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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i camlp4deps: "grammar/grammar.cma" i*)
open Names
open Pp
open Errors
open Util
open Nameops
open Namegen
open Term
open Vars
open Reduction
open Tacticals
open Tacmach
open Tactics
open Clenv
open Typeclasses
open Typeclasses_errors
open Classes
open Constrexpr
open Globnames
open Evd
open Misctypes
open Locus
open Locusops
open Decl_kinds
open Elimschemes
open Goal
open Environ
open Tacinterp
open Termops
open Genarg
open Extraargs
open Pcoq.Constr
open Entries
open Libnames
open Evarutil
(** Typeclass-based generalized rewriting. *)
(** Constants used by the tactic. *)
let classes_dirpath =
Names.DirPath.make (List.map Id.of_string ["Classes";"Coq"])
let init_setoid () =
if is_dirpath_prefix_of classes_dirpath (Lib.cwd ()) then ()
else Coqlib.check_required_library ["Coq";"Setoids";"Setoid"]
let make_dir l = DirPath.make (List.rev_map Id.of_string l)
let try_find_global_reference dir s =
let sp = Libnames.make_path (make_dir ("Coq"::dir)) (Id.of_string s) in
Nametab.global_of_path sp
let find_reference dir s =
let gr = lazy (try_find_global_reference dir s) in
fun () -> Lazy.force gr
type evars = evar_map * Evar.Set.t (* goal evars, constraint evars *)
let find_global dir s =
let gr = lazy (try_find_global_reference dir s) in
fun (evd,cstrs) ->
let evd, c = Evarutil.new_global evd (Lazy.force gr) in
(evd, cstrs), c
(** Utility for dealing with polymorphic applications *)
(** Global constants. *)
let gen_reference dir s = Coqlib.gen_reference "rewrite" dir s
let coq_eq_ref = find_reference ["Init"; "Logic"] "eq"
let coq_eq = find_global ["Init"; "Logic"] "eq"
let coq_f_equal = find_global ["Init"; "Logic"] "f_equal"
let coq_all = find_global ["Init"; "Logic"] "all"
let impl = find_global ["Program"; "Basics"] "impl"
(* let coq_inverse = lazy (gen_constant ["Program"; "Basics"] "flip") *)
(* let inverse car rel = mkApp (Lazy.force coq_inverse, [| car ; car; mkProp; rel |]) *)
(* let forall_relation = lazy (gen_constant ["Classes"; "Morphisms"] "forall_relation") *)
(* let pointwise_relation = lazy (gen_constant ["Classes"; "Morphisms"] "pointwise_relation") *)
(* let respectful = lazy (gen_constant ["Classes"; "Morphisms"] "respectful") *)
(* let default_relation = lazy (gen_constant ["Classes"; "SetoidTactics"] "DefaultRelation") *)
(* let subrelation = lazy (gen_constant ["Classes"; "RelationClasses"] "subrelation") *)
(* let do_subrelation = lazy (gen_constant ["Classes"; "Morphisms"] "do_subrelation") *)
(* let apply_subrelation = lazy (gen_constant ["Classes"; "Morphisms"] "apply_subrelation") *)
(* let coq_relation = lazy (gen_constant ["Relations";"Relation_Definitions"] "relation") *)
(* let mk_relation a = mkApp (Lazy.force coq_relation, [| a |]) *)
(* let proper_type = lazy (Universes.constr_of_global (Lazy.force proper_class).cl_impl) *)
(* let proper_proxy_type = lazy (Universes.constr_of_global (Lazy.force proper_proxy_class).cl_impl) *)
(** Bookkeeping which evars are constraints so that we can
remove them at the end of the tactic. *)
let goalevars evars = fst evars
let cstrevars evars = snd evars
let new_cstr_evar (evd,cstrs) env t =
let s = Typeclasses.set_resolvable Evd.Store.empty false in
let evd', t = Evarutil.new_evar ~store:s evd env t in
let ev, _ = destEvar t in
(evd', Evar.Set.add ev cstrs), t
(** Building or looking up instances. *)
let e_new_cstr_evar evars env t =
let evd', t = new_cstr_evar !evars env t in evars := evd'; t
let new_goal_evar (evd,cstrs) env t =
let evd', t = Evarutil.new_evar evd env t in
(evd', cstrs), t
let e_new_goal_evar evars env t =
let evd', t = new_goal_evar !evars env t in evars := evd'; t
(** Building or looking up instances. *)
let extends_undefined evars evars' =
let f ev evi found = found || not (Evd.mem evars ev)
in fold_undefined f evars' false
let app_poly_check env evars f args =
let (evars, cstrs), fc = f evars in
let evdref = ref evars in
let t = Typing.solve_evars env evdref (mkApp (fc, args)) in
(!evdref, cstrs), t
let app_poly_nocheck env evars f args =
let evars, fc = f evars in
evars, mkApp (fc, args)
let app_poly_sort b =
if b then app_poly_nocheck
else app_poly_check
let find_class_proof proof_type proof_method env evars carrier relation =
try
let evars, goal = app_poly_check env evars proof_type [| carrier ; relation |] in
let evars', c = Typeclasses.resolve_one_typeclass env (goalevars evars) goal in
if extends_undefined (goalevars evars) evars' then raise Not_found
else app_poly_check env (evars',cstrevars evars) proof_method [| carrier; relation; c |]
with e when Logic.catchable_exception e -> raise Not_found
(** Utility functions *)
module GlobalBindings (M : sig
val relation_classes : string list
val morphisms : string list
val relation : string list * string
val app_poly : env -> evars -> (evars -> evars * constr) -> constr array -> evars * constr
val arrow : evars -> evars * constr
val coq_inverse : evars -> evars * constr
end) = struct
open M
let relation : evars -> evars * constr = find_global (fst relation) (snd relation)
let reflexive_type = find_global relation_classes "Reflexive"
let reflexive_proof = find_global relation_classes "reflexivity"
let symmetric_type = find_global relation_classes "Symmetric"
let symmetric_proof = find_global relation_classes "symmetry"
let transitive_type = find_global relation_classes "Transitive"
let transitive_proof = find_global relation_classes "transitivity"
let forall_relation = find_global morphisms "forall_relation"
let pointwise_relation = find_global morphisms "pointwise_relation"
let forall_relation_ref = find_reference morphisms "forall_relation"
let pointwise_relation_ref = find_reference morphisms "pointwise_relation"
let respectful = find_global morphisms "respectful"
let respectful_ref = find_reference morphisms "respectful"
let default_relation = find_global ["Classes"; "SetoidTactics"] "DefaultRelation"
let coq_forall = find_global morphisms "forall_def"
let subrelation = find_global relation_classes "subrelation"
let do_subrelation = find_global morphisms "do_subrelation"
let apply_subrelation = find_global morphisms "apply_subrelation"
let rewrite_relation_class = find_global relation_classes "RewriteRelation"
let proper_class = lazy (class_info (try_find_global_reference morphisms "Proper"))
let proper_proxy_class = lazy (class_info (try_find_global_reference morphisms "ProperProxy"))
let proper_proj = lazy (mkConst (Option.get (pi3 (List.hd (Lazy.force proper_class).cl_projs))))
let proper_type =
let l = lazy (Lazy.force proper_class).cl_impl in
fun (evd,cstrs) ->
let evd, c = Evarutil.new_global evd (Lazy.force l) in
(evd, cstrs), c
let proper_proxy_type =
let l = lazy (Lazy.force proper_proxy_class).cl_impl in
fun (evd,cstrs) ->
let evd, c = Evarutil.new_global evd (Lazy.force l) in
(evd, cstrs), c
let proper_proof env evars carrier relation x =
let evars, goal = app_poly env evars proper_proxy_type [| carrier ; relation; x |] in
new_cstr_evar evars env goal
let get_reflexive_proof env = find_class_proof reflexive_type reflexive_proof env
let get_symmetric_proof env = find_class_proof symmetric_type symmetric_proof env
let get_transitive_proof env = find_class_proof transitive_type transitive_proof env
let mk_relation env evd a =
app_poly env evd relation [| a |]
(** Build an infered signature from constraints on the arguments and expected output
relation *)
let build_signature evars env m (cstrs : (types * types option) option list)
(finalcstr : (types * types option) option) =
let mk_relty evars newenv ty obj =
match obj with
| None | Some (_, None) ->
let evars, relty = mk_relation env evars ty in
if closed0 ty then
let env' = Environ.reset_with_named_context (Environ.named_context_val env) env in
new_cstr_evar evars env' relty
else new_cstr_evar evars newenv relty
| Some (x, Some rel) -> evars, rel
in
let rec aux env evars ty l =
let t = Reductionops.whd_betadeltaiota env (goalevars evars) ty in
match kind_of_term t, l with
| Prod (na, ty, b), obj :: cstrs ->
if noccurn 1 b (* non-dependent product *) then
let ty = Reductionops.nf_betaiota (goalevars evars) ty in
let (evars, b', arg, cstrs) = aux env evars (subst1 mkProp b) cstrs in
let evars, relty = mk_relty evars env ty obj in
let evars, newarg = app_poly env evars respectful [| ty ; b' ; relty ; arg |] in
evars, mkProd(na, ty, b), newarg, (ty, Some relty) :: cstrs
else
let (evars, b, arg, cstrs) =
aux (Environ.push_rel (na, None, ty) env) evars b cstrs
in
let ty = Reductionops.nf_betaiota (goalevars evars) ty in
let pred = mkLambda (na, ty, b) in
let liftarg = mkLambda (na, ty, arg) in
let evars, arg' = app_poly env evars forall_relation [| ty ; pred ; liftarg |] in
