(************************************************************************) (* * The Rocq Prover / The Rocq Development Team *) (* v * Copyright INRIA, CNRS and contributors *) (* <O___,, * (see version control and CREDITS file for authors & dates) *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) (* * (see LICENSE file for the text of the license) *) (************************************************************************)
open Pp open Util open Names open Term open Constr open Termops open EConstr open Tactics open Typeclasses open Evd open Locus open Proofview.Notations open Hints
module NamedDecl = Context.Named.Declaration
(** Hint database named "typeclass_instances", created in prelude *) let typeclasses_db = "typeclass_instances"
(** Options handling *)
let typeclasses_depth_opt_name = ["Typeclasses";"Depth"] let { Goptions.get = get_typeclasses_depth } =
Goptions.declare_intopt_option_and_ref
~key:typeclasses_depth_opt_name
~value:None
()
let set_typeclasses_depth =
Goptions.set_int_option_value typeclasses_depth_opt_name
(** When this flag is enabled, the resolution of type classes tries to avoid useless introductions. This is no longer useful since we have eta, but is here for compatibility purposes. Another compatibility issues is that the
cost (in terms of search depth) can differ. *) let { Goptions.get = get_typeclasses_limit_intros } =
Goptions.declare_bool_option_and_ref
~key:["Typeclasses";"Limit";"Intros"]
~value:true
()
let iterative_deepening_opt_name = ["Typeclasses";"Iterative";"Deepening"] let { Goptions.get = get_typeclasses_iterative_deepening } =
Goptions.declare_bool_option_and_ref
~key:iterative_deepening_opt_name
~value:false
()
module Debug : sig val ppdebug : int -> (unit -> Pp.t) -> unit
val get_debug : unit -> int
val set_typeclasses_debug : bool -> unit end = struct let typeclasses_debug = ref 0
let set_typeclasses_debug d = (:=) typeclasses_debug (if d then 1 else 0) let get_typeclasses_debug () = if !typeclasses_debug > 0 thentrueelsefalse
let set_typeclasses_verbose = function
| None -> typeclasses_debug := 0
| Some n -> typeclasses_debug := n let get_typeclasses_verbose () = if !typeclasses_debug = 0 then None else Some !typeclasses_debug
let ppdebug lvl pp = if !typeclasses_debug > lvl then Feedback.msg_debug (pp())
let get_debug () = !typeclasses_debug end open Debug let set_typeclasses_debug = set_typeclasses_debug
type search_strategy = Dfs | Bfs
let set_typeclasses_strategy = function
| Dfs -> Goptions.set_bool_option_value iterative_deepening_opt_name false
| Bfs -> Goptions.set_bool_option_value iterative_deepening_opt_name true
let pr_ev evs ev = let evi = Evd.find_undefined evs ev in let env = Evd.evar_filtered_env (Global.env ()) evi in
Printer.pr_econstr_env env evs (Evd.evar_concl evi)
let pr_ev_with_id evs ev =
Evar.print ev ++ str " : " ++ pr_ev evs ev
let auto_unif_flags ?(allowed_evars = Evarsolve.AllowedEvars.all) st = let fl = auto_core_unif_flags st allowed_evars in
{ core_unify_flags = fl;
merge_unify_flags = fl;
subterm_unify_flags = fl;
allow_K_in_toplevel_higher_order_unification = false;
resolve_evars = false
}
let e_give_exact flags h = letopen Tacmach in
Proofview.Goal.enter beginfun gl -> let env = Proofview.Goal.env gl in let sigma = project gl in let sigma, c = Hints.fresh_hint env sigma h in let (sigma, t1) = Typing.type_of (pf_env gl) sigma c in
Proofview.Unsafe.tclEVARS sigma <*>
Clenv.unify ~flags ~cv_pb:CUMUL t1 <*> exact_no_check c end
let unify_resolve ~with_evars flags h diff = match diff with
| None ->
Hints.hint_res_pf ~with_evars ~with_classes:false ~flags h
| Some (diff, ty) -> let () = assert (Option.is_empty (fst @@ hint_as_term @@ h)) in
Proofview.Goal.enter beginfun gl -> let env = Proofview.Goal.env gl in let sigma = Tacmach.project gl in let sigma, c = Hints.fresh_hint env sigma h in let clenv = Clenv.mk_clenv_from_n env sigma diff (c, ty) in
Clenv.res_pf ~with_evars ~with_classes:false ~flags clenv end
(** Dealing with goals of the form A -> B and hints of the form C -> A -> B.
*) let with_prods nprods h f = if get_typeclasses_limit_intros () then
Proofview.Goal.enter beginfun gl -> ifOption.has_some (fst @@ hint_as_term h) || Int.equal nprods 0 then f None else let sigma = Tacmach.project gl in let ty = Retyping.get_type_of (Proofview.Goal.env gl) sigma (snd @@ hint_as_term h) in let diff = nb_prod sigma ty - nprods in if (>=) diff 0 then f (Some (diff, ty)) else Tacticals.tclZEROMSG (str"Not enough premisses") end else Proofview.Goal.enter beginfun gl -> if Int.equal nprods 0 then f None else Tacticals.tclZEROMSG (str"Not enough premisses") end
(** Semantics of type class resolution lemma application:
- Use unification to find a well-typed substitution. There might be evars in the goal and the lemma. Evars in the goal can get refined. - Independent evars are turned into goals, whatever their kind is. - Dependent evars of the lemma corresponding to arguments which appear in independent goals or the conclusion are turned into subgoals iff they are of typeclass kind. - The remaining dependent evars not of typeclass type are shelved, and resolution must fill them for it to succeed, otherwise we backtrack.
