Source file class_tactics.ml
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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 { Goptions.get = get_typeclasses_dependency_order } =
Goptions.declare_bool_option_and_ref
~key:["Typeclasses";"Dependency";"Order"]
~value:false
()
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 then true else false
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 () =
let open Goptions in
declare_bool_option
{ optstage = Summary.Stage.Interp;
optdepr = None;
optkey = ["Typeclasses";"Debug"];
optread = get_typeclasses_debug;
optwrite = set_typeclasses_debug; }
let () =
let open Goptions in
declare_int_option
{ optstage = Summary.Stage.Interp;
optdepr = None;
optkey = ["Typeclasses";"Debug";"Verbosity"];
optread = get_typeclasses_verbose;
optwrite = set_typeclasses_verbose; }
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
(** Typeclasses instance search tactic / eauto *)
open Auto
open Unification
let auto_core_unif_flags st allowed_evars = {
modulo_conv_on_closed_terms = Some st;
use_metas_eagerly_in_conv_on_closed_terms = true;
use_evars_eagerly_in_conv_on_closed_terms = false;
modulo_delta = st;
modulo_delta_types = st;
check_applied_meta_types = false;
use_pattern_unification = true;
use_meta_bound_pattern_unification = true;
allowed_evars;
restrict_conv_on_strict_subterms = false;
modulo_betaiota = true;
modulo_eta = false;
}
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 =
let open Tacmach in
Proofview.Goal.enter begin fun 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 begin fun 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 begin fun gl ->
if Option.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
begin fun 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 =
let open 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 only_classes db_list local_db secvars =
let open Tacticals in
let open Tacmach in
let trivial_fail =
Proofview.Goal.enter
begin fun 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 only_classes db_list hints secvars
end
in
let trivial_resolve =
Proofview.Goal.enter
begin fun gl ->
let tacs = e_trivial_resolve db_list local_db secvars only_classes
(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 only_classes env sigma concl0 =
let prods, concl = EConstr.decompose_prod_decls sigma concl0 in
let nprods = List.length prods in
let allowed_evars =
let all = Evarsolve.AllowedEvars.all in
match hdc with
| Some (hd,_) when only_classes ->
begin match 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
else all
| 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 only_classes 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
if List.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
| [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 only_classes 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 only_classes env sigma concl with
| Some (_,l) -> l
| None -> [])
with Not_found -> []
let e_possible_resolve db_list local_db secvars only_classes 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 only_classes 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 ->
begin match 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
while not (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 = Evarutil.nf_evar sigma (NamedDecl.get_type decl) in
let iscl env ty =
let ctx, ar = decompose_prod_decls sigma ty 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 is_class = iscl env cty 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 true in
List.fold_right
(fun hyp hints ->
let consider =
not only_classes ||
try let t = hyp |> NamedDecl.get_id |> Global.lookup_named |> NamedDecl.get_type in
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
module Intpart = Unionfind.Make(Evar.Set)(Evar.Map)
type solver = { solver :
Environ.env ->
Evd.evar_map ->
depth:int option ->
unique:bool ->
best_effort:bool ->
goals:Evar.t list ->
(bool * Evd.evar_map)
}
module Search = struct
type autoinfo =
{ search_depth : int list;
last_tac : Pp.t Lazy.t;
search_dep : bool;
search_only_classes : bool;
search_cut : hints_path;
search_hints : hint_db;
search_best_effort : bool;
}
(** Local hints *)
let autogoal_cache = Summary.ref ~name:"autogoal_cache"
(DirPath.empty, true, Context.Named.empty, GlobRef.Map.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 DirPath.equal 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 then false else
if indep || is_Prop env evd concl then
occur_existential evd concl
else true
exception NonStuckFailure
let pr_goals s =
let open 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
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 =
let open Pp in
let open Proofview in
let open 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 <*>
fixpoint progress tacs ((glid, ev, status, tac) :: stuck) fk
| 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
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
| [] ->
match stuck with
| [] ->
tclOR (tclUNIT ()) fk
| stuck ->
if progress then fixpoint false stuck [] fk
else
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
if best_effort then
let stuckgls, failedgls = List.partition (fun (_, _, status, _) ->
match status with
| IsStuckGoal -> true
| IsNonStuckFailure -> false
| IsInitial -> assert false)
stuck
in
pr_goals (str "best_effort is on and remaining goals are: ") <*>
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 ->
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 =
let open Proofview in
let open 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
info.search_only_classes env sigma concl with
| None ->
Proofview.tclZERO StuckGoal
| Some (all_mode_match, poss) ->
let ortac = if backtrack then Proofview.tclOR else Proofview.tclORELSE in
let idx = ref 1 in
let foundone = ref false in
let rec onetac e (tac, pat, b, name, pp) tl =
let derivs = path_derivate 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 =
pr_depth (idx :: info.search_depth) ++ str": " ++
Lazy.force pp ++
(if !foundone != true then
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 begin fun 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 =
let filter 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
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 () = if not (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 <*>
if List.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 == false then
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 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 =
let open 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 =
let open 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 =
let open Proofview in
let tac sigma gls i =
Goal.enter
begin fun 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 =
let open 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 =
let open 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" ++
(if Option.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 eauto_tac mst ?unique ~only_classes ~best_effort ?strategy ~depth ~dep hints =
Hints.wrap_hint_warning @@
eauto_tac_stuck mst ?unique ~only_classes
~best_effort ?strategy ~depth ~dep hints
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, Evd.meta_list 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
let name, poly =
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 ~old_metas ~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.meta_merge old_metas (Evd.clear_metas sigma) 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 = true in
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 (GlobRef.Map.union (fun _ m1 m2 -> Some (m1@m2))) GlobRef.Map.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)
(** 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 evm =
let p = Intpart.create () in
evar_dependencies pred evm p;
deps_of_constraints (snd (extract_all_conv_pbs evm)) evm p;
Intpart.partition p
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
else true
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))
else false
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 =
if not 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" ([] : string list)
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 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
match evars_to_goals p evd with
| Some (goals, nongoals) ->
let solver = find_solver env evd comp in
let evd, old_metas, 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 ~old_metas ~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
with Not_found ->
raise (Unresolved evd))
with Unresolved evd' ->
if fail && is_mandatory (p evd') comp evd'
then
error_unresolvable env evd' comp
else
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))) &&
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 solve_inst env evd filter unique fail =
let ((), sigma) = Hints.wrap_hint_warning_fun env evd begin fun evd ->
(), resolve_typeclass_evars
(get_typeclasses_depth ())
unique env evd filter fail
end in
sigma
let () =
Typeclasses.set_solve_all_instances solve_inst
let resolve_one_typeclass env ?(sigma=Evd.from_env env) concl unique =
let (term, sigma) = Hints.wrap_hint_warning_fun env sigma begin fun 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 false in
term, evd
end in
(sigma, term)
let () =
Typeclasses.set_solve_one_instance
(fun x y z w -> resolve_one_typeclass x ~sigma:y z w)
(** 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 =
let open Tacticals in
Proofview.tclEVARMAP >>= fun sigma ->
if Evarutil.is_ground_term sigma c then tclIDTAC
else tclFAIL (str"Not ground")
let autoapply c i =
let open Proofview.Notations in
Hints.wrap_hint_warning @@
Proofview.Goal.enter begin fun 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 =
let open 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
let filter = (fun ev _ -> Evar.Set.mem ev evars) in
let fail = true in
let sigma = resolve_all_evars depth unique env (initial_select_evars filter) sigma fail in
Proofview.Unsafe.tclEVARS sigma