-(* cOpyright (C) 2005, HELM Team.
+(* Copyright (C) 2005, HELM Team.
*
* This file is part of HELM, an Hypertextual, Electronic
* Library of Mathematics, developed at the Computer Science
* http://cs.unibo.it/helm/.
*)
-(* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
-
-
-(******* CIC substitution ***************************************************)
-
-type cic_substitution = Cic.substitution
-let cic_apply_subst = CicMetaSubst.apply_subst
-let cic_apply_subst_metasenv = CicMetaSubst.apply_subst_metasenv
-let cic_ppsubst = CicMetaSubst.ppsubst
-let cic_buildsubst n context t ty tail = (n,(context,t,ty)) :: tail
-let cic_flatten_subst subst =
- List.map
- (fun (i, (context, term, ty)) ->
- let context = (* cic_apply_subst_context subst*) context in
- let term = cic_apply_subst subst term in
- let ty = cic_apply_subst subst ty in
- (i, (context, term, ty))) subst
-let rec cic_lookup_subst meta subst =
- match meta with
- | Cic.Meta (i, _) -> (
- try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst
- in cic_lookup_subst t subst
- with Not_found -> meta
- )
- | _ -> meta
-;;
-
-let cic_merge_subst_if_possible s1 s2 =
- let already_in = Hashtbl.create 13 in
- let rec aux acc = function
- | ((i,_,x) as s)::tl ->
- (try
- let x' = Hashtbl.find already_in i in
- if x = x' then aux acc tl else None
- with
- | Not_found ->
- Hashtbl.add already_in i x;
- aux (s::acc) tl)
- | [] -> Some acc
- in
- aux [] (s1@s2)
-;;
-
-(******** NAIF substitution **************************************************)
-(*
- * naif version of apply subst; the local context of metas is ignored;
- * we assume the substituted term must be lifted according to the nesting
- * depth of the meta.
- * Alternatively, we could used implicit instead of metas
- *)
-
-type naif_substitution = (int * Cic.term) list
-
-let naif_apply_subst subst term =
- let rec aux k t =
- match t with
- Cic.Rel _ -> t
- | Cic.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, aux k t)) exp_named_subst
- in
- Cic.Var (uri, exp_named_subst')
- | Cic.Meta (i, l) ->
- (try
- aux k (CicSubstitution.lift k (List.assoc i subst))
- with Not_found -> t)
- | Cic.Sort _
- | Cic.Implicit _ -> t
- | Cic.Cast (te,ty) -> Cic.Cast (aux k te, aux k ty)
- | Cic.Prod (n,s,t) -> Cic.Prod (n, aux k s, aux (k+1) t)
- | Cic.Lambda (n,s,t) -> Cic.Lambda (n, aux k s, aux (k+1) t)
- | Cic.LetIn (n,s,t) -> Cic.LetIn (n, aux k s, aux (k+1) t)
- | Cic.Appl [] -> assert false
- | Cic.Appl l -> Cic.Appl (List.map (aux k) l)
- | Cic.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, aux k t)) exp_named_subst
- in
- if exp_named_subst' != exp_named_subst then
- Cic.Const (uri, exp_named_subst')
- else
- t (* TODO: provare a mantenere il piu' possibile sharing *)
- | Cic.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, aux k t)) exp_named_subst
- in
- Cic.MutInd (uri,typeno,exp_named_subst')
- | Cic.MutConstruct (uri,typeno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (fun (uri, t) -> (uri, aux k t)) exp_named_subst
- in
- Cic.MutConstruct (uri,typeno,consno,exp_named_subst')
- | Cic.MutCase (sp,i,outty,t,pl) ->
- let pl' = List.map (aux k) pl in
- Cic.MutCase (sp, i, aux k outty, aux k t, pl')
- | Cic.Fix (i, fl) ->
- let len = List.length fl in
- let fl' =
- List.map
- (fun (name, i, ty, bo) -> (name, i, aux k ty, aux (k+len) bo)) fl
- in
- Cic.Fix (i, fl')
- | Cic.CoFix (i, fl) ->
- let len = List.length fl in
- let fl' =
- List.map (fun (name, ty, bo) -> (name, aux k ty, aux (k+len) bo)) fl
- in
- Cic.CoFix (i, fl')
-in
- aux 0 term
-;;
-
-(* naif version of apply_subst_metasenv: we do not apply the
-substitution to the context *)
-
-let naif_apply_subst_metasenv subst metasenv =
- List.map
- (fun (n, context, ty) ->
- (n, context, naif_apply_subst subst ty))
- (List.filter
- (fun (i, _, _) -> not (List.mem_assoc i subst))
- metasenv)
-
-let naif_ppsubst names subst =
- "{" ^ String.concat "; "
- (List.map
- (fun (idx, t) ->
- Printf.sprintf "%d:= %s" idx (CicPp.pp t names))
- subst) ^ "}"
-;;
-
-let naif_buildsubst n context t ty tail = (n,t) :: tail ;;
-
-let naif_flatten_subst subst =
- List.map (fun (i,t) -> i, naif_apply_subst subst t ) subst
-;;
-
-let rec naif_lookup_subst meta subst =
- match meta with
- | Cic.Meta (i, _) ->
- (try
- naif_lookup_subst (List.assoc i subst) subst
- with
- Not_found -> meta)
- | _ -> meta
-;;
-
-let naif_merge_subst_if_possible s1 s2 =
- let already_in = Hashtbl.create 13 in
- let rec aux acc = function
- | ((i,x) as s)::tl ->
- (try
- let x' = Hashtbl.find already_in i in
- if x = x' then aux acc tl else None
- with
- | Not_found ->
- Hashtbl.add already_in i x;
- aux (s::acc) tl)
- | [] -> Some acc
- in
- aux [] (s1@s2)
-;;
-
-(********** ACTUAL SUBSTITUTION IMPLEMENTATION *******************************)
-
-type substitution = naif_substitution
-let apply_subst = naif_apply_subst
-let apply_subst_metasenv = naif_apply_subst_metasenv
-let ppsubst ~names l = naif_ppsubst (names:(Cic.name option)list) l
-let buildsubst = naif_buildsubst
-let flatten_subst = naif_flatten_subst
-let lookup_subst = naif_lookup_subst
-
-(* filter out from metasenv the variables in substs *)
-let filter subst metasenv =
- List.filter
- (fun (m, _, _) ->
- try let _ = List.find (fun (i, _) -> m = i) subst in false
- with Not_found -> true)
- metasenv
-;;
-
-let is_in_subst i subst = List.mem_assoc i subst;;
-
-let merge_subst_if_possible = naif_merge_subst_if_possible;;
-
-let empty_subst = [];;
+(* let _profiler = <:profiler<_profiler>>;; *)
-(********* EQUALITY **********************************************************)
+(* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
type rule = SuperpositionRight | SuperpositionLeft | Demodulation
type uncomparable = int -> int
+
type equality =
uncomparable * (* trick to break structural equality *)
int * (* weight *)
Utils.comparison) * (* ordering *)
Cic.metasenv * (* environment for metas *)
int (* id *)
-and proof = new_proof * old_proof
-
-and new_proof =
+and proof =
| Exact of Cic.term
- | Step of substitution * (rule * int*(Utils.pos*int)* Cic.term) (* eq1, eq2,predicate *)
-and old_proof =
- | NoProof (* term is the goal missing a proof *)
- | BasicProof of substitution * Cic.term
- | ProofBlock of
- substitution * UriManager.uri *
- (Cic.name * Cic.term) * Cic.term * (Utils.pos * equality) * old_proof
- | ProofGoalBlock of old_proof * old_proof
- | ProofSymBlock of Cic.term list * old_proof
- | SubProof of Cic.term * int * old_proof
-and goal_proof = (Utils.pos * int * substitution * Cic.term) list
+ | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
+ (* subst, (rule,eq1, eq2,predicate) *)
+and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