*)
let pr_gls sigma gls =
prlist_with_sep spc
(fun ev -> int (Evar.repr ev) ++ spc () ++ pr_ev sigma ev) gls
(** Ensure the dependent subgoals are shelved after an apply/eapply. *) let shelve_dependencies gls = letopen Proofview in if CList.is_empty gls then tclUNIT () else
tclEVARMAP >>= fun sigma ->
ppdebug 1 (fun () -> str" shelving dependent subgoals: " ++ pr_gls sigma gls);
shelve_goals gls
let hintmap_of env sigma hdc secvars concl = match hdc with
| None -> fun db -> ModeMatch (NoMode, Hint_db.map_none ~secvars db)
| Some hdc -> fun db -> Hint_db.map_eauto env sigma ~secvars hdc concl db
(** Hack to properly solve dependent evars that are typeclasses *) let rec e_trivial_fail_db db_list local_db secvars = letopen Tacticals in letopen Tacmach in let trivial_fail =
Proofview.Goal.enter beginfun gl -> let env = Proofview.Goal.env gl in let sigma = Tacmach.project gl in let d = NamedDecl.get_id @@ pf_last_hyp gl in let hints = push_resolve_hyp env sigma d local_db in
e_trivial_fail_db db_list hints secvars end in let trivial_resolve =
Proofview.Goal.enter beginfun gl -> let tacs = e_trivial_resolve db_list local_db secvars
(pf_env gl) (project gl) (pf_concl gl) in
tclFIRST (List.map (fun (x,_,_,_,_) -> x) tacs) end in let tacl =
Eauto.e_assumption ::
(tclTHEN Tactics.intro trivial_fail :: [trivial_resolve]) in
tclSOLVE tacl
and e_my_find_search db_list local_db secvars hdc complete env sigma concl0 = let prods, concl = EConstr.decompose_prod_decls sigma concl0 in let nprods = List.length prods in let allowed_evars = letall = Evarsolve.AllowedEvars.allin match hdc with
| Some (hd,_) -> beginmatch Typeclasses.class_info hd with
| Some cl -> if cl.cl_strict then let undefined = lazy (Evarutil.undefined_evars_of_term sigma concl) in let allowed evk = not (Evar.Set.mem evk (Lazy.force undefined)) in
Evarsolve.AllowedEvars.from_pred allowed elseall
| None -> all end
| _ -> all in let tac_of_hint = fun (flags, h) -> let name = FullHint.name h in let tac = function
| Res_pf h -> let tac =
with_prods nprods h (unify_resolve ~with_evars:false flags h) in
Proofview.tclBIND (Proofview.with_shelf tac)
(fun (gls, ()) -> shelve_dependencies gls)
| ERes_pf h -> let tac =
with_prods nprods h (unify_resolve ~with_evars:true flags h) in
Proofview.tclBIND (Proofview.with_shelf tac)
(fun (gls, ()) -> shelve_dependencies gls)
| Give_exact h ->
e_give_exact flags h
| Res_pf_THEN_trivial_fail h -> let fst = with_prods nprods h (unify_resolve ~with_evars:true flags h) in let snd = if complete then Tacticals.tclIDTAC else e_trivial_fail_db db_list local_db secvars in
Tacticals.tclTHEN fst snd
| Unfold_nth c ->
Proofview.tclPROGRESS (unfold_in_concl [AllOccurrences,c])
| Extern (p, tacast) -> conclPattern concl0 p tacast in let tac = FullHint.run h tac in let tac = if complete then Tacticals.tclCOMPLETE tac else tac in let extern = match FullHint.repr h with
| Extern _ -> true
| _ -> false in
(tac, FullHint.priority h, extern, name, lazy (FullHint.print env sigma h)) in let hint_of_db = hintmap_of env sigma hdc secvars concl in let hintl = List.map_filter (fun db -> match hint_of_db db with
| ModeMatch (m, l) -> Some (db, m, l)
| ModeMismatch -> None)
(local_db :: db_list) in (* In case there is a mode mismatch in all the databases we get stuck. Otherwise we consider the hints that match.
Recall the local database uses the union of all the modes in the other databases. *) ifList.is_empty hintl then None else let hintl =
CList.map
(fun (db, m, tacs) -> let flags = auto_unif_flags ~allowed_evars (Hint_db.transparent_state db) in
m, List.map (fun x -> tac_of_hint (flags, x)) tacs)
hintl in let modes, hintl = List.split hintl in let all_mode_match = List.for_all (fun m -> m != NoMode) modes in let hintl = match hintl with (* Optim: only sort if multiple hint sources were involved *)
| [hintl] -> hintl
| _ -> let hintl = List.flatten hintl in let hintl = List.stable_sort
(fun (_, pri1, _, _, _) (_, pri2, _, _, _) -> Int.compare pri1 pri2)
hintl in
hintl in
Some (all_mode_match, hintl)
and e_trivial_resolve db_list local_db secvars env sigma concl = let hd = try Some (decompose_app_bound sigma concl) with Bound -> None in try
(match e_my_find_search db_list local_db secvars hd true env sigma concl with
| Some (_,l) -> l
| None -> []) with Not_found -> []
let e_possible_resolve db_list local_db secvars env sigma concl = let hd = try Some (decompose_app_bound sigma concl) with Bound -> None in try
e_my_find_search db_list local_db secvars hd false env sigma concl with Not_found -> Some (true, [])
let cut_of_hints h = List.fold_left (fun cut db -> PathOr (Hint_db.cut db, cut)) PathEmpty h
let pr_depth l = let rec fmt elts = match elts with
| [] -> []
| [n] -> [string_of_int n]
| n1::n2::rest ->
(string_of_int n1 ^ "." ^ string_of_int n2) :: fmt rest in
prlist_with_sep (fun () -> str "-") str (fmt (List.rev l))
let is_Prop env sigma concl = let ty = Retyping.get_type_of env sigma concl in match EConstr.kind sigma ty with
| Sort s -> beginmatch ESorts.kind sigma s with
| Prop -> true
| _ -> false end
| _ -> false
let is_unique env sigma concl = try let (cl,u), args = dest_class_app env sigma concl in
