From: Alberto Griggio <griggio@fbk.eu>
Date: Thu, 9 Jun 2005 17:19:17 +0000 (+0000)
Subject: prima implementazione di demodulate, superposition_left e superposition_right
X-Git-Tag: PRE_INDEX_1~1
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=acf29bdbdcdc6ad8c2d9d27e8a47500981b605cd;p=helm.git

prima implementazione di demodulate, superposition_left e superposition_right
con gli "indici"...
---

diff --git a/helm/ocaml/paramodulation/indexing.ml b/helm/ocaml/paramodulation/indexing.ml
index 8ed8f49a1..85821097d 100644
--- a/helm/ocaml/paramodulation/indexing.ml
+++ b/helm/ocaml/paramodulation/indexing.ml
@@ -2,39 +2,388 @@
     (Cic.term * ((bool * Inference.equality) list)) list 
 ;; *)
 
-type pos = Left | Right 
-;;
+type pos = Left | Right ;;
 
-let head_of_term =
-  function 
-    | Cic.Appl hd::tl -> hd
-    | t -> t
+let head_of_term = function
+  | Cic.Appl (hd::tl) -> hd
+  | t -> t
 ;;
 
-let index table eq =
-  let (_,(_,l,r,ordering),_,_) = eq in
+
+let index table (sign, eq) =
+  let _, (_, l, r, ordering), _, _ = eq in
   let hl = head_of_term l in
   let hr = head_of_term r in
   let index x pos = 
-    let x_entry = 
-      try Hashtbl.find table x
-      with Not_found -> [] in
-      Hashtbl.replace table x (pos,eq)::x_entry in
-  (match ordering with
-    | Utils.Gt -> 
-	index hl Left
-    | Utils.Lt -> 
-	index hr Right
-    | _ -> index hl Left;
-	index hr Right);
+    let x_entry = try Hashtbl.find table x with Not_found -> [] in
+    Hashtbl.replace table x ((pos, sign, eq)::x_entry)
+  in
+(*   (match ordering with *)
+(*    | Utils.Gt ->  *)
+(*        index hl Left *)
+(*    | Utils.Lt ->  *)
+(*        index hr Right *)
+(*    | _ -> index hl Left; *)
+(*        index hr Right); *)
+  index hl Left;
+  index hr Right;
   table
 ;;
 