if Option.is_empty obj then evars, mkProd(na, ty, b), arg', (ty, None) :: cstrs
else error "build_signature: no constraint can apply on a dependent argument"
| _, obj :: _ -> anomaly ~label:"build_signature" (Pp.str "not enough products")
| _, [] ->
(match finalcstr with
| None | Some (_, None) ->
let t = Reductionops.nf_betaiota (fst evars) ty in
let evars, rel = mk_relty evars env t None in
evars, t, rel, [t, Some rel]
| Some (t, Some rel) -> evars, t, rel, [t, Some rel])
in aux env evars m cstrs
(** Folding/unfolding of the tactic constants. *)
let unfold_impl t =
match kind_of_term t with
| App (arrow, [| a; b |])(* when eq_constr arrow (Lazy.force impl) *) ->
mkProd (Anonymous, a, lift 1 b)
| _ -> assert false
let unfold_all t =
match kind_of_term t with
| App (id, [| a; b |]) (* when eq_constr id (Lazy.force coq_all) *) ->
(match kind_of_term b with
| Lambda (n, ty, b) -> mkProd (n, ty, b)
| _ -> assert false)
| _ -> assert false
let unfold_forall t =
match kind_of_term t with
| App (id, [| a; b |]) (* when eq_constr id (Lazy.force coq_all) *) ->
(match kind_of_term b with
| Lambda (n, ty, b) -> mkProd (n, ty, b)
| _ -> assert false)
| _ -> assert false
let arrow_morphism env evd ta tb a b =
let ap = is_Prop ta and bp = is_Prop tb in
if ap && bp then app_poly env evd impl [| a; b |], unfold_impl
else if ap then (* Domain in Prop, CoDomain in Type *)
(evd, mkProd (Anonymous, a, b)), (fun x -> x)
else if bp then (* Dummy forall *)
(app_poly env evd coq_all [| a; mkLambda (Anonymous, a, b) |]), unfold_forall
else (* None in Prop, use arrow *)
(app_poly env evd arrow [| a; b |]), unfold_impl
let rec decomp_pointwise n c =
if Int.equal n 0 then c
else
match kind_of_term c with
| App (f, [| a; b; relb |]) when Globnames.is_global (pointwise_relation_ref ()) f ->
decomp_pointwise (pred n) relb
| App (f, [| a; b; arelb |]) when Globnames.is_global (forall_relation_ref ()) f ->
decomp_pointwise (pred n) (Reductionops.beta_applist (arelb, [mkRel 1]))
| _ -> invalid_arg "decomp_pointwise"
let rec apply_pointwise rel = function
| arg :: args ->
(match kind_of_term rel with
| App (f, [| a; b; relb |]) when Globnames.is_global (pointwise_relation_ref ()) f ->
apply_pointwise relb args
| App (f, [| a; b; arelb |]) when Globnames.is_global (forall_relation_ref ()) f ->
apply_pointwise (Reductionops.beta_applist (arelb, [arg])) args
| _ -> invalid_arg "apply_pointwise")
| [] -> rel
let pointwise_or_dep_relation env evd n t car rel =
if noccurn 1 car && noccurn 1 rel then
app_poly env evd pointwise_relation [| t; lift (-1) car; lift (-1) rel |]
else
app_poly env evd forall_relation
[| t; mkLambda (n, t, car); mkLambda (n, t, rel) |]
let lift_cstr env evars (args : constr list) c ty cstr =
let start evars env car =
match cstr with
| None | Some (_, None) ->
let evars, rel = mk_relation env evars car in
new_cstr_evar evars env rel
| Some (ty, Some rel) -> evars, rel
in
let rec aux evars env prod n =
if Int.equal n 0 then start evars env prod
else
match kind_of_term (Reduction.whd_betadeltaiota env prod) with
| Prod (na, ty, b) ->
if noccurn 1 b then
let b' = lift (-1) b in
let evars, rb = aux evars env b' (pred n) in
app_poly env evars pointwise_relation [| ty; b'; rb |]
else
let evars, rb = aux evars (Environ.push_rel (na, None, ty) env) b (pred n) in
app_poly env evars forall_relation
[| ty; mkLambda (na, ty, b); mkLambda (na, ty, rb) |]
| _ -> raise Not_found
in
let rec find env c ty = function
| [] -> None
| arg :: args ->
try let evars, found = aux evars env ty (succ (List.length args)) in
Some (evars, found, c, ty, arg :: args)
with Not_found ->
let ty = whd_betadeltaiota env ty in
find env (mkApp (c, [| arg |])) (prod_applist ty [arg]) args
in find env c ty args
let unlift_cstr env sigma = function
| None -> None
| Some codom -> Some (decomp_pointwise 1 codom)
end
(* let my_type_of env evars c = Typing.e_type_of env evars c *)
(* let mytypeofkey = Profile.declare_profile "my_type_of";; *)
(* let my_type_of = Profile.profile3 mytypeofkey my_type_of *)
let type_app_poly env env evd f args =
let evars, c = app_poly_nocheck env evd f args in
let evd', t = Typing.e_type_of env (goalevars evars) c in
(evd', cstrevars evars), c
module PropGlobal = struct
module Consts =
struct
let relation_classes = ["Classes"; "RelationClasses"]
let morphisms = ["Classes"; "Morphisms"]
let relation = ["Relations";"Relation_Definitions"], "relation"
let app_poly = app_poly_nocheck
let arrow = find_global ["Program"; "Basics"] "arrow"
let coq_inverse = find_global ["Program"; "Basics"] "flip"
end
module G = GlobalBindings(Consts)
include G
include Consts
let inverse env evd car rel =
type_app_poly env env evd coq_inverse [| car ; car; mkProp; rel |]
(* app_poly env evd coq_inverse [| car ; car; mkProp; rel |] *)
end
module TypeGlobal = struct
module Consts =
struct
let relation_classes = ["Classes"; "CRelationClasses"]
let morphisms = ["Classes"; "CMorphisms"]
let relation = relation_classes, "crelation"
let app_poly = app_poly_check
let arrow = find_global ["Classes"; "CRelationClasses"] "arrow"
let coq_inverse = find_global ["Classes"; "CRelationClasses"] "flip"
end
module G = GlobalBindings(Consts)
include G
include Consts
let inverse env (evd,cstrs) car rel =
let evd, (sort,_) = Evarutil.new_type_evar Evd.univ_flexible evd env in
app_poly_check env (evd,cstrs) coq_inverse [| car ; car; sort; rel |]
end
let sort_of_rel env evm rel =
Reductionops.sort_of_arity env evm (Retyping.get_type_of env evm rel)
(** Looking up declared rewrite relations (instances of [RewriteRelation]) *)
let is_applied_rewrite_relation env sigma rels t =
match kind_of_term t with
| App (c, args) when Array.length args >= 2 ->
let head = if isApp c then fst (destApp c) else c in
if Globnames.is_global (coq_eq_ref ()) head then None
else
(try
let params, args = Array.chop (Array.length args - 2) args in
let env' = Environ.push_rel_context rels env in
let evars, (evar, _) = Evarutil.new_type_evar Evd.univ_flexible sigma env' in
let evars, inst =
app_poly_check env (evars,Evar.Set.empty)
TypeGlobal.rewrite_relation_class [| evar; mkApp (c, params) |] in
let _ = Typeclasses.resolve_one_typeclass env' (goalevars evars) inst in
Some (it_mkProd_or_LetIn t rels)
with e when Errors.noncritical e -> None)
| _ -> None
(* let _ = *)
(* Hook.set Equality.is_applied_rewrite_relation is_applied_rewrite_relation *)
let split_head = function
hd :: tl -> hd, tl
| [] -> assert(false)
let evd_convertible env evd x y =
try ignore(Evarconv.the_conv_x env x y evd); true
with e when Errors.noncritical e -> false
let convertible env evd x y =
Reductionops.is_conv env evd x y
type hypinfo = {
cl : clausenv;
prf : constr;
car : constr;
rel : constr;
sort : bool; (* true = Prop; false = Type *)
l2r : bool;
c1 : constr;
c2 : constr;
c : (Tacinterp.interp_sign * Tacexpr.glob_constr_and_expr with_bindings) option;
abs : (constr * types) option;
flags : Unification.unify_flags;
}
let get_symmetric_proof b =
if b then PropGlobal.get_symmetric_proof else TypeGlobal.get_symmetric_proof
let rec decompose_app_rel env evd t =
match kind_of_term t with
| App (f, args) ->
if Array.length args > 1 then
let fargs, args = Array.chop (Array.length args - 2) args in
mkApp (f, fargs), args
else
let (f', args) = decompose_app_rel env evd args.(0) in
let ty = Typing.type_of env evd args.(0) in
let f'' = mkLambda (Name default_dependent_ident, ty,
mkLambda (Name (Id.of_string "y"), lift 1 ty,
mkApp (lift 2 f, [| mkApp (lift 2 f', [| mkRel 2; mkRel 1 |]) |])))
in (f'', args)
| _ -> error "The term provided is not an applied relation."
let decompose_applied_relation env origsigma sigma flags orig (c,l) left2right =
let c' = c in
let ctype = Retyping.get_type_of env sigma c' in
let find_rel ty =
let eqclause = Clenv.make_clenv_binding_env_apply env sigma None (c',ty) l in
let (equiv, args) = decompose_app_rel env eqclause.evd (Clenv.clenv_type eqclause) in
let c1 = args.(0) and c2 = args.(1) in
let ty1, ty2 =
Retyping.get_type_of env eqclause.evd c1, Retyping.get_type_of env eqclause.evd c2
in
if not (evd_convertible env eqclause.evd ty1 ty2) then None
else
let sort = sort_of_rel env eqclause.evd equiv in
let value = Clenv.clenv_value eqclause in
let eqclause = { eqclause with evd = Evd.diff eqclause.evd origsigma } in
Some { cl=eqclause; prf=value;
car=ty1; rel = equiv; sort = Sorts.is_prop sort;
l2r=left2right; c1=c1; c2=c2; c=orig; abs=None;
flags = flags }
in
match find_rel ctype with
| Some c -> c
| None ->
let ctx,t' = Reductionops.splay_prod env sigma ctype in (* Search for underlying eq *)
match find_rel (it_mkProd_or_LetIn t' (List.map (fun (n,t) -> n, None, t) ctx)) with
| Some c -> c
| None -> error "The term does not end with an applied homogeneous relation."
