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|
(************************************************************************)
(* 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 $Id: classes.ml 6748 2005-02-18 22:17:50Z herbelin $ i*)
(*i*)
open Names
open Decl_kinds
open Term
open Termops
open Sign
open Entries
open Evd
open Environ
open Nametab
open Mod_subst
open Util
open Typeclasses_errors
open Typeclasses
open Libnames
open Constrintern
open Rawterm
open Topconstr
(*i*)
open Decl_kinds
open Entries
let hint_db = "typeclass_instances"
let add_instance_hint inst =
Auto.add_hints false [hint_db]
(Vernacexpr.HintsResolve [CAppExpl (dummy_loc, (None, Ident (dummy_loc, inst)), [])])
let declare_instance (_,id) =
add_instance_hint id
let mismatched_params env n m = mismatched_ctx_inst env Parameters n m
(* let mismatched_defs env n m = mismatched_ctx_inst env Definitions n m *)
let mismatched_props env n m = mismatched_ctx_inst env Properties n m
type binder_list = (identifier located * bool * constr_expr) list
let interp_binders_evars isevars env avoid l =
List.fold_left
(fun (env, ids, params) ((loc, i), t) ->
let n = Name i in
let t' = interp_binder_evars isevars env n t in
let d = (i,None,t') in
(push_named d env, i :: ids, d::params))
(env, avoid, []) l
let interp_typeclass_context_evars isevars env avoid l =
List.fold_left
(fun (env, ids, params) (iid, bk, l) ->
let t' = interp_binder_evars isevars env (snd iid) l in
let i = match snd iid with
| Anonymous -> Nameops.next_name_away (Termops.named_hd env t' Anonymous) ids
| Name id -> id
in
let d = (i,None,t') in
(push_named d env, i :: ids, d::params))
(env, avoid, []) l
let interp_constrs_evars isevars env avoid l =
List.fold_left
(fun (env, ids, params) t ->
let t' = interp_binder_evars isevars env Anonymous t in
let id = Nameops.next_name_away (Termops.named_hd env t' Anonymous) ids in
let d = (id,None,t') in
(push_named d env, id :: ids, d::params))
(env, avoid, []) l
let raw_assum_of_binders k =
List.map (fun ((loc,i),t) -> LocalRawAssum ([(loc, Name i)], k, t))
let raw_assum_of_constrs k =
List.map2 (fun t (n,_,_) -> LocalRawAssum ([(dummy_loc, Name n)], k, t))
let raw_assum_of_anonymous_constrs k =
List.map (fun t -> LocalRawAssum ([(dummy_loc, Anonymous)], k, t))
let decl_expr_of_binders =
List.map (fun ((loc,i),t) -> false, Vernacexpr.AssumExpr ((loc, Name i), t))
let rec unfold n f acc =
match n with
| 0 -> f 0 acc
| n -> unfold (n - 1) f (f n acc)
(* Declare everything in the parameters as implicit, and the class instance as well *)
open Topconstr
let declare_implicit_proj c proj imps sub =
let len = List.length c.cl_context in
let (ctx, _) = decompose_prod_n (len + 1) (Typeops.type_of_constant (Global.env()) proj) in
let expls =
let rec aux i expls = function
[] -> expls
| (Name n, _) :: tl ->
let impl = ExplByPos (i, Some n), (true, true) in
aux (succ i) (impl :: List.remove_assoc (ExplByName n) expls) tl
| (Anonymous,_) :: _ -> assert(false)
in
aux 1 [] ctx
in
let expls = expls @ List.map (function (ExplByPos (i, n), f) -> (ExplByPos (succ len + i, n)), f | _ -> assert(false)) imps in
if sub then add_instance_hint (id_of_label (con_label proj));
Impargs.declare_manual_implicits true (ConstRef proj) true expls
let declare_implicits impls subs cl =
let projs = Recordops.lookup_projections cl.cl_impl in
Util.list_iter3
(fun c imps sub ->
match c with
| None -> assert(false)