cl.cl_unique with e when CErrors.noncritical e -> false
(** Sort the undefined variables from the least-dependent to most dependent. *) let top_sort evm undefs = let l' = ref [] in let tosee = ref undefs in let cache = Evarutil.create_undefined_evars_cache () in let rec visit ev evi = let evs = Evarutil.filtered_undefined_evars_of_evar_info ~cache evm evi in
tosee := Evar.Set.remove ev !tosee;
Evar.Set.iter (fun ev -> if Evar.Set.mem ev !tosee then
visit ev (Evd.find_undefined evm ev)) evs;
l' := ev :: !l'; in whilenot (Evar.Set.is_empty !tosee) do let ev = Evar.Set.choose !tosee in
visit ev (Evd.find_undefined evm ev)
done; List.rev !l'
(** We transform the evars that are concerned by this resolution (according to predicate p) into goals. Invariant: function p only manipulates and returns undefined evars
*)
let evars_to_goals p evm = let goals, nongoals = Evar.Set.partition (p evm) (Evd.get_typeclass_evars evm) in if Evar.Set.is_empty goals then None else Some (goals, nongoals)
(** Making local hints *) let make_resolve_hyp env sigma st only_classes decl db = let id = NamedDecl.get_id decl in let cty = NamedDecl.get_type decl in let is_class = let ctx, ar = decompose_prod_decls sigma cty in match EConstr.kind sigma (fst (decompose_app sigma ar)) with
| Const (c,_) -> is_class (GlobRef.ConstRef c)
| Ind (i,_) -> is_class (GlobRef.IndRef i)
| _ -> false in let keep = not only_classes || is_class in if keep then let id = GlobRef.VarRef id in
push_resolves env sigma id db else db
let make_hints env sigma (modes,st) only_classes sign = let db = Hint_db.add_modes modes @@ Hint_db.empty st truein List.fold_right
(fun hyp hints -> let consider = not only_classes || trylet t = hyp |> NamedDecl.get_id |> Global.lookup_named |> NamedDecl.get_type in (* Section variable, reindex only if the type changed *) not (EConstr.eq_constr sigma (EConstr.of_constr t) (NamedDecl.get_type hyp)) with Not_found -> true in if consider then
make_resolve_hyp env sigma st only_classes hyp hints else hints)
sign db
(** Local hints *) let autogoal_cache = Summary.ref ~name:"autogoal_cache"
(Libnames.dummy_full_path, true, Context.Named.empty, Hints.Modes.empty,
Hint_db.empty TransparentState.full true)
let make_autogoal_hints only_classes (modes,st as mst) gl = let env = Proofview.Goal.env gl in let sigma = Proofview.Goal.sigma gl in let sign = EConstr.named_context env in let (dir, onlyc, sign', cached_modes, cached_hints) = !autogoal_cache in let cwd = Lib.cwd () in let eq c1 c2 = EConstr.eq_constr sigma c1 c2 in if Libnames.eq_full_path cwd dir &&
(onlyc == only_classes) &&
Context.Named.equal (ERelevance.equal sigma) eq sign sign' &&
cached_modes == modes then cached_hints else let hints = make_hints env sigma mst only_classes sign in
autogoal_cache := (cwd, only_classes, sign, modes, hints); hints
let make_autogoal mst only_classes dep cut best_effort i g = let hints = make_autogoal_hints only_classes mst g in
{ search_hints = hints;
search_depth = [i]; last_tac = lazy (str"none");
search_dep = dep;
search_only_classes = only_classes;
search_cut = cut;
search_best_effort = best_effort }
(** In the proof engine failures are represented as exceptions *)
exception ReachedLimit
exception NoApplicableHint
exception StuckGoal
(** ReachedLimit has priority over NoApplicableHint to handle iterative deepening: it should fail when no hints are applicable,
but go to a deeper depth otherwise. *) let merge_exceptions e e' = match fst e, fst e' with
| ReachedLimit, _ -> e
| _, ReachedLimit -> e'
| _, _ -> e
(** Determine if backtracking is needed for this goal. We generally backtrack except in the following (possibly overlapping) cases: - [unique_instances] is [true]. This is the case when the goal's class has [Unique Instances]. - [indep] is [true] and the current goal has no evars. [indep] is generally [true] and only gets set to [false] if the current goal's evar is mentioned in other goals. ([indep] is the negation of [search_dep].)
- The current goal is a [Prop] and has no evars. *) let needs_backtrack env evd ~unique_instances ~indep concl = if unique_instances thenfalseelse if indep || is_Prop env evd concl then
occur_existential evd concl elsetrue
let pr_goals s = letopen Proofview in if get_debug() > 1 then
tclEVARMAP >>= fun sigma ->
Unsafe.tclGETGOALS >>= fun gls -> let gls = CList.map Proofview.drop_state gls in let j = List.length gls in let pr_goal gl = pr_ev_with_id sigma gl in
Feedback.msg_debug
(s ++ int j ++ str" goals:" ++ spc () ++
prlist_with_sep Pp.fnl pr_goal gls);
tclUNIT () else
tclUNIT ()
let pr_internal_exception ie = match fst ie with
| ReachedLimit -> str "Proof-search reached its limit."
| NoApplicableHint -> str "Proof-search failed."
| StuckGoal | NonStuckFailure -> str "Proof-search got stuck."
| e -> CErrors.iprint ie
(* XXX Is this handler needed for something? *) let () = CErrors.register_handler begin function
| NonStuckFailure -> Some (str "NonStuckFailure")
| NoApplicableHint -> Some (str "NoApplicableHint")
| _ -> None end
(** For each success of tac1 try tac2. If tac2 raises NonStuckFailure, try the next success of tac1 until depleted. If tac1 finally fails, returns the result of the first tac1 success, if any.
