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|
(* -*- compile-command: "make -C .. bin/coqtop.byte" -*- *)
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i camlp4deps: "parsing/grammar.cma" i*)
(* $Id$ *)
open Pp
open Util
open Names
open Nameops
open Term
open Termops
open Sign
open Reduction
open Proof_type
open Proof_trees
open Declarations
open Tacticals
open Tacmach
open Evar_refiner
open Tactics
open Pattern
open Clenv
open Auto
open Rawterm
open Hiddentac
open Typeclasses
open Typeclasses_errors
open Classes
open Topconstr
open Pfedit
open Command
open Libnames
open Evd
let default_eauto_depth = 100
let typeclasses_db = "typeclass_instances"
let _ = Auto.auto_init := (fun () ->
Auto.create_hint_db false typeclasses_db full_transparent_state true)
exception Found of evar_map
let is_dependent ev evm =
Evd.fold (fun ev' evi dep ->
if ev = ev' then dep
else dep || occur_evar ev evi.evar_concl)
evm false
let valid goals p res_sigma l =
let evm =
List.fold_left2
(fun sigma (ev, evi) prf ->
let cstr, obls = Refiner.extract_open_proof !res_sigma prf in
if not (Evd.is_defined sigma ev) then
Evd.define ev cstr sigma
else sigma)
!res_sigma goals l
in raise (Found evm)
let evars_to_goals p evm =
let goals, evm' =
Evd.fold
(fun ev evi (gls, evm') ->
if evi.evar_body = Evar_empty
&& Typeclasses.is_resolvable evi
(* && not (is_dependent ev evm) *)
&& p ev evi then ((ev,evi) :: gls, Evd.add evm' ev (Typeclasses.mark_unresolvable evi)) else
(gls, Evd.add evm' ev evi))
evm ([], Evd.empty)
in
if goals = [] then None
else
let goals = List.rev goals in
Some (goals, evm')
(** Typeclasses instance search tactic / eauto *)
let intersects s t =
Intset.exists (fun el -> Intset.mem el t) s
open Auto
let e_give_exact flags c gl =
let t1 = (pf_type_of gl c) and t2 = pf_concl gl in
if occur_existential t1 or occur_existential t2 then
tclTHEN (Clenvtac.unify ~flags t1) (exact_no_check c) gl
else exact_check c gl
(* let t1 = (pf_type_of gl c) in *)
(* tclTHEN (Clenvtac.unify ~flags t1) (exact_no_check c) gl *)
let assumption flags id = e_give_exact flags (mkVar id)
open Unification
let auto_unif_flags = {
modulo_conv_on_closed_terms = Some full_transparent_state;
use_metas_eagerly = true;
modulo_delta = var_full_transparent_state;
resolve_evars = false;
use_evars_pattern_unification = true;
}
let rec eq_constr_mod_evars x y =
match kind_of_term x, kind_of_term y with
| Evar (e1, l1), Evar (e2, l2) when e1 <> e2 -> true
| _, _ -> compare_constr eq_constr_mod_evars x y
let progress_evars t gl =
let concl = pf_concl gl in
let check gl' =
let newconcl = pf_concl gl' in
if eq_constr_mod_evars concl newconcl
then tclFAIL 0 (str"No progress made (modulo evars)") gl'
else tclIDTAC gl'
in tclTHEN t check gl
TACTIC EXTEND progress_evars
[ "progress_evars" tactic(t) ] -> [ progress_evars (snd t) ]
END
let unify_e_resolve flags (c,clenv) gls =
let clenv' = connect_clenv gls clenv in
let clenv' = clenv_unique_resolver false ~flags clenv' gls in
Clenvtac.clenv_refine true ~with_classes:false clenv' gls
let unify_resolve flags (c,clenv) gls =
let clenv' = connect_clenv gls clenv in
let clenv' = clenv_unique_resolver false ~flags clenv' gls in