let decompose_applied_relation_expr env sigma flags (is, (c,l)) left2right =
let sigma', cbl = Tacinterp.interp_open_constr_with_bindings is env sigma (c,l) in
decompose_applied_relation env sigma sigma' flags (Some (is, (c,l))) cbl left2right
let rewrite_db = "rewrite"
let conv_transparent_state = (Id.Pred.empty, Cpred.full)
let _ =
Auto.add_auto_init
(fun () ->
Auto.create_hint_db false rewrite_db conv_transparent_state true)
let rewrite_transparent_state () =
Auto.Hint_db.transparent_state (Auto.searchtable_map rewrite_db)
let rewrite_unif_flags = {
Unification.modulo_conv_on_closed_terms = None;
Unification.use_metas_eagerly_in_conv_on_closed_terms = true;
Unification.modulo_delta = empty_transparent_state;
Unification.modulo_delta_types = full_transparent_state;
Unification.modulo_delta_in_merge = None;
Unification.check_applied_meta_types = true;
Unification.resolve_evars = false;
Unification.use_pattern_unification = true;
Unification.use_meta_bound_pattern_unification = true;
Unification.frozen_evars = Evar.Set.empty;
Unification.restrict_conv_on_strict_subterms = false;
Unification.modulo_betaiota = false;
Unification.modulo_eta = true;
Unification.allow_K_in_toplevel_higher_order_unification = true
}
let rewrite2_unif_flags =
{ Unification.modulo_conv_on_closed_terms = Some conv_transparent_state;
Unification.use_metas_eagerly_in_conv_on_closed_terms = true;
Unification.modulo_delta = empty_transparent_state;
Unification.modulo_delta_types = conv_transparent_state;
Unification.modulo_delta_in_merge = None;
Unification.check_applied_meta_types = true;
Unification.resolve_evars = false;
Unification.use_pattern_unification = true;
Unification.use_meta_bound_pattern_unification = true;
Unification.frozen_evars = Evar.Set.empty;
Unification.restrict_conv_on_strict_subterms = false;
Unification.modulo_betaiota = true;
Unification.modulo_eta = true;
Unification.allow_K_in_toplevel_higher_order_unification = true
}
let general_rewrite_unif_flags () =
let ts = rewrite_transparent_state () in
{ Unification.modulo_conv_on_closed_terms = Some ts;
Unification.use_metas_eagerly_in_conv_on_closed_terms = true;
Unification.modulo_delta = ts;
Unification.modulo_delta_types = ts;
Unification.modulo_delta_in_merge = None;
Unification.check_applied_meta_types = true;
Unification.resolve_evars = false;
Unification.use_pattern_unification = true;
Unification.use_meta_bound_pattern_unification = true;
Unification.frozen_evars = Evar.Set.empty;
Unification.restrict_conv_on_strict_subterms = false;
Unification.modulo_betaiota = true;
Unification.modulo_eta = true;
Unification.allow_K_in_toplevel_higher_order_unification = true }
let refresh_hypinfo env sigma hypinfo =
if Option.is_empty hypinfo.abs then
let {l2r=l2r; c=c;cl=cl;flags=flags} = hypinfo in
match c with
| Some c ->
(* Refresh the clausenv to not get the same meta twice in the goal. *)
decompose_applied_relation_expr env sigma flags c l2r;
| _ -> hypinfo
else hypinfo
let solve_remaining_by by env prf =
match by with
| None -> env, prf
| Some tac ->
let indep = clenv_independent env in
let tac = eval_tactic tac in
let evd' =
List.fold_right (fun mv evd ->
let ty = Clenv.clenv_nf_meta env (meta_type evd mv) in
let c,_,_ = Pfedit.build_by_tactic env.env (ty,Univ.ContextSet.empty) (Tacticals.New.tclCOMPLETE tac) in
meta_assign mv (fst c (*FIXME*), (Conv,TypeNotProcessed)) evd)
indep env.evd
in { env with evd = evd' }, prf
let extend_evd sigma ext sigma' =
Evar.Set.fold (fun i acc ->
Evd.add acc i (Evarutil.nf_evar_info sigma' (Evd.find sigma' i)))
ext sigma
let shrink_evd sigma ext =
Evar.Set.fold (fun i acc -> Evd.remove acc i) ext sigma
let no_constraints cstrs =
fun ev _ -> not (Evar.Set.mem ev cstrs)
let all_constraints cstrs =
fun ev _ -> Evar.Set.mem ev cstrs
let poly_inverse sort =
if sort then PropGlobal.inverse else TypeGlobal.inverse
let unify_eqn env (sigma, cstrs) hypinfo by t =
if isEvar t then None
else try
let {cl=cl; prf=prf; car=car; rel=rel; l2r=l2r; c1=c1; c2=c2; c=c; abs=abs} =
!hypinfo in
let left = if l2r then c1 else c2 in
let evd' = Evd.merge sigma cl.evd in
let cl = { cl with evd = evd' } in
let evd', prf, c1, c2, car, rel =
match abs with
| Some (absprf, absprfty) ->
let env' = clenv_unify ~flags:rewrite_unif_flags CONV left t cl in
env'.evd, prf, c1, c2, car, rel
| None ->
let env' = clenv_unify ~flags:!hypinfo.flags CONV left t cl in
let env' = Clenvtac.clenv_pose_dependent_evars true env' in
let evd' = Typeclasses.resolve_typeclasses ~filter:(no_constraints cstrs)
~fail:true env'.env env'.evd in
let env' = { env' with evd = evd' } in
let env', prf = solve_remaining_by by env' (Clenv.clenv_value env') in
let nf c = Evarutil.nf_evar env'.evd (Clenv.clenv_nf_meta env' c) in
let c1 = nf c1 and c2 = nf c2
and car = nf car and rel = nf rel
and prf = nf prf in
let ty1 = Retyping.get_type_of env'.env env'.evd c1
and ty2 = Retyping.get_type_of env'.env env'.evd c2
in
if convertible env env'.evd ty1 ty2 then
(* (if occur_meta_or_existential prf then *)
(hypinfo := refresh_hypinfo env env'.evd !hypinfo;
env'.evd, prf, c1, c2, car, rel)
(* else (\** Evars have been solved, we can go back to the initial evd, *)
(* but keep the potential refinement of existing evars. *\) *)
(* env'.evd, prf, c1, c2, car, rel) *)
else raise Reduction.NotConvertible
in
let evars = evd', cstrs in
let evd, res =
if l2r then evars, (prf, (car, rel, c1, c2))
else
try
let evars, symprf = get_symmetric_proof !hypinfo.sort env evars car rel in
evars, (mkApp (symprf, [| c1 ; c2 ; prf |]),
(car, rel, c2, c1))
with Not_found ->
let evars, rel' = poly_inverse !hypinfo.sort env evars car rel in
evars, (prf, (car, rel', c2, c1))
in Some (evd, res)
with e when Class_tactics.catchable e -> None
type rewrite_flags = { under_lambdas : bool; on_morphisms : bool }
let default_flags = { under_lambdas = true; on_morphisms = true; }
type rewrite_proof =
| RewPrf of constr * constr
| RewCast of cast_kind
let map_rewprf f p = match p with
| RewPrf (x, y) -> RewPrf (f x, f y)
| RewCast _ -> p
let get_opt_rew_rel = function RewPrf (rel, prf) -> Some rel | _ -> None
type rewrite_result_info = {
rew_car : constr;
rew_from : constr;
rew_to : constr;
rew_prf : rewrite_proof;
rew_evars : evars;
}
type rewrite_result = rewrite_result_info option
type strategy = Environ.env -> Id.t list -> constr -> types ->
(bool (* prop *) * constr option) -> evars -> rewrite_result option
let make_eq () =
(*FIXME*) Universes.constr_of_global (Coqlib.build_coq_eq ())
let make_eq_refl () =
(*FIXME*) Universes.constr_of_global (Coqlib.build_coq_eq_refl ())
let get_rew_rel r = match r.rew_prf with
| RewPrf (rel, prf) -> rel
| RewCast c -> mkApp (make_eq (),[| r.rew_car; r.rew_from; r.rew_to |])
let get_rew_prf r = match r.rew_prf with
| RewPrf (rel, prf) -> rel, prf
| RewCast c ->
let rel = mkApp (make_eq (), [| r.rew_car |]) in
rel, mkCast (mkApp (make_eq_refl (), [| r.rew_car; r.rew_from |]),
c, mkApp (rel, [| r.rew_from; r.rew_to |]))
let poly_subrelation sort =
if sort then PropGlobal.subrelation else TypeGlobal.subrelation
let resolve_subrelation env avoid car rel sort prf rel' res =
if eq_constr rel rel' then res
else
let evars, app = app_poly_check env res.rew_evars (poly_subrelation sort) [|car; rel; rel'|] in
let evars, subrel = new_cstr_evar evars env app in
let appsub = mkApp (subrel, [| res.rew_from ; res.rew_to ; prf |]) in
{ res with
rew_prf = RewPrf (rel', appsub);
rew_evars = evars }
let resolve_morphism env avoid oldt m ?(fnewt=fun x -> x) args args' (b,cstr) evars =
let evars, morph_instance, proj, sigargs, m', args, args' =
let first = match (Array.findi (fun _ b -> not (Option.is_empty b)) args') with
| Some i -> i
| None -> invalid_arg "resolve_morphism" in
let morphargs, morphobjs = Array.chop first args in
let morphargs', morphobjs' = Array.chop first args' in
let appm = mkApp(m, morphargs) in
let appmtype = Typing.type_of env (goalevars evars) appm in
let cstrs = List.map
(Option.map (fun r -> r.rew_car, get_opt_rew_rel r.rew_prf))
(Array.to_list morphobjs')
in
(* Desired signature *)
let evars, appmtype', signature, sigargs =
if b then PropGlobal.build_signature evars env appmtype cstrs cstr
else TypeGlobal.build_signature evars env appmtype cstrs cstr
in
(* Actual signature found *)
let cl_args = [| appmtype' ; signature ; appm |] in
let evars, app = app_poly_sort b env evars (if b then PropGlobal.proper_type else TypeGlobal.proper_type)
cl_args in
let env' =
let dosub, appsub =
if b then PropGlobal.do_subrelation, PropGlobal.apply_subrelation
else TypeGlobal.do_subrelation, TypeGlobal.apply_subrelation
in
Environ.push_named
(Id.of_string "do_subrelation",
Some (snd (app_poly_sort b env evars dosub [||])),
snd (app_poly_nocheck env evars appsub [||]))
env
in
let evars, morph = new_cstr_evar evars env' app in
evars, morph, morph, sigargs, appm, morphobjs, morphobjs'
in
let projargs, subst, evars, respars, typeargs =
Array.fold_left2
(fun (acc, subst, evars, sigargs, typeargs') x y ->
let (carrier, relation), sigargs = split_head sigargs in
match relation with
| Some relation ->
let carrier = substl subst carrier
and relation = substl subst relation in
(match y with
| None ->
let evars, proof =
(if b then PropGlobal.proper_proof else TypeGlobal.proper_proof)
env evars carrier relation x in
[ proof ; x ; x ] @ acc, subst, evars, sigargs, x :: typeargs'
| Some r ->
[ snd (get_rew_prf r); r.rew_to; x ] @ acc, subst, evars,
sigargs, r.rew_to :: typeargs')
| None ->
if not (Option.is_empty y) then
error "Cannot rewrite the argument of a dependent function";
x :: acc, x :: subst, evars, sigargs, x :: typeargs')
([], [], evars, sigargs, []) args args'
in
let proof = applistc proj (List.rev projargs) in
let newt = applistc m' (List.rev typeargs) in
match respars with
[ a, Some r ] -> evars, proof, a, r, oldt, fnewt newt
| _ -> assert(false)
let apply_constraint env avoid car rel prf cstr res =
match snd cstr with
| None -> res
| Some r -> resolve_subrelation env avoid car rel (fst cstr) prf r res
let eq_env x y = x == y
let apply_rule hypinfo by loccs : strategy =
let (nowhere_except_in,occs) = convert_occs loccs in
let is_occ occ =
if nowhere_except_in then List.mem occ occs else not (List.mem occ occs) in
let occ = ref 0 in
fun env avoid t ty cstr evars ->
if not (eq_env !hypinfo.cl.env env) then
hypinfo := refresh_hypinfo env (goalevars evars) !hypinfo;
let unif = unify_eqn env evars hypinfo by t in
if not (Option.is_empty unif) then incr occ;
match unif with
| Some (evars', (prf, (car, rel, c1, c2))) when is_occ !occ ->
begin
if eq_constr t c2 then Some None
else
let res = { rew_car = ty; rew_from = c1;
rew_to = c2; rew_prf = RewPrf (rel, prf);
rew_evars = evars' }
in Some (Some (apply_constraint env avoid car rel prf cstr res))
end
| _ -> None