| Some p -> declare_implicit_proj cl p imps sub)
projs impls subs;
let len = List.length cl.cl_context in
let indimps =
list_fold_left_i
(fun i acc (is, (na, b, t)) ->
if len - i <= cl.cl_params then acc
else
match is with
None | Some (_, false) -> (ExplByPos (i, Some na), (false, true)) :: acc
| _ -> acc)
1 [] (List.rev cl.cl_context)
in
Impargs.declare_manual_implicits true (IndRef cl.cl_impl) false indimps
let rel_of_named_context subst l =
List.fold_right
(fun (id, _, t) (ctx, acc) -> (Name id, None, subst_vars acc t) :: ctx, id :: acc)
l ([], subst)
let ids_of_rel_context subst l =
List.fold_right
(fun (id, _, t) acc -> Nameops.out_name id :: acc)
l subst
let degenerate_decl (na,b,t) =
let id = match na with
| Name id -> id
| Anonymous -> anomaly "Unnamed record variable" in
match b with
| None -> (id, Entries.LocalAssum t)
| Some b -> (id, Entries.LocalDef b)
let declare_structure env id idbuild params arity fields =
let nparams = List.length params and nfields = List.length fields in
let args = extended_rel_list nfields params in
let ind = applist (mkRel (1+nparams+nfields), args) in
let type_constructor = it_mkProd_or_LetIn ind fields in
let mie_ind =
{ mind_entry_typename = id;
mind_entry_arity = arity;
mind_entry_consnames = [idbuild];
mind_entry_lc = [type_constructor] } in
let mie =
{ mind_entry_params = List.map degenerate_decl params;
mind_entry_record = true;
mind_entry_finite = true;
mind_entry_inds = [mie_ind] } in
let kn = Command.declare_mutual_with_eliminations true mie in
let rsp = (kn,0) in (* This is ind path of idstruc *)
let kinds,sp_projs = Record.declare_projections rsp (List.map (fun _ -> false) fields) fields in
let _build = ConstructRef (rsp,1) in
Recordops.declare_structure(rsp,idbuild,List.rev kinds,List.rev sp_projs);
rsp
let interp_type_evars evdref env ?(impls=([],[])) typ =
let typ' = intern_gen true ~impls (Evd.evars_of !evdref) env typ in
let imps = Implicit_quantifiers.implicits_of_rawterm typ' in
imps, Pretyping.Default.understand_tcc_evars evdref env Pretyping.IsType typ'
let mk_interning_data env na impls typ =
let impl = Impargs.compute_implicits_with_manual env typ (Impargs.is_implicit_args()) impls
in (na, ([], impl, Notation.compute_arguments_scope typ))
let interp_fields_evars isevars env avoid l =
List.fold_left
(fun (env, uimpls, ids, params, impls) ((loc, i), _, t) ->
let impl, t' = interp_type_evars isevars env ~impls t in
let data = mk_interning_data env i impl t' in
let d = (i,None,t') in
(push_named d env, impl :: uimpls, Idset.add i ids, d::params, ([], data :: snd impls)))
(env, [], avoid, [], ([], [])) l
let name_typeclass_binder avoid = function
| LocalRawAssum ([loc, Anonymous], bk, c) ->
let name =
let id =
match c with
CApp (_, (_, CRef (Ident (loc,id))), _) -> id
| _ -> id_of_string "assum"
in Implicit_quantifiers.make_fresh avoid (Global.env ()) id
in LocalRawAssum ([loc, Name name], bk, c), Idset.add name avoid
| x -> x, avoid
let name_typeclass_binders avoid l =
let l', avoid =
List.fold_left
(fun (binders, avoid) b -> let b', avoid = name_typeclass_binder avoid b in
b' :: binders, avoid)
([], avoid) l
in List.rev l', avoid
let decompose_named_assum =
let rec prodec_rec subst l c =
match kind_of_term c with
| Prod (Name na,t,c) ->
let decl = (na,None,substl subst t) in
let subst' = mkVar na :: subst in
prodec_rec subst' (add_named_decl decl l) (substl subst' c)
| Cast (c,_,_) -> prodec_rec subst l c
