(*
    ||M||  This file is part of HELM, an Hypertextual, Electronic        
    ||A||  Library of Mathematics, developed at the Computer Science     
    ||T||  Department, University of Bologna, Italy.                     
    ||I||                                                                
    ||T||  HELM is free software; you can redistribute it and/or         
    ||A||  modify it under the terms of the GNU General Public License   
    \   /  version 2 or (at your option) any later version.              
     \ /   This software is distributed as is, NO WARRANTY.              
      V_______________________________________________________________ *)

module U  = NUri
module W  = Share
module L  = Log
module G  = Options
module H  = Hierarchy
module N  = Level
module E  = Entity
module O  = Output
module S  = Status
module B  = Brg
module BO = BrgOutput
module BE = BrgEnvironment

type kam = {
   e: B.lenv;                 (* environment              *)
   s: (B.lenv * B.term) list; (* stack                    *)
   l: int;                    (* level                    *)
   d: int;                    (* inferred type iterations *)
   n: int option;             (* expected type iterations *)
}

type message = (kam, B.term) L.message

(* Internal functions *******************************************************)

let level = 4

let sublevel = succ level

let log1 st s c t =
   let s1, s2 = s ^ " in the environment", "the term" in
   L.log st BO.specs level (L.et_items1 s1 c s2 t)

let log2 st s cu u ct t =
   let s1, s2, s3 = s ^ " in the environment (expected)", "the term", "and in the environment (inferred)" in
   L.log st BO.specs level (L.et_items2 s1 cu s2 u ~sc2:s3 ~c2:ct s2 t)

let rec list_and map = function
   | hd1 :: tl1, hd2 :: tl2 ->
      if map hd1 hd2 then list_and map (tl1, tl2) else false
   | l1, l2                 -> l1 = l2

let zero = Some 0

(* check closure *)
let are_alpha_convertible err f t1 t2 =
   let rec aux f = function
      | B.Sort (_, p1), B.Sort (_, p2)
      | B.LRef (_, p1), B.LRef (_, p2)         ->
         if p1 = p2 then f () else err ()
      | B.GRef (_, u1), B.GRef (_, u2)         ->
         if U.eq u1 u2 then f () else err ()
      | B.Cast (_, v1, t1), B.Cast (_, v2, t2)         
      | B.Appl (_, v1, t1), B.Appl (_, v2, t2) ->
         let f _ = aux f (t1, t2) in
	 aux f (v1, v2)
      | B.Bind (_, b1, t1), B.Bind (_, b2, t2) ->
         let f _ = aux f (t1, t2) in
	 aux_bind f (b1, b2)
      | _                                      -> err ()
   and aux_bind f = function
      | B.Abbr v1, B.Abbr v2                          -> aux f (v1, v2)
      | B.Abst (n1, v1), B.Abst (n2, v2) when n1 = n2 -> aux f (v1, v2)
      | B.Void, B.Void                                -> f ()
      | _                                             -> err ()
   in
   if W.eq t1 t2 then f () else aux f (t1, t2)

let assert_tstep m vo = match m.n with
   | Some n -> n > m.d
   | None   -> vo

let tstep m = {m with d = succ m.d}

let tsteps m = match m.n with
   | Some n when n > m.d -> n - m.d
   | _                   -> 0

let get m i =
   let _, c, a, b = B.get m.e i in c, a, b

(* to share *)
let rec step st m x = 
   if !G.trace >= sublevel then 
   log1 st.S.lenv (Printf.sprintf "entering R.step: l:%u d:%i n:%s" m.l m.d (match m.n with Some n -> string_of_int n | None -> "infinite")) m.e x;
   match x with
   | B.Sort (a, h)                ->
      if assert_tstep m false then
         step st (tstep m) (B.Sort (a, H.apply h))      
      else m, x, None
   | B.GRef (_, uri)              ->
      begin match BE.get_entity uri with
         | _, _, _, E.Abbr v ->
            if st.S.delta then begin
	       if !G.summary then O.add ~gdelta:1 ();
               step st m v
            end else
	       m, x, Some v
         | _, _, _, E.Abst w ->
            if assert_tstep m true then begin
               if !G.summary then O.add ~grt:1 (); 
               step st (tstep m) w
            end else
	     m, x, None   
	 | _, _, _, E.Void   ->
            assert false
      end
   | B.LRef (_, i)                ->
      begin match get m i with
	 | c, _, B.Abbr v      ->
	    if !G.summary then O.add ~ldelta:1 ();
	    step st {m with e = c} v
	 | c, a, B.Abst (_, w) ->
            if assert_tstep m true then begin
               if !G.summary then O.add ~lrt:1 ();
               step st {(tstep m) with e = c} w
            end else
	       m, B.LRef (a, i), None
	 | _, _, B.Void        ->
	    assert false
      end
   | B.Cast (_, u, t)             ->
      if assert_tstep m false then begin
         if !G.summary then O.add ~e:1 ();
         step st (tstep m) u
      end else begin
         if !G.summary then O.add ~epsilon:1 ();
         step st m t
      end
   | B.Appl (_, v, t)             ->
      step st {m with s = (m.e, v) :: m.s} t   
   | B.Bind (a, B.Abst (n, w), t) ->
      begin match m.s with
         | []          ->
            let i = tsteps m in
            if i = 0 then m, x, None else
            let n = N.minus st.S.lenv n i in
            m, B.Bind (a, B.Abst (n, w), t), None
	 | (c, v) :: s ->
            if !G.cc && not (N.assert_not_zero st.S.lenv n) then assert false;
	    if !G.summary then O.add ~beta:1 ~theta:(List.length s) ();
	    let v = if assert_tstep m false then B.Cast (E.empty_node, w, v) else v in
            let e = B.push m.e c a (B.abbr v) in
	    step st {m with e = e; s = s} t
      end
   | B.Bind (a, b, t)        ->
      if !G.summary then O.add ~theta:(List.length m.s) ();
      let e = B.push m.e m.e a b in 
      step st {m with e = e} t