;;
+(* the hashtbl eq_id -> proof, max_eq_id *)
+module IntOt = struct type t = int let compare = Pervasives.compare end
+module M = Map.Make(IntOt)
+type equality_bag = equality M.t * int
+
+type goal = goal_proof * Cic.metasenv * Cic.term
(* globals *)
-let maxid = ref 0;;
-let id_to_eq = Hashtbl.create 1024;;
+let mk_equality_bag () = M.empty, 10000 ;;
-let freshid () =
- incr maxid; !maxid
-;;
+let freshid (m,i) = (m,i+1), i+1 ;;
-let reset () =
- maxid := 0;
- Hashtbl.clear id_to_eq
-;;
+let add_to_bag (id_to_eq,i) id eq = M.add id eq id_to_eq,i ;;
let uncomparable = fun _ -> 0
-let mk_equality (weight,(newp,oldp),(ty,l,r,o),m) =
- let id = freshid () in
- let eq = (uncomparable,weight,(newp,oldp),(ty,l,r,o),m,id) in
- Hashtbl.add id_to_eq id eq;
- eq
+let mk_equality bag (weight,p,(ty,l,r,o),m) =
+ let bag, id = freshid bag in
+ let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
+ let bag = add_to_bag bag id eq in
+ bag, eq
;;
+let mk_tmp_equality (weight,(ty,l,r,o),m) =
+ let id = -1 in
+ uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
+;;
+
+
let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
(weight,proof,(ty,l,r,o),m,id)
+let id_of e =
+ let _,_,_,_,id = open_equality e in 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,_,_) =
Pervasives.compare s1 s2
;;
-let rec string_of_proof_old ?(names=[]) = function
- | NoProof -> "NoProof "
- | BasicProof (s, t) -> "BasicProof(" ^
- ppsubst ~names s ^ ", " ^ (CicPp.pp t names) ^ ")"
- | SubProof (t, i, p) ->
- Printf.sprintf "SubProof(%s, %s, %s)"
- (CicPp.pp t names) (string_of_int i) (string_of_proof_old p)
- | ProofSymBlock (_,p) ->
- Printf.sprintf "ProofSymBlock(%s)" (string_of_proof_old p)
- | ProofBlock (subst, _, _, _ ,(_,eq),old) ->
- let _,(_,p),_,_,_ = open_equality eq in
- "ProofBlock(" ^ (ppsubst ~names subst) ^ "," ^ (string_of_proof_old old) ^ "," ^
- string_of_proof_old p ^ ")"
- | ProofGoalBlock (p1, p2) ->
- Printf.sprintf "ProofGoalBlock(%s, %s)"
- (string_of_proof_old p1) (string_of_proof_old p2)
-;;
-
-
-let proof_of_id id =
+let rec max_weight_in_proof ((id_to_eq,_) as bag) current =
+ function
+ | Exact _ -> current
+ | Step (_, (_,id1,(_,id2),_)) ->
+ let eq1 = M.find id1 id_to_eq in
+ let eq2 = M.find id2 id_to_eq in
+ let (w1,p1,(_,_,_,_),_,_) = open_equality eq1 in
+ let (w2,p2,(_,_,_,_),_,_) = open_equality eq2 in
+ let current = max current w1 in
+ let current = max_weight_in_proof bag current p1 in
+ let current = max current w2 in
+ max_weight_in_proof bag current p2
+
+let max_weight_in_goal_proof ((id_to_eq,_) as bag) =
+ List.fold_left
+ (fun current (_,_,id,_,_) ->
+ let eq = M.find id id_to_eq in
+ let (w,p,(_,_,_,_),_,_) = open_equality eq in
+ let current = max current w in
+ max_weight_in_proof bag current p)
+
+let max_weight bag goal_proof proof =
+ let current = max_weight_in_proof bag 0 proof in
+ max_weight_in_goal_proof bag current goal_proof
+
+let proof_of_id (id_to_eq,_) id =
try
- let (_,(p,_),(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+ let (_,p,(_,l,r,_),_,_) = open_equality (M.find id id_to_eq) in
p,l,r
with
- Not_found -> assert false
+ Not_found ->
+ prerr_endline ("Unable to find the proof of " ^ string_of_int id);
+ assert false
+;;
+let is_in (id_to_eq,_) id =
+ M.mem id id_to_eq
+;;
-let string_of_proof_new ?(names=[]) p gp =
- let str_of_rule = function
- | SuperpositionRight -> "SupR"
- | SuperpositionLeft -> "SupL"
- | Demodulation -> "Demod"
- in
+
+let string_of_proof ?(names=[]) bag p gp =
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) (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 (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id bag eq1)) ^
+ aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id bag eq2))
in
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"
- (str_of_pos pos) i (ppsubst ~names s) (CicPp.pp t names)) ^
- aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
+ "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 bag i)))
gp)
;;
-let ppsubst = ppsubst ~names:[]
+let rec depend ((id_to_eq,_) as bag) eq id seen =
+ let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
+ if List.mem ideq seen then
+ false,seen
+ else
+ if id = ideq then
+ true,seen
+ else
+ match p with
+ | Exact _ -> false,seen
+ | Step (_,(_,id1,(_,id2),_)) ->
+ let seen = ideq::seen in
+ let eq1 = M.find id1 id_to_eq in
+ let eq2 = M.find id2 id_to_eq in
+ let b1,seen = depend bag eq1 id seen in
+ if b1 then b1,seen else depend bag eq2 id seen
+;;
+
+let depend bag eq id = fst (depend bag eq id []);;
+
+let ppsubst = Subst.ppsubst ~names:[];;
(* returns an explicit named subst and a list of arguments for sym_eq_URI *)
let build_ens uri termlist =
let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
match obj with
| Cic.Constant (_, _, _, uris, _) ->
- assert (List.length uris <= List.length termlist);
+ (* assert (List.length uris <= List.length termlist); *)
let rec aux = function
| [], tl -> [], tl
| (uri::uris), (term::tl) ->
| _ -> assert false
;;
-let build_proof_term_old ?(noproof=Cic.Implicit None) proof =
- let rec do_build_proof proof =
- match proof with
- | NoProof ->
- Printf.fprintf stderr "WARNING: no proof!\n";
- noproof
- | BasicProof (s,term) -> apply_subst s term
- | ProofGoalBlock (proofbit, proof) ->
- print_endline "found ProofGoalBlock, going up...";
- do_build_goal_proof proofbit proof
- | ProofSymBlock (termlist, proof) ->
- let proof = do_build_proof proof in
- let ens, args = build_ens (Utils.sym_eq_URI ()) termlist in
- Cic.Appl ([Cic.Const (Utils.sym_eq_URI (), ens)] @ args @ [proof])
- | ProofBlock (subst, eq_URI, (name, ty), bo, (pos, eq), eqproof) ->
- let t' = Cic.Lambda (name, ty, bo) in
- let _, (_,proof), (ty, what, other, _), menv',_ = open_equality eq in
- let proof' = do_build_proof proof in
- let eqproof = do_build_proof eqproof in
- let what, other =
- if pos = Utils.Left then what, other else other, what
- in
- apply_subst subst
- (Cic.Appl [Cic.Const (eq_URI, []); ty;
- what; t'; eqproof; other; proof'])
- | SubProof (term, meta_index, proof) ->
- let proof = do_build_proof proof in
- let eq i = function
- | Cic.Meta (j, _) -> i = j
- | _ -> false
- in
- ProofEngineReduction.replace
- ~equality:eq ~what:[meta_index] ~with_what:[proof] ~where:term
-
- and do_build_goal_proof proofbit proof =
- match proof with
- | ProofGoalBlock (pb, p) ->
- do_build_proof (ProofGoalBlock (replace_proof proofbit pb, p))
- | _ -> do_build_proof (replace_proof proofbit proof)
-
- and replace_proof newproof = function
- | ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof) ->
- let eqproof' = replace_proof newproof eqproof in
- ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof')