| _ -> l,c
in prodec_rec [] []
let push_named_context = List.fold_right push_named
let new_class id par ar sup props =
let env0 = Global.env() in
let isevars = ref (Evd.create_evar_defs Evd.empty) in
let bound = Implicit_quantifiers.ids_of_list (Termops.ids_of_context env0) in
let bound, ids = Implicit_quantifiers.free_vars_of_binders ~bound [] (sup @ par) in
let bound = Idset.union bound (Implicit_quantifiers.ids_of_list ids) in
let sup, bound = name_typeclass_binders bound sup in
let supnames =
List.fold_left (fun acc b ->
match b with
LocalRawAssum (nl, _, _) -> nl @ acc
| LocalRawDef _ -> assert(false))
[] sup
in
(* Interpret the arity *)
let arity_imps, fullarity =
let arity = CSort (fst ar, snd ar) in
let term = prod_constr_expr (prod_constr_expr arity par) sup in
interp_type_evars isevars env0 term
in
let ctx_params, arity = decompose_named_assum fullarity in
let env_params = push_named_context ctx_params env0 in
(* Interpret the definitions and propositions *)
let env_props, prop_impls, bound, ctx_props, _ =
interp_fields_evars isevars env_params bound props
in
let subs = List.map (fun ((loc, id), b, _) -> b) props in
(* Instantiate evars and check all are resolved *)
let isevars,_ = Evarconv.consider_remaining_unif_problems env_props !isevars in
let sigma = Evd.evars_of isevars in
let ctx_params = Evarutil.nf_named_context_evar sigma ctx_params in
let ctx_props = Evarutil.nf_named_context_evar sigma ctx_props in
let arity = Reductionops.nf_evar sigma arity in
let ce t = Evarutil.check_evars env0 Evd.empty isevars t in
let kn =
let idb = id_of_string ("Build_" ^ (string_of_id (snd id))) in
let params, subst = rel_of_named_context [] ctx_params (* @ ctx_super @ ctx_super_ctx) *) in
let fields, _ = rel_of_named_context subst ctx_props in
List.iter (fun (_,c,t) -> ce t; match c with Some c -> ce c | None -> ()) (params @ fields);
declare_structure env0 (snd id) idb params arity fields
in
let ctx_context =
List.map (fun ((na, b, t) as d) ->
match Typeclasses.class_of_constr t with
| Some cl -> (Some (cl.cl_name, List.exists (fun (_, n) -> n = Name na) supnames), d)
| None -> (None, d))
ctx_params
in
let k =
{ cl_name = snd id;
cl_params = List.length par;
cl_context = ctx_context;
cl_props = ctx_props;
cl_impl = kn }
in
declare_implicits (List.rev prop_impls) subs k;
add_class k
type binder_def_list = (identifier located * identifier located list * constr_expr) list
let binders_of_lidents l =
List.map (fun (loc, id) -> LocalRawAssum ([loc, Name id], Default Rawterm.Implicit, CHole (loc, None))) l
let subst_ids_in_named_context subst l =
let x, _ =
List.fold_right
(fun (id, _, t) (ctx, k) -> (id, None, substn_vars k subst t) :: ctx, succ k)
l ([], 1)
in x
let subst_one_named inst ids t =
substnl inst 0 (substn_vars 1 ids t)
let subst_named inst subst ctx =
let ids = List.map (fun (id, _, _) -> id) subst in
let ctx' = subst_ids_in_named_context ids ctx in
let ctx', _ =
List.fold_right
(fun (id, _, t) (ctx, k) -> (id, None, substnl inst k t) :: ctx, succ k)
ctx' ([], 0)
in ctx'
let destClass c =
match kind_of_term c with
App (c, args) ->
(match kind_of_term c with
| Ind ind -> (try class_of_inductive ind, args with _ -> assert false)
| _ -> assert false)
| _ -> assert false
let infer_super_instances env params params_ctx super =
let super = subst_named params params_ctx super in
List.fold_right
(fun (na, _, t) (sups, ids, supctx) ->