-let demodulate_term env table cmp term =
+
+let remove_index table (sign, eq) =
+  let _, (_, l, r, ordering), _, _ = eq in
+  let hl = head_of_term l
+  and hr = head_of_term r in
+  let remove_index x pos =
+    let x_entry = try Hashtbl.find table x with Not_found -> [] in
+    let newentry = List.filter (fun e -> e <> (pos, sign, eq)) x_entry in
+    Hashtbl.replace table x newentry
+  in
+  remove_index hl Left;
+  remove_index hr Right;
+  table
+;;
+
+
+let rec find_matches metasenv context ugraph lift_amount term =
+  let module C = Cic in
+  let module U = Utils in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let cmp = !Utils.compare_terms in
+  function
+    | [] -> None
+    | (_, U.Negative, _)::tl ->
+        find_matches metasenv context ugraph lift_amount term tl
+    | (pos, U.Positive, (_, (_, _, _, o), _, _))::tl
+        when (pos = Left && o = U.Lt) || (pos = Right && o = U.Gt) ->
+        find_matches metasenv context ugraph lift_amount term tl
+    | (pos, U.Positive, (proof, (ty, left, right, o), metas, args))::tl ->
+        let do_match c other eq_URI =
+          let subst', metasenv', ugraph' =
+            Inference.matching (metasenv @ metas) context term
+              (S.lift lift_amount c) ugraph
+          in
+          Some (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
+                (proof, ty, c, other, eq_URI))
+        in
+        let c, other, eq_URI =
+          if pos = Left then left, right, HL.Logic.eq_ind_URI
+          else right, left, HL.Logic.eq_ind_r_URI
+        in
+        if o <> U.Incomparable then
+          try do_match c other eq_URI
+          with e -> find_matches metasenv context ugraph lift_amount term tl
+        else
+          let res = try do_match c other eq_URI with e -> None in
+          match res with
+          | Some (_, s, _, _, _) -> 
+              if cmp (M.apply_subst s left) (M.apply_subst s right) =
+                (if pos = Left then U.Gt else U.Lt) then
+                  res
+              else
+                find_matches metasenv context ugraph lift_amount term tl
+          | None ->
+              find_matches metasenv context ugraph lift_amount term tl
+;;
+
+
+let rec demodulate_term metasenv context ugraph table lift_amount term =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
   let hd_term = head_of_term term in
-  let candidates = Hashtbl.find table hd_term in
-  
-    
-    
-      
-  
+  let candidates = try Hashtbl.find table hd_term with Not_found -> [] in
+  match term with
+  | C.Meta _ -> None
+  | term ->
+      let res =
+        find_matches metasenv context ugraph lift_amount term candidates
+      in
+      if res <> None then
+        res
+      else
+        match term with
+        | C.Appl l ->
+            let res, ll = 
+              List.fold_left
+                (fun (res, tl) t ->
+                   if res <> None then
+                     (res, tl @ [S.lift 1 t])
+                   else 
+                     let r =
+                       demodulate_term metasenv context ugraph table
+                         lift_amount t
+                     in
+                     match r with
+                     | None -> (None, tl @ [S.lift 1 t])
+                     | Some (rel, _, _, _, _) -> (r, tl @ [rel]))
+                (None, []) l
+            in (
+              match res with
+              | None -> None
+              | Some (_, subst, menv, ug, info) ->
+                  Some (C.Appl ll, subst, menv, ug, info)
+            )
+        | C.Prod (nn, s, t) ->
+            let r1 =
+              demodulate_term metasenv context ugraph table lift_amount s in (
+              match r1 with
+              | None ->
+                  let r2 =
+                    demodulate_term metasenv
+                      ((Some (nn, C.Decl s))::context) ugraph
+                      table (lift_amount+1) t
+                  in (
+                    match r2 with
+                    | None -> None
+                    | Some (t', subst, menv, ug, info) ->
+                        Some (C.Prod (nn, (S.lift 1 s), t'),
+                              subst, menv, ug, info)
+                  )
+              | Some (s', subst, menv, ug, info) ->
+                  Some (C.Prod (nn, s', (S.lift 1 t)), subst, menv, ug, info)
+            )
+        | t ->
+            Printf.printf "Ne` Appl ne` Prod: %s\n"
+              (CicPp.pp t (Utils.names_of_context context));
+            None
+;;
+
+
+let rec demodulate newmeta env table target =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let metasenv, context, ugraph = env in
+  let proof, (eq_ty, left, right, order), metas, args = target in
+  let metasenv = metasenv @ metas in
+  let build_newtarget is_left
+      (t, subst, menv, ug, (proof', ty, what, other, eq_URI)) = 
+    let newterm, newproof =
+      let bo = S.subst (M.apply_subst subst other) t in
+      let bo'' =
+        C.Appl ([C.MutInd (HL.Logic.eq_URI, 0, []);
+                 S.lift 1 eq_ty] @
+                  if is_left then [bo; S.lift 1 right] else [S.lift 1 left; bo])
+      in
+      let t' = C.Lambda (C.Anonymous, ty, bo'') in
+      bo,
+      M.apply_subst subst (C.Appl [C.Const (eq_URI, []); ty; what; t';
+                                   proof; other; proof'])
+    in
+    let newmeta, newtarget =
+      let left, right = if is_left then newterm, right else left, newterm in
+      let m =
+        (Inference.metas_of_term left) @ (Inference.metas_of_term right)
+      in
+      let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas
+      and newargs =
+        List.filter
+          (function C.Meta (i, _) -> List.mem i m | _ -> assert false)
+          args
+      in
+      let ordering = !Utils.compare_terms left right in
+      newmeta, (newproof, (eq_ty, left, right, ordering), newmetasenv, newargs)
+    in
+    newmeta, newtarget
+  in
+  let res = demodulate_term metasenv context ugraph table 0 left in
+  match res with
+  | Some t ->
+      let newmeta, newtarget = build_newtarget true t in
+      if Inference.is_identity (metasenv, context, ugraph) newtarget then
+        newmeta, newtarget
+      else
