From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Mon, 1 Jun 2009 11:57:04 +0000 (+0000)
Subject: we rewrite the paramodulation code!
X-Git-Tag: make_still_working~3936
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=ddd751449e73a22af523ce78ce1d8f0bb211e941;p=helm.git

we rewrite the paramodulation code!
---

diff --git a/helm/software/components/METAS/meta.helm-ng_paramodulation.src b/helm/software/components/METAS/meta.helm-ng_paramodulation.src
new file mode 100644
index 000000000..5c7e62b30
--- /dev/null
+++ b/helm/software/components/METAS/meta.helm-ng_paramodulation.src
@@ -0,0 +1,5 @@
+requires="helm-cic helm-ng_kernel"
+version="0.0.1"
+archive(byte)="ng_paramodulation.cma"
+archive(native)="ng_paramodulation.cmxa"
+linkopts=""
diff --git a/helm/software/components/ng_paramodulation/.depend b/helm/software/components/ng_paramodulation/.depend
new file mode 100644
index 000000000..db250f996
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/.depend
@@ -0,0 +1,12 @@
+terms.cmi: 
+pp.cmi: terms.cmi 
+founif.cmi: terms.cmi 
+index.cmi: terms.cmi 
+terms.cmo: terms.cmi 
+terms.cmx: terms.cmi 
+pp.cmo: pp.cmi 
+pp.cmx: pp.cmi 
+founif.cmo: founif.cmi 
+founif.cmx: founif.cmi 
+index.cmo: terms.cmi index.cmi 
+index.cmx: terms.cmx index.cmi 
diff --git a/helm/software/components/ng_paramodulation/Makefile b/helm/software/components/ng_paramodulation/Makefile
new file mode 100644
index 000000000..8612f4bfc
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/Makefile
@@ -0,0 +1,11 @@
+PACKAGE = ng_paramodulation
+
+INTERFACE_FILES = \
+	terms.mli pp.mli founif.mli index.mli orderings.mli
+
+IMPLEMENTATION_FILES = $(INTERFACE_FILES:%.mli=%.ml)
+
+all:
+
+include ../../Makefile.defs
+include ../Makefile.common
diff --git a/helm/software/components/ng_paramodulation/founif.ml b/helm/software/components/ng_paramodulation/founif.ml
new file mode 100644
index 000000000..125bded70
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/founif.ml
@@ -0,0 +1,14 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
+
+let unification = assert false
diff --git a/helm/software/components/ng_paramodulation/founif.mli b/helm/software/components/ng_paramodulation/founif.mli
new file mode 100644
index 000000000..d959fc309
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/founif.mli
@@ -0,0 +1,30 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
+
+val unification: 
+  Terms.varlist -> (* global varlist for both terms t1 and t2 *)
+  Terms.varlist -> (* locked variables: if equal to FV(t2) we match t1 with t2*)
+  'a Terms.foterm ->
+  'a Terms.foterm ->
+     'a Terms.substitution * Terms.varlist
+
+(*
+val unification: 
+  Terms.varlist -> 'a Terms.foterm -> 'a Terms.foterm -> 
+   'a Terms.substitution * Terms.varlist
+
+val matching:
+  Terms.varlist -> Terms.varlist -> 'a Terms.foterm -> 'a Terms.foterm -> 
+   'a Terms.substitution * Terms.varlist
+
+*)
diff --git a/helm/software/components/ng_paramodulation/index.ml b/helm/software/components/ng_paramodulation/index.ml
new file mode 100644
index 000000000..123c51650
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/index.ml
@@ -0,0 +1,78 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id$ *)
+
+module type Comparable =
+  sig
+    type t
+    val is_eq : t -> t -> bool
+  end
+
+module C : Comparable =
+  struct 
+    type t = NCic.term
+    let is_eq a b = Pervasives.compare a b = 0 (* TODO: optimize *)
+  end
+
+  (*
+module C : Comparable =
+  struct 
+    type t = Cic.term
+    let is_eq a b = Pervasives.compare a b = 0 (* TODO: optimize *)
+  end
+*)
+
+open Discrimination_tree