let t = subst_one_named sups ids t in
let inst =
try resolve_one_typeclass env t
with Not_found ->
let cl, args = destClass t in
no_instance (push_named_context supctx env) (dummy_loc, cl.cl_name) (Array.to_list args)
in
let d = (na, Some inst, t) in
inst :: sups, na :: ids, d :: supctx)
super ([], [], [])
(* let evars_of_context ctx id n env = *)
(* List.fold_right (fun (na, _, t) (n, env, nc) -> *)
(* let b = Evarutil.e_new_evar isevars env ~src:(dummy_loc, ImplicitArg (Ident id, (n * Some na))) t in *)
(* let d = (na, Some b, t) in *)
(* (succ n, push_named d env, d :: nc)) *)
(* ctx (n, env, []) *)
let type_ctx_instance isevars env ctx inst subst =
List.fold_left2
(fun (subst, instctx) (na, _, t) ce ->
let t' = replace_vars subst t in
let c = interp_casted_constr_evars isevars env ce t' in
let d = na, Some c, t' in
(na, c) :: subst, d :: instctx)
(subst, []) (List.rev ctx) inst
let substitution_of_constrs ctx cstrs =
List.fold_right2 (fun c (na, _, _) acc -> (na, c) :: acc) cstrs ctx []
let destClassApp cl =
match cl with
| CApp (loc, (None,CRef (Ident f)), l) -> f, List.map fst l
| _ -> raise Not_found
let refine_ref = ref (fun _ -> assert(false))
open Pp
let ($$) g f = fun x -> g (f x)
let new_instance ctx (instid, bk, cl) props =
let env = Global.env() in
let isevars = ref (Evd.create_evar_defs Evd.empty) in
let bound = Implicit_quantifiers.ids_of_list (Termops.ids_of_context env) in
let bound, fvs = Implicit_quantifiers.free_vars_of_binders ~bound [] ctx in
let tclass =
match bk with
| Explicit ->
let id, par = Implicit_quantifiers.destClassAppExpl cl in
let k =
try class_info (snd id)
with Not_found -> unbound_class env id
in
let applen = List.fold_left (fun acc (x, y) -> if y = None then succ acc else acc) 0 par in
let needlen = List.fold_left (fun acc (x, y) -> if x = None then succ acc else acc) 0 k.cl_context in
if needlen <> applen then
mismatched_params env (List.map fst par) (List.map snd k.cl_context);
let pars, _ = Implicit_quantifiers.combine_params Idset.empty (* need no avoid *)
(fun avoid (clname, (id, _, t)) ->
match clname with
Some (cl, b) ->
let t =
if b then
let _k = class_info cl in
CHole (Util.dummy_loc, Some Evd.InternalHole) (* (Evd.ImplicitArg (IndRef k.cl_impl, (1, None)))) *)
else CHole (Util.dummy_loc, None)
in t, avoid
| None -> failwith ("new instance: under-applied typeclass"))
par (List.rev k.cl_context)
in Topconstr.CAppExpl (Util.dummy_loc, (None, Ident id), pars)
| Implicit -> cl
in
let ctx_bound = Idset.union bound (Implicit_quantifiers.ids_of_list fvs) in
let gen_ids = Implicit_quantifiers.free_vars_of_constr_expr ~bound:ctx_bound tclass [] in
let bound = Idset.union (Implicit_quantifiers.ids_of_list gen_ids) ctx_bound in
let gen_ctx = Implicit_quantifiers.binder_list_of_ids gen_ids in
let ctx, avoid = name_typeclass_binders bound ctx in
let ctx = List.rev_append gen_ctx ctx in
let k, ctx', subst =
let c = Command.generalize_constr_expr tclass ctx in
let _imps, c' = interp_type_evars isevars env c in
let ctx, c = decompose_named_assum c' in
(match kind_of_term c with
App (c, args) ->
let cl = Option.get (class_of_constr c) in
cl, ctx, substitution_of_constrs (List.map snd cl.cl_context) (List.rev (Array.to_list args))
| _ ->
let cl = Option.get (class_of_constr c) in
cl, ctx, [])
in
let id =
match snd instid with
Name id ->
let sp = Lib.make_path id in
if Nametab.exists_cci sp then
