ->
    try String (Strings.sample d.strs) with Not_found ->
    try sample_rec_arrow d.arrow with Not_found ->

    let memo = Assumptions.add d memo in
    try sample_rec_times memo d.times with Not_found ->
    try sample_rec_record memo d.record with Not_found -> 
    raise Not_found


and sample_rec_times memo c = 
  find (sample_rec_times_aux memo) c

and sample_rec_times_aux memo (left,right) =
  let rec aux accu1 accu2 = function
    | (t1,t2)::right ->
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1' accu2 right else
          let accu2' = diff_t accu2 t2 in
          if non_empty accu2' then aux accu1 accu2' right else
	    raise Not_found
    | [] -> Pair (sample_rec memo accu1, sample_rec memo accu2)
  in
  let (accu1,accu2) = cap_product left in
  if (is_empty accu1) || (is_empty accu2) then raise Not_found;
  aux accu1 accu2 right

and sample_rec_arrow c =
  find sample_rec_arrow_aux c

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and check_empty_simple_arrow_line left (s1,s2) = 
  let rec aux accu1 accu2 = function
    | (t1,t2)::left ->
        let accu1' = diff_t accu1 t1 in
        if non_empty accu1' then aux accu1 accu2 left;
        let accu2' = cap_t accu2 t2 in
        if non_empty accu2' then aux accu1 accu2 left
    | [] -> raise NotEmpty
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  in
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  let accu1 = descr s1 in
  (is_empty accu1) ||
  (try aux accu1 (diff any (descr s2)) left; true with NotEmpty -> false)

and check_empty_arrow_line left right = 
  List.exists (check_empty_simple_arrow_line left) right

and sample_rec_arrow_aux (left,right) =
  if (check_empty_arrow_line left right) then raise Not_found
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  else Fun left


and sample_rec_record memo c =
  Record (find (sample_rec_record_aux memo) (get_record c))

and sample_rec_record_aux memo fields =
  let aux acc (l,(o,t)) = if o then acc else (l, sample_rec memo t) :: acc in
  List.fold_left aux [] fields

let get x = sample_rec Assumptions.empty x
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end


module Product =
struct
  type t = (descr * descr) list

  let get d =
    let line accu (left,right) =
      let rec aux accu d1 d2 = function
	| (t1,t2)::right ->
	    let accu = 
	      let d1 = diff_t d1 t1 in
              if is_empty d1 then accu else aux accu d1 d2 right in
	    let accu =
              let d2 = diff_t d2 t2 in
              if is_empty d2 then accu else aux accu d1 d2 right in
	    accu
	| [] ->  (d1,d2) :: accu
      in
      let (d1,d2) = cap_product left in
      if (is_empty d1) || (is_empty d2) then accu else aux accu d1 d2 right
    in
    List.fold_left line [] d.times

  let pi1 = List.fold_left (fun acc (t1,_) -> cup acc t1) empty
  let pi2 = List.fold_left (fun acc (_,t2) -> cup acc t2) empty

  let restrict_1 rects pi1 =
    let aux accu (t1,t2) = 
      let t1 = cap t1 pi1 in if is_empty t1 then accu else (t1,t2)::accu in
    List.fold_left aux [] rects
  
  type normal = t

  let normal d =
    let res = ref [] in

    let add (t1,t2) =
      let rec loop t1 t2 = function
	| [] -> res := (ref (t1,t2)) :: !res
	| ({contents = (d1,d2)} as r)::l ->
	    (*OPT*) 
	    if d1 = t1 then r := (d1,cup d2 t2) else
	      
	      let i = cap t1 d1 in
	      if is_empty i then loop t1 t2 l
	      else (
		r := (i, cup t2 d2);
		let k = diff d1 t1 in 
		if non_empty k then res := (ref (k,d2)) :: !res;
		
		let j = diff t1 d1 in 
		if non_empty j then loop j t2 l
	      )
      in
      loop t1 t2 !res
    in
    List.iter add (get d);
    List.map (!) !res

  let any = { empty with times = any.times }
end


module Record = 
struct
  type t = (label, (bool * descr)) SortedMap.t list

  let get d =
    let line r = List.for_all (fun (l,(o,d)) -> o || non_empty d) r in
    List.filter line (get_record d.record)


  let restrict_label_present t l =
    let aux = SortedMap.change l (fun (_,d) -> (false,d)) (false,any) in
    List.map aux t

  let restrict_label_absent t l =
    let restr = function (true, _) -> (true,empty) | _ -> raise Exit in
    let aux accu r =  
      try SortedMap.change l restr (true,empty) r :: accu
      with Exit -> accu in
    List.fold_left aux [] t

  let restrict_field t l d =
    let restr (_,d1) = 
      let d1 = cap d d1 in 
      if is_empty d1 then raise Exit else (false,d1) in
    let aux accu r = 
      try SortedMap.change l restr (false,d) r :: accu 
      with Exit -> accu in
    List.fold_left aux [] t