*)
type goal_status =
| IsInitial
| IsStuckGoal
| IsNonStuckFailure
let pr_goal_status = function
| IsInitial -> str "initial"
| IsStuckGoal -> str "stuck"
| IsNonStuckFailure -> str "stuck failure"
let pr_search_goal sigma (glid, ev, status, _) =
str"Goal " ++ int glid ++ str" evar: " ++ Evar.print ev ++ str " status: " ++ pr_goal_status status
let pr_search_goals sigma =
prlist_with_sep fnl (pr_search_goal sigma)
let search_fixpoint ~best_effort ~allow_out_of_order tacs = letopen Pp in letopen Proofview in letopen Proofview.Notations in let rec fixpoint progress tacs stuck fk = let next (glid, ev, status, tac) tacs stuck = let () = ppdebug 1 (fun () ->
str "considering goal " ++ int glid ++
str " of status " ++ pr_goal_status status) in let rec kont = function
| Fail ((NonStuckFailure | StuckGoal as exn), info) when allow_out_of_order -> let () = ppdebug 1 (fun () ->
str "Goal " ++ int glid ++
str" is stuck or failed without being stuck, trying other tactics.") in let status = match exn with
| NonStuckFailure -> IsNonStuckFailure
| StuckGoal -> IsStuckGoal
| _ -> assert false in
cycle 1 (* Puts the first goal last *) <*>
fixpoint progress tacs ((glid, ev, status, tac) :: stuck) fk (* Launches the search on the rest of the goals *)
| Fail ie -> let () = ppdebug 1 (fun () ->
str "Goal " ++ int glid ++ str" has no more solutions, returning exception: "
++ pr_internal_exception ie) in
fk ie
| Next (res, fk') -> let () = ppdebug 1 (fun () ->
str "Goal " ++ int glid ++ str" has a success, continuing resolution") in (* We try to solve the rest of the constraints, and if that fails we backtrack to the next result of tac, etc.... Ultimately if none of the solutions for tac work, we will come back to the failure continuation fk in one of
the above cases *)
fixpoint true tacs stuck (fun e -> tclCASE (fk' e) >>= kont) in tclCASE tac >>= kont in
tclEVARMAP >>= fun sigma -> let () = ppdebug 1 (fun () -> let stuck, failed = List.partition (fun (_, _, status, _) -> status = IsStuckGoal) stuck in
str"Calling fixpoint on : " ++
int (List.length tacs) ++ str" initial goals" ++
str", " ++ int (List.length stuck) ++ str" stuck goals" ++
str" and " ++ int (List.length failed) ++ str" non-stuck failures kept" ++
str" with " ++ str(if progress then""else"no ") ++
str"progress made in this run." ++ fnl () ++
str "Stuck: " ++ pr_search_goals sigma stuck ++ fnl () ++
str "Failed: " ++ pr_search_goals sigma failed ++ fnl () ++
str "Initial: " ++ pr_search_goals sigma tacs) in
tclCHECKINTERRUPT <*> match tacs with
| tac :: tacs -> next tac tacs stuck
| [] -> (* All remaining goals are stuck *) match stuck with
| [] -> (* We found a solution! Great, but in case it's not good for the rest of the proof search,
we might have other solutions available through fk. *)
tclOR (tclUNIT ()) fk
| stuck -> if progress then fixpoint false stuck [] fk else(* No progress can be made on the stuck goals arising from this resolution,
try a different solution on the non-stuck goals, if any. *) begin
tclORELSE (fk (NoApplicableHint, Exninfo.null))
(fun (e, info) -> let () = ppdebug 1 (fun () -> int (List.length stuck) ++ str " remaining goals left, no progress, calling continuation failed") in (* We keep the stuck goals to display to the user *) if best_effort then let stuckgls, failedgls = List.partition (fun (_, _, status, _) -> match status with
| IsStuckGoal -> true
| IsNonStuckFailure -> false (* There should remain no initial goals at this point *)
| IsInitial -> assert false)
stuck in
pr_goals (str "best_effort is on and remaining goals are: ") <*> (* We shelve the stuck goals but we keep the non-stuck failures in the goal list. This is for compat with Coq 8.12 but might not be the wisest choice in the long run.
*) let to_shelve = List.map (fun (glid, ev, _, _) -> ev) stuckgls in let () = ppdebug 1 (fun () ->
str "Shelving subgoals: " ++
prlist_with_sep spc Evar.print to_shelve) in
Unsafe.tclNEWSHELVED to_shelve else tclZERO ~info e) end in
pr_goals (str"Launching resolution fixpoint on ") <*>
Unsafe.tclGETGOALS >>= fun gls -> (* We wrap all goals with their associated tactic. It might happen that an initial goal is solved during the resolution of another goal,
hence the `tclUNIT` in case there is no goal for the tactic to apply anymore. *) let tacs = List.map2_i
(fun i gls tac -> (succ i, Proofview.drop_state gls, IsInitial, tclFOCUS ~nosuchgoal:(tclUNIT ()) 1 1 tac))
0 gls tacs in
fixpoint false tacs [] (fun (e, info) -> tclZERO ~info e) <*>
pr_goals (str "Result goals after fixpoint: ")
(** The general hint application tactic. tac1 + tac2 .... The choice of OR or ORELSE is determined depending on the dependencies of the goal and the unique/Prop
status *) let hints_tac_gl hints info kont gl : unit Proofview.tactic = letopen Proofview in letopen Proofview.Notations in let env = Goal.env gl in let concl = Goal.concl gl in let sigma = Goal.sigma gl in let unique_instances = is_unique env sigma concl in let indep = not info.search_dep in let backtrack = needs_backtrack env sigma ~unique_instances ~indep concl in let () = ppdebug 0 (fun () ->
pr_depth info.search_depth ++ str": looking for " ++
Printer.pr_econstr_env (Goal.env gl) sigma concl ++
(if backtrack then str" with backtracking" else str" without backtracking")) in let secvars = compute_secvars gl in match e_possible_resolve hints info.search_hints secvars
env sigma concl with
| None ->
Proofview.tclZERO StuckGoal
