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|
open Printf
open Pp
open Subtac_utils
open Command
open Term
open Names
open Libnames
open Summary
open Libobject
open Entries
open Decl_kinds
open Util
open Evd
type definition_hook = constant -> unit
let pperror cmd = Util.errorlabstrm "Program" cmd
let error s = pperror (str s)
exception NoObligations of identifier option
let explain_no_obligations = function
Some ident -> str "No obligations for program " ++ str (string_of_id ident)
| None -> str "No obligations remaining"
type obligation_info = (Names.identifier * Term.types * bool * Intset.t) array
type obligation =
{ obl_name : identifier;
obl_type : types;
obl_body : constr option;
obl_opaque : bool;
obl_deps : Intset.t;
}
type obligations = (obligation array * int)
type notations = (string * Topconstr.constr_expr * Topconstr.scope_name option) list
type program_info = {
prg_name: identifier;
prg_body: constr;
prg_type: constr;
prg_obligations: obligations;
prg_deps : identifier list;
prg_fixkind : Command.fixpoint_kind option ;
prg_implicits : (Topconstr.explicitation * (bool * bool)) list;
prg_notations : notations ;
prg_kind : definition_object_kind;
prg_hook : definition_hook;
}
let assumption_message id =
Flags.if_verbose message ((string_of_id id) ^ " is assumed")
let default_tactic : Proof_type.tactic ref = ref Refiner.tclIDTAC
let default_tactic_expr : Tacexpr.glob_tactic_expr ref = ref (Obj.magic ())
let set_default_tactic t = default_tactic_expr := t; default_tactic := Tacinterp.eval_tactic t
let evar_of_obligation o = make_evar (Global.named_context_val ()) o.obl_type
let subst_deps obls deps t =
Intset.fold
(fun x acc ->
let xobl = obls.(x) in
debug 3 (str "Trying to get body of obligation " ++ int x);
let oblb =
try Option.get xobl.obl_body
with _ ->
debug 3 (str "Couldn't get body of obligation " ++ int x);
assert(false)
in
Term.subst1 oblb (Term.subst_var xobl.obl_name acc))
deps t
let subst_deps_obl obls obl =
let t' = subst_deps obls obl.obl_deps obl.obl_type in
{ obl with obl_type = t' }
module ProgMap = Map.Make(struct type t = identifier let compare = compare end)
let map_replace k v m = ProgMap.add k v (ProgMap.remove k m)
let map_cardinal m =
let i = ref 0 in
ProgMap.iter (fun _ _ -> incr i) m;
!i
exception Found of program_info
let map_first m =
try
ProgMap.iter (fun _ v -> raise (Found v)) m;
assert(false)
with Found x -> x
let from_prg : program_info ProgMap.t ref = ref ProgMap.empty
let freeze () = !from_prg, !default_tactic_expr
let unfreeze (v, t) = from_prg := v; set_default_tactic t
let init () =
from_prg := ProgMap.empty; set_default_tactic (Subtac_utils.tactics_call "obligations_tactic" [])
let _ =
Summary.declare_summary "program-tcc-table"
{ Summary.freeze_function = freeze;
Summary.unfreeze_function = unfreeze;
Summary.init_function = init;
Summary.survive_module = false;
Summary.survive_section = false }
let progmap_union = ProgMap.fold ProgMap.add
let cache (_, (infos, tac)) =
from_prg := infos;
set_default_tactic tac
let (input,output) =
declare_object
{ (default_object "Program state") with
cache_function = cache;
load_function = (fun _ -> cache);
open_function = (fun _ -> cache);
classify_function = (fun _ -> Dispose);
export_function = (fun x -> Some x) }
open Evd
let rec intset_to = function
-1 -> Intset.empty
| n -> Intset.add n (intset_to (pred n))
let subst_body prg =
let obls, _ = prg.prg_obligations in
let ints = intset_to (pred (Array.length obls)) in
subst_deps obls ints prg.prg_body,
subst_deps obls ints (Termops.refresh_universes prg.prg_type)
let declare_definition prg =
let body, typ = subst_body prg in
(try trace (str "Declaring: " ++ Ppconstr.pr_id prg.prg_name ++ spc () ++
my_print_constr (Global.env()) body ++ str " : " ++
my_print_constr (Global.env()) prg.prg_type);
with _ -> ());
let ce =
{ const_entry_body = body;
const_entry_type = Some typ;
const_entry_opaque = false;
const_entry_boxed = false}
in
let c = Declare.declare_constant
prg.prg_name (DefinitionEntry ce,IsDefinition prg.prg_kind)
in
let gr = ConstRef c in
if Impargs.is_implicit_args () || prg.prg_implicits <> [] then
Impargs.declare_manual_implicits false gr (Impargs.is_implicit_args ()) prg.prg_implicits;
print_message (Subtac_utils.definition_message c);
prg.prg_hook c;
c
open Pp
open Ppconstr
let compute_possible_guardness_evidences (n,_) fixtype =
match n with
| Some n -> [n]
| None ->
(* If recursive argument was not given by user, we try all args.