- | ProofGoalBlock (pb, p) ->
- let pb' = replace_proof newproof pb in
- ProofGoalBlock (pb', p)
- | BasicProof _ -> newproof
- | SubProof (term, meta_index, p) ->
- SubProof (term, meta_index, replace_proof newproof p)
- | p -> p
- in
- do_build_proof proof
-;;
-
let mk_sym uri ty t1 t2 p =
let ens, args = build_ens uri [ty;t1;t2;p] in
Cic.Appl (Cic.Const(uri, ens) :: args)
;;
let mk_eq_ind uri ty what pred p1 other p2 =
- Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
+ let ens, args = build_ens uri [ty; what; pred; p1; other; p2] in
+ Cic.Appl (Cic.Const (uri, ens) :: args)
;;
let p_of_sym ens tl =
| _ -> assert false
;;
-let canonical t =
+let open_sym ens tl =
+ let args = List.map snd ens @ tl in
+ match args with
+ | [ty;l;r;p] -> ty,l,r,p
+ | _ -> assert false
+;;
+
+let open_eq_ind args =
+ match args with
+ | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
+ | _ -> assert false
+;;
+
+let open_pred pred =
+ match pred with
+ | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]))
+ when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
+ | _ -> Utils.debug_print (lazy (CicPp.ppterm pred)); assert false
+;;
+
+let is_not_fixed t =
+ CicSubstitution.subst (Cic.Implicit None) t <>
+ CicSubstitution.subst (Cic.Rel 1) t
+;;
+
+let canonical t context menv =
+ let remove_cycles t =
+ let is_transitive =
+ function
+ Cic.Appl (Cic.Const (uri_trans,_)::_)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ true
+ | _ -> false in
+ let rec collect =
+ function
+ Cic.Appl (Cic.Const (uri_trans,ens)::tl)
+ when LibraryObjects.is_trans_eq_URI uri_trans ->
+ let ty,l,m,r,p1,p2 = open_trans ens tl in
+ (if is_transitive p1 then fst (collect p1) else [l,p1]) @
+ (if is_transitive p2 then fst (collect p2) else [m,p2]),
+ (r, uri_trans, ty)
+ | t -> assert false in
+ let rec cut_to_last_duplicate l acc =
+ function
+ [] -> List.rev acc
+ | (l',p)::tl when l=l' ->
+if acc <> [] then
+Utils.debug_print (lazy ("!!! RISPARMIO " ^ string_of_int (List.length acc) ^ " PASSI"));
+ cut_to_last_duplicate l [l',p] tl
+ | (l',p)::tl ->
+ cut_to_last_duplicate l ((l',p)::acc) tl
+ in
+ let rec rebuild =
+ function
+ (l,_)::_::_ as steps, ((r,uri_trans,ty) as last) ->
+ (match cut_to_last_duplicate l [] steps with
+ (l,p1)::((m,_)::_::_ as tl) ->
+ mk_trans uri_trans ty l m r p1 (rebuild (tl,last))
+ | [l,p1 ; m,p2] -> mk_trans uri_trans ty l m r p1 p2
+ | [l,p1] -> p1
+ | [] -> assert false)
+ | _ -> assert false
+ in
+ if is_transitive t then
+ rebuild (collect t)
+ else
+ t
+ in
let rec remove_refl t =
match t with
| Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
remove_refl p1
| _ -> Cic.Appl (List.map remove_refl args))
| Cic.Appl l -> Cic.Appl (List.map remove_refl l)
+ | Cic.LetIn (name,bo,ty,rest) ->
+ Cic.LetIn (name,remove_refl bo,remove_refl ty,remove_refl rest)
| _ -> t
in
- let rec canonical t =
+ let rec canonical_trough_lambda context = function
+ | Cic.Lambda(name,ty,bo) ->
+ let context' = (Some (name,Cic.Decl ty))::context in
+ Cic.Lambda(name,ty,canonical_trough_lambda context' bo)
+ | t -> canonical context t
+
+ and canonical context t =
match t with
+ | Cic.LetIn(name,bo,ty,rest) ->
+ let bo = canonical_trough_lambda context bo in
+ let ty = canonical_trough_lambda context ty in
+ let context' = (Some (name,Cic.Def (bo,ty)))::context in
+ Cic.LetIn(name,bo,ty,canonical context' 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
| Cic.Appl ((Cic.Const(uri,ens))::tl)
when LibraryObjects.is_sym_eq_URI uri ->
- canonical (p_of_sym ens tl)
+ canonical context (p_of_sym ens tl)
| Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
when LibraryObjects.is_trans_eq_URI uri_trans ->
let ty,l,m,r,p1,p2 = open_trans ens tl in
mk_trans uri_trans ty r m l
- (canonical (mk_sym uri_sym ty m r p2))
- (canonical (mk_sym uri_sym ty l m p1))
- | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl)
- when LibraryObjects.is_eq_ind_URI uri_ind ||
- LibraryObjects.is_eq_ind_r_URI uri_ind ->
- let ty, what, pred, p1, other, p2 =
- match tl with
- | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
- | _ -> assert false
- in
- let pred,l,r =
- match pred with
- | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
- when LibraryObjects.is_eq_URI uri ->
- Cic.Lambda
- (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
- | _ ->
- prerr_endline (CicPp.ppterm pred);
- assert false
+ (canonical context (mk_sym uri_sym ty m r p2))
+ (canonical context (mk_sym uri_sym ty l m p1))
+ | Cic.Appl (([Cic.Const(uri_feq,ens);ty1;ty2;f;x;y;p]))
+ when LibraryObjects.is_eq_f_URI uri_feq ->
+ let eq = LibraryObjects.eq_URI_of_eq_f_URI uri_feq in
+ let eq_f_sym =
+ Cic.Const (LibraryObjects.eq_f_sym_URI ~eq, [])
in
- let l = CicSubstitution.subst what l in
- let r = CicSubstitution.subst what r in
- Cic.Appl
- [he;ty;what;pred;
- canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
+ let rc = Cic.Appl [eq_f_sym;ty1;ty2;f;x;y;p] in
+ Utils.debug_print (lazy ("CANONICAL " ^ CicPp.ppterm rc));
+ rc
| Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
when LibraryObjects.is_eq_URI uri -> t
- | _ -> Cic.Appl (List.map canonical args))
- | Cic.Appl l -> Cic.Appl (List.map canonical l)
+ | _ -> Cic.Appl (List.map (canonical context) args))
+ | Cic.Appl l -> Cic.Appl (List.map (canonical context) l)
| _ -> t
in
- remove_refl (canonical t)
+ remove_cycles (remove_refl (canonical context t))
+;;
+
+let compose_contexts ctx1 ctx2 =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun _ ->(=)) ~context:[] ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
+;;
+
+let put_in_ctx ctx t =
+ ProofEngineReduction.replace_lifting
+ ~equality:(fun _ -> (=)) ~context:[] ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
+;;
+
+let mk_eq uri ty l r =
+ let ens, args = build_ens uri [ty; l; r] in
+ Cic.Appl (Cic.MutInd(uri,0,ens) :: args)
+;;
+
+let mk_refl uri ty t =
+ let ens, args = build_ens uri [ty; t] in
+ Cic.Appl (Cic.MutConstruct(uri,0,1,ens) :: args)
;;
-let build_proof_step subst p1 p2 pos l r pred =
- let p1 = apply_subst subst p1 in
- let p2 = apply_subst subst p2 in
- let l = apply_subst subst l in
- let r = apply_subst subst r in
- let pred = apply_subst subst pred in
- let ty,body = (* Cic.Implicit None *)
+let open_eq = function
+ | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
+ uri, ty, l ,r
+ | _ -> assert false
+;;
+
+let mk_feq uri_feq ty ty1 left pred right t =
+ let ens, args = build_ens uri_feq [ty;ty1;pred;left;right;t] in
+ Cic.Appl (Cic.Const(uri_feq,ens) :: args)
+;;
+
+let rec look_ahead aux = function
+ | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) as t
+ when LibraryObjects.is_eq_ind_URI uri_ind ||
