| Exact of Cic.term
| Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
(* subst, (rule,eq1, eq2,predicate) *)
-and goal_proof = (Utils.pos * int * Subst.substitution * Cic.term) list
+and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
;;
(* globals *)
let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
(weight,proof,(ty,l,r,o),m,id)
+let string_of_rule = function
+ | SuperpositionRight -> "SupR"
+ | SuperpositionLeft -> "SupL"
+ | Demodulation -> "Demod"
+;;
+
let string_of_equality ?env eq =
match env with
| None ->
- let w, _, (ty, left, right, o), _ , id = open_equality eq in
- Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s"
+ let w, _, (ty, left, right, o), m , id = open_equality eq in
+ Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
id w (CicPp.ppterm ty)
(CicPp.ppterm left)
(Utils.string_of_comparison o) (CicPp.ppterm right)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
| Some (_, context, _) ->
let names = Utils.names_of_context context in
- let w, _, (ty, left, right, o), _ , id = open_equality eq in
- Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s"
+ let w, _, (ty, left, right, o), m , id = open_equality eq in
+ Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
id w (CicPp.pp ty names)
(CicPp.pp left names) (Utils.string_of_comparison o)
(CicPp.pp right names)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
;;
let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
let string_of_proof ?(names=[]) p gp =
- let str_of_rule = function
- | SuperpositionRight -> "SupR"
- | SuperpositionLeft -> "SupL"
- | Demodulation -> "Demod"
- in
let str_of_pos = function
| Utils.Left -> "left"
| Utils.Right -> "right"
prefix (CicPp.pp t names)
| Step (subst,(rule,eq1,(pos,eq2),pred)) ->
Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
- prefix (str_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
+ prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
(CicPp.pp pred names)^
aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^
aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2))
aux 0 "" p ^
String.concat "\n"
(List.map
- (fun (pos,i,s,t) ->
+ (fun (r,pos,i,s,t) ->
(Printf.sprintf
- "GOAL: %s %d %s %s\n"
+ "GOAL: %s %s %d %s %s\n" (string_of_rule r)
(str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
gp)
remove_refl p1
| _ -> Cic.Appl (List.map remove_refl args))
| Cic.Appl l -> Cic.Appl (List.map remove_refl l)
+ | Cic.LetIn (name,bo,rest) ->
+ Cic.LetIn (name,remove_refl bo,remove_refl rest)
| _ -> t
in
let rec canonical t =
match t with
+ | Cic.LetIn(name,bo,rest) -> Cic.LetIn(name,canonical bo,canonical rest)
| Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
when LibraryObjects.is_sym_eq_URI uri_sym ->
(match p_of_sym ens tl with
* ctx is a term with an open (Rel 1). (Rel 1) is the empty context
*)
let rec aux uri ty left right ctx_d = function
+ | Cic.LetIn (name,body,rest) ->
+ (* we should go in body *)
+ Cic.LetIn (name,body,aux uri ty left right ctx_d rest)
| Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
when LibraryObjects.is_eq_ind_URI uri_ind ||
LibraryObjects.is_eq_ind_r_URI uri_ind ->
contextualize eq ty l r t
;;
-let build_proof_step subst p1 p2 pos l r pred =
- let p1 = Subst.apply_subst subst p1 in
- let p2 = Subst.apply_subst subst p2 in
- let l = Subst.apply_subst subst l in
- let r = Subst.apply_subst subst r in
- let pred = Subst.apply_subst subst pred in
+let build_proof_step ?(sym=false) lift subst p1 p2 pos l r pred =
+ let p1 = Subst.apply_subst_lift lift subst p1 in