| Some (all_mode_match, poss) -> (* If no goal depends on the solution of this one or the instances are irrelevant/assumed to be unique, then we don't need to backtrack, as long as no evar appears in the goal This is an overapproximation. Evars could appear in this goal only
and not any other *) let ortac = if backtrack then Proofview.tclOR else Proofview.tclORELSE in let idx = ref 1 in let foundone = reffalsein let rec onetac e (tac, pat, b, name, pp) tl = let derivs = path_derivate env info.search_cut name in let pr_error ie =
ppdebug 1 (fun () -> let idx = if fst ie == NoApplicableHint then pred !idx else !idx in let header =
pr_depth (idx :: info.search_depth) ++ str": " ++
Lazy.force pp ++
(if !foundone != truethen
str" on" ++ spc () ++ pr_ev sigma (Proofview.Goal.goal gl) else mt ()) in
(header ++ str " failed with: " ++ pr_internal_exception ie)) in let tac_of gls i j = Goal.enter beginfun gl' -> let sigma' = Goal.sigma gl'in let () = ppdebug 0 (fun () ->
pr_depth (succ j :: i :: info.search_depth) ++ str" : " ++
pr_ev sigma' (Proofview.Goal.goal gl')) in let eq c1 c2 = EConstr.eq_constr sigma' c1 c2 in let hints' = if b && not (Context.Named.equal (ERelevance.equal sigma) eq (Goal.hyps gl') (Goal.hyps gl)) then let st = Hint_db.transparent_state info.search_hints in let modes = Hint_db.modes info.search_hints in
make_autogoal_hints info.search_only_classes (modes,st) gl' else info.search_hints in let dep' = info.search_dep || Proofview.unifiable sigma' (Goal.goal gl') gls in let info' =
{ search_depth = succ j :: i :: info.search_depth;
last_tac = pp;
search_dep = dep';
search_only_classes = info.search_only_classes;
search_hints = hints';
search_cut = derivs;
search_best_effort = info.search_best_effort } in kont info' end in let rec result (shelf, ()) i k =
foundone := true;
Proofview.Unsafe.tclGETGOALS >>= fun gls -> let gls = CList.map Proofview.drop_state gls in let j = List.length gls in let () = ppdebug 0 (fun () ->
pr_depth (i :: info.search_depth) ++ str": " ++ Lazy.force pp
++ str" on" ++ spc () ++ pr_ev sigma (Proofview.Goal.goal gl)
++ str", " ++ int j ++ str" subgoal(s)" ++
(Option.cata (fun k -> str " in addition to the first " ++ int k)
(mt()) k)) in let res = if j = 0 then tclUNIT () else search_fixpoint ~best_effort:false ~allow_out_of_order:false
(List.init j (fun j' -> (tac_of gls i (Option.default 0 k + j')))) in let finish nestedshelf sigma = letfilter ev = try let evi = Evd.find_undefined sigma ev in if info.search_only_classes then
Some (ev, not (is_class_evar sigma evi)) else Some (ev, true) with Not_found -> None in let remaining = CList.map_filter filter shelf in let () = ppdebug 1 (fun () -> let prunsolved (ev, _) = int (Evar.repr ev) ++ spc () ++ pr_ev sigma ev in let unsolved = prlist_with_sep spc prunsolved remaining in
pr_depth (i :: info.search_depth) ++
str": after " ++ Lazy.force pp ++ str" finished, " ++
int (List.length remaining) ++
str " goals are shelved and unsolved ( " ++
unsolved ++ str")") in begin (* Some existentials produced by the original tactic were not solved
in the subgoals, turn them into subgoals now. *) let shelved, goals = List.partition (fun (ev, s) -> s) remaining in let shelved = List.map fst shelved @ nestedshelf and goals = List.map fst goals in let () = ifnot (List.is_empty shelved && List.is_empty goals) then
ppdebug 1 (fun () ->
str"Adding shelved subgoals to the search: " ++
prlist_with_sep spc (pr_ev sigma) goals ++
str" while shelving " ++
prlist_with_sep spc (pr_ev sigma) shelved) in
shelve_goals shelved <*> ifList.is_empty goals then tclUNIT () else let make_unresolvables = tclEVARMAP >>= fun sigma -> let sigma = make_unresolvables (fun x -> List.mem_f Evar.equal x goals) sigma in
Unsafe.tclEVARS sigma in let goals = CList.map Proofview.with_empty_state goals in
with_shelf (make_unresolvables <*> Unsafe.tclNEWGOALS goals) >>= fun s ->
result s i (Some (Option.default 0 k + j)) end in
with_shelf res >>= fun (sh, ()) ->
tclEVARMAP >>= finish sh in if path_matches_epsilon derivs then aux e tl else
ortac
(with_shelf tac >>= fun s -> let i = !idx in incr idx; result s i None)
(fun e' ->
(pr_error e'; aux (merge_exceptions e e') tl)) and aux e = function
| tac :: tacs -> onetac e tac tacs
| [] -> let () = if !foundone == falsethen
ppdebug 0 (fun () ->
pr_depth info.search_depth ++ str": no match for " ++
Printer.pr_econstr_env (Goal.env gl) sigma concl ++
str ", " ++ int (List.length poss) ++
str" possibilities") in match e with
| (ReachedLimit,ie) -> Proofview.tclZERO ~info:ie ReachedLimit
| (StuckGoal,ie) -> Proofview.tclZERO ~info:ie StuckGoal
| (NoApplicableHint,ie) -> (* If the constraint abides by the (non-trivial) modes but no solution could be found, we consider it a failed goal, and let proof search proceed on the rest of the
constraints, thus giving a more precise error message. *) if all_mode_match &&
info.search_best_effort then
Proofview.tclZERO ~info:ie NonStuckFailure else Proofview.tclZERO ~info:ie NoApplicableHint
| (_,ie) -> Proofview.tclZERO ~info:ie NoApplicableHint in if backtrack then aux (NoApplicableHint,Exninfo.null) poss else tclONCE (aux (NoApplicableHint,Exninfo.null) poss)
let hints_tac hints info kont : unit Proofview.tactic =
Proofview.Goal.enter
(fun gl -> hints_tac_gl hints info kont gl)
let intro_tac info kont gl = letopen Proofview in let env = Goal.env gl in let sigma = Goal.sigma gl in let decl = Tacmach.pf_last_hyp gl in let ldb =
make_resolve_hyp env sigma (Hint_db.transparent_state info.search_hints)
info.search_only_classes decl info.search_hints in let info' =