An earlier approach was to look only for inductive arguments,
but doing it properly involves delta-reduction, and it finally
doesn't seem to worth the effort (except for huge mutual
fixpoints ?) *)
let m = Term.nb_prod fixtype in
let ctx = fst (Sign.decompose_prod_n_assum m fixtype) in
list_map_i (fun i _ -> i) 0 ctx
let declare_mutual_definition l =
let len = List.length l in
let fixdefs, fixtypes, fiximps =
list_split3
(List.map (fun x ->
let subs, typ = (subst_body x) in
snd (decompose_lam_n len subs), snd (decompose_prod_n len typ), x.prg_implicits) l)
in
let fixkind = Option.get (List.hd l).prg_fixkind in
let arrrec, recvec = Array.of_list fixtypes, Array.of_list fixdefs in
let fixdecls = (Array.of_list (List.map (fun x -> Name x.prg_name) l), arrrec, recvec) in
let boxed = true (* TODO *) in
let fixnames = (List.hd l).prg_deps in
let kind = if fixkind <> IsCoFixpoint then Fixpoint else CoFixpoint in
let indexes, fixdecls =
match fixkind with
| IsFixpoint wfl ->
let possible_indexes =
List.map2 compute_possible_guardness_evidences wfl fixtypes in
let indexes = Pretyping.search_guard dummy_loc (Global.env ()) possible_indexes fixdecls in
Some indexes, list_map_i (fun i _ -> mkFix ((indexes,i),fixdecls)) 0 l
| IsCoFixpoint ->
None, list_map_i (fun i _ -> mkCoFix (i,fixdecls)) 0 l
in
(* Declare the recursive definitions *)
let kns = list_map4 (declare_fix boxed kind) fixnames fixdecls fixtypes fiximps in
(* Declare notations *)
List.iter (Command.declare_interning_data ([],[])) (List.hd l).prg_notations;
Flags.if_verbose ppnl (Command.recursive_message kind indexes fixnames);
(match List.hd kns with ConstRef kn -> kn | _ -> assert false)
let declare_obligation obl body =
let ce =
{ const_entry_body = body;
const_entry_type = Some obl.obl_type;
const_entry_opaque = obl.obl_opaque;
const_entry_boxed = false}
in
let constant = Declare.declare_constant obl.obl_name
(DefinitionEntry ce,IsProof Property)
in
print_message (Subtac_utils.definition_message constant);
{ obl with obl_body = Some (mkConst constant) }
let try_tactics obls =
Array.map
(fun obl ->
match obl.obl_body with
None ->
(try
let ev = evar_of_obligation obl in
let c = Subtac_utils.solve_by_tac ev Auto.default_full_auto in
declare_obligation obl c
with _ -> obl)
| _ -> obl)
obls
let red = Reductionops.nf_betaiota
let init_prog_info n b t deps fixkind notations obls impls kind hook =
let obls' =
Array.mapi
(fun i (n, t, o, d) ->
debug 2 (str "Adding obligation " ++ int i ++ str " with deps : " ++ str (string_of_intset d));
{ obl_name = n ; obl_body = None;
obl_type = red t; obl_opaque = o;
obl_deps = d })
obls
in
{ prg_name = n ; prg_body = b; prg_type = red t; prg_obligations = (obls', Array.length obls');
prg_deps = deps; prg_fixkind = fixkind ; prg_notations = notations ;
prg_implicits = impls; prg_kind = kind; prg_hook = hook; }
let get_prog name =
let prg_infos = !from_prg in
match name with
Some n ->
(try ProgMap.find n prg_infos
with Not_found -> raise (NoObligations (Some n)))
| None ->
(let n = map_cardinal prg_infos in
match n with
0 -> raise (NoObligations None)
| 1 -> map_first prg_infos
| _ -> error "More than one program with unsolved obligations")
let get_prog_err n =
try get_prog n with NoObligations id -> pperror (explain_no_obligations id)
let obligations_solved prg = (snd prg.prg_obligations) = 0
let update_state s =
(* msgnl (str "Updating obligations info"); *)
Lib.add_anonymous_leaf (input s)
type progress =
| Remain of int
| Dependent
| Defined of constant
let obligations_message rem =
if rem > 0 then
if rem = 1 then