+ LibraryObjects.is_eq_ind_r_URI uri_ind ->
+ let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
+ let ty2,eq,lp,rp = open_pred pred in
+ let hole = Cic.Implicit (Some `Hole) in
+ let ty2 = CicSubstitution.subst hole ty2 in
+ aux ty1 (CicSubstitution.subst other lp) (CicSubstitution.subst other rp) hole ty2 t
+ | Cic.Lambda (n,s,t) -> Cic.Lambda (n,s,look_ahead aux t)
+ | t -> t
+;;
+
+let contextualize uri ty left right t =
+ let hole = Cic.Implicit (Some `Hole) in
+ (* aux [uri] [ty] [left] [right] [ctx] [ctx_ty] [t]
+ *
+ * the parameters validate this invariant
+ * t: eq(uri) ty left right
+ * that is used only by the base case
+ *
+ * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
+ * ctx_ty is the type of ctx
+ *)
+ let rec aux uri ty left right ctx_d ctx_ty t =
+ match t with
+ | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
+ when LibraryObjects.is_sym_eq_URI uri_sym ->
+ let ty,l,r,p = open_sym ens tl in
+ mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
+ | Cic.LetIn (name,body,bodyty,rest) ->
+ Cic.LetIn
+ (name,look_ahead (aux uri) body, bodyty,
+ aux uri ty left right ctx_d ctx_ty 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 ->
+ let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
+ let ty2,eq,lp,rp = open_pred pred in
+ let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
+ let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
+ let is_not_fixed_lp = is_not_fixed lp in
+ let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
+ (* extract the context and the fixed term from the predicate *)
+ let m, ctx_c, ty2 =
+ let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
+ (* they were under a lambda *)
+ let m = CicSubstitution.subst hole m in
+ let ctx_c = CicSubstitution.subst hole ctx_c in
+ let ty2 = CicSubstitution.subst hole ty2 in
+ m, ctx_c, ty2
+ in
+ (* create the compound context and put the terms under it *)
+ let ctx_dc = compose_contexts ctx_d ctx_c in
+ let dc_what = put_in_ctx ctx_dc what in
+ let dc_other = put_in_ctx ctx_dc other in
+ (* m is already in ctx_c so it is put in ctx_d only *)
+ let d_m = put_in_ctx ctx_d m in
+ (* we also need what in ctx_c *)
+ let c_what = put_in_ctx ctx_c what in
+ (* now put the proofs in the compound context *)
+ let p1 = (* p1: dc_what = d_m *)
+ if is_not_fixed_lp then
+ aux uri ty2 c_what m ctx_d ctx_ty p1
+ else
+ mk_sym uri_sym ctx_ty d_m dc_what
+ (aux uri ty2 m c_what ctx_d ctx_ty p1)
+ in
+ let p2 = (* p2: dc_other = dc_what *)
+ if avoid_eq_ind then
+ mk_sym uri_sym ctx_ty dc_what dc_other
+ (aux uri ty1 what other ctx_dc ctx_ty p2)
+ else
+ aux uri ty1 other what ctx_dc ctx_ty p2
+ in
+ (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
+ if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
+ let a,b,c,paeqb,pbeqc =
+ if is_not_fixed_lp then
+ dc_other,dc_what,d_m,p2,p1
+ else
+ d_m,dc_what,dc_other,
+ (mk_sym uri_sym ctx_ty dc_what d_m p1),
+ (mk_sym uri_sym ctx_ty dc_other dc_what p2)
+ in
+ mk_trans uri_trans ctx_ty a b c paeqb pbeqc
+ | t when ctx_d = hole -> t
+ | t ->
+(* let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in *)
+(* let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in *)
+
+ let uri_feq = LibraryObjects.eq_f_URI ~eq:uri in
+ let pred =
+(* let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in *)
+ let l =
+ let ctx_d = CicSubstitution.lift 1 ctx_d in
+ put_in_ctx ctx_d (Cic.Rel 1)
+ in
+(* let lty = CicSubstitution.lift 1 ctx_ty in *)
+(* Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r)) *)
+ Cic.Lambda (Cic.Name "foo",ty,l)
+ in
+(* let d_left = put_in_ctx ctx_d left in *)
+(* let d_right = put_in_ctx ctx_d right in *)
+(* let refl_eq = mk_refl uri ctx_ty d_left in *)
+(* mk_sym uri_sym ctx_ty d_right d_left *)
+(* (mk_eq_ind uri_ind ty left pred refl_eq right t) *)
+ (mk_feq uri_feq ty ctx_ty left pred right t)
+ in
+ aux uri ty left right hole ty t
+;;
+
+let contextualize_rewrites t ty =
+ let eq,ty,l,r = open_eq ty in
+ contextualize eq ty l r t
+;;
+
+let add_subst subst =
+ function
+ | Exact t -> Exact (Subst.apply_subst subst t)
+ | Step (s,(rule, id1, (pos,id2), pred)) ->
+ Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
+;;
+
+let build_proof_step eq 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
| _ -> assert false
in
- let what, other = (* Cic.Implicit None, Cic.Implicit None *)
+ let what, other =
if pos = Utils.Left then l,r else r,l
in
- let is_not_fixed t =
- CicSubstitution.subst (Cic.Implicit None) t <>
- CicSubstitution.subst (Cic.Rel 1) t
+ let p =
+ match pos with
+ | Utils.Left ->
+ mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
+ | Utils.Right ->
+ mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
in
- match body,pos with
- |Cic.Appl [Cic.MutInd(eq,_,_);_;Cic.Rel 1;third],Utils.Left ->
- let third = CicSubstitution.subst (Cic.Implicit None) third in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let uri_sym = LibraryObjects.sym_eq_URI ~eq in
- mk_trans uri_trans ty other what third
- (mk_sym uri_sym ty what other p2) p1
- |Cic.Appl [Cic.MutInd(eq,_,_);_;Cic.Rel 1;third],Utils.Right ->
- let third = CicSubstitution.subst (Cic.Implicit None) third in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- mk_trans uri_trans ty other what third p2 p1
- |Cic.Appl [Cic.MutInd(eq,_,_);_;third;Cic.Rel 1],Utils.Left ->
- let third = CicSubstitution.subst (Cic.Implicit None) third in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- mk_trans uri_trans ty third what other p1 p2
- |Cic.Appl [Cic.MutInd(eq,_,_);_;third;Cic.Rel 1],Utils.Right ->
- let third = CicSubstitution.subst (Cic.Implicit None) third in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let uri_sym = LibraryObjects.sym_eq_URI ~eq in
- mk_trans uri_trans ty third what other p1
- (mk_sym uri_sym ty other what p2)
- | Cic.Appl [Cic.MutInd(eq,_,_);_;lhs;rhs],Utils.Left when is_not_fixed lhs
- ->
- let rhs = CicSubstitution.subst (Cic.Implicit None) rhs in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let pred_of t = CicSubstitution.subst t lhs in
- let pred_of_what = pred_of what in
- let pred_of_other = pred_of other in
- (* p2 : what = other
- * ====================================
- * inject p2: P(what) = P(other)
- *)
- let rec inject ty lhs what other p2 =
- match p2 with
- | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
- when LibraryObjects.is_trans_eq_URI uri_trans ->
- let ty,l,m,r,plm,pmr = open_trans ens tl in
- mk_trans uri_trans ty (pred_of r) (pred_of m) (pred_of l)
- (inject ty lhs m r pmr) (inject ty lhs l m plm)
- | _ ->
- let liftedty = CicSubstitution.lift 1 ty in
- let lifted_pred_of_other = CicSubstitution.lift 1 (pred_of other) in
- let refl_eq_part =