+ let p2 = Subst.apply_subst_lift lift subst p2 in
+ let l = CicSubstitution.lift lift l in
+ let l = Subst.apply_subst_lift lift subst l in
+ let r = CicSubstitution.lift lift r in
+ let r = Subst.apply_subst_lift lift subst r in
+ let pred = CicSubstitution.lift lift pred in
+ let pred = Subst.apply_subst_lift lift subst pred in
let ty,body =
match pred with
| Cic.Lambda (_,ty,body) -> ty,body
let what, other =
if pos = Utils.Left then l,r else r,l
in
+ let p =
match pos with
| Utils.Left ->
mk_eq_ind (Utils.eq_ind_URI ()) ty what pred p1 other p2
| Utils.Right ->
mk_eq_ind (Utils.eq_ind_r_URI ()) ty what pred p1 other p2
+ in
+ if sym then
+ let uri,pl,pr =
+ let eq,_,pl,pr = open_eq body in
+ LibraryObjects.sym_eq_URI ~eq, pl, pr
+ in
+ let l = CicSubstitution.subst other pl in
+ let r = CicSubstitution.subst other pr in
+ mk_sym uri ty l r p
+ else
+ p
;;
-let build_proof_term proof =
- let rec aux = function
- | Exact term -> term
- | Step (subst,(_, id1, (pos,id2), pred)) ->
- let p,_,_ = proof_of_id id1 in
- let p1 = aux p in
- let p,l,r = proof_of_id id2 in
- let p2 = aux p in
- build_proof_step subst p1 p2 pos l r pred
+let parametrize_proof p l r ty =
+ let parameters = CicUtil.metas_of_term p
+@ CicUtil.metas_of_term l
+@ CicUtil.metas_of_term r
+in (* ?if they are under a lambda? *)
+ let parameters =
+ HExtlib.list_uniq (List.sort Pervasives.compare parameters)
in
- aux proof
+ let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
+ let with_what, lift_no =
+ List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
+ in
+ let p = CicSubstitution.lift (lift_no-1) p in
+ let p =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun t1 t2 ->
+ match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
+ ~what ~with_what ~where:p
+ in
+ let ty_of_m _ = ty (*function
+ | Cic.Meta (i,_) -> List.assoc i menv
+ | _ -> assert false *)
+ in
+ let args, proof,_ =
+ List.fold_left
+ (fun (instance,p,n) m ->
+ (instance@[m],
+ Cic.Lambda
+ (Cic.Name ("x"^string_of_int n),
+ CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
+ p),
+ n+1))
+ ([Cic.Rel 1],p,1)
+ what
+ in
+ let instance = match args with | [x] -> x | _ -> Cic.Appl args in
+ proof, instance
;;
-let wfo goalproof proof =
+let wfo goalproof proof id =
let rec aux acc id =
let p,_,_ = proof_of_id id in
match p with
in
let acc =
match proof with
- | Exact _ -> []
- | Step (_,(_,id1, (_,id2), _)) -> aux (aux [] id1) id2
+ | Exact _ -> [id]
+ | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
in
- List.fold_left (fun acc (_,id,_,_) -> aux acc id) acc goalproof
+ List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
;;
let string_of_id names id =
+ if id = 0 then "" else
try
- let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+ let (_,p,(_,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
match p with
| Exact t ->
- Printf.sprintf "%d = %s: %s = %s" id
+ Printf.sprintf "%d = %s: %s = %s [%s]" id
(CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
| Step (_,(step,id1, (_,id2), _) ) ->
- Printf.sprintf "%6d: %s %6d %6d %s = %s" id
- (if step = SuperpositionRight then "SupR" else "Demo")
+ Printf.sprintf "%6d: %s %6d %6d %s = %s [%s]" id
+ (string_of_rule step)
id1 id2 (CicPp.pp l names) (CicPp.pp r names)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
with
Not_found -> assert false
-let pp_proof names goalproof proof =
- String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof)) ^
- "\ngoal is demodulated with " ^
- (String.concat " "
- ((List.map (fun (_,i,_,_) -> string_of_int i) goalproof)))