+
+module ClauseOT : Set.OrderedType 
+                with type t = Terms.direction * C.t Terms.unit_clause = 
+ struct 
+  type t = Terms.direction * C.t Terms.unit_clause
+  let compare (d1,(id1,_,_,_)) (d2,(id2,_,_,_)) = 
+          Pervasives.compare (d1,id1) (d2,id2)
+ end
+
+module ClauseSet = Set.Make(ClauseOT)
+
+module FotermIndexable : Indexable
+with type input = C.t Terms.foterm and 
+     type constant_name = C.t = struct
+
+type input = C.t Terms.foterm
+type constant_name = C.t
+
+let path_string_of =
+  let rec aux arity = function
+    | Terms.Leaf a -> [Constant (a, arity)]
+    | Terms.Var i -> assert (arity = 0); [Variable]
+    | Terms.Node (Terms.Var _::_) -> assert false
+    | Terms.Node ([] | [ _ ] ) -> assert false
+    | Terms.Node (Terms.Node _::_) -> assert false
+    | Terms.Node (hd::tl) ->
+        aux (List.length tl) hd @ List.flatten (List.map (aux 0) tl) 
+  in 
+    aux 0
+;;
+
+let compare e1 e2 = 
+  match e1,e2 with 
+  | Constant (a1,ar1), Constant (a2,ar2) ->
+      if C.is_eq a1 a2 then Pervasives.compare ar1 ar2
+      else Pervasives.compare e1 e2 (* TODO: OPTIMIZE *)
+  | _ -> Pervasives.compare e1 e2
+;;
+
+let string_of_path l = String.concat "." (List.map (fun _ -> "*") l) ;;
+
+end
+
+module DiscriminationTree = Make(FotermIndexable)(ClauseSet)
diff --git a/helm/software/components/ng_paramodulation/index.mli b/helm/software/components/ng_paramodulation/index.mli
new file mode 100644
index 000000000..fdecba91f
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/index.mli
@@ -0,0 +1,31 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id$ *)
+
+module type Comparable =
+  sig
+    type t
+    val is_eq : t -> t -> bool
+  end
+
+module C : Comparable 
+
+module FotermIndexable : Discrimination_tree.Indexable
+with type constant_name = C.t and
+     type input = C.t Terms.foterm 
+
+module ClauseSet : Set.S with type elt = Terms.direction * C.t Terms.unit_clause
+
+module DiscriminationTree : Discrimination_tree.DiscriminationTree 
+with type constant_name = C.t
+and type input = C.t Terms.foterm
+and type data = ClauseSet.elt and type dataset = ClauseSet.t
diff --git a/helm/software/components/ng_paramodulation/orderings.ml b/helm/software/components/ng_paramodulation/orderings.ml
new file mode 100644
index 000000000..f15454c62
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/orderings.ml
@@ -0,0 +1,276 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id$ *)
+
+(* (weight of constants, [(meta, weight_of_meta)]) *)
+type weight = int * (int * int) list;;
+
+let string_of_weight (cw, mw) =
+  let s =
+    String.concat ", "
+      (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
+  in
+  Printf.sprintf "[%d; %s]" cw s
+;;
+
+let weight_of_term term =
+  let vars_dict = Hashtbl.create 5 in
+  let rec aux = function
+    | Terms.Var i -> 
+        (try
+           let oldw = Hashtbl.find vars_dict i in
+           Hashtbl.replace vars_dict i (oldw+1)
+         with Not_found ->
+           Hashtbl.add vars_dict i 1);
+        0
+    | Terms.Leaf _ -> 1
+    | Terms.Node l -> List.fold_left (+) 0 (List.map aux l)
+  in
+  let w = aux term in
+  let l =
+    Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict [] 
+  in
+  let compare w1 w2 = 
+    match w1, w2 with
+    | (m1, _), (m2, _) -> m2 - m1 
+  in 
+  (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
+;;
+
+let compute_clause_weight = assert false (*
+  let factor = 2 in
+  match o with
+    | Lt -> 
+	let w, m = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false right) in
+	  w + (factor * (List.length m)) ;