let reset m ?(e=m.e) n =
   {m with e = e; n = n; s = []; d = 0} 

let assert_iterations m1 m2 = match m1.n, m2.n with
      | Some n1, Some n2 -> n1 - m1.d = n2 - m2.d
      | _                -> false 

let push m a b = 
   let a, l = match b with
      | B.Abst _ -> {a with E.n_apix = m.l}, succ m.l
      | b        -> a, m.l
   in
   let e = B.push m.e m.e a b in
   {m with e = e; l = l}

let rec ac_nfs st (m1, t1, r1) (m2, t2, r2) =
   if !G.trace >= level then log2 st.S.lenv "Now converting nfs" m1.e t1 m2.e t2;
   match t1, r1, t2, r2 with
      | B.Sort (_, h1), _, B.Sort (_, h2), _                ->
         h1 = h2
      | B.LRef ({E.n_apix = e1}, _), _, 
        B.LRef ({E.n_apix = e2}, _), _                      ->
	 if e1 = e2 then ac_stacks st m1 m2 else false
      | B.GRef (_, u1), None, B.GRef (_, u2), None          ->
	 if U.eq u1 u2 && assert_iterations m1 m2 then ac_stacks st m1 m2 else false
      | B.GRef ({E.n_apix = e1}, u1), Some v1, 
        B.GRef ({E.n_apix = e2}, u2), Some v2               ->
         if e1 < e2 then begin 
            if !G.summary then O.add ~gdelta:1 ();
	    ac_nfs st (m1, t1, r1) (step st m2 v2)
	 end else if e2 < e1 then begin
	    if !G.summary then O.add ~gdelta:1 ();
	    ac_nfs st (step st m1 v1) (m2, t2, r2) 
         end else if U.eq u1 u2 && assert_iterations m1 m2 && ac_stacks st m1 m2 then true
         else begin
	    if !G.summary then O.add ~gdelta:2 ();
	    ac st m1 v1 m2 v2
         end 
      | _, _, B.GRef _, Some v2                             ->
         if !G.summary then O.add ~gdelta:1 ();
	 ac_nfs st (m1, t1, r1) (step st m2 v2)
      | B.GRef _, Some v1, _, _                             ->
	 if !G.summary then O.add ~gdelta:1 ();
	 ac_nfs st (step st m1 v1) (m2, t2, r2)
      | B.Bind (a1, (B.Abst (n1, w1) as b1), t1), _, 
        B.Bind (a2, (B.Abst (n2, w2) as b2), t2), _         ->
	 if !G.cc && not (N.assert_equal st.S.lenv n1 n2) then false else
         if ac {st with S.si = false} (reset m1 zero) w1 (reset m2 zero) w2 then
	    ac st (push m1 a1 b1) t1 (push m2 a2 b2) t2
	 else false
      | B.Sort _, _, B.Bind (a, (B.Abst (n, _) as b), t), _ ->
         if st.S.si then
            if !G.cc && not (N.assert_zero st.S.lenv n) then false else begin
	    if !G.summary then O.add ~si:1 ();
	    ac st (push m1 a b) t1 (push m2 a b) t end
         else false
      | _                                                   -> false

and ac st m1 t1 m2 t2 =
(*   L.warn "entering R.are_convertible"; *)
   ac_nfs st (step st m1 t1) (step st m2 t2)

and ac_stacks st m1 m2 =
(*   L.warn "entering R.are_convertible_stacks"; *)
   if List.length m1.s <> List.length m2.s then false else
   let map (c1, v1) (c2, v2) =
      let m1, m2 = reset m1 ~e:c1 zero, reset m2 ~e:c2 zero in
      ac {st with S.si = false} m1 v1 m2 v2
   in
   list_and map (m1.s, m2.s)

(* Interface functions ******************************************************)

let empty_kam = { 
   e = B.empty; s = []; l = 0; d = 0; n = None
}

let get m i =
   assert (m.s = []);
   let _, _, _, b = B.get m.e i in b

let xwhd st m n t =
   if !G.trace >= level then log1 st.S.lenv "Now scanning" m.e t;   
   let m, t, _ = step {st with S.delta = true} (reset m n) t in
   m, t

let are_convertible st m1 n1 t1 m2 n2 t2 = 
   if !G.trace >= level then log2 st.S.lenv "Now converting" m1.e t1 m2.e t2;
   let r = ac {st with S.delta = !G.expand} (reset m1 n1) t1 (reset m2 n2) t2 in
   r
(*    let err _ = in 
      if W.eq mu mw then are_alpha_convertible err f u w else err () *)

(* error reporting **********************************************************)

let pp_term st m och t = BO.specs.L.pp_term st m.e och t

let pp_lenv st och m = BO.specs.L.pp_lenv st och m.e

let specs = {
   L.pp_term = pp_term; L.pp_lenv = pp_lenv
}