let apply_lemma flags (evm,c) left2right by loccs : strategy =
fun env avoid t ty cstr evars ->
let hypinfo =
let evars' = Evd.merge (goalevars evars) evm in
ref (decompose_applied_relation env (goalevars evars) evars'
flags None c left2right)
in
apply_rule hypinfo by loccs env avoid t ty cstr evars
let e_app_poly env evars f args =
let evars', c = app_poly_nocheck env !evars f args in
evars := evars';
c
let make_leibniz_proof env c ty r =
let evars = ref r.rew_evars in
let prf =
match r.rew_prf with
| RewPrf (rel, prf) ->
let rel = e_app_poly env evars coq_eq [| ty |] in
let prf =
e_app_poly env evars coq_f_equal
[| r.rew_car; ty;
mkLambda (Anonymous, r.rew_car, c);
r.rew_from; r.rew_to; prf |]
in RewPrf (rel, prf)
| RewCast k -> r.rew_prf
in
{ rew_car = ty; rew_evars = !evars;
rew_from = subst1 r.rew_from c; rew_to = subst1 r.rew_to c; rew_prf = prf }
let reset_env env =
let env' = Global.env_of_context (Environ.named_context_val env) in
Environ.push_rel_context (Environ.rel_context env) env'
let fold_match ?(force=false) env sigma c =
let (ci, p, c, brs) = destCase c in
let cty = Retyping.get_type_of env sigma c in
let dep, pred, exists, (sk,eff) =
let env', ctx, body =
let ctx, pred = decompose_lam_assum p in
let env' = Environ.push_rel_context ctx env in
env', ctx, pred
in
let sortp = Retyping.get_sort_family_of env' sigma body in
let sortc = Retyping.get_sort_family_of env sigma cty in
let dep = not (noccurn 1 body) in
let pred = if dep then p else
it_mkProd_or_LetIn (subst1 mkProp body) (List.tl ctx)
in
let sk =
if sortp == InProp then
if sortc == InProp then
if dep then case_dep_scheme_kind_from_prop
else case_scheme_kind_from_prop
else (
if dep
then case_dep_scheme_kind_from_type_in_prop
else case_scheme_kind_from_type)
else ((* sortc <> InProp by typing *)
if dep
then case_dep_scheme_kind_from_type
else case_scheme_kind_from_type)
in
let exists = Ind_tables.check_scheme sk ci.ci_ind in
if exists || force then
dep, pred, exists, Ind_tables.find_scheme sk ci.ci_ind
else raise Not_found
in
let app =
let ind, args = Inductive.find_rectype env cty in
let pars, args = List.chop ci.ci_npar args in
let meths = List.map (fun br -> br) (Array.to_list brs) in
applist (mkConst sk, pars @ [pred] @ meths @ args @ [c])
in
sk, (if exists then env else reset_env env), app, eff
let unfold_match env sigma sk app =
match kind_of_term app with
| App (f', args) when eq_constant (fst (destConst f')) sk ->
let v = Environ.constant_value_in (Global.env ()) (sk,Univ.Instance.empty)(*FIXME*) in
Reductionops.whd_beta sigma (mkApp (v, args))
| _ -> app
let is_rew_cast = function RewCast _ -> true | _ -> false
let coerce env avoid cstr res =
let rel, prf = get_rew_prf res in
apply_constraint env avoid res.rew_car rel prf cstr res
let subterm all flags (s : strategy) : strategy =
let rec aux env avoid t ty (prop, cstr) evars =
let cstr' = Option.map (fun c -> (ty, Some c)) cstr in
match kind_of_term t with
| App (m, args) ->
let rewrite_args success =
let args', evars', progress =
Array.fold_left
(fun (acc, evars, progress) arg ->
if not (Option.is_empty progress) && not all then (None :: acc, evars, progress)
else
let argty = Retyping.get_type_of env (goalevars evars) arg in
let res = s env avoid arg argty (prop,None) evars in
match res with
| Some None -> (None :: acc, evars,
if Option.is_empty progress then Some false else progress)
| Some (Some r) ->
(Some r :: acc, r.rew_evars, Some true)
| None -> (None :: acc, evars, progress))
([], evars, success) args
in
match progress with
| None -> None
| Some false -> Some None
| Some true ->
let args' = Array.of_list (List.rev args') in
if Array.exists
(function
| None -> false
| Some r -> not (is_rew_cast r.rew_prf)) args'
then
let evars', prf, car, rel, c1, c2 =
resolve_morphism env avoid t m args args' (prop, cstr') evars'
in
let res = { rew_car = ty; rew_from = c1;
rew_to = c2; rew_prf = RewPrf (rel, prf);
rew_evars = evars' }
in Some (Some res)
else
let args' = Array.map2
(fun aorig anew ->
match anew with None -> aorig
| Some r -> r.rew_to) args args'
in
let res = { rew_car = ty; rew_from = t;
rew_to = mkApp (m, args'); rew_prf = RewCast DEFAULTcast;
rew_evars = evars' }
in Some (Some res)
in
if flags.on_morphisms then
let mty = Retyping.get_type_of env (goalevars evars) m in
let evars, cstr', m, mty, argsl, args =
let argsl = Array.to_list args in
let lift = if prop then PropGlobal.lift_cstr else TypeGlobal.lift_cstr in
match lift env evars argsl m mty None with
| Some (evars, cstr', m, mty, args) ->
evars, Some cstr', m, mty, args, Array.of_list args
| None -> evars, None, m, mty, argsl, args
in
let m' = s env avoid m mty (prop, cstr') evars in
match m' with
| None -> rewrite_args None (* Standard path, try rewrite on arguments *)
| Some None -> rewrite_args (Some false)
| Some (Some r) ->
(* We rewrote the function and get a proof of pointwise rel for the arguments.
We just apply it. *)
let prf = match r.rew_prf with
| RewPrf (rel, prf) ->
let app = if prop then PropGlobal.apply_pointwise
else TypeGlobal.apply_pointwise
in
RewPrf (app rel argsl, mkApp (prf, args))
| x -> x
in
let res =
{ rew_car = prod_appvect r.rew_car args;
rew_from = mkApp(r.rew_from, args); rew_to = mkApp(r.rew_to, args);
rew_prf = prf; rew_evars = r.rew_evars }
in
match prf with
| RewPrf (rel, prf) ->
Some (Some (apply_constraint env avoid res.rew_car
rel prf (prop,cstr) res))
| _ -> Some (Some res)
else rewrite_args None
| Prod (n, x, b) when noccurn 1 b ->
let b = subst1 mkProp b in
let tx = Retyping.get_type_of env (goalevars evars) x
and tb = Retyping.get_type_of env (goalevars evars) b in
let arr = if prop then PropGlobal.arrow_morphism
else TypeGlobal.arrow_morphism
in
let (evars', mor), unfold = arr env evars tx tb x b in
let res = aux env avoid mor ty (prop,cstr) evars' in
(match res with
| Some (Some r) -> Some (Some { r with rew_to = unfold r.rew_to })
| _ -> res)
(* if x' = None && flags.under_lambdas then *)
(* let lam = mkLambda (n, x, b) in *)
(* let lam', occ = aux env lam occ None in *)
(* let res = *)
(* match lam' with *)
(* | None -> None *)
(* | Some (prf, (car, rel, c1, c2)) -> *)
(* Some (resolve_morphism env sigma t *)
(* ~fnewt:unfold_all *)
(* (Lazy.force coq_all) [| x ; lam |] [| None; lam' |] *)
(* cstr evars) *)
(* in res, occ *)
(* else *)
| Prod (n, dom, codom) ->
let lam = mkLambda (n, dom, codom) in
let (evars', app), unfold =
if eq_constr ty mkProp then
(app_poly_sort prop env evars coq_all [| dom; lam |]), TypeGlobal.unfold_all
else
let forall = if prop then PropGlobal.coq_forall else TypeGlobal.coq_forall in
(app_poly_sort prop env evars forall [| dom; lam |]), TypeGlobal.unfold_forall
in
let res = aux env avoid app ty (prop,cstr) evars' in
(match res with
| Some (Some r) -> Some (Some { r with rew_to = unfold r.rew_to })
| _ -> res)
(* TODO: real rewriting under binders: introduce x x' (H : R x x') and rewrite with
H at any occurrence of x. Ask for (R ==> R') for the lambda. Formalize this.
B. Barras' idea is to have a context of relations, of length 1, with Σ for gluing
dependent relations and using projections to get them out.
*)
(* | Lambda (n, t, b) when flags.under_lambdas -> *)
(* let n' = name_app (fun id -> Tactics.fresh_id_in_env avoid id env) n in *)
(* let n'' = name_app (fun id -> Tactics.fresh_id_in_env avoid id env) n' in *)
(* let n''' = name_app (fun id -> Tactics.fresh_id_in_env avoid id env) n'' in *)
(* let rel = new_cstr_evar cstr env (mkApp (Lazy.force coq_relation, [|t|])) in *)
(* let env' = Environ.push_rel_context [(n'',None,lift 2 rel);(n'',None,lift 1 t);(n', None, t)] env in *)
(* let b' = s env' avoid b (Typing.type_of env' (goalevars evars) (lift 2 b)) (unlift_cstr env (goalevars evars) cstr) evars in *)
(* (match b' with *)
(* | Some (Some r) -> *)
(* let prf = match r.rew_prf with *)
(* | RewPrf (rel, prf) -> *)
(* let rel = pointwise_or_dep_relation n' t r.rew_car rel in *)
(* let prf = mkLambda (n', t, prf) in *)
(* RewPrf (rel, prf) *)
(* | x -> x *)
(* in *)
(* Some (Some { r with *)
(* rew_prf = prf; *)
(* rew_car = mkProd (n, t, r.rew_car); *)
(* rew_from = mkLambda(n, t, r.rew_from); *)
(* rew_to = mkLambda (n, t, r.rew_to) }) *)
(* | _ -> b') *)
| Lambda (n, t, b) when flags.under_lambdas ->
let n' = name_app (fun id -> Tactics.fresh_id_in_env avoid id env) n in
let env' = Environ.push_rel (n', None, t) env in
let bty = Retyping.get_type_of env' (goalevars evars) b in
let unlift = if prop then PropGlobal.unlift_cstr else TypeGlobal.unlift_cstr in
let b' = s env' avoid b bty (prop, unlift env evars cstr) evars in
(match b' with
| Some (Some r) ->
let r = match r.rew_prf with
| RewPrf (rel, prf) ->
let point = if prop then PropGlobal.pointwise_or_dep_relation else
TypeGlobal.pointwise_or_dep_relation
in
let evars, rel = point env r.rew_evars n' t r.rew_car rel in
let prf = mkLambda (n', t, prf) in
{ r with rew_prf = RewPrf (rel, prf); rew_evars = evars }
| x -> r
in
Some (Some { r with
rew_car = mkProd (n, t, r.rew_car);
rew_from = mkLambda(n, t, r.rew_from);
rew_to = mkLambda (n, t, r.rew_to) })
| _ -> b')
| Case (ci, p, c, brs) ->
let cty = Retyping.get_type_of env (goalevars evars) c in
let evars', eqty = app_poly_sort prop env evars coq_eq [| cty |] in
let cstr' = Some eqty in
let c' = s env avoid c cty (prop, cstr') evars' in
let res =
match c' with
| Some (Some r) ->
let case = mkCase (ci, lift 1 p, mkRel 1, Array.map (lift 1) brs) in
let res = make_leibniz_proof env case ty r in
Some (Some (coerce env avoid (prop,cstr) res))
| x ->
if Array.for_all (Int.equal 0) ci.ci_cstr_ndecls then
let evars', eqty = app_poly_sort prop env evars coq_eq [| ty |] in
let cstr = Some eqty in
let found, brs' = Array.fold_left
(fun (found, acc) br ->
if not (Option.is_empty found) then (found, fun x -> lift 1 br :: acc x)
else
match s env avoid br ty (prop,cstr) evars with
| Some (Some r) -> (Some r, fun x -> mkRel 1 :: acc x)
| _ -> (None, fun x -> lift 1 br :: acc x))
(None, fun x -> []) brs
in
match found with
| Some r ->
let ctxc = mkCase (ci, lift 1 p, lift 1 c, Array.of_list (List.rev (brs' x))) in
Some (Some (make_leibniz_proof env ctxc ty r))
| None -> x
else
match try Some (fold_match env (goalevars evars) t) with Not_found -> None with
| None -> x
| Some (cst, _, t', eff (*FIXME*)) ->
match aux env avoid t' ty (prop,cstr) evars with
| Some (Some prf) ->
Some (Some { prf with
rew_from = t;
rew_to = unfold_match env (goalevars evars) cst prf.rew_to })
| x' -> x
in
(match res with
| Some (Some r) ->
let rel, prf = get_rew_prf r in
Some (Some (apply_constraint env avoid r.rew_car rel prf (prop,cstr) r))
| x -> x)
| _ -> None
in aux
let all_subterms = subterm true default_flags
let one_subterm = subterm false default_flags
(** Requires transitivity of the rewrite step, if not a reduction.