- Cic.Appl [Cic.MutConstruct(eq,0,1,[]);ty;pred_of other]
- in
- (mk_eq_ind (Utils.eq_ind_r_URI ()) ty other
- (Cic.Lambda (Cic.Name "foo",ty,
- (Cic.Appl
- [Cic.MutInd(eq,0,[]);liftedty;lifted_pred_of_other;lhs])))
- refl_eq_part what p2)
- in
- mk_trans uri_trans ty pred_of_other pred_of_what rhs
- (inject ty lhs what other p2) p1
- | Cic.Appl[Cic.MutInd(eq,_,_);_;lhs;rhs],Utils.Right when is_not_fixed lhs
- ->
- let rhs = CicSubstitution.subst (Cic.Implicit None) rhs in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let pred_of t = CicSubstitution.subst t lhs in
- let pred_of_what = pred_of what in
- let pred_of_other = pred_of other in
- (* p2 : what = other
- * ====================================
- * inject p2: P(what) = P(other)
- *)
- let rec inject ty lhs what other p2 =
- match p2 with
- | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
- when LibraryObjects.is_trans_eq_URI uri_trans ->
- let ty,l,m,r,plm,pmr = open_trans ens tl in
- mk_trans uri_trans ty (pred_of l) (pred_of m) (pred_of r)
- (inject ty lhs m l plm)
- (inject ty lhs r m pmr)
- | _ ->
- let liftedty = CicSubstitution.lift 1 ty in
- let lifted_pred_of_other =
- CicSubstitution.lift 1 (pred_of other) in
- let refl_eq_part =
- Cic.Appl [Cic.MutConstruct(eq,0,1,[]);ty;pred_of other]
- in
- mk_eq_ind (Utils.eq_ind_URI ()) ty other
- (Cic.Lambda (Cic.Name "foo",ty,
- (Cic.Appl
- [Cic.MutInd(eq,0,[]);liftedty;lifted_pred_of_other;lhs])))
- refl_eq_part what p2
- in
- mk_trans uri_trans ty pred_of_other pred_of_what rhs
- (inject ty lhs what other p2) p1
- | Cic.Appl[Cic.MutInd(eq,_,_);_;lhs;rhs],Utils.Right when is_not_fixed rhs
- ->
- let lhs = CicSubstitution.subst (Cic.Implicit None) lhs in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let pred_of t = CicSubstitution.subst t rhs in
- let pred_of_what = pred_of what in
- let pred_of_other = pred_of other in
- (* p2 : what = other
- * ====================================
- * inject p2: P(what) = P(other)
- *)
- let rec inject ty lhs what other p2 =
- match p2 with
- | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
- when LibraryObjects.is_trans_eq_URI uri_trans ->
- let ty,l,m,r,plm,pmr = open_trans ens tl in
- mk_trans uri_trans ty (pred_of r) (pred_of m) (pred_of l)
- (inject ty lhs m r pmr)
- (inject ty lhs l m plm)
- | _ ->
- let liftedty = CicSubstitution.lift 1 ty in
- let lifted_pred_of_other = CicSubstitution.lift 1 (pred_of other) in
- let refl_eq_part =
- Cic.Appl [Cic.MutConstruct(eq,0,1,[]);ty;pred_of other]
- in
- (mk_eq_ind (Utils.eq_ind_r_URI ()) ty other
- (Cic.Lambda (Cic.Name "foo",ty,
- (Cic.Appl
- [Cic.MutInd(eq,0,[]);liftedty;lifted_pred_of_other;lhs])))
- refl_eq_part what p2)
- in
- mk_trans uri_trans ty lhs pred_of_what pred_of_other
- p1 (inject ty rhs other what p2)
- | Cic.Appl[Cic.MutInd(eq,_,_);_;lhs;rhs],Utils.Left when is_not_fixed rhs
- ->
- let lhs = CicSubstitution.subst (Cic.Implicit None) lhs in
- let uri_trans = LibraryObjects.trans_eq_URI ~eq in
- let pred_of t = CicSubstitution.subst t rhs in
- let pred_of_what = pred_of what in
- let pred_of_other = pred_of other in
- (* p2 : what = other
- * ====================================
- * inject p2: P(what) = P(other)
- *)
- let rec inject ty lhs what other p2 =
- match p2 with
- | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
- when LibraryObjects.is_trans_eq_URI uri_trans ->
- let ty,l,m,r,plm,pmr = open_trans ens tl in
- (mk_trans uri_trans ty (pred_of l) (pred_of m) (pred_of r)
- (inject ty lhs m l plm)
- (inject ty lhs r m pmr))
- | _ ->
- let liftedty = CicSubstitution.lift 1 ty in
- let lifted_pred_of_other = CicSubstitution.lift 1 (pred_of other) in
- let refl_eq_part =
- Cic.Appl [Cic.MutConstruct(eq,0,1,[]);ty;pred_of other]
- in
- mk_eq_ind (Utils.eq_ind_URI ()) ty other
- (Cic.Lambda (Cic.Name "foo",ty,
- (Cic.Appl
- [Cic.MutInd(eq,0,[]);liftedty;lifted_pred_of_other;lhs])))
- refl_eq_part what p2
- in
- mk_trans uri_trans ty lhs pred_of_what pred_of_other
- p1 (inject ty rhs other what p2)
- | _, 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
+ p
;;
-let build_proof_term_new 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 =
+ let uniq l = HExtlib.list_uniq (List.sort (fun (i,_) (j,_) -> Pervasives.compare i j) l) in
+ let mot = CicUtil.metas_of_term_set in
+ let parameters = uniq (mot p @ mot l @ mot r) in
+ (* ?if they are under a lambda? *)
+(*
+ let parameters =
+ HExtlib.list_uniq (List.sort Pervasives.compare parameters)
in
- aux proof
+*)
+ (* resorts l such that *hopefully* dependencies can be inferred *)
+ let guess_dependency p l =
+ match p with
+ | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
+ when LibraryObjects.is_eq_ind_URI uri_ind ||
+ LibraryObjects.is_eq_ind_r_URI uri_ind ->
+ let ty,_,_,_,_,_ = open_eq_ind tl in
+ let metas = CicUtil.metas_of_term ty in
+ let nondep, dep =
+ List.partition (fun (i,_) -> List.exists (fun (j,_) -> j=i) metas) l
+ in
+ nondep@dep
+ | _ -> l
+ in
+ let parameters = guess_dependency p parameters in
+ 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)
+ ~context:[]
+ ~what ~with_what ~where:p
+ in
+ let ty_of_m _ = Cic.Implicit (Some `Type) 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 =
+let wfo bag goalproof proof id =
let rec aux acc id =
- let p,_,_ = proof_of_id id in
+ let p,_,_ = proof_of_id bag id in
match p with
- | Exact _ -> id :: acc
+ | Exact _ -> if (List.mem id acc) then acc else id :: acc
| Step (_,(_,id1, (_,id2), _)) ->
let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
id :: acc
in
- List.fold_left (fun acc (_,id,_,_) -> aux acc id) [] goalproof
+ let acc =
+ match proof with
+ | Exact _ -> [id]
+ | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
+ in
+ List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
;;
-let string_of_id names id =
+let string_of_id (id_to_eq,_) names id =
+ if id = 0 then "" else
try
- let (_,(p,_),(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+ let (_,p,(t,l,r,_),m,_) = open_equality (M.find id id_to_eq) 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)
- | Step (_,(step,id1, (_,id2), _) ) ->
- Printf.sprintf "%5d: %s %4d %4d %s = %s" id
- (if step = SuperpositionRight then "SupR" else "Demo")
- id1 id2 (CicPp.pp l names) (CicPp.pp r names)
+(* "..." *)
+ (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
+ | Step (_,(step,id1, (dir,id2), p) ) ->
+ Printf.sprintf "%6d: %s %6d %6d %s =(%s) %s [%s]" id
+ (string_of_rule step)
+ id1 id2 (CicPp.pp l names) (CicPp.pp t 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 =
- String.concat "\n" (List.map (string_of_id names) (wfo goalproof))
+let pp_proof bag names goalproof proof subst id initial_goal =