+        demodulate newmeta env table newtarget
+  | None ->
+      let res = demodulate_term metasenv context ugraph table 0 right in
+      match res with
+      | Some t ->
+          let newmeta, newtarget = build_newtarget false t in
+          if Inference.is_identity (metasenv, context, ugraph) newtarget then
+            newmeta, newtarget
+          else
+            demodulate newmeta env table newtarget
+      | None ->
+          newmeta, target
+;;
+
+
+let rec betaexpand_term metasenv context ugraph table lift_amount term =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let hd_term = head_of_term term in
+  let candidates = try Hashtbl.find table hd_term with Not_found -> [] in
+  let res, lifted_term = 
+    match term with
+    | C.Meta (i, l) ->
+        let l = 
+          List.map (function
+                      | Some t -> Some (S.lift lift_amount t)
+                      | None -> None) l
+        in
+        [], C.Meta (i, l)
+          
+    | C.Rel m ->
+        [], if m <= lift_amount then C.Rel m else C.Rel (m+1)
+          
+    | C.Prod (nn, s, t) ->
+        let l1, lifted_s =
+          betaexpand_term metasenv context ugraph table lift_amount s in
+        let l2, lifted_t =
+          betaexpand_term metasenv ((Some (nn, C.Decl s))::context) ugraph
+            table (lift_amount+1) t in
+        let l1' =
+          List.map
+            (fun (t, s, m, ug, info) ->
+               C.Prod (nn, t, lifted_t), s, m, ug, info) l1
+        and l2' =
+          List.map
+            (fun (t, s, m, ug, info) ->
+               C.Prod (nn, lifted_s, t), s, m, ug, info) l2 in
+        l1' @ l2', C.Prod (nn, lifted_s, lifted_t)
+          
+    | C.Appl l ->
+        let l', lifted_l =
+          List.fold_right
+            (fun arg (res, lifted_tl) ->
+               let arg_res, lifted_arg =
+                 betaexpand_term metasenv context ugraph table lift_amount arg
+               in
+               let l1 =
+                 List.map
+                   (fun (a, s, m, ug, info) -> a::lifted_tl, s, m, ug, info)
+                   arg_res
+               in
+               (l1 @
+                  (List.map
+                     (fun (r, s, m, ug, info) -> lifted_arg::r, s, m, ug, info)
+                     res),
+                lifted_arg::lifted_tl)
+            ) l ([], [])
+        in
+        (List.map (fun (l, s, m, ug, info) -> (C.Appl l, s, m, ug, info)) l',
+         C.Appl lifted_l)
+
+    | t -> [], (S.lift lift_amount t)
+  in
+  match term with
+  | C.Meta _ -> res, lifted_term
+  | _ ->
+      match
+        find_matches metasenv context ugraph lift_amount term candidates
+      with
+      | None -> res, lifted_term
+      | Some r -> r::res, lifted_term
+;;
+
+
+let superposition_left (metasenv, context, ugraph) table target =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let module CR = CicReduction in
+  let module U = Utils in
+  let proof, (eq_ty, left, right, ordering), _, _ = target in
+  let expansions, _ =
+    let term = if ordering = U.Gt then left else right in
+    betaexpand_term metasenv context ugraph table 0 term
+  in
+  let build_new (bo, s, m, ug, (proof', ty, what, other, eq_URI)) =
+    let newgoal, newproof =
+      let bo' = S.subst (M.apply_subst s other) bo in
+      let bo'' =
+        C.Appl (
+          [C.MutInd (HL.Logic.eq_URI, 0, []);
+           S.lift 1 eq_ty] @
+            if ordering = U.Gt then [bo'; S.lift 1 right]
+            else [S.lift 1 left; bo'])
+      in
+      let t' = C.Lambda (C.Anonymous, ty, bo'') in
+      S.subst (M.apply_subst s other) bo,
+      M.apply_subst s
+        (C.Appl [C.Const (eq_URI, []); ty; what; t';
+                 proof; other; proof'])
+    in
+    let left, right, newordering =
+      if ordering = U.Gt then
+        newgoal, right, !Utils.compare_terms newgoal right
+      else
+        left, newgoal, !Utils.compare_terms left newgoal
+    in
+    (newproof, (eq_ty, left, right, ordering), [], [])
+  in
+  List.map build_new expansions
+;;
+
+
+let superposition_right newmeta (metasenv, context, ugraph) table target =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let module CR = CicReduction in
+  let module U = Utils in
+  let eqproof, (eq_ty, left, right, ordering), newmetas, args = target in
+  let maxmeta = ref newmeta in
+  let res1, res2 =
+    match ordering with
+    | U.Gt -> fst (betaexpand_term metasenv context ugraph table 0 left), []
+    | U.Lt -> [], fst (betaexpand_term metasenv context ugraph table 0 right)
+    | _ ->
+        let res l r =
+          List.filter
+            (fun (_, subst, _, _, _) ->
+               let subst = M.apply_subst subst in
+               let o = !Utils.compare_terms (subst l) (subst r) in
+               o <> U.Lt && o <> U.Le)
+            (fst (betaexpand_term metasenv context ugraph table 0 l))
+        in
+        (res left right), (res right left)
+  in
+  let build_new ordering (bo, s, m, ug, (proof', ty, what, other, eq_URI)) =
+    let newgoal, newproof =
+      let bo' = S.subst (M.apply_subst s other) bo in
+      let bo'' =
+        C.Appl (
+          [C.MutInd (HL.Logic.eq_URI, 0, []);
+           S.lift 1 eq_ty] @
+            if ordering = U.Gt then [bo'; S.lift 1 right]
+            else [S.lift 1 left; bo'])
+      in
+      let t' = C.Lambda (C.Anonymous, ty, bo'') in
+      S.subst (M.apply_subst s other) bo,
+      M.apply_subst s
+        (C.Appl [C.Const (eq_URI, []); ty; what; t';
+                 eqproof; other; proof'])
+    in
+    let newmeta, newequality = 
+      let left, right, newordering =
+        if ordering = U.Gt then
+          newgoal, right, !Utils.compare_terms newgoal right
+        else
+          left, newgoal, !Utils.compare_terms left newgoal
+      in
+      Inference.fix_metas !maxmeta
+        (newproof, (eq_ty, left, right, ordering), [], [])
+    in
+    maxmeta := newmeta;
+    newequality
+  in
+  let new1 = List.map (build_new U.Gt) res1
+  and new2 = List.map (build_new U.Lt) res2 in
+  let ok = function
+    | _, (_, left, right, _), _, _ ->
+        not (fst (CR.are_convertible context left right ugraph))
+  in
+  (!maxmeta,
+   (List.filter ok (new1 @ new2)))
+;;