Flags.if_verbose msgnl (int rem ++ str " obligation remaining")
else
Flags.if_verbose msgnl (int rem ++ str " obligations remaining")
else
Flags.if_verbose msgnl (str "No more obligations remaining")
let update_obls prg obls rem =
let prg' = { prg with prg_obligations = (obls, rem) } in
from_prg := map_replace prg.prg_name prg' !from_prg;
obligations_message rem;
let res =
if rem > 0 then Remain rem
else (
match prg'.prg_deps with
[] ->
let kn = declare_definition prg' in
from_prg := ProgMap.remove prg.prg_name !from_prg;
Defined kn
| l ->
let progs = List.map (fun x -> ProgMap.find x !from_prg) prg'.prg_deps in
if List.for_all (fun x -> obligations_solved x) progs then
(let kn = declare_mutual_definition progs in
from_prg := List.fold_left
(fun acc x ->
ProgMap.remove x.prg_name acc) !from_prg progs;
Defined kn)
else Dependent);
in
update_state (!from_prg, !default_tactic_expr);
res
let is_defined obls x = obls.(x).obl_body <> None
let deps_remaining obls deps =
Intset.fold
(fun x acc ->
if is_defined obls x then acc
else x :: acc)
deps []
let kind_of_opacity o =
if o then Subtac_utils.goal_proof_kind
else Subtac_utils.goal_kind
let obligations_of_evars evars =
let arr =
Array.of_list
(List.map
(fun (n, t) ->
{ obl_name = n;
obl_type = t;
obl_body = None;
obl_opaque = false;
obl_deps = Intset.empty;
}) evars)
in arr, Array.length arr
let rec solve_obligation prg num =
let user_num = succ num in
let obls, rem = prg.prg_obligations in
let obl = obls.(num) in
if obl.obl_body <> None then
pperror (str "Obligation" ++ spc () ++ int user_num ++ str "already" ++ spc() ++ str "solved.")
else
match deps_remaining obls obl.obl_deps with
[] ->
let obl = subst_deps_obl obls obl in
Command.start_proof obl.obl_name (kind_of_opacity obl.obl_opaque) obl.obl_type
(fun strength gr ->
debug 2 (str "Proof of obligation " ++ int user_num ++ str " finished");
let obl = { obl with obl_body = Some (Libnames.constr_of_global gr) } in
let obls = Array.copy obls in
let _ = obls.(num) <- obl in
match update_obls prg obls (pred rem) with
Remain n when n > 0 ->
ignore(auto_solve_obligations (Some prg.prg_name))
| _ -> ());
trace (str "Started obligation " ++ int user_num ++ str " proof: " ++
Subtac_utils.my_print_constr (Global.env ()) obl.obl_type);
Pfedit.by !default_tactic;
Flags.if_verbose (fun () -> msg (Printer.pr_open_subgoals ())) ()
| l -> pperror (str "Obligation " ++ int user_num ++ str " depends on obligation(s) "
++ str (string_of_list ", " (fun x -> string_of_int (succ x)) l))
and subtac_obligation (user_num, name, typ) =
let num = pred user_num in
let prg = get_prog_err name in
let obls, rem = prg.prg_obligations in
if num < Array.length obls then
let obl = obls.(num) in
match obl.obl_body with
None -> solve_obligation prg num
| Some r -> error "Obligation already solved"
else error (sprintf "Unknown obligation number %i" (succ num))
and solve_obligation_by_tac prg obls i tac =
let obl = obls.(i) in
match obl.obl_body with
Some _ -> false
| None ->
(try
if deps_remaining obls obl.obl_deps = [] then
let obl = subst_deps_obl obls obl in
let t = Subtac_utils.solve_by_tac (evar_of_obligation obl) tac in
if obl.obl_opaque then
obls.(i) <- declare_obligation obl t
else
obls.(i) <- { obl with obl_body = Some t };
true
else false
with _ -> false)
and solve_prg_obligations prg tac =
let obls, rem = prg.prg_obligations in
let rem = ref rem in
let obls' = Array.copy obls in
let _ =
Array.iteri (fun i x ->
if solve_obligation_by_tac prg obls' i tac then
decr rem)
obls'
in
update_obls prg obls' !rem
and solve_obligations n tac =