Clenvtac.clenv_refine false ~with_classes:false clenv' gls
(** Hack to properly solve dependent evars that are typeclasses *)
let flags_of_state st =
{auto_unif_flags with
modulo_conv_on_closed_terms = Some st; modulo_delta = st}
let rec e_trivial_fail_db db_list local_db goal =
let tacl =
Eauto.registered_e_assumption ::
(tclTHEN Tactics.intro
(function g'->
let d = pf_last_hyp g' in
let hintl = make_resolve_hyp (pf_env g') (project g') d in
(e_trivial_fail_db db_list
(Hint_db.add_list hintl local_db) g'))) ::
(List.map pi1 (e_trivial_resolve db_list local_db (pf_concl goal)) )
in
tclFIRST (List.map tclCOMPLETE tacl) goal
and e_my_find_search db_list local_db hdc concl =
let hdc = head_of_constr_reference hdc in
let hintl =
list_map_append
(fun db ->
if Hint_db.use_dn db then
let flags = flags_of_state (Hint_db.transparent_state db) in
List.map (fun x -> (flags, x)) (Hint_db.map_auto (hdc,concl) db)
else
let flags = flags_of_state (Hint_db.transparent_state db) in
List.map (fun x -> (flags, x)) (Hint_db.map_all hdc db))
(local_db::db_list)
in
let tac_of_hint =
fun (flags, {pri=b; pat = p; code=t}) ->
let tac =
match t with
| Res_pf (term,cl) -> unify_resolve flags (term,cl)
| ERes_pf (term,cl) -> unify_e_resolve flags (term,cl)
| Give_exact (c) -> e_give_exact flags c
| Res_pf_THEN_trivial_fail (term,cl) ->
tclTHEN (unify_e_resolve flags (term,cl))
(e_trivial_fail_db db_list local_db)
| Unfold_nth c -> unfold_in_concl [all_occurrences,c]
| Extern tacast -> conclPattern concl p tacast
in
(tac,b,pr_autotactic t)
in
List.map tac_of_hint hintl
and e_trivial_resolve db_list local_db gl =
try
e_my_find_search db_list local_db
(fst (head_constr_bound gl)) gl
with Bound | Not_found -> []
let e_possible_resolve db_list local_db gl =
try
e_my_find_search db_list local_db
(fst (head_constr_bound gl)) gl
with Bound | Not_found -> []
let rec catchable = function
| Refiner.FailError _ -> true
| Stdpp.Exc_located (_, e) -> catchable e
| e -> Logic.catchable_exception e
let is_dep gl gls =
let evs = Evarutil.evars_of_term gl.evar_concl in
if evs = Intset.empty then false
else
List.fold_left
(fun b gl ->
if b then b
else
let evs' = Evarutil.evars_of_term gl.evar_concl in
intersects evs evs')
false gls
let is_ground gl =
Evarutil.is_ground_term (project gl) (pf_concl gl)
let nb_empty_evars s =
Evd.fold (fun ev evi acc -> if evi.evar_body = Evar_empty then succ acc else acc) s 0
let pr_ev evs ev = Printer.pr_constr_env (Evd.evar_env ev) (Evarutil.nf_evar evs ev.Evd.evar_concl)
let typeclasses_debug = ref false
type validation = evar_map -> proof_tree list -> proof_tree
let pr_depth l = prlist_with_sep (fun () -> str ".") pr_int (List.rev l)
type autoinfo = { hints : Auto.hint_db; auto_depth: int list; auto_last_tac: std_ppcmds }
type autogoal = goal * autoinfo
type 'ans fk = unit -> 'ans
type ('a,'ans) sk = 'a -> 'ans fk -> 'ans
type 'a tac = { skft : 'ans. ('a,'ans) sk -> 'ans fk -> autogoal sigma -> 'ans }
type auto_result = autogoal list sigma * validation
type atac = auto_result tac
let lift_tactic tac (f : goal list sigma -> autoinfo -> autogoal list sigma) : 'a tac =