+ String.concat "\n" (List.map (string_of_id bag names) (wfo bag 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
+;;
+
+let rec find_deps bag m i =
+ if M.mem i m then m
+ else
+ let p,_,_ = proof_of_id bag i in
+ match p with
+ | Exact _ -> M.add i [] m
+ | Step (_,(_,id1,(_,id2),_)) ->
+ let m = find_deps bag m id1 in
+ let m = find_deps bag m id2 in
+ (* without the uniq there is a stack overflow doing concatenation *)
+ let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in
+ let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
+ M.add i xxx m
+;;
-let build_goal_proof l initial =
- 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_new 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 topological_sort bag l =
+ (* build the partial order relation *)
+ let m = List.fold_left (fun m i -> find_deps bag m i) M.empty l in
+ let m = (* keep only deps inside l *)
+ List.fold_left
+ (fun m' i ->
+ M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m')
+ M.empty l
in
- canonical proof
+ let m = M.map (fun x -> Some x) m in
+ (* utils *)
+ let keys m = M.fold (fun i _ acc -> i::acc) m [] in
+ let split l m = List.filter (fun i -> M.find i m = Some []) l in
+ let purge l m =
+ M.mapi
+ (fun k v -> if List.mem k l then None else
+ match v with
+ | None -> None
+ | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
+ m
+ in
+ let rec aux m res =
+ let keys = keys m in
+ let ok = split keys m in
+ let m = purge ok m in
+ let res = ok @ res in
+ if ok = [] then res else aux m res
+ in
+ let rc = List.rev (aux m []) in
+ rc
+;;
+
+(* returns the list of ids that should be factorized *)
+let get_duplicate_step_in_wfo bag 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 =
+ let p,_,_ = proof_of_id bag i in
+ match p with
+ | Exact _ -> true
+ | _ ->
+ try
+ let no = Hashtbl.find h i in
+ Hashtbl.replace h i (no+1);
+ false
+ with Not_found -> Hashtbl.add h i 1;true
+ in
+ let rec aux = function
+ | Exact _ -> ()
+ | Step (_,(_,i1,(_,i2),_)) ->
+ let go_on_1 = add i1 in
+ let go_on_2 = add i2 in
+ if go_on_1 then aux (let p,_,_ = proof_of_id bag i1 in p);
+ if go_on_2 then aux (let p,_,_ = proof_of_id bag i2 in p)
+ in
+ aux p;
+ List.iter
+ (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id bag id in p))
+ ol;
+ (* now h is complete *)
+ let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
+ let proofs = List.filter (fun (_,c) -> c > 1) proofs in
+ let res = topological_sort bag (List.map (fun (i,_) -> i) proofs) in
+ res
;;
-let refl_proof ty term =
- Cic.Appl
- [Cic.MutConstruct
- (LibraryObjects.eq_URI (), 0, 1, []);
- ty; term]
+let build_proof_term bag eq h lift proof =
+ let proof_of_id aux id =
+ let p,l,r = proof_of_id bag 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,(rule, id1, (pos,id2), pred)) ->
+ let p1,_,_ = proof_of_id aux id1 in
+ let p2,l,r = proof_of_id aux id2 in
+ let varname =
+ match rule with
+ | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
+ | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
+ | _ -> assert false
+ in
+ let pred =
+ match pred with
+ | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+ | _ -> assert false
+ in
+ let p = build_proof_step eq 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
+ aux proof
;;
-let metas_of_proof p = Utils.metas_of_term (build_proof_term_old (snd p)) ;;
+let build_goal_proof ?(contextualize=true) ?(forward=false) bag eq l initial ty se context menv =
+ let se = List.map (fun i -> Cic.Meta (i,[])) se in
+ let lets = get_duplicate_step_in_wfo bag l initial in
+ let letsno = List.length lets in
+ let l = if forward then List.rev l else l 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 bag id in
+ let cic = build_proof_term bag eq h n p in
+ let real_cic,instance =
+ parametrize_proof cic l r
+ in
+ let h = (id, instance)::lift_list h in
+ acc@[id,real_cic],n+1,h)
+ ([],0,[]) lets
+ in
+ let lets =
+ List.map (fun (id,cic) -> id,cic,Cic.Implicit (Some `Type)) 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 bag id in
+ let p = build_proof_term bag eq h letsno p in
+ let pos = if forward then pos else
+ if pos = Utils.Left then Utils.Right else Utils.Left in
+ let varname =
+ match rule with
+ | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
+ | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
+ | _ -> assert false
+ in
+ let pred =
+ match pred with
+ | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+ | _ -> assert false
+ in
+ let proof =
+ build_proof_step eq 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 bag eq h letsno initial) l
+ in
+ let n,proof =
+ let initial = proof in
+ List.fold_right
+ (fun (id,cic,ty) (n,p) ->
+ n-1,
+ Cic.LetIn (
+ Cic.Name ("H"^string_of_int id),
+ cic,
+ ty,
+ p))
+ lets (letsno-1,initial)
+ in
+ let proof =
+ if contextualize
+ then contextualize_rewrites proof (CicSubstitution.lift letsno ty)
+ else proof in
+ canonical proof context menv, se
+;;
+
+let refl_proof eq_uri ty term =
+ Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
+;;
+
+let metas_of_proof bag p =
+ let eq =
+ match LibraryObjects.eq_URI () with
+ | Some u -> u
+ | None ->
+ raise
+ (ProofEngineTypes.Fail
+ (lazy "No default equality defined when calling metas_of_proof"))
+ in
+ let p = build_proof_term bag eq [] 0 p in
+ Utils.metas_of_term p
+;;
+
+let remove_local_context eq =
+ let w, p, (ty, left, right, o), menv,id = open_equality eq in
+ let p = Utils.remove_local_context p in
+ let ty = Utils.remove_local_context ty in
+ let left = Utils.remove_local_context left in
+ let right = Utils.remove_local_context right in
+ w, p, (ty, left, right, o), menv, id
+;;
-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 = buildsubst i context (Cic.Meta(maxmeta,irl)) ty subst in
- let newmeta = maxmeta, context, ty in
- newsubst, newmeta::menv, maxmeta+1)
- menv ([], [], newmeta+1)
- in
- let metasenv = apply_subst_metasenv subst metasenv in
- let subst = flatten_subst subst in
- subst, metasenv, newmeta
-
-
-let fix_metas newmeta eq =
- let w, (p1,p2), (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 ty = apply_subst subst ty in
- let left = apply_subst subst left in
- let right = apply_subst subst right in
+ (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) *)
+ newsubst, (maxmeta,[],ty)::metasenv, maxmeta+1)
+ to_be_relocated (Subst.empty_subst, [], newmeta+1)
+ in
+ (* let subst = Subst.flatten_subst subst in *)
+ let menv = Subst.apply_subst_metasenv subst (menv @ newmetasenv) in
+ subst, menv, newmeta
+
+let fix_metas_goal (id_to_eq,newmeta) goal =
+ let (proof, menv, ty) = goal in
+ let to_be_relocated = List.map (fun i ,_,_ -> i) menv in
+ let subst, menv, newmeta = relocate newmeta menv to_be_relocated in