-;;
-
-let build_goal_proof l initial ty =
- let proof =
- List.fold_left
- (fun current_proof (pos,id,subst,pred) ->
- let p,l,r = proof_of_id id in
- let p = build_proof_term p in
- let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
- build_proof_step subst current_proof p pos l r pred)
- initial l
+let pp_proof names goalproof proof subst id initial_goal =
+ prerr_endline ("AAAAA" ^ string_of_int id);
+ prerr_endline (String.concat "+" (List.map string_of_int (wfo goalproof proof
+ id)));
+ String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof id)) ^
+ "\ngoal:\n " ^
+ (String.concat "\n "
+ (fst (List.fold_right
+ (fun (r,pos,i,s,pred) (acc,g) ->
+ let _,_,left,right = open_eq g in
+ let ty =
+ match pos with
+ | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
+ | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
+ in
+ let ty = Subst.apply_subst s ty in
+ ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
+ ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
+ "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
+;;
+
+(* returns the list of ids that should be factorized *)
+let get_duplicate_step_in_wfo l p =
+ let ol = List.rev l in
+ let h = Hashtbl.create 13 in
+ (* NOTE: here the n parameter is an approximation of the dependency
+ between equations. To do things seriously we should maintain a
+ dependency graph. This approximation is not perfect. *)
+ let add i n =
+ let p,_,_ = proof_of_id i in
+ match p with
+ | Exact _ -> true
+ | _ ->
+ try let (pos,no) = Hashtbl.find h i in Hashtbl.replace h i (pos,no+1);false
+ with Not_found -> Hashtbl.add h i (n,1);true
+ in
+ let rec aux n = function
+ | Exact _ -> n
+ | Step (_,(_,i1,(_,i2),_)) ->
+ let go_on_1 = add i1 n in
+ let go_on_2 = add i2 n in
+ max
+ (if go_on_1 then aux (n+1) (let p,_,_ = proof_of_id i1 in p) else n+1)
+ (if go_on_2 then aux (n+1) (let p,_,_ = proof_of_id i2 in p) else n+1)
+ in
+ let i = aux 0 p in
+ let _ =
+ List.fold_left
+ (fun acc (_,_,id,_,_) -> aux acc (let p,_,_ = proof_of_id id in p))
+ i ol
+ in
+ (* now h is complete *)
+ let proofs = Hashtbl.fold (fun k (pos,count) acc->(k,pos,count)::acc) h [] in
+ let proofs = List.filter (fun (_,_,c) -> c > 1) proofs in
+ let proofs =
+ List.sort (fun (_,c1,_) (_,c2,_) -> Pervasives.compare c2 c1) proofs
+ in
+ List.map (fun (i,_,_) -> i) proofs
+;;
+
+let build_proof_term h lift proof =
+ let proof_of_id aux id =
+ let p,l,r = proof_of_id id in
+ try List.assoc id h,l,r with Not_found -> aux p, l, r
+ in
+ let rec aux = function
+ | Exact term -> CicSubstitution.lift lift term
+ | Step (subst,(_, id1, (pos,id2), pred)) ->
+ let p1,_,_ = proof_of_id aux id1 in
+ let p2,l,r = proof_of_id aux id2 in
+ let p = build_proof_step lift subst p1 p2 pos l r pred in
+(* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
+ if not cond then
+ prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
+ assert cond;*)
+ p
in
- proof
- (*canonical (contextualize_rewrites proof ty)*)
+ aux proof
+;;
+
+let build_goal_proof l initial ty se =
+ let se = List.map (fun i -> Cic.Meta (i,[])) se in
+ let lets = get_duplicate_step_in_wfo l initial in
+ let letsno = List.length lets in
+ let _,mty,_,_ = open_eq ty in
+ let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l
+ in
+ let lets,_,h =
+ List.fold_left
+ (fun (acc,n,h) id ->
+ let p,l,r = proof_of_id id in
+ let cic = build_proof_term h n p in
+ let real_cic,instance =
+ parametrize_proof cic l r (CicSubstitution.lift n mty)
+ in