let prg = get_prog_err n in
solve_prg_obligations prg tac
and solve_all_obligations tac =
ProgMap.iter (fun k v -> ignore(solve_prg_obligations v tac)) !from_prg
and try_solve_obligation n prg tac =
let prg = get_prog prg in
let obls, rem = prg.prg_obligations in
let obls' = Array.copy obls in
if solve_obligation_by_tac prg obls' n tac then
ignore(update_obls prg obls' (pred rem));
and try_solve_obligations n tac =
try ignore (solve_obligations n tac) with NoObligations _ -> ()
and auto_solve_obligations n : progress =
Flags.if_verbose msgnl (str "Solving obligations automatically...");
try solve_obligations n !default_tactic with NoObligations _ -> Dependent
open Pp
let show_obligations ?(msg=true) n =
let prg = get_prog_err n in
let n = prg.prg_name in
let obls, rem = prg.prg_obligations in
if msg then msgnl (int rem ++ str " obligation(s) remaining: ");
Array.iteri (fun i x ->
match x.obl_body with
None -> msgnl (str "Obligation" ++ spc() ++ int (succ i) ++ spc () ++ str "of" ++ spc() ++ str (string_of_id n) ++ str ":" ++ spc () ++
my_print_constr (Global.env ()) x.obl_type ++ str "." ++ fnl ())
| Some _ -> ())
obls
let show_term n =
let prg = get_prog_err n in
let n = prg.prg_name in
msgnl (str (string_of_id n) ++ spc () ++ str":" ++ spc () ++ my_print_constr (Global.env ()) prg.prg_type ++ spc () ++ str ":=" ++ fnl ()
++ my_print_constr (Global.env ()) prg.prg_body)
let add_definition n b t ?(implicits=[]) ?(kind=Definition) ?(hook=fun x -> ()) obls =
Flags.if_verbose pp (str (string_of_id n) ++ str " has type-checked");
let prg = init_prog_info n b t [] None [] obls implicits kind hook in
let obls,_ = prg.prg_obligations in
if Array.length obls = 0 then (
Flags.if_verbose ppnl (str ".");
let cst = declare_definition prg in
from_prg := ProgMap.remove prg.prg_name !from_prg;
Defined cst)
else (
let len = Array.length obls in
let _ = Flags.if_verbose ppnl (str ", generating " ++ int len ++ str " obligation(s)") in
from_prg := ProgMap.add n prg !from_prg;
let res = auto_solve_obligations (Some n) in
match res with
| Remain rem when rem < 5 -> Flags.if_verbose (fun () -> show_obligations ~msg:false (Some n)) (); res
| _ -> res)
let add_mutual_definitions l ?(kind=Definition) notations fixkind =
let deps = List.map (fun (n, b, t, imps, obls) -> n) l in
let upd = List.fold_left
(fun acc (n, b, t, imps, obls) ->
let prg = init_prog_info n b t deps (Some fixkind) notations obls imps kind (fun x -> ()) in
ProgMap.add n prg acc)
!from_prg l
in
from_prg := upd;
let _defined =
List.fold_left (fun finished x ->
if finished then finished
else
match auto_solve_obligations (Some x) with
Defined _ -> (* If one definition is turned into a constant, the whole block is defined. *) true
| _ -> false)
false deps
in ()
let admit_obligations n =
let prg = get_prog_err n in
let obls, rem = prg.prg_obligations in
Array.iteri (fun i x ->
match x.obl_body with
None ->
let x = subst_deps_obl obls x in
let kn = Declare.declare_constant x.obl_name (ParameterEntry (x.obl_type,false), IsAssumption Conjectural) in
assumption_message x.obl_name;
obls.(i) <- { x with obl_body = Some (mkConst kn) }
| Some _ -> ())
obls;
ignore(update_obls prg obls 0)
exception Found of int
let array_find f arr =
try Array.iteri (fun i x -> if f x then raise (Found i)) arr;
raise Not_found
with Found i -> i
let next_obligation n =
let prg = get_prog_err n in
let obls, rem = prg.prg_obligations in
let i =
array_find (fun x -> x.obl_body = None && deps_remaining obls x.obl_deps = [])
obls
in solve_obligation prg i
let default_tactic () = !default_tactic
|