{ info with search_hints = ldb; last_tac = lazy (str"intro");
search_depth = 1 :: 1 :: info.search_depth } in kont info'
let intro info kont =
Proofview.tclBIND Tactics.intro
(fun _ -> Proofview.Goal.enter (fun gl -> intro_tac info kont gl))
let rec search_tac hints limit depth = let kont info =
Proofview.numgoals >>= fun i -> let () = ppdebug 1 (fun () ->
str "calling eauto recursively at depth " ++ int (succ depth) ++
str " on " ++ int i ++ str " subgoals") in
search_tac hints limit (succ depth) info in fun info -> if Int.equal depth (succ limit) then let info = Exninfo.reify () in
Proofview.tclZERO ~info ReachedLimit else
Proofview.tclOR (hints_tac hints info kont)
(fun e -> Proofview.tclOR (intro info kont)
(fun e' -> let (e, info) = merge_exceptions e e'in
Proofview.tclZERO ~info e))
let search_tac_gl mst only_classes dep hints best_effort depth i sigma gls gl :
unit Proofview.tactic = letopen Proofview in let dep = dep || Proofview.unifiable sigma (Goal.goal gl) gls in let info = make_autogoal mst only_classes dep (cut_of_hints hints)
best_effort i gl in
search_tac hints depth 1 info
let search_tac mst only_classes best_effort dep hints depth = letopen Proofview in let tac sigma gls i =
Goal.enter beginfun gl ->
search_tac_gl mst only_classes dep hints best_effort depth (succ i) sigma gls gl end in
Proofview.Unsafe.tclGETGOALS >>= fun gls -> let gls = CList.map Proofview.drop_state gls in
Proofview.tclEVARMAP >>= fun sigma -> let j = List.length gls in
search_fixpoint ~best_effort ~allow_out_of_order:true (List.init j (fun i -> tac sigma gls i))
let fix_iterative t = let rec aux depth =
Proofview.tclOR
(t depth)
(function
| (ReachedLimit,_) -> aux (succ depth)
| (e,ie) -> Proofview.tclZERO ~info:ie e) in aux 1
let fix_iterative_limit limit t = letopen Proofview in let rec aux depth = if Int.equal depth (succ limit) then let info = Exninfo.reify () in
tclZERO ~info ReachedLimit else tclOR (t depth) (function
| (ReachedLimit, _) -> aux (succ depth)
| (e,ie) -> Proofview.tclZERO ~info:ie e) in aux 1
let eauto_tac_stuck mst ?(unique=false)
~only_classes
~best_effort
?strategy ~depth ~dep hints = letopen Proofview in let tac = let search = search_tac mst only_classes best_effort dep hints in let dfs = match strategy with
| None -> not (get_typeclasses_iterative_deepening ())
| Some Dfs -> true
| Some Bfs -> false in if dfs then let depth = match depth with None -> -1 | Some d -> d in
search depth else match depth with
| None -> fix_iterative search
| Some l -> fix_iterative_limit l search in let error (e, info) = match e with
| ReachedLimit ->
Tacticals.tclFAIL ~info (str"Proof search reached its limit")
| NoApplicableHint ->
Tacticals.tclFAIL ~info (str"Proof search failed" ++
(ifOption.is_empty depth then mt() else str" without reaching its limit"))
| Proofview.MoreThanOneSuccess ->
Tacticals.tclFAIL ~info (str"Proof search failed: " ++
str"more than one success found")
| e -> Proofview.tclZERO ~info e in let tac = Proofview.tclOR tac error in let tac = if unique then
Proofview.tclEXACTLY_ONCE Proofview.MoreThanOneSuccess tac else tac in
with_shelf numgoals >>= fun (initshelf, i) -> let () = ppdebug 1 (fun () ->
str"Starting resolution with " ++ int i ++
str" goal(s) under focus and " ++
int (List.length initshelf) ++ str " shelved goal(s)" ++
(if only_classes then str " in only_classes mode"else str " in regular mode") ++ match depth with
| None -> str ", unbounded"
| Some i -> str ", with depth limit " ++ int i) in
tac <*> pr_goals (str "after eauto_tac_stuck: ")
let preprocess_goals evm goals = let sorted_goals = if get_typeclasses_dependency_order () then
top_sort evm goals else Evar.Set.elements goals in let evm = Evd.set_typeclass_evars evm Evar.Set.empty in let evm = Evd.push_future_goals evm in
evm, sorted_goals
let run_on_goals env evm tac ~goals = let goalsl = List.map Proofview.with_empty_state goals in let tac = Proofview.Unsafe.tclNEWGOALS goalsl <*> tac in let _, pv = Proofview.init evm [] in (* Instance may try to call this before a proof is set up!
Thus, give_me_the_proof will fail. Beware! *) let name, poly = (* try * let Proof.{ name; poly } = Proof.data Proof_global.(give_me_the_proof ()) in * name, poly
* with | Proof_global.NoCurrentProof -> *)
Id.of_string "instance", false in let tac = if get_debug () > 1 then Proofview.Trace.record_info_trace tac else tac in let (), pv', _, unsafe, info = try Proofview.apply ~name ~poly env tac pv with Logic_monad.TacticFailure _ -> raise Not_found in let () =
ppdebug 1 (fun () ->
str"The tactic trace is: " ++ hov 0 (Proofview.Trace.pr_info env evm ~lvl:1 info)) in let finished = Proofview.finished pv' in let evm' = Proofview.return pv'in
(finished, evm')
let post_process_goals ~goals ~nongoals ~sigma ~finished = let _, sigma = Evd.pop_future_goals sigma in let tc_evars = Evd.get_typeclass_evars sigma in let () = ppdebug 1 (fun () ->
str"Finished resolution with " ++ str(if finished then"a complete"else"an incomplete") ++
str" solution." ++ fnl() ++
str"Old typeclass evars not concerned by this resolution = " ++
hov 0 (prlist_with_sep spc (pr_ev_with_id sigma)
(Evar.Set.elements tc_evars)) ++ fnl() ++
str"Shelf = " ++
hov 0 (prlist_with_sep spc (pr_ev_with_id sigma)
(Evar.Set.elements tc_evars))) in let nongoals =
Evar.Set.fold (fun ev acc -> match Evarutil.advance sigma ev with
| Some ev -> Evar.Set.add ev acc
| None -> acc) (Evar.Set.union goals nongoals) tc_evars in let sigma = Evd.set_typeclass_evars sigma nongoals in let () = ppdebug 1 (fun () ->
