(* Copyright (C) 2004-2005, HELM Team.
 * 
 * This file is part of HELM, an Hypertextual, Electronic
 * Library of Mathematics, developed at the Computer Science
 * Department, University of Bologna, Italy.
 * 
 * HELM is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 * 
 * HELM is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HELM; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA  02111-1307, USA.
 * 
 * For details, see the HELM World-Wide-Web page,
 * http://helm.cs.unibo.it/
 *)

open Printf

type pattern_id = int
type interpretation_id = pattern_id

type term_info =
  { sort: (Cic.id, CicNotationPt.sort_kind) Hashtbl.t;
    uri: (Cic.id, string) Hashtbl.t;
  }

exception No_match

module OrderedInt =
  struct
  type t = int
  let compare (x1:t) (x2:t) = Pervasives.compare x2 x1  (* reverse order *)
  end

module IntSet = Set.Make (OrderedInt)

let int_set_of_int_list l =
  List.fold_left (fun acc i -> IntSet.add i acc) IntSet.empty l

let warning s = prerr_endline ("CicNotation WARNING: " ^ s)

module Patterns =
  struct
  type row_t = CicNotationPt.cic_appl_pattern list * pattern_id
  type t = row_t list

  let empty = []

  let first_column t = List.map (fun (patterns, _) -> List.hd patterns) t
  let pattern_ids t = List.map snd t

  let prepend_column t column =
    try
      List.map2 (fun elt (pl, pid) -> (elt :: pl), pid) column t

    with Invalid_argument _ -> assert false

  let prepend_columns t columns =
    List.fold_right
      (fun column rows -> prepend_column rows column)
      columns t

  let partition t pidl =
    let partitions = Hashtbl.create 11 in
    let add pid row = Hashtbl.add partitions pid row in
    (try
      List.iter2 add pidl t
    with Invalid_argument _ -> assert false);
    let pidset = int_set_of_int_list pidl in
    IntSet.fold
      (fun pid acc ->
        match Hashtbl.find_all partitions pid with
        | [] -> acc
        | patterns -> (pid, List.rev patterns) :: acc)
      pidset []

  let are_empty t = fst (List.hd t) = []
    (* if first row has an empty list of patterns, then others will as well *)

    (* return 2 lists of rows, first one containing homogeneous rows according
     * to "compatible" below *)
  let horizontal_split t =
    let compatible ap1 ap2 =
      match ap1, ap2 with
      | CicNotationPt.UriPattern _, CicNotationPt.UriPattern _
      | CicNotationPt.ArgPattern _, CicNotationPt.ArgPattern _
      | CicNotationPt.ApplPattern _, CicNotationPt.ApplPattern _ -> true
      | _ -> false
    in
    let ap =
      match t with
      | [] -> assert false
      | ([], _) :: _ ->
          assert false  (* are_empty should have been invoked in advance *)
      | (hd :: _ , _) :: _ -> hd
    in
    let rec aux prev_t = function
      | [] -> List.rev prev_t, []
      | ([], _) :: _ -> assert false
      | (((hd :: _), _) as row) :: tl when compatible ap hd ->
          aux (row :: prev_t) tl
      | t -> List.rev prev_t, t
    in
    aux [] t

    (* return 2 lists, first one representing first column, second one
     * representing rows stripped of the first element *)
  let vertical_split t =
    let l =
      List.map
        (function
          | (hd :: tl, pid) -> hd, (tl, pid)
          | _ -> assert false)
        t
    in
    List.split l
  end

  (* acic -> ast auxiliary function s *)

let get_types uri =
  let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
    match o with
      | Cic.InductiveDefinition (l,_,_,_) -> l 
      | _ -> assert false

let name_of_inductive_type uri i = 
  let types = get_types uri in
  let (name, _, _, _) = try List.nth types i with Not_found -> assert false in
  name

  (* returns <name, type> pairs *)
let constructors_of_inductive_type uri i =
  let types = get_types uri in
  let (_, _, _, constructors) = 
    try List.nth types i with Not_found -> assert false
  in
  constructors