+    | Le -> assert false
+    | Gt -> 
+	let w, m = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false left) in
+	  w + (factor * (List.length m)) ;
+  | Ge -> assert false
+  | Eq 
+  | Incomparable -> 
+      let w1, m1 = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false right) in
+      let w2, m2 = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false left) in
+      w1 + w2 + (factor * (List.length m1)) + (factor * (List.length m2))
+*)
+;;
+
+(* returns a "normalized" version of the polynomial weight wl (with type
+ * weight list), i.e. a list sorted ascending by meta number,
+ * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
+ * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
+ *      (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
+let normalize_weight maxmeta (cw, wl) =
+  let rec aux = function
+    | 0 -> []
+    | m -> (m, 0)::(aux (m-1))
+  in
+  let tmpl = aux maxmeta in
+  let wl =
+    List.sort
+      (fun (m, _) (n, _) -> Pervasives.compare m n)
+      (List.fold_left
+         (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
+  in
+  (cw, wl)
+;;
+
+
+let normalize_weights (cw1, wl1) (cw2, wl2) =
+  let rec aux wl1 wl2 =
+    match wl1, wl2 with
+    | [], [] -> [], []
+    | (m, w)::tl1, (n, w')::tl2 when m = n ->
+        let res1, res2 = aux tl1 tl2 in
+        (m, w)::res1, (n, w')::res2
+    | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
+        let res1, res2 = aux tl1 wl2 in
+        (m, w)::res1, (m, 0)::res2
+    | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
+        let res1, res2 = aux wl1 tl2 in
+        (n, 0)::res1, (n, w')::res2
+    | [], (n, w)::tl2 ->
+        let res1, res2 = aux [] tl2 in
+        (n, 0)::res1, (n, w)::res2
+    | (m, w)::tl1, [] ->
+        let res1, res2 = aux tl1 [] in
+        (m, w)::res1, (m, 0)::res2
+    | _, _ -> assert false
+  in
+  let cmp (m, _) (n, _) = compare m n in
+  let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
+  (cw1, wl1), (cw2, wl2)
+;;
+
+(* Riazanov: 3.1.5 pag 38 *)
+let compare_weights ((h1, w1) as weight1) ((h2, w2) as weight2)=
+  let res, diffs =
+    try
+      List.fold_left2
+        (fun ((lt, eq, gt), diffs) w1 w2 ->
+           match w1, w2 with
+           | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
+               let diffs = (w1 - w2) + diffs in 
+               let r = compare w1 w2 in
+               if r < 0 then (lt+1, eq, gt), diffs
+               else if r = 0 then (lt, eq+1, gt), diffs
+               else (lt, eq, gt+1), diffs
+           | _ -> assert false)
+        ((0, 0, 0), 0) w1 w2
+    with Invalid_argument _ -> assert false
+  in
+  let hdiff = h1 - h2 in 
+  match res with
+  | (0, _, 0) ->
+      if hdiff < 0 then Lt
+      else if hdiff > 0 then Gt
+      else Eq 
+  | (m, _, 0) ->
+      if hdiff <= 0 then Lt
+      else if (- diffs) >= hdiff then Le else Incomparable
+  | (0, _, m) ->
+      if hdiff >= 0 then Gt
+      else if diffs >= (- hdiff) then Ge else Incomparable
+  | (m, _, n) when m > 0 && n > 0 ->
+      Incomparable
+  | _ -> assert false 
+;;
+
+
+let rec aux_ordering ?(recursion=true) t1 t2 =
+  let module C = Cic in
+  let compare_uris u1 u2 =
+    let res =
+      compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
+    if res < 0 then Lt
+    else if res = 0 then Eq
+    else Gt
+  in
+  match t1, t2 with
+  | C.Meta _, _
+  | _, C.Meta _ -> Incomparable
+
+  | t1, t2 when t1 = t2 -> Eq
+
+  | C.Rel n, C.Rel m -> if n > m then Lt else Gt
+  | C.Rel _, _ -> Lt
+  | _, C.Rel _ -> Gt
+