str"New typeclass evars are: " ++
hov 0 (prlist_with_sep spc (pr_ev_with_id sigma) (Evar.Set.elements nongoals))) in
sigma
(** Typeclasses eauto is an eauto which tries to resolve only goals of typeclass type, and assumes that the initially selected
evars in evd are independent of the rest of the evars *) let typeclasses_eauto env evd ~goals ?depth ~unique ~best_effort st hints = let only_classes = truein let dep = unique in
NewProfile.profile "typeclass search" (fun () ->
run_on_goals env evd (eauto_tac_stuck st ~unique ~only_classes ~best_effort ~depth ~dep hints) ~goals) ()
let typeclasses_resolve : solver = { solver = fun env evd ~depth ~unique ~best_effort ~goals -> let db = searchtable_map typeclasses_db in let st = Hint_db.transparent_state db in let modes = Hint_db.modes db in
typeclasses_eauto env evd ~goals ?depth ~best_effort ~unique (modes,st) [db]
} end
let typeclasses_eauto ?(only_classes=false)
?(best_effort=false)
?(st=TransparentState.full)
?strategy ~depth dbs = let dbs = List.map_filter
(fun db -> try Some (searchtable_map db) with e when CErrors.noncritical e -> None)
dbs in let st = match dbs with x :: _ -> Hint_db.transparent_state x | _ -> st in let modes = List.map Hint_db.modes dbs in let modes = List.fold_left Modes.union Modes.empty modes in let depth = match depth with None -> get_typeclasses_depth () | Some l -> Some l in
Proofview.tclIGNORE
(Search.eauto_tac (modes,st) ~only_classes ?strategy
~best_effort ~depth ~dep:true dbs) (* Stuck goals can remain here, we could shelve them, but this way the user can use `solve [typeclasses eauto]` to check there are
no stuck goals remaining, or use [typeclasses eauto; shelve] himself. *)
(** We compute dependencies via a union-find algorithm. Beware of the imperative effects on the partition structure,
it should not be shared, but only used locally. *)
let deps_of_constraints cstrs evm p = List.iter (fun (_, _, x, y) -> let evx = Evarutil.undefined_evars_of_term evm x in let evy = Evarutil.undefined_evars_of_term evm y in
Intpart.union_set (Evar.Set.union evx evy) p)
cstrs
let evar_dependencies pred evm p = let cache = Evarutil.create_undefined_evars_cache () in
Evd.fold_undefined
(fun ev evi _ -> if Evd.is_typeclass_evar evm ev && pred evm ev evi then let evars = Evar.Set.add ev (Evarutil.filtered_undefined_evars_of_evar_info ~cache evm evi) in Intpart.union_set evars p else ())
evm ()
(** [split_evars] returns groups of undefined evars according to dependencies *)
let split_evars pred env evm = let p = Intpart.create () in
evar_dependencies pred evm p;
deps_of_constraints (snd (extract_all_conv_pbs evm)) evm p; let part = Intpart.partition p in let is_strictly_unique ev = let evi = Evd.find_undefined evm ev in let concl = Evd.evar_concl evi in match Typeclasses.class_of_constr env evm concl with
| None -> false
| Some (_, ((cl, _), _)) ->
cl.cl_strict && cl.cl_unique in let fn evs = let (strictly_uniques, rest) = Evar.Set.partition is_strictly_unique evs in List.rev_append (List.rev_map Evar.Set.singleton (Evar.Set.elements strictly_uniques)) [rest] in List.concat_map fn part
let is_inference_forced p evd ev = try if Evar.Set.mem ev (Evd.get_typeclass_evars evd) && p ev then let (loc, k) = evar_source (Evd.find_undefined evd ev) in match k with
| Evar_kinds.ImplicitArg (_, _, b) -> b
| Evar_kinds.QuestionMark _ -> false
| _ -> true elsetrue with Not_found -> assert false
let is_mandatory p comp evd =
Evar.Set.exists (is_inference_forced p evd) comp
(** Check if an evar is concerned by the current resolution attempt, (and in particular is in the current component).
Invariant : this should only be applied to undefined evars. *)
let select_and_update_evars p oevd in_comp evd ev = try if Evd.is_typeclass_evar oevd ev then
(in_comp ev && p evd ev (Evd.find_undefined evd ev)) elsefalse with Not_found -> false
(** Do we still have unresolved evars that should be resolved ? *)
let has_undefined p oevd evd = let check ev evi = p oevd ev in
Evar.Map.exists check (Evd.undefined_map evd) let find_undefined p oevd evd = let check ev evi = p oevd ev in
Evar.Map.domain (Evar.Map.filter check (Evd.undefined_map evd))
exception Unresolved of evar_map
type condition = Environ.env -> evar_map -> Evar.Set.t -> bool
type tc_solver = solver * condition
let class_solvers = ref (CString.Map.empty : tc_solver CString.Map.t)
let register_solver ~name ?(override=false) h = ifnot override && CString.Map.mem name !class_solvers then
CErrors.anomaly ~label:"Class_tactics.register_solver"
Pp.(str (Printf.sprintf {|Solver "%s" is already registered|} name));
class_solvers := CString.Map.add name h !class_solvers
let active_solvers = Summary.ref ~name:"typeclass_solvers" ([] : stringlist)
let deactivate_solver ~name =
active_solvers := List.filter (fun s -> not (String.equal s name)) !active_solvers
let activate_solver ~name =
assert (CString.Map.mem name !class_solvers);
deactivate_solver ~name;
active_solvers := name :: !active_solvers
let find_solver env evd (s : Intpart.set) = let rec find_solver = function
| [] -> Search.typeclasses_resolve
| hd :: tl -> try let (solver,cond) = CString.Map.find hd !class_solvers in if cond env evd s then solver else find_solver tl with Not_found -> find_solver tl in
find_solver !active_solvers
(** If [do_split] is [true], we try to separate the problem in
several components and then solve them separately *) let resolve_all_evars depth unique env p oevd fail = let () =
ppdebug 0 (fun () ->
str"Calling typeclass resolution with flags: "++