  let project_field t l =
    let aux accu x =
      match List.assoc l x with
	| (false,t) -> cup accu t
	| _ -> raise Not_found
    in
    List.fold_left aux empty t

  type normal = 
      [ `Success
      | `Fail
      | `Label of label * (descr * normal) list * normal ]

  let rec merge_record n r =
    match (n, r) with
      | (`Success, _) | (_, []) -> `Success
      | (`Fail, r) ->
	  let aux (l,(o,t)) n = `Label (l, [t,n], if o then n else `Fail) in
	  List.fold_right aux r `Success
      | (`Label (l1,present,absent), (l2,(o,t2))::r') ->
	  if (l1 < l2) then
	    let pr =  List.map (fun (t,x) -> (t, merge_record x r)) present in
	    `Label (l1,pr,merge_record absent r)
	  else if (l2 < l1) then
	    let n' = merge_record n r' in
	    `Label (l2, [t2, n'], if o then n' else n)
	  else
	    let res = ref [] in
	    let aux a (t,x) = 
	      (let t = diff t t2 in 
	       if non_empty t then res := (t,x) :: !res);
	      (let t = cap t t2 in
	       if non_empty t then res := (t, merge_record x r') :: !res);
	      diff a t 
	    in
	    let t2 = List.fold_left aux t2 present in
	    let () = 
	      if non_empty t2 then 
	      res := (t2, merge_record `Fail r') :: !res in
	    let abs = if o then merge_record absent r' else absent in
	    `Label (l1, !res, abs)


  let normal d =
    List.fold_left merge_record `Fail (get d)

  let project d l =
    let aux accu x =
      match List.assoc l x with
	| (false,t) -> cup accu t
	| _ -> raise Not_found
    in
    List.fold_left aux empty (get_record d.record)

  let any = { empty with record = any.record }
  let is_empty d = d = []
end


module MapDescr = Map.Make(struct type t = descr let compare = compare end)

let memo_normalize = ref MapDescr.empty

let map_sort f l =
  SortedList.from_list (List.map f l)

let rec rec_normalize d =
  try MapDescr.find d !memo_normalize
  with Not_found ->
    let n = make () in
    memo_normalize := MapDescr.add d n !memo_normalize;
    let times = 
      map_sort
	(fun (d1,d2) -> [(rec_normalize d1, rec_normalize d2)],[])
	(Product.normal d)
    in
    let record = 
      map_sort
	(fun f -> map_sort (fun (l,(o,d)) -> (l,o,rec_normalize d)) f, [])
	(Record.get d)
    in
    define n { d with times = times; record = record };
    n

let normalize n =
  internalize (rec_normalize (descr n))
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module Print =
struct
  let marks = Hashtbl.create 63
  let wh = ref []
  let count_name = ref 0
  let name () =
    incr count_name;
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    "X" ^ (string_of_int !count_name)
(* TODO: 
   check that these generated names does not conflict with declared types *)
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  let bool_iter f b =
    List.iter (fun (p,n) -> List.iter f p; List.iter f n) b

  let trivial b = b = Boolean.empty || b = Boolean.full

  let worth_abbrev d = 
    not (trivial d.times && trivial d.arrow && trivial d.record) 

  let rec mark n =
    let i = id n and d = descr n in
    try 
      let r = Hashtbl.find marks i in
      if (!r = None) && (worth_abbrev d) then 
	(let na = name () in 
	 r := Some na;
	 wh := (na,d) :: !wh
	)
    with Not_found -> 
      Hashtbl.add marks i (ref None);
      mark_descr d
  and mark_descr d = 
    bool_iter (fun (n1,n2) -> mark n1; mark n2) d.times;
    bool_iter (fun (n1,n2) -> mark n1; mark n2) d.arrow;
    bool_iter (fun (l,o,n) -> mark n) d.record

    
  let rec print_union ppf = function
    | [] -> Format.fprintf ppf "Empty"
    | [h] -> h ppf
    | h::t -> Format.fprintf ppf "@[%t |@ %a@]" h print_union t

  let print_atom ppf a = Format.fprintf ppf "`%s" (atom_name a)

  let rec print ppf n =
(*    Format.fprintf ppf "[%i]" (id n); *)
    match !(Hashtbl.find marks (id n)) with
      | Some n -> Format.fprintf ppf "%s" n
      | None -> print_descr ppf (descr n)
  and print_descr ppf d = 
    if d = any then Format.fprintf ppf "Any" else
    print_union ppf 
      (Intervals.print d.ints @
       Strings.print d.strs @
       Atoms.print "AnyAtom" print_atom d.atoms @
       Boolean.print "(Any,Any)" print_times d.times @
       Boolean.print "(Empty -> Any)" print_arrow d.arrow @
       Boolean.print "{ }" print_record d.record
      )
  and print_times ppf (t1,t2) =
    Format.fprintf ppf "@[(%a,%a)@]" print t1 print t2
  and print_arrow ppf (t1,t2) =
    Format.fprintf ppf "@[(%a -> %a)@]" print t1 print t2
  and print_record ppf (l,o,t) =
    Format.fprintf ppf "@[{ %s =%s %a }@]" 
      (label_name l) (if o then "?" else "") print t