+  | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
+  | C.Const _, _ -> Lt
+  | _, C.Const _ -> Gt
+
+  | C.MutInd (u1, tno1, _), C.MutInd (u2, tno2, _) -> 
+       let res =  compare_uris u1 u2 in
+       if res <> Eq then res 
+       else 
+          let res = compare tno1 tno2 in
+          if res = 0 then Eq else if res < 0 then Lt else Gt
+  | C.MutInd _, _ -> Lt
+  | _, C.MutInd _ -> Gt
+
+  | C.MutConstruct (u1, tno1, cno1, _), C.MutConstruct (u2, tno2, cno2, _) ->
+       let res =  compare_uris u1 u2 in
+       if res <> Eq then res 
+       else 
+          let res = compare (tno1,cno1) (tno2,cno2) in
+          if res = 0 then Eq else if res < 0 then Lt else Gt
+  | C.MutConstruct _, _ -> Lt
+  | _, C.MutConstruct _ -> Gt
+
+  | C.Appl l1, C.Appl l2 when recursion ->
+      let rec cmp t1 t2 =
+        match t1, t2 with
+        | [], [] -> Eq
+        | _, [] -> Gt
+        | [], _ -> Lt
+        | hd1::tl1, hd2::tl2 ->
+            let o = aux_ordering hd1 hd2 in
+            if o = Eq then cmp tl1 tl2
+            else o
+      in
+      cmp l1 l2
+  | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
+      aux_ordering h1 h2
+        
+  | t1, t2 ->
+      debug_print
+        (lazy
+           (Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
+              (CicPp.ppterm t1) (CicPp.ppterm t2)));
+      Incomparable
+;;
+
+let nonrec_kbo t1 t2 =
+  let w1 = weight_of_term t1 in
+  let w2 = weight_of_term t2 in
+  match compare_weights ~normalize:true w1 w2 with
+  | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
+  | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
+  | Eq -> aux_ordering t1 t2
+  | res -> res
+;;
+
+let rec kbo t1 t2 =
+  let aux = aux_ordering ~recursion:false in
+  let w1 = weight_of_term t1
+  and w2 = weight_of_term t2 in
+  let rec cmp t1 t2 =
+    match t1, t2 with
+    | [], [] -> Eq
+    | _, [] -> Gt
+    | [], _ -> Lt
+    | hd1::tl1, hd2::tl2 ->
+        let o =
+          kbo hd1 hd2
+        in
+        if o = Eq then cmp tl1 tl2
+        else o
+  in
+  let comparison = compare_weights ~normalize:true w1 w2 in
+  match comparison with
+  | Le ->
+      let r = aux t1 t2 in
+      if r = Lt then Lt
+      else if r = Eq then (
+        match t1, t2 with
+        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
+            if cmp tl1 tl2 = Lt then Lt else Incomparable
+        | _, _ ->  Incomparable
+      ) else Incomparable
+  | Ge ->
+      let r = aux t1 t2 in
+      if r = Gt then Gt
+      else if r = Eq then (
+        match t1, t2 with
+        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
+            if cmp tl1 tl2 = Gt then Gt else Incomparable
+        | _, _ ->  Incomparable
+      ) else Incomparable
+  | Eq ->
+      let r = aux t1 t2 in
+      if r = Eq then (
+        match t1, t2 with
+        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
+            cmp tl1 tl2
+        | _, _ ->  Incomparable
+      ) else r 
+  | res -> res
+;;
+          
+let compare_terms = nonrec_kbo;; 
+
diff --git a/helm/software/components/ng_paramodulation/orderings.mli b/helm/software/components/ng_paramodulation/orderings.mli
new file mode 100644
index 000000000..9d0f47d22
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/orderings.mli
@@ -0,0 +1,13 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
+
diff --git a/helm/software/components/ng_paramodulation/pp.ml b/helm/software/components/ng_paramodulation/pp.ml
new file mode 100644
index 000000000..aff9224e0
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/pp.ml
@@ -0,0 +1,19 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