  (* returns name only *)
let constructor_of_inductive_type uri i j =
  (try
    fst (List.nth (constructors_of_inductive_type uri i) (j-1))
  with Not_found -> assert false)

module Ast = CicNotationPt

let string_of_name = function
  | Cic.Name s -> s
  | Cic.Anonymous -> "_"

let ident_of_name n = Ast.Ident (string_of_name n, None)

let idref id t = Ast.AttributedTerm (`IdRef id, t)

let ast_of_acic0 term_info acic k =
(*   prerr_endline "ast_of_acic0"; *)
  let k = k term_info in
  let register_uri id uri = Hashtbl.add term_info.uri id uri in
  let sort_of_id id =
    try
      Hashtbl.find term_info.sort id
    with Not_found -> assert false
  in
  let aux_substs substs =
    Some
      (List.map
        (fun (uri, annterm) -> (UriManager.name_of_uri uri, k annterm))
        substs)
  in
  let aux_context context =
    List.map
      (function
        | None -> None
        | Some annterm -> Some (k annterm))
      context
  in
  let aux = function
    | Cic.ARel (id,_,_,b) -> idref id (Ast.Ident (b, None))
    | Cic.AVar (id,uri,substs) ->
        register_uri id (UriManager.string_of_uri uri);
        idref id (Ast.Ident (UriManager.name_of_uri uri, aux_substs substs))
    | Cic.AMeta (id,n,l) -> idref id (Ast.Meta (n, aux_context l))
    | Cic.ASort (id,Cic.Prop) -> idref id (Ast.Sort `Prop)
    | Cic.ASort (id,Cic.Set) -> idref id (Ast.Sort `Set)
    | Cic.ASort (id,Cic.Type _) -> idref id (Ast.Sort `Type)
    | Cic.ASort (id,Cic.CProp) -> idref id (Ast.Sort `CProp)
    | Cic.AImplicit _ -> assert false
    | Cic.AProd (id,n,s,t) ->
        let binder_kind =
          match sort_of_id id with
          | `Set | `Type -> `Pi
          | `Prop | `CProp -> `Forall
        in
        idref id (Ast.Binder (binder_kind, (ident_of_name n, Some (k s)), k t))
    | Cic.ACast (id,v,t) ->
        idref id (Ast.Appl [idref id (Ast.Symbol ("cast", 0)); k v; k t])
    | Cic.ALambda (id,n,s,t) ->
        idref id (Ast.Binder (`Lambda, (ident_of_name n, Some (k s)), k t))
    | Cic.ALetIn (id,n,s,t) ->
        idref id (Ast.LetIn ((ident_of_name n, None), k s, k t))
    | Cic.AAppl (aid,args) -> idref aid (Ast.Appl (List.map k args))
    | Cic.AConst (id,uri,substs) ->
        register_uri id (UriManager.string_of_uri uri);
        idref id (Ast.Ident (UriManager.name_of_uri uri, aux_substs substs))
    | Cic.AMutInd (id,uri,i,substs) as t ->
        let name = name_of_inductive_type uri i in
        let uri_str = UriManager.string_of_uri uri in
        let puri_str =
          uri_str ^ "#xpointer(1/" ^ (string_of_int (i + 1)) ^ ")"
        in
        register_uri id puri_str;
        idref id (Ast.Ident (name, aux_substs substs))
    | Cic.AMutConstruct (id,uri,i,j,substs) ->
        let name = constructor_of_inductive_type uri i j in
        let uri_str = UriManager.string_of_uri uri in
        let puri_str = sprintf "%s#xpointer(1/%d/%d)" uri_str (i + 1) j in
        register_uri id puri_str;
        idref id (Ast.Ident (name, aux_substs substs))
    | Cic.AMutCase (id,uri,typeno,ty,te,patterns) ->
        let name = name_of_inductive_type uri typeno in
        let constructors = constructors_of_inductive_type uri typeno in
        let rec eat_branch ty pat =
          match (ty, pat) with
          | Cic.Prod (_, _, t), Cic.ALambda (_, name, s, t') ->
              let (cv, rhs) = eat_branch t t' in
              (ident_of_name name, Some (k s)) :: cv, rhs
          | _, _ -> [], k pat
        in
        let patterns =
          List.map2
            (fun (name, ty) pat ->
              let (capture_variables, rhs) = eat_branch ty pat in
              ((name, capture_variables), rhs))
            constructors patterns
        in
        idref id (Ast.Case (k te, Some name, Some (k ty), patterns))
    | Cic.AFix (id, no, funs) -> 
        let defs = 
          List.map
            (fun (_, n, decr_idx, ty, bo) ->
              ((Ast.Ident (n, None), Some (k ty)), k bo, decr_idx))
            funs
        in
        let name =
          try
            (match List.nth defs no with
            | (Ast.Ident (n, _), _), _, _ when n <> "_" -> n
            | _ -> assert false)
          with Not_found -> assert false
        in
        idref id (Ast.LetRec (`Inductive, defs, Ast.Ident (name, None)))
    | Cic.ACoFix (id, no, funs) -> 
        let defs = 
          List.map
            (fun (_, n, ty, bo) -> ((Ast.Ident (n, None), Some (k ty)), k bo, 0))
            funs
        in
        let name =
          try
            (match List.nth defs no with
            | (Ast.Ident (n, _), _), _, _ when n <> "_" -> n
            | _ -> assert false)
          with Not_found -> assert false
        in
        idref id (Ast.LetRec (`CoInductive, defs, Ast.Ident (name, None)))
  in
  aux acic