Not tail-recursive. *)
let transitivity env avoid prop (res : rewrite_result_info) (next : strategy) :
rewrite_result option =
let nextres =
next env avoid res.rew_to res.rew_car
(prop, get_opt_rew_rel res.rew_prf) res.rew_evars
in
match nextres with
| None -> None
| Some None -> Some (Some res)
| Some (Some res') ->
match res.rew_prf with
| RewCast c -> Some (Some { res' with rew_from = res.rew_from })
| RewPrf (rew_rel, rew_prf) ->
match res'.rew_prf with
| RewCast _ -> Some (Some ({ res with rew_to = res'.rew_to }))
| RewPrf (res'_rel, res'_prf) ->
let trans =
if prop then PropGlobal.transitive_type
else TypeGlobal.transitive_type
in
let evars, prfty =
app_poly_sort prop env res'.rew_evars trans [| res.rew_car; rew_rel |]
in
let evars, prf = new_cstr_evar evars env prfty in
let prf = mkApp (prf, [|res.rew_from; res'.rew_from; res'.rew_to;
rew_prf; res'_prf |])
in Some (Some { res' with rew_from = res.rew_from;
rew_evars = evars; rew_prf = RewPrf (res'_rel, prf) })
(** Rewriting strategies.
Inspired by ELAN's rewriting strategies:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.4049
*)
module Strategies =
struct
let fail : strategy =
fun env avoid t ty cstr evars -> None
let id : strategy =
fun env avoid t ty cstr evars -> Some None
let refl : strategy =
fun env avoid t ty (prop,cstr) evars ->
let evars, rel = match cstr with
| None ->
let mkr = if prop then PropGlobal.mk_relation else TypeGlobal.mk_relation in
let evars, rty = mkr env evars ty in
new_cstr_evar evars env rty
| Some r -> evars, r
in
let evars, proof =
let proxy =
if prop then PropGlobal.proper_proxy_type
else TypeGlobal.proper_proxy_type
in
let evars, mty = app_poly_sort prop env evars proxy [| ty ; rel; t |] in
new_cstr_evar evars env mty
in
Some (Some { rew_car = ty; rew_from = t; rew_to = t;
rew_prf = RewPrf (rel, proof); rew_evars = evars })
let progress (s : strategy) : strategy =
fun env avoid t ty cstr evars ->
match s env avoid t ty cstr evars with
| None -> None
| Some None -> None
| r -> r
let seq first snd : strategy =
fun env avoid t ty cstr evars ->
match first env avoid t ty cstr evars with
| None -> None
| Some None -> snd env avoid t ty cstr evars
| Some (Some res) -> transitivity env avoid (fst cstr) res snd
let choice fst snd : strategy =
fun env avoid t ty cstr evars ->
match fst env avoid t ty cstr evars with
| None -> snd env avoid t ty cstr evars
| res -> res
let try_ str : strategy = choice str id
let fix (f : strategy -> strategy) : strategy =
let rec aux env = f (fun env -> aux env) env in aux
let any (s : strategy) : strategy =
fix (fun any -> try_ (seq s any))
let repeat (s : strategy) : strategy =
seq s (any s)
let bu (s : strategy) : strategy =
fix (fun s' -> seq (choice (progress (all_subterms s')) s) (try_ s'))
let td (s : strategy) : strategy =
fix (fun s' -> seq (choice s (progress (all_subterms s'))) (try_ s'))
let innermost (s : strategy) : strategy =
fix (fun ins -> choice (one_subterm ins) s)
let outermost (s : strategy) : strategy =
fix (fun out -> choice s (one_subterm out))
let lemmas flags cs : strategy =
List.fold_left (fun tac (l,l2r,by) ->
choice tac (apply_lemma flags l l2r by AllOccurrences))
fail cs
let inj_open hint =
(Evd.from_env ~ctx:hint.Autorewrite.rew_ctx (Global.env()),
(hint.Autorewrite.rew_lemma, NoBindings))
let old_hints (db : string) : strategy =
let rules = Autorewrite.find_rewrites db in
lemmas rewrite_unif_flags
(List.map (fun hint -> (inj_open hint, hint.Autorewrite.rew_l2r,
hint.Autorewrite.rew_tac)) rules)
let hints (db : string) : strategy =
fun env avoid t ty cstr evars ->
let rules = Autorewrite.find_matches db t in
let lemma hint = (inj_open hint, hint.Autorewrite.rew_l2r,
hint.Autorewrite.rew_tac) in
let lems = List.map lemma rules in
lemmas rewrite_unif_flags lems env avoid t ty cstr evars
let reduce (r : Redexpr.red_expr) : strategy =
fun env avoid t ty cstr evars ->
let rfn, ckind = Redexpr.reduction_of_red_expr env r in
let t' = rfn env (goalevars evars) t in
if eq_constr t' t then
Some None
else
Some (Some { rew_car = ty; rew_from = t; rew_to = t';
rew_prf = RewCast ckind; rew_evars = evars })
let fold c : strategy =
fun env avoid t ty cstr evars ->
(* let sigma, (c,_) = Tacinterp.interp_open_constr_with_bindings is env (goalevars evars) c in *)
let sigma, c = Constrintern.interp_open_constr (goalevars evars) env c in
let unfolded =
try Tacred.try_red_product env sigma c
with e when Errors.noncritical e ->
error "fold: the term is not unfoldable !"
in
try
let sigma = Unification.w_unify env sigma CONV ~flags:(Unification.elim_flags ())
unfolded t in
let c' = Evarutil.nf_evar sigma c in
Some (Some { rew_car = ty; rew_from = t; rew_to = c';
rew_prf = RewCast DEFAULTcast;
rew_evars = (sigma, snd evars) })
with e when Errors.noncritical e -> None
let fold_glob c : strategy =
fun env avoid t ty cstr evars ->
(* let sigma, (c,_) = Tacinterp.interp_open_constr_with_bindings is env (goalevars evars) c in *)
let sigma, c = Pretyping.understand_tcc (goalevars evars) env c in
let unfolded =
try Tacred.try_red_product env sigma c
with e when Errors.noncritical e ->
error "fold: the term is not unfoldable !"
in
try
let sigma = Unification.w_unify env sigma CONV ~flags:(Unification.elim_flags ()) unfolded t in
let c' = Evarutil.nf_evar sigma c in
Some (Some { rew_car = ty; rew_from = t; rew_to = c';
rew_prf = RewCast DEFAULTcast;
rew_evars = (sigma, snd evars) })
with e when Errors.noncritical e -> None
end
(** The strategy for a single rewrite, dealing with occurences. *)
let rewrite_strat flags occs hyp =
let app = apply_rule hyp None occs in
let rec aux () =
Strategies.choice app (subterm true flags (fun env -> aux () env))
in aux ()
let get_hypinfo_ids {c = opt} =
match opt with
| None -> []
| Some (is, gc) ->
let avoid = Option.default [] (TacStore.get is.extra f_avoid_ids) in
Id.Map.fold (fun id _ accu -> id :: accu) is.lfun avoid
let rewrite_with flags c left2right loccs : strategy =
fun env avoid t ty cstr evars ->
let gevars = goalevars evars in
let hypinfo = ref (decompose_applied_relation_expr env gevars flags c left2right) in
let avoid = get_hypinfo_ids !hypinfo @ avoid in
rewrite_strat default_flags loccs hypinfo env avoid t ty cstr (gevars, cstrevars evars)
let apply_strategy (s : strategy) env avoid concl (prop, cstr) evars =
let res =
s env avoid concl (Retyping.get_type_of env (goalevars evars) concl)
(prop, Some cstr) evars
in
match res with
| None -> None
| Some None -> Some None
| Some (Some res) ->
Some (Some (res.rew_prf, res.rew_evars, res.rew_car, res.rew_from, res.rew_to))
let solve_constraints env (evars,cstrs) =
Typeclasses.resolve_typeclasses env ~split:false ~fail:true
(Typeclasses.mark_resolvables ~filter:(all_constraints cstrs) evars)
let nf_zeta =
Reductionops.clos_norm_flags (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA])
exception RewriteFailure of Pp.std_ppcmds
type result = (evar_map * constr option * types) option option
let cl_rewrite_clause_aux ?(abs=None) strat env avoid sigma concl is_hyp : result =
let evars = (sigma, Evar.Set.empty) in
let evars, cstr =
let sort = Typing.sort_of env (goalevars evars) concl in
let prop, (evars, arrow) =
if is_prop_sort sort then true, app_poly_sort true env evars impl [||]
else false, app_poly_sort false env evars TypeGlobal.arrow [||]
in
match is_hyp with
| None ->
let evars, t = poly_inverse prop env evars (mkSort sort) arrow in
evars, (prop, t)
| Some _ -> evars, (prop, arrow)
in
let eq = apply_strategy strat env avoid concl cstr evars in
match eq with
| Some (Some (p, (evars, cstrs), car, oldt, newt)) ->
let evars' = solve_constraints env (evars, cstrs) in
let p = map_rewprf (fun p -> nf_zeta env evars' (Evarutil.nf_evar evars' p)) p in
let newt = Evarutil.nf_evar evars' newt in
let abs = Option.map (fun (x, y) ->
Evarutil.nf_evar evars' x, Evarutil.nf_evar evars' y) abs in
let evars = (* Keep only original evars (potentially instantiated) and goal evars,
the rest has been defined and substituted already. *)
Evar.Set.fold (fun ev acc -> Evd.remove acc ev) cstrs evars'
in
let res =
match is_hyp with
| Some id ->
(match p with
| RewPrf (rel, p) ->
let term =
match abs with
| None -> p
| Some (t, ty) ->
mkApp (mkLambda (Name (Id.of_string "lemma"), ty, p), [| t |])
in
Some (evars, Some (mkApp (term, [| mkVar id |])), newt)
| RewCast c ->
Some (evars, None, newt))
| None ->
(match p with
| RewPrf (rel, p) ->
(match abs with
| None -> Some (evars, Some p, newt)
| Some (t, ty) ->
let proof = mkApp (mkLambda (Name (Id.of_string "lemma"), ty, p), [| t |]) in
Some (evars, Some proof, newt))
| RewCast c -> Some (evars, None, newt))
in Some res
| Some None -> Some None
| None -> None
let rewrite_refine (evd,c) =
Tacmach.refine c
let cl_rewrite_clause_tac ?abs strat meta clause gl =
let evartac evd = Refiner.tclEVARS (Evd.clear_metas evd) in
let treat res =
match res with
| None -> tclFAIL 0 (str "Nothing to rewrite")
| Some None -> tclIDTAC
| Some (Some (undef, p, newt)) ->
let tac =
match clause, p with
| Some id, Some p ->
cut_replacing id newt (Tacmach.refine p)
| Some id, None ->
change_in_hyp None newt (id, InHypTypeOnly)
| None, Some p ->
let name = next_name_away_with_default "H" Anonymous (pf_ids_of_hyps gl) in
tclTHENLAST
(Tacmach.internal_cut false name newt)
(tclTHEN (Proofview.V82.of_tactic (Tactics.revert [name])) (Tacmach.refine p))
| None, None -> change_in_concl None newt
in tclTHEN (evartac undef) tac
in
let tac =
try
let concl, is_hyp =
match clause with
| Some id -> pf_get_hyp_typ gl id, Some id
| None -> pf_concl gl, None
in
let sigma = project gl in
let concl = Evarutil.nf_evar sigma concl in
let res = cl_rewrite_clause_aux ?abs strat (pf_env gl) [] sigma concl is_hyp in
treat res
with
| TypeClassError (env, (UnsatisfiableConstraints _ as e)) ->
Refiner.tclFAIL 0
(str"Unable to satisfy the rewriting constraints."