	  
  let end_print ppf =
    (match List.rev !wh with
       | [] -> ()
       | (na,d)::t ->
	   Format.fprintf ppf " where@ @[%s = %a" na print_descr d;
	   List.iter 
	     (fun (na,d) -> Format.fprintf ppf " and@ %s = %a" na print_descr d)
	     t;
	   Format.fprintf ppf "@]"
    );
    Format.fprintf ppf "@]";
    count_name := 0;
    wh := [];
    Hashtbl.clear marks

  let print ppf n =
    mark n;
    Format.fprintf ppf "@[%a" print n;
    end_print ppf

  let print_descr ppf d =
    mark_descr d;
    Format.fprintf ppf "@[%a" print_descr d;
    end_print ppf
 
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  let rec print_sep f sep ppf = function
    | [] -> ()
    | [x] -> f ppf x
    | x::rem -> f ppf x; Format.fprintf ppf "%s" sep; print_sep f sep ppf rem


  let rec print_sample ppf = function
    | Sample.Int i -> Format.fprintf ppf "%i" i
    | Sample.Atom a -> Format.fprintf ppf "`%s" (atom_name a)
    | Sample.String s -> Format.fprintf ppf "%S" s
    | Sample.Pair (x1,x2) -> 
	Format.fprintf ppf "(%a,%a)" 
        print_sample x1
        print_sample x2
    | Sample.Record r ->
	Format.fprintf ppf "{ %a }"
	  (print_sep 
	     (fun ppf (l,x) -> 
		Format.fprintf ppf "%s = %a"
		(label_name l)
		print_sample x
	     )
	     " ; "
	  ) r
    | Sample.Fun iface ->
	Format.fprintf ppf "(fun ( %a ) x -> ...)"
	  (print_sep
	     (fun ppf (t1,t2) ->
		Format.fprintf ppf "%a -> %a; "
		print t1 print t2
	     )
	     " ; "
	  ) iface
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end

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module Arrow =
struct
  type t = descr * (descr * descr) list list

  let get t =
    List.fold_left
      (fun ((dom,arr) as accu) (left,right) ->
	 if Sample.check_empty_arrow_line left right 
	 then accu
	 else (
	   let left =
	     List.map 
	       (fun (t,s) -> (descr t, descr s)) left in
	   let d = List.fold_left (fun d (t,_) -> cup d t) empty left in
	   (cap dom d, left :: arr)
	 )
      )
      (any, [])
      t.arrow

  let domain (dom,_) = dom

  let apply_simple t result left = 
    let rec aux result accu1 accu2 = function
      | (t1,s1)::left ->
          let result = 
	    let accu1 = diff accu1 t1 in
            if non_empty accu1 then aux result accu1 accu2 left
            else result in
          let result =
	    let accu2 = cap accu2 s1 in
            aux result accu1 accu2 left in
	  result
      | [] -> 
          if subtype accu2 result 
	  then result
	  else cup result accu2
    in
    aux result t any left
      
  let apply (_,arr) t =
    List.fold_left (apply_simple t) empty arr

  let any = { empty with arrow = any.arrow }
end
  


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(*
let rec print_normal_record ppf = function
  | Success -> Format.fprintf ppf "Yes"
  | Fail -> Format.fprintf ppf "No"
  | FirstLabel (l,present,absent) ->
      Format.fprintf ppf "%s?@[<v>@\n" (label_name l);
      List.iter
        (fun (t,n) ->
	   Format.fprintf ppf "(%a)=>@[%a@]@\n" 
	     Print.print_descr t
	     print_normal_record n
	) present;
      if absent <> Fail then
	Format.fprintf ppf "(absent)=>@[%a@]@\n" print_normal_record absent;
      Format.fprintf ppf "@]" 
*)


(* 
let pr s = Types.Print.print Format.std_formatter (Syntax.make_type (Syntax.parse s));;

let pr' s = Types.Print.print Format.std_formatter 
   (Types.normalize (Syntax.make_type (Syntax.parse s)));;

BUG:
pr "'a | 'b where 'a = ('a , 'a) and 'b= ('b , 'b)";;
*)


(*
  let nr s =
    let t = Types.descr (Syntax.make_type (Syntax.parse s)) in
    let n = Types.normal_record' t.Types.record in
    Types.print_normal_record Format.std_formatter n;;
*)