  (* persistent state *)

let level2_patterns = Hashtbl.create 211

let (compiled32: (term_info -> Cic.annterm -> CicNotationPt.term) option ref) =
  ref None

let pattern_matrix = ref Patterns.empty

let get_compiled32 () =
  match !compiled32 with
  | None -> assert false
  | Some f -> f

let set_compiled32 f = compiled32 := Some f

  (* "envl" is a list of triples:
   *   <name environment, term environment, pattern id>, where
   *   name environment: (string * string) list
   *   term environment: (string * Cic.annterm) list *)
let return_closure success_k =
  (fun term_info terms envl ->
(*     prerr_endline "return_closure"; *)
    match terms with
    | [] ->
        (try
          success_k term_info (List.hd envl)
        with Failure _ -> assert false)
    | _ -> assert false)

let variable_closure names k =
  (fun term_info terms envl ->
(*     prerr_endline "variable_closure"; *)
    match terms with
    | hd :: tl ->
        let envl' =
          List.map2
            (fun arg (name_env, term_env, pid) ->
              let rec aux name_env term_env pid arg term =
                match arg, term with
                  Ast.IdentArg name, _ ->
                    (name_env, (name, term) :: term_env, pid)
                | Ast.EtaArg (Some name, arg'),
                  Cic.ALambda (id, name', ty, body) ->
                    aux
                      ((name, (string_of_name name', Some (ty, id))) :: name_env)
                      term_env pid arg' body
                | Ast.EtaArg (Some name, arg'), _ ->
                    let name' = CicNotationUtil.fresh_name () in
                    aux ((name, (name', None)) :: name_env)
                      term_env pid arg' term
                | Ast.EtaArg (None, arg'), Cic.ALambda (id, name, ty, body) ->
                    assert false
                | Ast.EtaArg (None, arg'), _ ->
                    assert false
              in
                aux name_env term_env pid arg hd)
            names envl
        in
        k term_info tl envl'
    | _ -> assert false)

let appl_closure ks k =
  (fun term_info terms envl ->
(*     prerr_endline "appl_closure"; *)
    (match terms with
    | Cic.AAppl (_, args) :: tl ->
        (try
          let k' = List.assoc (List.length args) ks in
          k' term_info (args @ tl) envl
        with Not_found -> k term_info terms envl)
    | [] -> assert false
    | _ -> k term_info terms envl))

let uri_of_term t = CicUtil.uri_of_term (Deannotate.deannotate_term t)

let uri_closure ks k =
  (fun term_info terms envl ->
(*     prerr_endline "uri_closure"; *)
    (match terms with
    | [] -> assert false
    | hd :: tl ->
(*         prerr_endline (sprintf "uri_of_term = %s" (uri_of_term hd)); *)
        begin
          try
            let k' = List.assoc (uri_of_term hd) ks in
            k' term_info tl envl
          with
          | Invalid_argument _  (* raised by uri_of_term *)
          | Not_found -> k term_info terms envl
        end))