+ let h = (id, instance)::lift_list h in
+ acc@[id,real_cic],n+1,h)
+ ([],0,[]) lets
+ in
+ let proof,se =
+ let rec aux se current_proof = function
+ | [] -> current_proof,se
+ | (rule,pos,id,subst,pred)::tl ->
+ let p,l,r = proof_of_id id in
+ let p = build_proof_term h letsno p in
+ let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
+ let sym,pred =
+ match rule with
+ | SuperpositionLeft when pos = Utils.Left ->
+ let pred =
+ match pred with
+ | Cic.Lambda (name,ty,Cic.Appl[eq;ty1;l;r]) ->
+ Cic.Lambda (name,ty,Cic.Appl[eq;ty1;r;l])
+ | _ -> assert false
+ in
+ true, pred
+ | _ -> false,pred
+ in
+ let proof =
+ build_proof_step ~sym letsno subst current_proof p pos l r pred
+ in
+ let proof,se = aux se proof tl in
+ Subst.apply_subst_lift letsno subst proof,
+ List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
+ in
+ aux se (build_proof_term h letsno initial) l
+ in
+ let n,proof =
+ let initial = proof in
+ List.fold_right
+ (fun (id,cic) (n,p) ->
+ n-1,
+ Cic.LetIn (
+ Cic.Name ("H"^string_of_int id),
+ cic, p))
+ lets (letsno-1,initial)
+ in
+ (*canonical (contextualize_rewrites proof (CicSubstitution.lift letsno ty))*)proof, se
;;
let refl_proof ty term =
ty; term]
;;
-let metas_of_proof p =
- Utils.metas_of_term (build_proof_term p)
+let metas_of_proof p =
+ let p = build_proof_term [] 0 p in
+ Utils.metas_of_term p
;;
-let relocate newmeta menv =
- let subst, metasenv, newmeta =
+let relocate newmeta menv to_be_relocated =
+ let subst, newmetasenv, newmeta =
List.fold_right
- (fun (i, context, ty) (subst, menv, maxmeta) ->
- let irl = [] (*
- CicMkImplicit.identity_relocation_list_for_metavariable context *)
- in
- let newsubst = Subst.buildsubst i context (Cic.Meta(maxmeta,irl)) ty subst in
- let newmeta = maxmeta, context, ty in
- newsubst, newmeta::menv, maxmeta+1)
- menv (Subst.empty_subst, [], newmeta+1)
+ (fun i (subst, metasenv, maxmeta) ->
+ let _,context,ty = CicUtil.lookup_meta i menv in
+ let irl = [] in
+ let newmeta = Cic.Meta(maxmeta,irl) in
+ let newsubst = Subst.buildsubst i context newmeta ty subst in
+ newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1)
+ to_be_relocated (Subst.empty_subst, [], newmeta+1)
in
- let metasenv = Subst.apply_subst_metasenv subst metasenv in
- let subst = Subst.flatten_subst subst in
- subst, metasenv, newmeta
+ let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
+ subst, menv, newmeta
let fix_metas newmeta eq =
let w, p, (ty, left, right, o), menv,_ = open_equality eq in
- (* debug
- let _ , eq =
- fix_metas_old newmeta (w, p, (ty, left, right, o), menv, args) in
- prerr_endline (string_of_equality eq); *)
- let subst, metasenv, newmeta = relocate newmeta menv in
+ let to_be_relocated =
+ HExtlib.list_uniq
+ (List.sort Pervasives.compare
+ (Utils.metas_of_term left @ Utils.metas_of_term right))
+ in
+ let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
let ty = Subst.apply_subst subst ty in
let left = Subst.apply_subst subst left in
let right = Subst.apply_subst subst right in
let fix_proof = function
| Exact p -> Exact (Subst.apply_subst subst p)
| Step (s,(r,id1,(pos,id2),pred)) ->
- Step (Subst.concat_substs s subst,(r,id1,(pos,id2), pred))
+ Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
in
let p = fix_proof p in
- let eq = mk_equality (w, p, (ty, left, right, o), metasenv) in
- (* debug prerr_endline (string_of_equality eq); *)
- newmeta+1, eq
+ let eq' = mk_equality (w, p, (ty, left, right, o), metasenv) in
+ newmeta+1, eq'
exception NotMetaConvertible;;
projects / helm.git / blobdiff