{ skft = fun sk fk {it = gl,hints; sigma=s} ->
let res = try Some (tac {it=gl; sigma=s}) with e when catchable e -> None in
match res with
| Some (gls,v) -> sk (f gls hints, fun _ -> v) fk
| None -> fk () }
let intro_tac : atac =
lift_tactic Tactics.intro
(fun {it = gls; sigma = s} info ->
let gls' =
List.map (fun g' ->
let env = evar_env g' in
let hint = make_resolve_hyp env s (List.hd (evar_context g')) in
let ldb = Hint_db.add_list hint info.hints in
(g', { info with hints = ldb; auto_last_tac = str"intro" })) gls
in {it = gls'; sigma = s})
let id_tac : atac =
{ skft = fun sk fk {it = gl; sigma = s} ->
sk ({it = [gl]; sigma = s}, fun _ pfs -> List.hd pfs) fk }
(* Ordering of states is lexicographic on the number of remaining goals. *)
let compare (pri, _, (res, _)) (pri', _, (res', _)) =
let nbgoals s =
List.length (sig_it s) + nb_empty_evars (sig_sig s)
in
let pri = pri - pri' in
if pri <> 0 then pri
else nbgoals res - nbgoals res'
let or_tac (x : 'a tac) (y : 'a tac) : 'a tac =
{ skft = fun sk fk gls -> x.skft sk (fun () -> y.skft sk fk gls) gls }
let solve_tac (x : 'a tac) : 'a tac =
{ skft = fun sk fk gls -> x.skft (fun ({it = gls},_ as res) fk -> if gls = [] then sk res fk else fk ()) fk gls }
let hints_tac hints =
{ skft = fun sk fk {it = gl,info; sigma = s} ->
(* if !typeclasses_debug then msgnl (str"depth=" ++ int info.auto_depth ++ str": " ++ info.auto_last_tac *)
(* ++ spc () ++ str "->" ++ spc () ++ pr_ev s gl); *)
let possible_resolve ((lgls,v) as res, pri, pp) =
(pri, pp, res)
in
let tacs =
let concl = Evarutil.nf_evar s gl.evar_concl in
let poss = e_possible_resolve hints info.hints concl in
let l =
Util.list_map_append (fun (tac, pri, pptac) ->
try [tac {it = gl; sigma = s}, pri, pptac] with e when catchable e -> [])
poss
in
if l = [] && !typeclasses_debug then
msgnl (pr_depth info.auto_depth ++ str": no match for " ++
Printer.pr_constr_env (Evd.evar_env gl) concl ++
spc () ++ int (List.length poss) ++ str" possibilities");
List.map possible_resolve l
in
let tacs = List.sort compare tacs in
let rec aux i = function
| (_, pp, ({it = gls; sigma = s}, v)) :: tl ->
if !typeclasses_debug then msgnl (pr_depth (i :: info.auto_depth) ++ str": " ++ pp
++ str" on" ++ spc () ++ pr_ev s gl);
let fk =
(fun () -> (* if !typeclasses_debug then msgnl (str"backtracked after " ++ pp); *)
aux (succ i) tl)
in
let glsv = {it = list_map_i (fun j g -> g,
{ info with auto_depth = j :: i :: info.auto_depth;
auto_last_tac = pp }) 1 gls; sigma = s}, fun _ -> v in
sk glsv fk
| [] -> fk ()
in aux 1 tacs }
let then_list (second : atac) (sk : (auto_result, 'a) sk) : (auto_result, 'a) sk =
let rec aux s (acc : (autogoal list * validation) list) fk = function
| (gl,info) :: gls ->
second.skft (fun ({it=gls';sigma=s'},v') fk' ->
let fk'' = if gls' = [] && Evarutil.is_ground_term s gl.evar_concl then
(if !typeclasses_debug then msgnl (str"no backtrack on" ++ pr_ev s gl); fk) else fk' in
aux s' ((gls',v')::acc) fk'' gls) fk {it = (gl,info); sigma = s}
| [] -> Some (List.rev acc, s, fk)
in fun ({it = gls; sigma = s},v) fk ->
let rec aux' = function
| None -> fk ()
| Some (res, s', fk') ->
let goals' = List.concat (List.map (fun (gls,v) -> gls) res) in