  (* compiler from level 3 to level 2 *)
let compiler32 (t: Patterns.t) success_k fail_k =
  let rec aux t k = (* k is a continuation *)
    if t = [] then
      k
    else if Patterns.are_empty t then begin
      (match t with
      | _::_::_ ->
          (* optimization possible here: throw away all except one of the rules
           * which lead to ambiguity *)
          warning "Ambiguous patterns"
      | _ -> ());
      return_closure success_k
    end else
      match Patterns.horizontal_split t with
      | t', [] ->
          (match t' with
          | []
          | ([], _) :: _ -> assert false
          | (Ast.ArgPattern (Ast.IdentArg _) :: _, _) :: _
          | (Ast.ArgPattern (Ast.EtaArg _) :: _, _) :: _ ->
              let first_column, t'' = Patterns.vertical_split t' in
              let names =
                List.map
                  (function
                    | Ast.ArgPattern arg -> arg
                    | _ -> assert false)
                  first_column
              in
              variable_closure names (aux t'' k)
          | (Ast.ApplPattern _ :: _, _) :: _ ->
              let pidl =
                List.map
                  (function
                    | (Ast.ApplPattern args) :: _, _ -> List.length args
                    | _ -> assert false)
                  t'
              in
                (* arity partitioning *)
              let clusters = Patterns.partition t' pidl in
              let ks =  (* k continuation list *)
                List.map
                  (fun (len, cluster) ->
                    let cluster' =
                      List.map  (* add args as patterns heads *)
                        (function
                          | (Ast.ApplPattern args) :: tl, pid ->
                              (* let's throw away "teste di cluster" *)
                              args @ tl, pid
                          | _ -> assert false)
                        cluster
                    in
                    len, aux cluster' k)
                  clusters
              in
              appl_closure ks k
          | (Ast.UriPattern _ :: _, _) :: _ ->
              let uidmap, pidl =
                let urimap = ref [] in
                let uidmap = ref [] in
                let get_uri_id uri =
                  try
                    List.assoc uri !urimap
                  with
                    Not_found ->
                      let uid = List.length !urimap in
                      urimap := (uri, uid) :: !urimap ;
                      uidmap := (uid, uri) :: !uidmap ;
                      uid
                in
                let uidl =
                  List.map
                    (function
                      | (Ast.UriPattern uri) :: _, _ -> get_uri_id uri
                      | _ -> assert false)
                    t'
                in
                  !uidmap, uidl
              in
              let clusters = Patterns.partition t' pidl in
              let ks =
                List.map
                  (fun (uid, cluster) ->
                    let cluster' =
                      List.map
                        (function
                        | (Ast.UriPattern uri) :: tl, pid -> tl, pid
                        | _ -> assert false)
                      cluster
                    in
                    List.assoc uid uidmap, aux cluster' k)
                  clusters
              in
              uri_closure ks k)
      | t', tl -> aux t' (aux tl k)
  in
  let matcher = aux t (fun _ _ -> raise No_match) in
  (fun term_info annterm ->
    try
      matcher term_info [annterm] (List.map (fun (_, pid) -> [], [], pid) t)
    with No_match -> fail_k term_info annterm)

let ast_of_acic1 term_info annterm = (get_compiled32 ()) term_info annterm

let instantiate term_info name_env term_env pid =
  let symbol, args =
    try
      Hashtbl.find level2_patterns pid
    with Not_found -> assert false
  in
  let rec instantiate_arg = function
    | Ast.IdentArg name ->
        (try List.assoc name term_env with Not_found -> assert false)
    | Ast.EtaArg (None, _) -> assert false  (* TODO *)
    | Ast.EtaArg (Some name, arg) ->
        let (name', ty_opt) =
          try List.assoc name name_env with Not_found -> assert false
        in
        let body = instantiate_arg arg in
        let name' = Ast.Ident (name', None) in
        match ty_opt with
        | None -> Ast.Binder (`Lambda, (name', None), body)
        | Some (ty, id) ->
            idref id (Ast.Binder (`Lambda, (name', Some ty), body))
  in
  let args' = List.map instantiate_arg args in
  Ast.Appl (Ast.Symbol (symbol, 0) :: args')

let load_patterns t =
  let ast_env_of_name_env term_info name_env =
    List.map
      (fun (name, (name', ty_opt)) ->
        let ast_ty_opt =
          match ty_opt with
          | None -> None
          | Some (annterm, id) -> Some (ast_of_acic1 term_info annterm, id)
        in
        (name, (name', ast_ty_opt)))
      name_env
  in
  let ast_env_of_term_env term_info =
    List.map (fun (name, term) -> (name, ast_of_acic1 term_info term))
  in
  let fail_k term_info annterm = ast_of_acic0 term_info annterm ast_of_acic1 in
  let success_k term_info (name_env, term_env, pid) =
    instantiate
      term_info
      (ast_env_of_name_env term_info name_env)
      (ast_env_of_term_env term_info term_env)
      pid
  in
  let compiled32 = compiler32 t success_k fail_k in
  set_compiled32 compiled32

let ast_of_acic id_to_sort annterm =
  let term_info = { sort = id_to_sort; uri = Hashtbl.create 211 } in
  let ast = ast_of_acic1 term_info annterm in
  ast, term_info.uri

let fresh_id =
  let counter = ref ~-1 in
  fun () ->
    incr counter;
    !counter

let add_interpretation (symbol, args) appl_pattern =
  let id = fresh_id () in
  Hashtbl.add level2_patterns id (symbol, args);
  pattern_matrix := ([appl_pattern], id) :: !pattern_matrix;
  load_patterns !pattern_matrix;
  id

exception Interpretation_not_found

let remove_interpretation id =
  (try
    Hashtbl.remove level2_patterns id;
  with Not_found -> raise Interpretation_not_found);
  pattern_matrix := List.filter (fun (_, id') -> id <> id') !pattern_matrix;
  load_patterns !pattern_matrix

let _ = load_patterns []