+
+let pp_foterm = assert false
+let pp_proof = assert false
+let pp_substitution = assert false
+let pp_unit_clause = assert false
+
+
diff --git a/helm/software/components/ng_paramodulation/pp.mli b/helm/software/components/ng_paramodulation/pp.mli
new file mode 100644
index 000000000..46c588676
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/pp.mli
@@ -0,0 +1,19 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *)
+
+val pp_foterm: ('a -> string) -> 'a Terms.foterm -> string
+val pp_proof: ('a -> string) -> 'a Terms.bag -> 'a Terms.proof -> string
+val pp_substitution: ('a -> string) -> 'a Terms.substitution -> string
+val pp_unit_clause: ('a -> string) -> 'a Terms.unit_clause -> string
+
+
diff --git a/helm/software/components/ng_paramodulation/terms.ml b/helm/software/components/ng_paramodulation/terms.ml
new file mode 100644
index 000000000..91ca56271
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/terms.ml
@@ -0,0 +1,59 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id$ *)
+
+type 'a foterm = 
+  | Leaf of 'a
+  | Var of int
+  | Node of ('a foterm) list
+
+type 'a substitution = (int * 'a foterm) list
+
+type comparison = Lt | Le | Eq | Ge | Gt | Incomparable
+
+type rule = SuperpositionRight | SuperpositionLeft | Demodulation
+type direction = Left2Right | Right2Left | Nodir
+type position = int list
+
+type 'a proof =
+  | Exact of 'a
+  | Step of rule * int * int * direction * position * 'a substitution
+         (* rule, eq1, eq2, direction of eq2, position, substitution *)
+
+type 'a literal = 
+ | Equation of    'a foterm  (* lhs *)
+                * 'a foterm  (* rhs *)
+                * 'a foterm  (* type *)
+                * comparison (* orientation *)
+ | Predicate of   'a foterm 
+
+type varlist = int list
+
+type 'a unit_clause =
+   int        (* ID *)
+ * 'a literal
+ * varlist       (* variable list *)
+ * 'a proof      (* proof *)
+
+type 'a passive_clause = int * 'a unit_clause (* weight * equation *)
+
+
+module OT =
+ struct
+   type t = int 
+   let compare = Pervasives.compare
+ end
+
+module M : Map.S with type key = int 
+  = Map.Make(OT) 
+
+type 'a bag = 'a unit_clause M.t
diff --git a/helm/software/components/ng_paramodulation/terms.mli b/helm/software/components/ng_paramodulation/terms.mli
new file mode 100644
index 000000000..c49eaff83
--- /dev/null
+++ b/helm/software/components/ng_paramodulation/terms.mli
@@ -0,0 +1,52 @@
+(*
+    ||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_______________________________________________________________ *)
+
+(* $Id$ *)
+
+type 'a foterm = 
+  | Leaf of 'a
+  | Var of int
+  | Node of ('a foterm) list
+
+type 'a substitution = (int * 'a foterm) list
+
+type comparison = Lt | Le | Eq | Ge | Gt | Incomparable
+
+type rule = SuperpositionRight | SuperpositionLeft | Demodulation
+type direction = Left2Right | Right2Left | Nodir
+type position = int list
+
+type 'a proof =
+  | Exact of 'a
+  | Step of rule * int * int * direction * position * 'a substitution
+         (* rule, eq1, eq2, direction of eq2, position, substitution *)
+
+type 'a literal = 
+ | Equation of    'a foterm  (* lhs *)
+                * 'a foterm  (* rhs *)
+                * 'a foterm  (* type *)
+                * comparison (* orientation *)
+ | Predicate of   'a foterm 
+
+type varlist = int list
+
+type 'a unit_clause =
+   int        (* ID *)
+ * 'a literal
+ * varlist
+ * 'a proof      (* proof *)
+
+type 'a passive_clause = int * 'a unit_clause (* weight * equation *)
+
+module M : Map.S with type key = int 
+
+type 'a bag = 'a unit_clause M.t
+