errorlabstrm "new_instance" (Nameops.pr_id id ++ Pp.str " already exists");
id
| Anonymous ->
let i = Nameops.add_suffix k.cl_name "_instance_0" in
Termops.next_global_ident_away false i (Termops.ids_of_context env)
in
let env' = push_named_context ctx' env in
isevars := Evarutil.nf_evar_defs !isevars;
let sigma = Evd.evars_of !isevars in
isevars := resolve_typeclasses env sigma !isevars;
let sigma = Evd.evars_of !isevars in
let substctx = Typeclasses.nf_substitution sigma subst in
let subst, _propsctx =
let props =
List.map (fun (x, l, d) ->
x, Topconstr.abstract_constr_expr d (binders_of_lidents l))
props
in
if List.length props > List.length k.cl_props then
mismatched_props env' (List.map snd props) k.cl_props;
let props, rest =
List.fold_left
(fun (props, rest) (id,_,_) ->
try
let (_, c) = List.find (fun ((_,id'), c) -> id' = id) rest in
let rest' = List.filter (fun ((_,id'), c) -> id' <> id) rest in
c :: props, rest'
with Not_found -> (CHole (Util.dummy_loc, None) :: props), rest)
([], props) k.cl_props
in
if rest <> [] then
unbound_method env' k.cl_name (fst (List.hd rest))
else
type_ctx_instance isevars env' k.cl_props props substctx
in
let app =
applistc (mkConstruct (k.cl_impl, 1)) (List.rev_map snd subst)
in
let term = Termops.it_mkNamedLambda_or_LetIn app ctx' in
isevars := Evarutil.nf_evar_defs !isevars;
let term = Evarutil.nf_isevar !isevars term in
let termtype =
let app = applistc (mkInd (k.cl_impl)) (List.rev_map snd substctx) in
let t = it_mkNamedProd_or_LetIn app ctx' in
Evarutil.nf_isevar !isevars t
in
let imps =
Util.list_map_i
(fun i (na, b, t) -> ExplByPos (i, Some na), (true, true))
1 ctx'
in
let hook cst =
let inst =
{ is_class = k;
is_name = id;
is_impl = cst;
}
in
add_instance_hint id;
Impargs.declare_manual_implicits false (ConstRef cst) false imps;
Typeclasses.add_instance inst
in
let evm = Evd.evars_of (undefined_evars !isevars) in
if evm = Evd.empty then
let cdecl =
let kind = IsDefinition Instance in
let entry =
{ const_entry_body = term;
const_entry_type = Some termtype;
const_entry_opaque = false;
const_entry_boxed = false }
in DefinitionEntry entry, kind
in
let kn = Declare.declare_constant id cdecl in
Flags.if_verbose Command.definition_message id;
hook kn;
id
else
let kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Instance in
Command.start_proof id kind termtype (fun _ -> function ConstRef cst -> hook cst | _ -> assert false);
Pfedit.by (* (Refiner.tclTHEN (Refiner.tclEVARS (Evd.evars_of !isevars)) *)
(!refine_ref (evm, term));
Flags.if_verbose (msg $$ Printer.pr_open_subgoals) ();
id
let goal_kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Definition
let solve_by_tac env evd evar evi t =
let goal = {it = evi; sigma = (Evd.evars_of evd) } in
let (res, valid) = t goal in
if res.it = [] then
let prooftree = valid [] in
let proofterm, obls = Refiner.extract_open_proof res.sigma prooftree in
if obls = [] then
let evd' = evars_reset_evd res.sigma evd in
let evd' = evar_define evar proofterm evd' in
evd', true
else evd, false
else evd, false
let context l =
let env = Global.env() in
let isevars = ref (Evd.create_evar_defs Evd.empty) in
let avoid = Termops.ids_of_context env in
let ctx, l = Implicit_quantifiers.resolve_class_binders (vars_of_env env) l in
let env', avoid, ctx = interp_binders_evars isevars env avoid ctx in
let env', avoid, l = interp_typeclass_context_evars isevars env' avoid l in
isevars := Evarutil.nf_evar_defs !isevars;