let v' s' pfs' : proof_tree =
let (newpfs, rest) = List.fold_left (fun (newpfs,pfs') (gls,v) ->
let before, after = list_split_at (List.length gls) pfs' in
(v s' before :: newpfs, after))
([], pfs') res
in assert(rest = []); v s' (List.rev newpfs)
in sk ({it = goals'; sigma = s'}, v') (fun () -> aux' (fk' ()))
in aux' (aux s [] (fun () -> None) gls)
let then_tac (first : atac) (second : atac) : atac =
{ skft = fun sk fk -> first.skft (then_list second sk) fk }
let run_tac (t : 'a tac) (gl : autogoal sigma) : auto_result option =
t.skft (fun x _ -> Some x) (fun _ -> None) gl
type run_list_res = (auto_result * run_list_res fk) option
let run_list_tac (t : 'a tac) p goals (gl : autogoal list sigma) : run_list_res =
(then_list t (fun x fk -> Some (x, fk)))
(gl, fun s pfs -> valid goals p (ref s) pfs)
(fun _ -> None)
let rec fix (t : 'a tac) : 'a tac =
then_tac t { skft = fun sk fk -> (fix t).skft sk fk }
(* A special one for getting everything into a dnet. *)
let is_transparent_gr (ids, csts) = function
| VarRef id -> Idpred.mem id ids
| ConstRef cst -> Cpred.mem cst csts
| IndRef _ | ConstructRef _ -> false
let make_resolve_hyp env sigma st flags pri (id, _, cty) =
let cty = Evarutil.nf_evar sigma cty in
let ctx, ar = decompose_prod cty in
let keep =
match kind_of_term (fst (decompose_app ar)) with
| Const c -> is_class (ConstRef c)
| Ind i -> is_class (IndRef i)
| _ -> false
in
if keep then let c = mkVar id in
map_succeed
(fun f -> f (c,cty))
[make_exact_entry pri; make_apply_entry env sigma flags pri]
else []
let make_autogoal ?(st=full_transparent_state) g =
let sign = pf_hyps g in
let hintlist = list_map_append (pf_apply make_resolve_hyp g st (true,false,false) None) sign in
let st = List.fold_left (fun (ids, csts) (n, b, t) ->
(if b <> None then Idpred.add else Idpred.remove) n ids, csts)
st sign
in
let hints = Hint_db.add_list hintlist (Hint_db.empty st true) in
(g.it, { hints = hints ; auto_depth = []; auto_last_tac = mt() })
let make_autogoals ?(st=full_transparent_state) gs evm' =
{ it = list_map_i (fun i g ->
let (gl, auto) = make_autogoal ~st {it = snd g; sigma = evm'} in
(gl, { auto with auto_depth = [i]})) 1 gs; sigma = evm' }
let get_result r =
match r with
| None -> None
| Some ((gls, v), fk) ->
try ignore(v (sig_sig gls) []); assert(false)
with Found evm' -> Some (evm', fk)
let run_on_evars ?(st=full_transparent_state) p evm tac =
match evars_to_goals p evm with
| None -> None (* This happens only because there's no evar having p *)
| Some (goals, evm') ->
let res = run_list_tac tac p goals (make_autogoals ~st goals evm') in
match get_result res with
| None -> raise Not_found
| Some (evm', fk) -> Some (Evd.evars_reset_evd evm' evm, fk)
let eauto_tac hints = fix (or_tac intro_tac (hints_tac hints))
let eauto hints g =
let gl = { it = make_autogoal ~st:(Hint_db.transparent_state (List.hd hints)) g; sigma = project g } in
match run_tac (eauto_tac hints) gl with
| None -> raise Not_found
| Some ({it = goals; sigma = s}, valid) ->
{it = List.map fst goals; sigma = s}, valid s
let real_eauto st hints p evd =
let rec aux evd fails =
let res, fails =