++ fnl () ++ Himsg.explain_typeclass_error env e)
in tac gl
let bind_gl_info f =
bind concl (fun c -> bind env (fun v -> bind defs (fun ev -> f c v ev)))
let new_refine c : Goal.subgoals Goal.sensitive =
let refable = Goal.Refinable.make
(fun handle -> Goal.Refinable.constr_of_open_constr handle true c)
in Goal.bind refable Goal.refine
let assert_replacing id newt tac =
let prf = Proofview.Goal.enter begin fun gl ->
let concl = Proofview.Goal.concl gl in
let env = Proofview.Goal.env gl in
let nc' =
Environ.fold_named_context
(fun _ (n, b, t as decl) nc' ->
if Id.equal n id then (n, b, newt) :: nc'
else decl :: nc')
env ~init:[]
in
Proofview.Refine.refine begin fun h ->
let env' = Environ.reset_with_named_context (val_of_named_context nc') env in
let h, ev = Proofview.Refine.new_evar h env' concl in
let h, ev' = Proofview.Refine.new_evar h env newt in
let inst =
fold_named_context
(fun _ (n, b, t) inst ->
if Id.equal n id then ev' :: inst
else if Option.is_empty b then mkVar n :: inst else inst)
env ~init:[]
in
let (e, args) = destEvar ev in
h, mkEvar (e, Array.of_list inst)
end
end in
Proofview.tclTHEN prf (Proofview.tclFOCUS 2 2 tac)
let newfail n s =
Proofview.tclZERO (Refiner.FailError (n, lazy s))
let cl_rewrite_clause_newtac ?abs strat clause =
let treat (res, is_hyp) =
match res with
| None -> newfail 0 (str "Nothing to rewrite")
| Some None -> Proofview.tclUNIT ()
| Some (Some res) ->
match is_hyp, res with
| Some id, (undef, Some p, newt) ->
assert_replacing id newt (Proofview.tclSENSITIVE (new_refine (undef, p)))
| Some id, (undef, None, newt) ->
Proofview.tclSENSITIVE (Goal.convert_hyp false (id, None, newt))
| None, (undef, Some p, newt) ->
let refable = Goal.Refinable.make
(fun handle ->
Goal.bind env
(fun env -> Goal.bind (Refinable.mkEvar handle env newt)
(fun ev ->
Goal.Refinable.constr_of_open_constr handle true
(undef, mkApp (p, [| ev |])))))
in
Proofview.tclSENSITIVE (Goal.bind refable Goal.refine)
| None, (undef, None, newt) ->
Proofview.tclSENSITIVE (Goal.convert_concl false newt)
in
let info =
bind_gl_info
(fun concl env sigma ->
let ty, is_hyp =
match clause with
| Some id -> Environ.named_type id env, Some id
| None -> concl, None
in
try
let res =
cl_rewrite_clause_aux ?abs strat env [] sigma ty is_hyp
in return (res, is_hyp)
with
| TypeClassError (env, (UnsatisfiableConstraints _ as e)) ->
raise (RewriteFailure (str"Unable to satisfy the rewriting constraints."
++ fnl () ++ Himsg.explain_typeclass_error env e)))
in Proofview.Goal.lift info (fun i -> treat i)
let newtactic_init_setoid () =
try init_setoid (); Proofview.tclUNIT ()
with e when Errors.noncritical e -> Proofview.tclZERO e
let tactic_init_setoid () =
try init_setoid (); tclIDTAC
with e when Errors.noncritical e -> tclFAIL 0 (str"Setoid library not loaded")
let cl_rewrite_clause_new_strat ?abs strat clause =
Proofview.tclTHEN (newtactic_init_setoid ())
(try cl_rewrite_clause_newtac ?abs strat clause
with RewriteFailure s ->
newfail 0 (str"setoid rewrite failed: " ++ s))
let cl_rewrite_clause_newtac' l left2right occs clause =
Proofview.tclFOCUS 1 1
(cl_rewrite_clause_new_strat (rewrite_with rewrite_unif_flags l left2right occs) clause)
let cl_rewrite_clause_strat strat clause =
tclTHEN (tactic_init_setoid ())
(fun gl ->
let meta = Evarutil.new_meta() in
(* let gl = { gl with sigma = Typeclasses.mark_unresolvables gl.sigma } in *)
try cl_rewrite_clause_tac strat (mkMeta meta) clause gl
with RewriteFailure e ->
tclFAIL 0 (str"setoid rewrite failed: " ++ e) gl
| Refiner.FailError (n, pp) ->
tclFAIL n (str"setoid rewrite failed: " ++ Lazy.force pp) gl)
let cl_rewrite_clause l left2right occs clause gl =
cl_rewrite_clause_strat (rewrite_with (general_rewrite_unif_flags ()) l left2right occs) clause gl
let occurrences_of = function
| n::_ as nl when n < 0 -> (false,List.map abs nl)
| nl ->
if List.exists (fun n -> n < 0) nl then
error "Illegal negative occurrence number.";
(true,nl)
open Extraargs
let apply_constr_expr c l2r occs = fun env avoid t ty cstr evars ->
let evd, c = Constrintern.interp_open_constr (goalevars evars) env c in
apply_lemma (general_rewrite_unif_flags ()) (Evd.empty, (c, NoBindings))
l2r None occs env avoid t ty cstr (evd, cstrevars evars)
let apply_glob_constr c l2r occs = fun env avoid t ty cstr evars ->
let evd, c = (Pretyping.understand_tcc (goalevars evars) env c) in
apply_lemma (general_rewrite_unif_flags ()) (Evd.empty, (c, NoBindings))
l2r None occs env avoid t ty cstr (evd, cstrevars evars)
let interp_constr_list env sigma =
List.map (fun c ->
let evd, c = Constrintern.interp_open_constr sigma env c in
(evd, (c, NoBindings)), true, None)
let interp_glob_constr_list env sigma =
List.map (fun c ->
let evd, c = Pretyping.understand_tcc sigma env c in
(evd, (c, NoBindings)), true, None)
(* Syntax for rewriting with strategies *)
type ('constr,'redexpr) strategy_ast =
| StratId | StratFail | StratRefl
| StratUnary of string * ('constr,'redexpr) strategy_ast
| StratBinary of string * ('constr,'redexpr) strategy_ast * ('constr,'redexpr) strategy_ast
| StratConstr of 'constr * bool
| StratTerms of 'constr list
| StratHints of bool * string
| StratEval of 'redexpr
| StratFold of 'constr
let rec map_strategy (f : 'a -> 'a2) (g : 'b -> 'b2) : ('a,'b) strategy_ast -> ('a2,'b2) strategy_ast = function
| StratId | StratFail | StratRefl as s -> s
| StratUnary (s, str) -> StratUnary (s, map_strategy f g str)
| StratBinary (s, str, str') -> StratBinary (s, map_strategy f g str, map_strategy f g str')
| StratConstr (c, b) -> StratConstr (f c, b)
| StratTerms l -> StratTerms (List.map f l)
| StratHints (b, id) -> StratHints (b, id)
| StratEval r -> StratEval (g r)
| StratFold c -> StratFold (f c)
let rec strategy_of_ast = function
| StratId -> Strategies.id
| StratFail -> Strategies.fail
| StratRefl -> Strategies.refl
| StratUnary (f, s) ->
let s' = strategy_of_ast s in
let f' = match f with
| "subterms" -> all_subterms
| "subterm" -> one_subterm
| "innermost" -> Strategies.innermost
| "outermost" -> Strategies.outermost
| "bottomup" -> Strategies.bu
| "topdown" -> Strategies.td
| "progress" -> Strategies.progress
| "try" -> Strategies.try_
| "any" -> Strategies.any
| "repeat" -> Strategies.repeat
| _ -> anomaly ~label:"strategy_of_ast" (str"Unkwnon strategy: " ++ str f)
in f' s'
| StratBinary (f, s, t) ->
let s' = strategy_of_ast s in
let t' = strategy_of_ast t in
let f' = match f with
| "compose" -> Strategies.seq
| "choice" -> Strategies.choice
| _ -> anomaly ~label:"strategy_of_ast" (str"Unkwnon strategy: " ++ str f)
in f' s' t'
| StratConstr (c, b) -> apply_glob_constr (fst c) b AllOccurrences
| StratHints (old, id) -> if old then Strategies.old_hints id else Strategies.hints id
| StratTerms l ->
(fun env avoid t ty cstr evars ->
let l' = interp_glob_constr_list env (goalevars evars) (List.map fst l) in
Strategies.lemmas rewrite_unif_flags l' env avoid t ty cstr evars)
| StratEval r ->
(fun env avoid t ty cstr evars ->
let (sigma,r_interp) = Tacinterp.interp_redexp env (goalevars evars) r in
Strategies.reduce r_interp env avoid t ty cstr (sigma,cstrevars evars))
| StratFold c -> Strategies.fold_glob (fst c)
(* By default the strategy for "rewrite_db" is top-down *)
let mkappc s l = CAppExpl (Loc.ghost,(None,(Libnames.Ident (Loc.ghost,Id.of_string s)),None),l)
let declare_an_instance n s args =
((Loc.ghost,Name n), Explicit,
CAppExpl (Loc.ghost, (None, Qualid (Loc.ghost, qualid_of_string s),None),
args))
let declare_instance a aeq n s = declare_an_instance n s [a;aeq]
let anew_instance global binders instance fields =
new_instance (Flags.is_universe_polymorphism ())
binders instance (Some (true, CRecord (Loc.ghost,None,fields)))
~global ~generalize:false None
let declare_instance_refl global binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Reflexive") "Coq.Classes.RelationClasses.Reflexive"
in anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "reflexivity"),lemma)]
let declare_instance_sym global binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Symmetric") "Coq.Classes.RelationClasses.Symmetric"
in anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "symmetry"),lemma)]
let declare_instance_trans global binders a aeq n lemma =
let instance = declare_instance a aeq (add_suffix n "_Transitive") "Coq.Classes.RelationClasses.Transitive"
in anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "transitivity"),lemma)]
let declare_relation ?(binders=[]) a aeq n refl symm trans =
init_setoid ();
let global = not (Locality.make_section_locality (Locality.LocalityFixme.consume ())) in