+ let ty = Subst.apply_subst subst ty in
+ let proof =
+ match proof with
+ | [] -> assert false (* is a nonsense to relocate the initial goal *)
+ | (r,pos,id,s,p) :: tl -> (r,pos,id,Subst.concat subst s,p) :: tl
+ in
+ (id_to_eq,newmeta+1),(proof, menv, ty)
+;;
+
+let fix_metas (id_to_eq, newmeta) eq =
+ let w, p, (ty, left, right, o), menv,_ = open_equality eq in
+ let to_be_relocated = List.map (fun i ,_,_ -> i) menv 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
- | NoProof -> NoProof
- | BasicProof (subst',term) -> BasicProof (subst@subst',term)
- | ProofBlock (subst', eq_URI, namety, bo, (pos, eq), p) ->
- (*
- let newsubst =
- List.map
- (fun (i, (context, term, ty)) ->
- let context = apply_subst_context subst context in
- let term = apply_subst subst term in
- let ty = apply_subst subst ty in
- (i, (context, term, ty))) subst' in *)
- ProofBlock (subst@subst', eq_URI, namety, bo, (pos, eq), p)
- | p -> assert false
- in
- let fix_new_proof = function
- | Exact p -> Exact (apply_subst subst p)
+ | Exact p -> Exact (Subst.apply_subst subst p)
| Step (s,(r,id1,(pos,id2),pred)) ->
- Step (s@subst,(r,id1,(pos,id2),(*apply_subst subst*) pred))
+ Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
in
- let new_p = fix_new_proof p1 in
- let old_p = fix_proof p2 in
- let eq = mk_equality (w, (new_p,old_p), (ty, left, right, o), metasenv) in
- (* debug prerr_endline (string_of_equality eq); *)
- newmeta+1, eq
+ let p = fix_proof p in
+ let bag = id_to_eq, newmeta in
+ let bag, e = mk_equality bag (w, p, (ty, left, right, o), metasenv) in
+ bag, e
+;;
exception NotMetaConvertible;;
let meta_convertibility_aux table t1 t2 =
let module C = Cic in
- let rec aux ((table_l, table_r) as table) t1 t2 =
+ let rec aux ((table_l,table_r) as table) t1 t2 =
match t1, t2 with
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 = m2 -> table
+ | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 < m2 -> aux table t2 t1
| C.Meta (m1, tl1), C.Meta (m2, tl2) ->
let m1_binding, table_l =
try List.assoc m1 table_l, table_l
in
if (m1_binding <> m2) || (m2_binding <> m1) then
raise NotMetaConvertible
- else (
- try
- List.fold_left2
- (fun res t1 t2 ->
- match t1, t2 with
- | None, Some _ | Some _, None -> raise NotMetaConvertible
- | None, None -> res
- | Some t1, Some t2 -> (aux res t1 t2))
- (table_l, table_r) tl1 tl2
- with Invalid_argument _ ->
- raise NotMetaConvertible
- )
+ else table_l,table_r
| C.Var (u1, ens1), C.Var (u2, ens2)
| C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
aux_ens table ens1 ens2
| C.Cast (s1, t1), C.Cast (s2, t2)
| C.Prod (_, s1, t1), C.Prod (_, s2, t2)
- | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
- | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
+ | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2) ->
+ let table = aux table s1 s2 in
+ aux table t1 t2
+ | C.LetIn (_, s1, ty1, t1), C.LetIn (_, s2, ty2, t2) ->
let table = aux table s1 s2 in
+ let table = aux table ty1 ty2 in
aux table t1 t2
| C.Appl l1, C.Appl l2 -> (
try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
true
else
try
- let table = meta_convertibility_aux ([], []) left left' in
+ let table = meta_convertibility_aux ([],[]) left left' in
let _ = meta_convertibility_aux table right right' in
true
with NotMetaConvertible ->
try
- let table = meta_convertibility_aux ([], []) left right' in
+ let table = meta_convertibility_aux ([],[]) left right' in
let _ = meta_convertibility_aux table right left' in
true
with NotMetaConvertible ->
false
;;
-
let meta_convertibility t1 t2 =
if t1 = t2 then
true
else
try
- ignore(meta_convertibility_aux ([], []) t1 t2);
+ ignore(meta_convertibility_aux ([],[]) t1 t2);
true
with NotMetaConvertible ->
false
;;
+let meta_convertibility_subst t1 t2 menv =
+ if t1 = t2 then
+ Some([])
+ else
+ try
+ let (l,_) = meta_convertibility_aux ([],[]) t1 t2 in
+ let subst =
+ List.map
+ (fun (x,y) ->
+ try
+ let (_,c,t) = CicUtil.lookup_meta x menv in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable c in
+ (y,(c,Cic.Meta(x,irl),t))
+ with CicUtil.Meta_not_found _ ->
+ try
+ let (_,c,t) = CicUtil.lookup_meta y menv in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable c in
+ (x,(c,Cic.Meta(y,irl),t))
+ with CicUtil.Meta_not_found _ -> assert false) l in
+ Some subst
+ with NotMetaConvertible ->
+ None
+;;
+
exception TermIsNotAnEquality;;
let term_is_equality term =
- let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in
match term with
- | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
+ | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
+ when LibraryObjects.is_eq_URI uri -> true
| _ -> false
;;
-let equality_of_term proof term =
- let eq_uri = LibraryObjects.eq_URI () in
- let iseq uri = UriManager.eq uri eq_uri in
+let equality_of_term bag proof term newmetas =
match term with
- | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
+ | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
let o = !Utils.compare_terms t1 t2 in
let stat = (ty,t1,t2,o) in
let w = Utils.compute_equality_weight stat in
- let e = mk_equality (w, (Exact proof, BasicProof ([],proof)),stat,[]) in
- e
+ let bag, e = mk_equality bag (w, Exact proof, stat,newmetas) in
+ bag, e
| _ ->
raise TermIsNotAnEquality
;;
let is_weak_identity eq =
let _,_,(_,left, right,_),_,_ = open_equality eq in
- left = right || meta_convertibility left right
+ left = right
+ (* doing metaconv here is meaningless *)
;;
let is_identity (_, context, ugraph) eq =
let _,_,(ty,left,right,_),menv,_ = open_equality eq in
- left = right ||
- (* (meta_convertibility left right)) *)
- fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
+ (* doing metaconv here is meaningless *)
+ left = right
+(* fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
+ * *)
;;
-let term_of_equality equality =
+let term_of_equality eq_uri equality =
let _, _, (ty, left, right, _), menv, _= open_equality equality in
let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
let argsno = List.length menv in
let t =
CicSubstitution.lift argsno
- (Cic.Appl [Cic.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right])
+ (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
in
snd (
List.fold_right
menv (argsno, t))
;;
+let symmetric bag eq_ty l id uri m =
+ let eq = Cic.MutInd(uri,0,[]) in
+ let pred =
+ Cic.Lambda (Cic.Name "Sym",eq_ty,
+ Cic.Appl [CicSubstitution.lift 1 eq ;
+ CicSubstitution.lift 1 eq_ty;
+ Cic.Rel 1;CicSubstitution.lift 1 l])
+ in
+ let prefl =
+ Exact (Cic.Appl
+ [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
+ in
+ let bag, id1 =
+ let bag, eq = mk_equality bag (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