try run_on_evars ~st p evd (eauto_tac hints), fails
with Not_found ->
List.fold_right (fun fk (res, fails) ->
match res with
| Some r -> res, fk :: fails
| None -> get_result (fk ()), fails)
fails (None, [])
in
match res with
| None -> evd
| Some (evd', fk) -> aux evd' (fk :: fails)
in aux evd []
let resolve_all_evars_once debug (mode, depth) p evd =
let db = searchtable_map typeclasses_db in
real_eauto (Hint_db.transparent_state db) [db] p evd
exception FoundTerm of constr
let resolve_one_typeclass env ?(sigma=Evd.empty) gl =
let gls = { it = Evd.make_evar (Environ.named_context_val env) gl; sigma = sigma } in
let gls', v = eauto [searchtable_map typeclasses_db] gls in
let term = v [] in
let evd = sig_sig gls' in
let term = fst (Refiner.extract_open_proof evd term) in
let term = Evarutil.nf_evar evd term in
evd, term
let _ =
Typeclasses.solve_instanciation_problem := (fun x y z -> resolve_one_typeclass x ~sigma:y z)
let has_undefined p oevd evd =
Evd.fold (fun ev evi has -> has ||
(evi.evar_body = Evar_empty && p ev evi &&
(try Typeclasses.is_resolvable (Evd.find oevd ev) with _ -> true)))
evd false
let rec merge_deps deps = function
| [] -> [deps]
| hd :: tl ->
if intersects deps hd then
merge_deps (Intset.union deps hd) tl
else hd :: merge_deps deps tl
let evars_of_evi evi =
Intset.union (Evarutil.evars_of_term evi.evar_concl)
(match evi.evar_body with
| Evar_defined b -> Evarutil.evars_of_term b
| Evar_empty -> Intset.empty)
let split_evars evm =
Evd.fold (fun ev evi acc ->
let deps = Intset.union (Intset.singleton ev) (evars_of_evi evi) in
merge_deps deps acc)
evm []
let select_evars evs evm =
Evd.fold (fun ev evi acc ->
if Intset.mem ev evs then Evd.add acc ev evi else acc)
evm Evd.empty
let resolve_all_evars debug m env p oevd do_split fail =
let oevm = oevd in
let split = if do_split then split_evars oevd else [Intset.empty] in
let p = if do_split then
fun comp ev evi -> (Intset.mem ev comp || not (Evd.mem oevm ev)) && p ev evi
else fun _ -> p
in
let rec aux n p evd =
if has_undefined p oevm evd then
if n > 0 then
let evd' = resolve_all_evars_once debug m p evd in
aux (pred n) p evd'
else None
else Some evd
in
let rec docomp evd = function
| [] -> evd
| comp :: comps ->
let res = try aux 1 (p comp) evd with Not_found -> None in
match res with
| None ->
if fail then
let evd = Evarutil.nf_evars evd in
(* Unable to satisfy the constraints. *)
let evm = if do_split then select_evars comp evd else evd in
let _, ev = Evd.fold
(fun ev evi (b,acc) ->
(* focus on one instance if only one was searched for *)
if class_of_constr evi.evar_concl <> None then
if not b (* || do_split *) then
true, Some ev
else b, None
else b, acc) evm (false, None)
in
Typeclasses_errors.unsatisfiable_constraints (Evarutil.nf_env_evar evm env) evm ev
else (* Best effort: do nothing *) oevd
| Some evd' -> docomp evd' comps
in docomp oevd split
let resolve_typeclass_evars d p env evd onlyargs split fail =
let pred =
if onlyargs then
(fun ev evi -> Typeclasses.is_implicit_arg (snd (Evd.evar_source ev evd)) &&
Typeclasses.is_class_evar evd evi)
else (fun ev evi -> Typeclasses.is_class_evar evd evi)
in resolve_all_evars d p env pred evd split fail