let instance = declare_instance a aeq (add_suffix n "_relation") "Coq.Classes.RelationClasses.RewriteRelation"
in ignore(anew_instance global binders instance []);
match (refl,symm,trans) with
(None, None, None) -> ()
| (Some lemma1, None, None) ->
ignore (declare_instance_refl global binders a aeq n lemma1)
| (None, Some lemma2, None) ->
ignore (declare_instance_sym global binders a aeq n lemma2)
| (None, None, Some lemma3) ->
ignore (declare_instance_trans global binders a aeq n lemma3)
| (Some lemma1, Some lemma2, None) ->
ignore (declare_instance_refl global binders a aeq n lemma1);
ignore (declare_instance_sym global binders a aeq n lemma2)
| (Some lemma1, None, Some lemma3) ->
let _lemma_refl = declare_instance_refl global binders a aeq n lemma1 in
let _lemma_trans = declare_instance_trans global binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PreOrder"
in ignore(
anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "PreOrder_Reflexive"), lemma1);
(Ident (Loc.ghost,Id.of_string "PreOrder_Transitive"),lemma3)])
| (None, Some lemma2, Some lemma3) ->
let _lemma_sym = declare_instance_sym global binders a aeq n lemma2 in
let _lemma_trans = declare_instance_trans global binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PER"
in ignore(
anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "PER_Symmetric"), lemma2);
(Ident (Loc.ghost,Id.of_string "PER_Transitive"),lemma3)])
| (Some lemma1, Some lemma2, Some lemma3) ->
let _lemma_refl = declare_instance_refl global binders a aeq n lemma1 in
let _lemma_sym = declare_instance_sym global binders a aeq n lemma2 in
let _lemma_trans = declare_instance_trans global binders a aeq n lemma3 in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.Equivalence"
in ignore(
anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "Equivalence_Reflexive"), lemma1);
(Ident (Loc.ghost,Id.of_string "Equivalence_Symmetric"), lemma2);
(Ident (Loc.ghost,Id.of_string "Equivalence_Transitive"), lemma3)])
let cHole = CHole (Loc.ghost, None, None)
let proper_projection r ty =
let ctx, inst = decompose_prod_assum ty in
let mor, args = destApp inst in
let instarg = mkApp (r, rel_vect 0 (List.length ctx)) in
let app = mkApp (Lazy.force PropGlobal.proper_proj,
Array.append args [| instarg |]) in
it_mkLambda_or_LetIn app ctx
let declare_projection n instance_id r =
let c,uctx = Universes.fresh_global_instance (Global.env()) r in
let poly = Global.is_polymorphic r in
let ty = Retyping.get_type_of (Global.env ()) Evd.empty c in
let term = proper_projection c ty in
let typ = Typing.type_of (Global.env ()) Evd.empty term in
let ctx, typ = decompose_prod_assum typ in
let typ =
let n =
let rec aux t =
match kind_of_term t with
| App (f, [| a ; a' ; rel; rel' |])
when Globnames.is_global (PropGlobal.respectful_ref ()) f ->
succ (aux rel')
| _ -> 0
in
let init =
match kind_of_term typ with
App (f, args) when Globnames.is_global (PropGlobal.respectful_ref ()) f ->
mkApp (f, fst (Array.chop (Array.length args - 2) args))
| _ -> typ
in aux init
in
let ctx,ccl = Reductionops.splay_prod_n (Global.env()) Evd.empty (3 * n) typ
in it_mkProd_or_LetIn ccl ctx
in
let typ = it_mkProd_or_LetIn typ ctx in
let cst =
Declare.definition_entry ~types:typ ~poly ~univs:(Univ.ContextSet.to_context uctx)
term
in
ignore(Declare.declare_constant n
(Entries.DefinitionEntry cst, Decl_kinds.IsDefinition Decl_kinds.Definition))
let build_morphism_signature m =
let env = Global.env () in
let m,ctx = Constrintern.interp_constr Evd.empty env m in
let sigma = Evd.from_env ~ctx:(Evd.evar_universe_context_set ctx) env in
let t = Typing.type_of env sigma m in
let cstrs =
let rec aux t =
match kind_of_term t with
| Prod (na, a, b) ->
None :: aux b
| _ -> []
in aux t
in
let evars, t', sig_, cstrs =
PropGlobal.build_signature (Evd.empty, Evar.Set.empty) env t cstrs None in
let evd = ref evars in
let _ = List.iter
(fun (ty, rel) ->
Option.iter (fun rel ->
let default = e_app_poly env evd PropGlobal.default_relation [| ty; rel |] in
ignore(e_new_cstr_evar evd env default))
rel)
cstrs
in
let morph = e_app_poly env evd PropGlobal.proper_type [| t; sig_; m |] in
let evd = solve_constraints env !evd in
let m = Evarutil.nf_evar evd morph in
Evarutil.check_evars env Evd.empty evd m; m
let default_morphism sign m =
let env = Global.env () in
let t = Typing.type_of env Evd.empty m in
let evars, _, sign, cstrs =
PropGlobal.build_signature (Evd.empty, Evar.Set.empty) env t (fst sign) (snd sign)
in
let evars, morph = app_poly_check env evars PropGlobal.proper_type [| t; sign; m |] in
let evars, mor = resolve_one_typeclass env (goalevars evars) morph in
mor, proper_projection mor morph
let add_setoid global binders a aeq t n =
init_setoid ();
let _lemma_refl = declare_instance_refl global binders a aeq n (mkappc "Seq_refl" [a;aeq;t]) in
let _lemma_sym = declare_instance_sym global binders a aeq n (mkappc "Seq_sym" [a;aeq;t]) in
let _lemma_trans = declare_instance_trans global binders a aeq n (mkappc "Seq_trans" [a;aeq;t]) in
let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.Equivalence"
in ignore(
anew_instance global binders instance
[(Ident (Loc.ghost,Id.of_string "Equivalence_Reflexive"), mkappc "Seq_refl" [a;aeq;t]);
(Ident (Loc.ghost,Id.of_string "Equivalence_Symmetric"), mkappc "Seq_sym" [a;aeq;t]);
(Ident (Loc.ghost,Id.of_string "Equivalence_Transitive"), mkappc "Seq_trans" [a;aeq;t])])
let make_tactic name =
let open Tacexpr in
let loc = Loc.ghost in
let tacpath = Libnames.qualid_of_string name in
let tacname = Qualid (loc, tacpath) in
TacArg (loc, TacCall (loc, tacname, []))
let add_morphism_infer glob m n =
init_setoid ();
let poly = Flags.is_universe_polymorphism () in
let instance_id = add_suffix n "_Proper" in
let instance = build_morphism_signature m in
let ctx = Univ.ContextSet.empty (*FIXME *) in
if Lib.is_modtype () then
let cst = Declare.declare_constant ~internal:Declare.KernelSilent instance_id
(Entries.ParameterEntry
(None,poly,(instance,Univ.UContext.empty),None),
Decl_kinds.IsAssumption Decl_kinds.Logical)
in
add_instance (Typeclasses.new_instance
(Lazy.force PropGlobal.proper_class) None glob
poly (ConstRef cst));
declare_projection n instance_id (ConstRef cst)
else
let kind = Decl_kinds.Global, poly,
Decl_kinds.DefinitionBody Decl_kinds.Instance
in
let tac = make_tactic "Coq.Classes.SetoidTactics.add_morphism_tactic" in
let hook _ = function
| Globnames.ConstRef cst ->
add_instance (Typeclasses.new_instance
(Lazy.force PropGlobal.proper_class) None
glob poly (ConstRef cst));
declare_projection n instance_id (ConstRef cst)
| _ -> assert false
in
let hook = Lemmas.mk_hook hook in
Flags.silently
(fun () ->
Lemmas.start_proof instance_id kind (instance, ctx) hook;
ignore (Pfedit.by (Tacinterp.interp tac))) ()
let add_morphism glob binders m s n =
init_setoid ();
let poly = Flags.is_universe_polymorphism () in
let instance_id = add_suffix n "_Proper" in
let instance =
((Loc.ghost,Name instance_id), Explicit,
CAppExpl (Loc.ghost,
(None, Qualid (Loc.ghost, Libnames.qualid_of_string "Coq.Classes.Morphisms.Proper"),None),
[cHole; s; m]))
in
let tac = Tacinterp.interp (make_tactic "add_morphism_tactic") in
ignore(new_instance ~global:glob poly binders instance
(Some (true, CRecord (Loc.ghost,None,[])))
~generalize:false ~tac ~hook:(declare_projection n instance_id) None)
(** Bind to "rewrite" too *)
(** Taken from original setoid_replace, to emulate the old rewrite semantics where
lemmas are first instantiated and then rewrite proceeds. *)
let check_evar_map_of_evars_defs evd =
let metas = Evd.meta_list evd in
let check_freemetas_is_empty rebus =
Evd.Metaset.iter
(fun m ->
if Evd.meta_defined evd m then () else
raise
(Logic.RefinerError (Logic.UnresolvedBindings [Evd.meta_name evd m])))
in
List.iter
(fun (_,binding) ->
match binding with
Evd.Cltyp (_,{Evd.rebus=rebus; Evd.freemetas=freemetas}) ->
check_freemetas_is_empty rebus freemetas
| Evd.Clval (_,({Evd.rebus=rebus1; Evd.freemetas=freemetas1},_),
{Evd.rebus=rebus2; Evd.freemetas=freemetas2}) ->
check_freemetas_is_empty rebus1 freemetas1 ;
check_freemetas_is_empty rebus2 freemetas2
) metas
let unification_rewrite flags l2r c1 c2 cl car rel but gl =
let env = pf_env gl in
let evd = Evd.merge (project gl) cl.evd in
let (evd',c') =
try
(* ~flags:(false,true) to allow to mark occurrences that must not be
rewritten simply by replacing them with let-defined definitions
in the context *)
Unification.w_unify_to_subterm
~flags:{ rewrite_unif_flags with Unification.resolve_evars = true } env
evd ((if l2r then c1 else c2),but)
with
Pretype_errors.PretypeError _ ->
(* ~flags:(true,true) to make Ring work (since it really