+ let (_,_,_,_,id) = open_equality eq in
+ bag, id
+ in
+ bag, Step(Subst.empty_subst,
+ (Demodulation,id1,(Utils.Left,id),pred))
+;;
+
+module IntOT = struct
+ type t = int
+ let compare = Pervasives.compare
+end
+
+module IntSet = Set.Make(IntOT);;
+
+let n_purged = ref 0;;
+
+let collect ((id_to_eq,maxmeta) as bag) alive1 alive2 alive3 =
+ let deps_of id =
+ let p,_,_ = proof_of_id bag id in
+ match p with
+ | Exact _ -> IntSet.empty
+ | Step (_,(_,id1,(_,id2),_)) ->
+ IntSet.add id1 (IntSet.add id2 IntSet.empty)
+ in
+ let rec close s =
+ let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
+ if IntSet.equal news s then s else close news
+ in
+ let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
+ let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
+ let closed_alive_set = close alive_set in
+ let to_purge =
+ M.fold
+ (fun k _ s ->
+ if not (IntSet.mem k closed_alive_set) then
+ k::s else s) id_to_eq []
+ in
+ n_purged := !n_purged + List.length to_purge;
+ List.fold_right M.remove to_purge id_to_eq, maxmeta
+;;
+
+let get_stats () = ""
+(*
+ <:show<Equality.>> ^
+ "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"
+*)
+;;
+
+let rec pp_proofterm name t context =
+ let rec skip_lambda tys ctx = function
+ | Cic.Lambda (n,s,t) -> skip_lambda (s::tys) ((Some n)::ctx) t
+ | t -> ctx,tys,t
+ in
+ let rename s name =
+ match name with
+ | Cic.Name s1 -> Cic.Name (s ^ s1)
+ | _ -> assert false
+ in
+ let rec skip_letin ctx = function
+ | Cic.LetIn (n,b,_,t) ->
+ pp_proofterm (Some (rename "Lemma " n)) b ctx::
+ skip_letin ((Some n)::ctx) t
+ | t ->
+ let ppterm t = CicPp.pp t ctx in
+ let rec pp inner = function
+ | Cic.Appl [Cic.Const (uri,[]);_;l;m;r;p1;p2]
+ when Pcre.pmatch ~pat:"trans_eq" (UriManager.string_of_uri uri)->
+ if not inner then
+ (" " ^ ppterm l) :: pp true p1 @
+ [ " = " ^ ppterm m ] @ pp true p2 @
+ [ " = " ^ ppterm r ]
+ else
+ pp true p1 @
+ [ " = " ^ ppterm m ] @ pp true p2
+ | Cic.Appl [Cic.Const (uri,[]);_;l;m;p]
+ when Pcre.pmatch ~pat:"sym_eq" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
+ when Pcre.pmatch ~pat:"eq_f" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p]
+ when Pcre.pmatch ~pat:"eq_OF_eq" (UriManager.string_of_uri uri)->
+ pp true p
+ | Cic.Appl [Cic.MutConstruct (uri,_,_,[]);_;_;t;p]
+ when Pcre.pmatch ~pat:"ex.ind" (UriManager.string_of_uri uri)->
+ [ "witness " ^ ppterm t ] @ pp true p
+ | Cic.Appl (t::_) ->[ " [by " ^ ppterm t ^ "]"]
+ | t ->[ " [by " ^ ppterm t ^ "]"]
+ in
+ let rec compat = function
+ | a::b::tl -> (b ^ a) :: compat tl
+ | h::[] -> [h]
+ | [] -> []
+ in
+ let compat l = List.hd l :: compat (List.tl l) in
+ compat (pp false t) @ ["";""]
+ in
+ let names, tys, body = skip_lambda [] context t in
+ let ppname name = (match name with Some (Cic.Name s) -> s | _ -> "") in
+ ppname name ^ ":\n" ^
+ (if context = [] then
+ let rec pp_l ctx = function
+ | (t,name)::tl ->
+ " " ^ ppname name ^ ": " ^ CicPp.pp t ctx ^ "\n" ^
+ pp_l (name::ctx) tl
+ | [] -> "\n\n"
+ in
+ pp_l [] (List.rev (List.combine tys names))
+ else "")
+ ^
+ String.concat "\n" (skip_letin names body)
+;;
+
+let pp_proofterm t =
+ "\n\n" ^
+ pp_proofterm (Some (Cic.Name "Hypothesis")) t []
+;;
+
+let initial_nameset_list = [
+ "x"; "y"; "z"; "t"; "u"; "v"; "a"; "b"; "c"; "d";
+ "e"; "l"; "m"; "n"; "o"; "p"; "q"; "r";
+]
+
+module S = Set.Make(String)
+
+let initial_nameset = List.fold_right S.add initial_nameset_list S.empty, [];;
+
+let freshname (nameset, subst) term =
+ let m = CicUtil.metas_of_term term in
+ let nameset, subst =
+ List.fold_left
+ (fun (set,rc) (m,_) ->
+ if List.mem_assoc m rc then set,rc else
+ let name = S.choose set in
+ let set = S.remove name set in
+ set,
+ (m,Cic.Const(UriManager.uri_of_string
+ ("cic:/"^name^".con"),[]))::rc)
+ (nameset,subst) m
+ in
+ let term =
+ ProofEngineReduction.replace
+ ~equality:(fun i t -> match t with Cic.Meta (j,_) -> i=j| _ -> false)
+ ~what:(List.map fst subst)
+ ~with_what:(List.map snd subst) ~where:term
+ in
+ (nameset, subst), term
+;;
+
+let remove_names_in_context (set,subst) names =
+ List.fold_left
+ (fun s n ->
+ match n with Some (Cic.Name n) -> S.remove n s | _ -> s)
+ set names, subst
+;;
+
+let string_of_id2 (id_to_eq,_) names nameset id =
+ if id = 0 then "" else
+ try
+ let (_,_,(_,l,r,_),_,_) = open_equality (M.find id id_to_eq) in
+ let nameset, l = freshname nameset l in
+ let nameset, r = freshname nameset r in
+ Printf.sprintf "%s = %s" (CicPp.pp l names) (CicPp.pp r names)
+ with
+ Not_found -> assert false
+;;
+
+let draw_proof bag names goal_proof proof id =
+ let b = Buffer.create 100 in
+ let fmt = Format.formatter_of_buffer b in
+ let sint = string_of_int in
+ let fst3 (x,_,_) = x in
+ let visited = ref [] in
+ let nameset = remove_names_in_context initial_nameset names in
+ let rec fact id = function
+ | Exact t ->
+ if not (List.mem id !visited) then
+ begin
+ visited := id :: !visited;
+ let nameset, t = freshname nameset t in
+ let t = CicPp.pp t names in
+ GraphvizPp.Dot.node (sint id)
+ ~attrs:["label",t^":"^string_of_id2 bag names nameset id;
+ "shape","rectangle"] fmt;
+ end
+ | Step (_,(_,id1,(_,id2),_)) ->
+ GraphvizPp.Dot.edge (sint id) (sint id1) fmt;
+ GraphvizPp.Dot.edge (sint id) (sint id2) fmt;
+ let p1,_,_ = proof_of_id bag id1 in
+ let p2,_,_ = proof_of_id bag id2 in
+ fact id1 p1;
+ fact id2 p2;
+ if not (List.mem id !visited); then
+ begin
+ visited := id :: !visited;
+ GraphvizPp.Dot.node (sint id)
+ ~attrs:["label",sint id^":"^string_of_id2 bag names nameset id;
+ "shape","ellipse"] fmt
+ end
+ in
+ let sleft acc (_,_,id,_,_) =
+ if acc != 0 then GraphvizPp.Dot.edge (sint acc) (sint id) fmt;
+ fact id (fst3 (proof_of_id bag id));
+ id
+ in
+ GraphvizPp.Dot.header ~node_attrs:["fontsize","10"; ] fmt;
+ ignore(List.fold_left sleft id goal_proof);
+ GraphvizPp.Dot.trailer fmt;
+ let oc = open_out "/tmp/matita_paramod.dot" in
+ Buffer.output_buffer oc b;
+ close_out oc;
+ Utils.debug_print (lazy "dot!");
+ ignore(Unix.system
+ "dot -Tps -o /tmp/matita_paramod.eps /tmp/matita_paramod.dot"
+(* "cat /tmp/matita_paramod.dot| tred | dot -Tps -o /tmp/matita_paramod.eps" *)
+ );
+ ignore(Unix.system "gv /tmp/matita_paramod.eps");
+;;
+
+let saturate_term (id_to_eq, maxmeta) metasenv subst context term =
+ let maxmeta = max maxmeta (CicMkImplicit.new_meta metasenv subst) in
+ let head, metasenv, args, newmeta =
+ TermUtil.saturate_term maxmeta metasenv context term 0
+ in
+ (id_to_eq, newmeta), head, metasenv, args
+;;
+
+let push_maxmeta (id_to_eq, maxmeta) m = id_to_eq, max maxmeta m ;;
+let filter_metasenv_gt_maxmeta (_,maxmeta) =
+ List.filter (fun (j,_,_) -> j >= maxmeta)
+;;
+let maxmeta = snd;;
projects / helm.git / blobdiff