let sigma = Evd.evars_of !isevars in
let fullctx = Evarutil.nf_named_context_evar sigma (l @ ctx) in
List.iter (function (id,_,t) ->
Command.declare_one_assumption false (Local (* global *), Definitional) t
[] false (* inline *) (dummy_loc, id))
(List.rev fullctx)
open Libobject
let module_qualid = qualid_of_dirpath (dirpath_of_string "Coq.Classes.Init")
let tactic_qualid = make_qualid (dirpath_of_string "Coq.Classes.Init") (id_of_string "typeclass_instantiation")
let tactic_expr = Tacexpr.TacArg (Tacexpr.Reference (Qualid (dummy_loc, tactic_qualid)))
let tactic = lazy (Tacinterp.interp tactic_expr)
let _ =
Typeclasses.solve_instanciation_problem :=
(fun env evd ev evi ->
Library.require_library [(dummy_loc, module_qualid)] None; (* may be inefficient *)
solve_by_tac env evd ev evi (Lazy.force tactic))
(* let prod = lazy_fun Coqlib.build_prod *)
(* let build_conjunction evm = *)
(* List.fold_left *)
(* (fun (acc, evs) (ev, evi) -> *)
(* if class_of_constr evi.evar_concl <> None then *)
(* mkApp ((Lazy.force prod).Coqlib.typ, [|evi.evar_concl; acc |]), evs *)
(* else acc, Evd.add evs ev evi) *)
(* (Coqlib.build_coq_True (), Evd.empty) evm *)
(* let destruct_conjunction evm_list evm evm' term = *)
(* let _, evm = *)
(* List.fold_right *)
(* (fun (ev, evi) (term, evs) -> *)
(* if class_of_constr evi.evar_concl <> None then *)
(* match kind_of_term term with *)
(* | App (x, [| _ ; _ ; proof ; term |]) -> *)
(* let evs' = Evd.define evs ev proof in *)
(* (term, evs') *)
(* | _ -> assert(false) *)
(* else *)
(* match (Evd.find evm' ev).evar_body with *)
(* Evar_empty -> raise Not_found *)
(* | Evar_defined c -> *)
(* let evs' = Evd.define evs ev c in *)
(* (term, evs')) *)
(* evm_list (term, evm) *)
(* in evm *)
(* let solve_by_tac env evd evar evi t = *)
(* let goal = {it = evi; sigma = (Evd.evars_of evd) } in *)
(* let (res, valid) = t goal in *)
(* if res.it = [] then *)
(* let prooftree = valid [] in *)
(* let proofterm, obls = Refiner.extract_open_proof res.sigma prooftree in *)
(* if obls = [] then *)
(* let evd' = evars_reset_evd res.sigma evd in *)
(* let evd' = evar_define evar proofterm evd' in *)
(* evd', true *)
(* else evd, false *)
(* else evd, false *)
(* let resolve_all_typeclasses env evd = *)
(* let evm = Evd.evars_of evd in *)
(* let evm_list = Evd.to_list evm in *)
(* let goal, typesevm = build_conjunction evm_list in *)
(* let evars = ref (Evd.create_evar_defs typesevm) in *)
(* let term = resolve_one_typeclass_evd env evars goal in *)
(* let evm' = destruct_conjunction evm_list evm (Evd.evars_of !evars) term in *)
(* Evd.create_evar_defs evm' *)
(* let _ = *)
(* Typeclasses.solve_instanciations_problem := *)
(* (fun env evd -> *)
(* Library.require_library [(dummy_loc, module_qualid)] None; (\* may be inefficient *\) *)
(* resolve_all_typeclasses env evd) *)
let solve_evars_by_tac env evd t =
let ev = make_evar empty_named_context_val mkProp in
let goal = {it = ev; sigma = (Evd.evars_of evd) } in
let (res, valid) = t goal in
let evd' = evars_reset_evd res.sigma evd in
evd'
(* Library.require_library [(dummy_loc, module_qualid)] None (a\* may be inefficient *\); *)
(* let _ = *)
(* Typeclasses.solve_instanciations_problem := *)
(* (fun env evd -> *)
(* Eauto.resolve_all_evars false (true, 15) env *)
(* (fun ev evi -> is_implicit_arg (snd (evar_source ev evd)) *)
(* && class_of_constr evi.evar_concl <> None) evd) *)
|