exploits conversion) *)
Unification.w_unify_to_subterm
~flags:{ flags with Unification.resolve_evars = true }
env evd ((if l2r then c1 else c2),but)
in
let cl' = {cl with evd = evd'} in
let cl' = Clenvtac.clenv_pose_dependent_evars true cl' in
let nf c = Evarutil.nf_evar cl'.evd (Clenv.clenv_nf_meta cl' c) in
let c1 = if l2r then nf c' else nf c1
and c2 = if l2r then nf c2 else nf c'
and car = nf car and rel = nf rel in
check_evar_map_of_evars_defs cl'.evd;
let prf = nf (Clenv.clenv_value cl') and prfty = nf (Clenv.clenv_type cl') in
let sort = sort_of_rel env evd' (pf_concl gl) in
let cl' = { cl' with templval = mk_freelisted prf ; templtyp = mk_freelisted prfty;
evd = Evd.diff cl'.evd (project gl) }
in
{cl=cl'; prf=(mkRel 1); car=car; rel=rel; l2r=l2r;
c1=c1; c2=c2; c=None; abs=Some (prf, prfty); sort = Sorts.is_prop sort; flags = flags}
let get_hyp gl evars (c,l) clause l2r =
let flags = rewrite2_unif_flags in
let hi = decompose_applied_relation (pf_env gl) evars evars flags None (c,l) l2r in
let but = match clause with
| Some id -> pf_get_hyp_typ gl id
| None -> Evarutil.nf_evar evars (pf_concl gl)
in
let unif = unification_rewrite flags hi.l2r hi.c1 hi.c2 hi.cl hi.car hi.rel but gl in
{ unif with flags = rewrite_unif_flags }
let general_rewrite_flags = { under_lambdas = false; on_morphisms = true }
let apply_lemma gl (c,l) cl l2r occs =
let sigma = project gl in
let hypinfo = ref (get_hyp gl sigma (c,l) cl l2r) in
let app = apply_rule hypinfo None occs in
let rec aux () =
Strategies.choice app (subterm true general_rewrite_flags (fun env -> aux () env))
in !hypinfo, aux ()
let cl_rewrite_clause_tac abs strat meta cl gl =
cl_rewrite_clause_tac ~abs strat meta cl gl
(* let rewriteclaustac_key = Profile.declare_profile "cl_rewrite_clause_tac";; *)
(* let cl_rewrite_clause_tac = Profile.profile5 rewriteclaustac_key cl_rewrite_clause_tac *)
let general_s_rewrite cl l2r occs (c,l) ~new_goals gl =
let meta = Evarutil.new_meta() in
let hypinfo, strat = apply_lemma gl (c,l) cl l2r occs in
try
tclWEAK_PROGRESS
(tclTHEN
(Refiner.tclEVARS (Evd.merge (project gl) hypinfo.cl.evd))
(cl_rewrite_clause_tac hypinfo.abs strat (mkMeta meta) cl)) gl
with RewriteFailure e ->
let {l2r=l2r; c1=x; c2=y} = hypinfo in
raise (Pretype_errors.PretypeError
(pf_env gl,project gl,
Pretype_errors.NoOccurrenceFound ((if l2r then x else y), cl)))
open Proofview.Notations
let general_s_rewrite_clause x =
match x with
| None -> general_s_rewrite None
| Some id -> general_s_rewrite (Some id)
let general_s_rewrite_clause x y z w ~new_goals =
newtactic_init_setoid () <*>
Proofview.V82.tactic (general_s_rewrite_clause x y z w ~new_goals)
let _ = Hook.set Equality.general_rewrite_clause general_s_rewrite_clause
(** [setoid_]{reflexivity,symmetry,transitivity} tactics *)
let not_declared env ty rel =
Tacticals.New.tclFAIL 0 (str" The relation " ++ Printer.pr_constr_env env rel ++ str" is not a declared " ++
str ty ++ str" relation. Maybe you need to require the Setoid library")
let setoid_proof ty fn fallback =
Proofview.Goal.enter begin fun gl ->
let env = Proofview.Goal.env gl in
let sigma = Proofview.Goal.sigma gl in
let concl = Proofview.Goal.concl gl in
Proofview.tclORELSE
begin
try
let rel, args = decompose_app_rel env sigma concl in
let evm = sigma in
let car = pi3 (List.hd (fst (Reduction.dest_prod env (Typing.type_of env evm rel)))) in
fn env sigma car rel
with e -> Proofview.tclZERO e
end
begin function
| e ->
Proofview.tclORELSE
fallback
begin function
| Hipattern.NoEquationFound ->
(* spiwack: [Errors.push] here is unlikely to do what
it's intended to, or anything meaningful for that
matter. *)
let e = Errors.push e in
begin match e with
| Not_found ->
let rel, args = decompose_app_rel env sigma concl in
not_declared env ty rel
| _ -> Proofview.tclZERO e
end
| e' -> Proofview.tclZERO e'
end
end
end
let tac_open ((evm,_), c) tac =
Proofview.V82.tactic
(tclTHEN (Refiner.tclEVARS evm) (tac c))
let poly_proof getp gett env evm car rel =
if Sorts.is_prop (sort_of_rel env evm rel) then
getp env (evm,Evar.Set.empty) car rel
else gett env (evm,Evar.Set.empty) car rel
let setoid_reflexivity =
setoid_proof "reflexive"
(fun env evm car rel ->
tac_open (poly_proof PropGlobal.get_reflexive_proof TypeGlobal.get_reflexive_proof
env evm car rel) apply)
(reflexivity_red true)
let setoid_symmetry =
setoid_proof "symmetric"
(fun env evm car rel ->
tac_open
(poly_proof PropGlobal.get_symmetric_proof TypeGlobal.get_symmetric_proof
env evm car rel)
apply)
(symmetry_red true)
let setoid_transitivity c =
setoid_proof "transitive"
(fun env evm car rel ->
tac_open (poly_proof PropGlobal.get_transitive_proof TypeGlobal.get_transitive_proof
env evm car rel)
(fun proof -> match c with
| None -> eapply proof
| Some c -> apply_with_bindings (proof,ImplicitBindings [ c ])))
(transitivity_red true c)
let setoid_symmetry_in id =
Proofview.V82.tactic (fun gl ->
let ctype = pf_type_of gl (mkVar id) in
let binders,concl = decompose_prod_assum ctype in
let (equiv, args) = decompose_app concl in
let rec split_last_two = function
| [c1;c2] -> [],(c1, c2)
| x::y::z -> let l,res = split_last_two (y::z) in x::l, res
| _ -> error "The term provided is not an equivalence."
in
let others,(c1,c2) = split_last_two args in
let he,c1,c2 = mkApp (equiv, Array.of_list others),c1,c2 in
let new_hyp' = mkApp (he, [| c2 ; c1 |]) in
let new_hyp = it_mkProd_or_LetIn new_hyp' binders in
tclTHENS (Proofview.V82.of_tactic (Tactics.cut new_hyp))
[ intro_replacing id;
tclTHENLIST [ Proofview.V82.of_tactic intros; Proofview.V82.of_tactic setoid_symmetry; apply (mkVar id); Proofview.V82.of_tactic Tactics.assumption ] ]
gl)
let _ = Hook.set Tactics.setoid_reflexivity setoid_reflexivity
let _ = Hook.set Tactics.setoid_symmetry setoid_symmetry
let _ = Hook.set Tactics.setoid_symmetry_in setoid_symmetry_in
let _ = Hook.set Tactics.setoid_transitivity setoid_transitivity
let implify id gl =
let (_, b, ctype) = pf_get_hyp gl id in
let binders,concl = decompose_prod_assum ctype in
let evm, ctype' =
match binders with
| (_, None, ty as hd) :: tl when noccurn 1 concl ->
let env = Environ.push_rel_context tl (pf_env gl) in
let sigma = project gl in
let tyhd = Retyping.get_type_of env sigma ty
and tyconcl = Retyping.get_type_of (Environ.push_rel hd env) sigma concl in
let ((sigma,_), app), unfold =
PropGlobal.arrow_morphism env (sigma, Evar.Set.empty) tyhd
(subst1 mkProp tyconcl) ty (subst1 mkProp concl)
in
sigma, it_mkProd_or_LetIn app tl
| _ -> project gl, ctype
in tclTHEN (Refiner.tclEVARS evm) (Tacmach.convert_hyp (id, b, ctype')) gl
let rec fold_matches env sigma c =
map_constr_with_full_binders Environ.push_rel
(fun env c ->
match kind_of_term c with
| Case _ ->
let cst, env, c', _eff = fold_match ~force:true env sigma c in
fold_matches env sigma c'
| _ -> fold_matches env sigma c)
env c
let fold_match_tac c gl =
let _, _, c', eff = fold_match ~force:true (pf_env gl) (project gl) c in
let gl = { gl with sigma = Evd.emit_side_effects eff gl.sigma } in
change (Some (snd (Patternops.pattern_of_constr (project gl) c))) c' onConcl gl
let fold_matches_tac c gl =
let c' = fold_matches (pf_env gl) (project gl) c in
(* let gl = { gl with sigma = Evd.emit_side_effects eff gl.sigma } in *)
change (Some (snd (Patternops.pattern_of_constr (project gl) c))) c' onConcl gl
let myapply id l gl =
let gr = id in
let _, impls = List.hd (Impargs.implicits_of_global gr) in
let env = pf_env gl in
let evars = ref (project gl) in
let evd, ty = fresh_global env !evars gr in
let _ = evars := evd in
let app =
let rec aux ty impls args args' =
match impls, kind_of_term ty with
| Some (_, _, (_, _)) :: impls, Prod (n, t, t') ->
let arg = Evarutil.e_new_evar evars env t in
aux (subst1 arg t') impls args (arg :: args')
| None :: impls, Prod (n, t, t') ->
(match args with
| [] ->
if dependent (mkRel 1) t' then
let arg = Evarutil.e_new_evar evars env t in
aux (subst1 arg t') impls args (arg :: args')
else
let arg = Evarutil.mk_new_meta () in
evars := meta_declare (destMeta arg) t !evars;
aux (subst1 arg t') impls args (arg :: args')
| arg :: args ->
aux (subst1 arg t') impls args (arg :: args'))
| _, _ -> mkApp (Universes.constr_of_global gr, Array.of_list (List.rev args'))
in aux ty impls l []
in
tclTHEN (Refiner.tclEVARS !evars) (apply app) gl
let get_lemma_proof f env evm x y =
let (evm, _), c = f env (evm,Evar.Set.empty) x y in
evm, c
let get_reflexive_proof =
get_lemma_proof PropGlobal.get_reflexive_proof
let get_symmetric_proof =
get_lemma_proof PropGlobal.get_symmetric_proof
let get_transitive_proof =
get_lemma_proof PropGlobal.get_transitive_proof
|