let solve_inst debug mode depth env evd onlyargs split fail =
resolve_typeclass_evars debug (mode, depth) env evd onlyargs split fail
let _ =
Typeclasses.solve_instanciations_problem :=
solve_inst false true default_eauto_depth
VERNAC COMMAND EXTEND Typeclasses_Unfold_Settings
| [ "Typeclasses" "Transparent" reference_list(cl) ] -> [
add_hints false [typeclasses_db]
(interp_hints (Vernacexpr.HintsTransparency (cl, true)))
]
END
VERNAC COMMAND EXTEND Typeclasses_Rigid_Settings
| [ "Typeclasses" "Opaque" reference_list(cl) ] -> [
add_hints false [typeclasses_db]
(interp_hints (Vernacexpr.HintsTransparency (cl, false)))
]
END
open Genarg
open Extraargs
let pr_debug _prc _prlc _prt b =
if b then Pp.str "debug" else Pp.mt()
ARGUMENT EXTEND debug TYPED AS bool PRINTED BY pr_debug
| [ "debug" ] -> [ true ]
| [ ] -> [ false ]
END
let pr_mode _prc _prlc _prt m =
match m with
Some b ->
if b then Pp.str "depth-first" else Pp.str "breadth-fist"
| None -> Pp.mt()
ARGUMENT EXTEND search_mode TYPED AS bool option PRINTED BY pr_mode
| [ "dfs" ] -> [ Some true ]
| [ "bfs" ] -> [ Some false ]
| [] -> [ None ]
END
let pr_depth _prc _prlc _prt = function
Some i -> Util.pr_int i
| None -> Pp.mt()
ARGUMENT EXTEND depth TYPED AS int option PRINTED BY pr_depth
| [ int_or_var_opt(v) ] -> [ match v with Some (ArgArg i) -> Some i | _ -> None ]
END
VERNAC COMMAND EXTEND Typeclasses_Settings
| [ "Typeclasses" "eauto" ":=" debug(d) search_mode(s) depth(depth) ] -> [
typeclasses_debug := d;
let mode = match s with Some t -> t | None -> true in
let depth = match depth with Some i -> i | None -> default_eauto_depth in
Typeclasses.solve_instanciations_problem :=
solve_inst d mode depth
]
END
TACTIC EXTEND typeclasses_eauto
| [ "typeclasses" "eauto" ] -> [ fun gl ->
try eauto [Auto.searchtable_map typeclasses_db] gl
with Not_found -> tclFAIL 0 (str" typeclasses eauto failed") gl ]
END
let _ = Classes.refine_ref := Refine.refine
(** Take the head of the arity af constr. *)
let rec head_of_constr t =
let t = strip_outer_cast(collapse_appl t) in
match kind_of_term t with
| Prod (_,_,c2) -> head_of_constr c2
| LetIn (_,_,_,c2) -> head_of_constr c2
| App (f,args) -> head_of_constr f
| _ -> t
TACTIC EXTEND head_of_constr
[ "head_of_constr" ident(h) constr(c) ] -> [
let c = head_of_constr c in
letin_tac None (Name h) c None allHyps
]
END
(** A tactic to help reification based on classes:
factorize all variables of a particular type into a varmap. *)
let gen_constant dir s = Coqlib.gen_constant "typeclass_tactics" dir s
let coq_List_nth = lazy (gen_constant ["Lists"; "List"] "nth")
let coq_List_cons = lazy (gen_constant ["Lists"; "List"] "cons")
let coq_List_nil = lazy (gen_constant ["Lists"; "List"] "nil")
let freevars c =
let rec frec acc c = match kind_of_term c with
| Var id -> Idset.add id acc
| _ -> fold_constr frec acc c
in
frec Idset.empty c
let coq_zero = lazy (gen_constant ["Init"; "Datatypes"] "O")
let coq_succ = lazy (gen_constant ["Init"; "Datatypes"] "S")
let coq_nat = lazy (gen_constant ["Init"; "Datatypes"] "nat")
let rec coq_nat_of_int = function
| 0 -> Lazy.force coq_zero
| n -> mkApp (Lazy.force coq_succ, [| coq_nat_of_int (pred n) |])