str"depth = " ++ (match depth with None -> str "∞" | Some d -> int d) ++ str"," ++
str"unique = " ++ bool unique ++ str"," ++
str"fail = " ++ bool fail);
ppdebug 2 (fun () ->
str"Initial evar map: " ++
Termops.pr_evar_map ~with_univs:!Detyping.print_universes None env oevd) in let split = split_evars p env oevd in let in_comp comp ev = Evar.Set.mem ev comp in let rec docomp evd = function
| [] -> let () = ppdebug 2 (fun () ->
str"Final evar map: " ++
Termops.pr_evar_map ~with_univs:!Detyping.print_universes None env evd) in
evd
| comp :: comps -> let p = select_and_update_evars p oevd (in_comp comp) in try
(try (* evars_to_goals p evd gives none when there's no evar having p *) match evars_to_goals p evd with
| Some (goals, nongoals) -> let solver = find_solver env evd comp in let evd, sorted_goals = Search.preprocess_goals evd goals in let finished, evd = solver.solver env evd ~goals:sorted_goals ~best_effort:true ~depth ~unique in let evd = Search.post_process_goals ~goals ~nongoals ~sigma:evd ~finished in if has_undefined p oevd evd then let () = if finished then ppdebug 1 (fun () ->
str"Proof is finished but there remain undefined evars: " ++
prlist_with_sep spc (pr_ev evd)
(Evar.Set.elements (find_undefined p oevd evd))) in raise (Unresolved evd) else docomp evd comps
| None -> docomp evd comps (* No typeclass evars left in this component *) with Not_found -> (* Typeclass resolution failed *) raise (Unresolved evd)) with Unresolved evd' -> if fail && is_mandatory (p evd') comp evd' then(* Unable to satisfy the constraints. *)
error_unresolvable env evd' comp else(* Best effort: use the best found solution on this component *)
docomp evd' comps in docomp oevd split
let initial_select_evars filter = fun evd ev evi -> filter ev (Lazy.from_val (snd (Evd.evar_source evi))) && (* Typeclass evars can contain evars whose conclusion is not
yet determined to be a class or not. *)
Typeclasses.is_class_evar evd evi
let classes_transparent_state () = try Hint_db.transparent_state (searchtable_map typeclasses_db) with Not_found -> TransparentState.empty
let resolve_typeclass_evars depth unique env evd filter fail = let evd = try Evarconv.solve_unif_constraints_with_heuristics
~flags:(Evarconv.default_flags_of (classes_transparent_state())) env evd with e when CErrors.noncritical e -> evd in
resolve_all_evars depth unique env
(initial_select_evars filter) evd fail
let () =
Typeclasses.set_solve_all_instances solve_inst
let resolve_one_typeclass env sigma concl = let (term, sigma) = Hints.wrap_hint_warning_fun env sigma beginfun sigma -> let hints = searchtable_map typeclasses_db in let st = Hint_db.transparent_state hints in let modes = Hint_db.modes hints in let depth = get_typeclasses_depth () in let tac = Tacticals.tclCOMPLETE (Search.eauto_tac (modes,st)
~only_classes:true ~best_effort:false
~depth [hints] ~dep:true) in let entry, pv = Proofview.init sigma [env, concl] in let pv = let name = Names.Id.of_string "legacy_pe"in match Proofview.apply ~name ~poly:false (Global.env ()) tac pv with
| (_, final, _, _, _) -> final
| exception (Logic_monad.TacticFailure (Tacticals.FailError _)) -> raise Not_found in let evd = Proofview.return pv in let term = match Proofview.partial_proof entry pv with [t] -> t | _ -> assert falsein
term, evd endin
(sigma, term)
let () = (Typeclasses.set_solve_one_instance[@warning "-3"]) resolve_one_typeclass
(** Take the head of the arity of a constr.
Used in the partial application tactic. *)
let rec head_of_constr sigma t = let t = strip_outer_cast sigma t in match EConstr.kind sigma t with
| Prod (_,_,c2) -> head_of_constr sigma c2
| LetIn (_,_,_,c2) -> head_of_constr sigma c2
| App (f,args) -> head_of_constr sigma f
| _ -> t
let head_of_constr h c =
Proofview.tclEVARMAP >>= fun sigma -> let c = head_of_constr sigma c in
letin_tac None (Name h) c None Locusops.allHyps
let not_evar c =
Proofview.tclEVARMAP >>= fun sigma -> match EConstr.kind sigma c with
| Evar _ -> Tacticals.tclFAIL (str"Evar")
| _ -> Proofview.tclUNIT ()
let is_ground c = letopen Tacticals in
Proofview.tclEVARMAP >>= fun sigma -> if Evarutil.is_ground_term sigma c then tclIDTAC else tclFAIL (str"Not ground")
let autoapply c i = letopen Proofview.Notations in
Hints.wrap_hint_warning @@
Proofview.Goal.enter beginfun gl -> let hintdb = try Hints.searchtable_map i with Not_found ->
CErrors.user_err (Pp.str ("Unknown hint database " ^ i ^ ".")) in let flags = auto_unif_flags
(Hints.Hint_db.transparent_state hintdb) in let cty = Tacmach.pf_get_type_of gl c in let env = Proofview.Goal.env gl in let sigma = Proofview.Goal.sigma gl in let ce = Clenv.mk_clenv_from env sigma (c,cty) in
Clenv.res_pf ~with_evars:true ~with_classes:false ~flags ce <*>
Proofview.tclEVARMAP >>= (fun sigma -> let sigma = Typeclasses.make_unresolvables
(fun ev -> Typeclasses.all_goals ev (Lazy.from_val (snd (Evd.evar_source (Evd.find_undefined sigma ev))))) sigma in
Proofview.Unsafe.tclEVARS sigma) end
let resolve_tc c = letopen Proofview.Notations in
Proofview.tclENV >>= fun env ->
Proofview.tclEVARMAP >>= fun sigma -> let depth = get_typeclasses_depth () in let unique = get_typeclasses_unique_solutions () in let evars = Evarutil.undefined_evars_of_term sigma c in letfilter = (fun ev _ -> Evar.Set.mem ev evars) in let fail = truein let sigma = resolve_all_evars depth unique env (initial_select_evars filter) sigma fail in
Proofview.Unsafe.tclEVARS sigma
¤ Dauer der Verarbeitung: 0.26 Sekunden
(vorverarbeitet)
¤
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