let varify_constr_list ty def varh c =
let vars = Idset.elements (freevars c) in
let mkaccess i =
mkApp (Lazy.force coq_List_nth,
[| ty; coq_nat_of_int i; varh; def |])
in
let l = List.fold_right (fun id acc ->
mkApp (Lazy.force coq_List_cons, [| ty ; mkVar id; acc |]))
vars (mkApp (Lazy.force coq_List_nil, [| ty |]))
in
let subst =
list_map_i (fun i id -> (id, mkaccess i)) 0 vars
in
l, replace_vars subst c
let coq_varmap_empty = lazy (gen_constant ["quote"; "Quote"] "Empty_vm")
let coq_varmap_node = lazy (gen_constant ["quote"; "Quote"] "Node_vm")
let coq_varmap_lookup = lazy (gen_constant ["quote"; "Quote"] "varmap_find")
let coq_index_left = lazy (gen_constant ["quote"; "Quote"] "Left_idx")
let coq_index_right = lazy (gen_constant ["quote"; "Quote"] "Right_idx")
let coq_index_end = lazy (gen_constant ["quote"; "Quote"] "End_idx")
let rec split_interleaved l r = function
| hd :: hd' :: tl' ->
split_interleaved (hd :: l) (hd' :: r) tl'
| hd :: [] -> (List.rev (hd :: l), List.rev r)
| [] -> (List.rev l, List.rev r)
let rec mkidx i p =
if i mod 2 = 0 then
if i = 0 then mkApp (Lazy.force coq_index_left, [|Lazy.force coq_index_end|])
else mkApp (Lazy.force coq_index_left, [|mkidx (i - p) (2 * p)|])
else if i = 1 then mkApp (Lazy.force coq_index_right, [|Lazy.force coq_index_end|])
else mkApp (Lazy.force coq_index_right, [|mkidx (i - p) (2 * p)|])
let varify_constr_varmap ty def varh c =
let vars = Idset.elements (freevars c) in
let mkaccess i =
mkApp (Lazy.force coq_varmap_lookup,
[| ty; def; i; varh |])
in
let rec vmap_aux l cont =
match l with
| [] -> [], mkApp (Lazy.force coq_varmap_empty, [| ty |])
| hd :: tl ->
let left, right = split_interleaved [] [] tl in
let leftvars, leftmap = vmap_aux left (fun x -> cont (mkApp (Lazy.force coq_index_left, [| x |]))) in
let rightvars, rightmap = vmap_aux right (fun x -> cont (mkApp (Lazy.force coq_index_right, [| x |]))) in
(hd, cont (Lazy.force coq_index_end)) :: leftvars @ rightvars,
mkApp (Lazy.force coq_varmap_node, [| ty; hd; leftmap ; rightmap |])
in
let subst, vmap = vmap_aux (def :: List.map (fun x -> mkVar x) vars) (fun x -> x) in
let subst = List.map (fun (id, x) -> (destVar id, mkaccess x)) (List.tl subst) in
vmap, replace_vars subst c
TACTIC EXTEND varify
[ "varify" ident(varh) ident(h') constr(ty) constr(def) constr(c) ] -> [
let vars, c' = varify_constr_varmap ty def (mkVar varh) c in
tclTHEN (letin_tac None (Name varh) vars None allHyps)
(letin_tac None (Name h') c' None allHyps)
]
END
TACTIC EXTEND not_evar
[ "not_evar" constr(ty) ] -> [
match kind_of_term ty with
| Evar _ -> tclFAIL 0 (str"Evar")
| _ -> tclIDTAC ]
END
TACTIC EXTEND is_ground
[ "is_ground" constr(ty) ] -> [ fun gl ->
if Evarutil.is_ground_term (project gl) ty then tclIDTAC gl
else tclFAIL 0 (str"Not ground") gl ]
END
TACTIC EXTEND autoapply
[ "autoapply" constr(c) "using" preident(i) ] -> [ fun gl ->
let flags = flags_of_state (Auto.Hint_db.transparent_state (Auto.searchtable_map i)) in
let cty = pf_type_of gl c in
let ce = mk_clenv_from gl (c,cty) in
unify_e_resolve flags (c,ce) gl ]
END
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