(************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* anomaly (str ("Global reference " ^ s ^ " not found in generalized rewriting")) 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 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 env evd t in let ev, _ = destEvar t in (evd', Evar.Set.add ev cstrs), t (** Building or looking up instances. *) let e_new_cstr_evar env evars t = let evd', t = new_cstr_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 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 *) (app_poly env evd arrow [| a; b |]), unfold_impl (* (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) (** 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 env' sigma Evd.univ_flexible in let evars, inst = app_poly env (evars,Evar.Set.empty) 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 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 env evd Evd.univ_flexible 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) let is_applied_rewrite_relation = PropGlobal.is_applied_rewrite_relation (* 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 let evd = Evarconv.the_conv_x env x y evd in (* Unfortunately, the_conv_x might say they are unifiable even if some unsolvable constraints remain, so we check them here *) let evd = Evarconv.consider_remaining_unif_problems env evd in let () = Evarconv.check_problems_are_solved env evd in Some evd with e when Errors.noncritical e -> None let convertible env evd x y = Reductionops.is_conv_leq env evd x y type hypinfo = { env : env; prf : constr; car : constr; rel : constr; sort : bool; (* true = Prop; false = Type *) c1 : constr; c2 : constr; holes : Clenv.hole list; } 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 = (** Head normalize for compatibility with the old meta mechanism *) let t = Reductionops.whd_betaiota evd t in match kind_of_term t with | App (f, [||]) -> assert false | App (f, [|arg|]) -> let (f', argl, argr) = decompose_app_rel env evd arg in let ty = Typing.type_of env evd argl 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'', argl, argr) | App (f, args) -> let len = Array.length args in let fargs = Array.sub args 0 (Array.length args - 2) in mkApp (f, fargs), args.(len - 2), args.(len - 1) | _ -> error "Cannot find a relation to rewrite." let decompose_applied_relation env sigma (c,l) = let ctype = Retyping.get_type_of env sigma c in let find_rel ty = let sigma, cl = Clenv.make_evar_clause env sigma ty in let sigma = Clenv.solve_evar_clause env sigma true cl l in let { Clenv.cl_holes = holes; Clenv.cl_concl = t } = cl in let (equiv, c1, c2) = decompose_app_rel env sigma t in let ty1 = Retyping.get_type_of env sigma c1 in let ty2 = Retyping.get_type_of env sigma c2 in match evd_convertible env sigma ty1 ty2 with | None -> None | Some sigma -> let sort = sort_of_rel env sigma equiv in let args = Array.map_of_list (fun h -> h.Clenv.hole_evar) holes in let value = mkApp (c, args) in Some (sigma, { env=env; prf=value; car=ty1; rel = equiv; sort = Sorts.is_prop sort; c1=c1; c2=c2; holes }) 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 "Cannot find an homogeneous relation to rewrite." let decompose_applied_relation_expr env sigma (is, (c,l)) = let sigma, cbl = Tacinterp.interp_open_constr_with_bindings is env sigma (c,l) in decompose_applied_relation env sigma cbl let rewrite_db = "rewrite" let conv_transparent_state = (Id.Pred.empty, Cpred.full) let _ = Hints.add_hints_init (fun () -> Hints.create_hint_db false rewrite_db conv_transparent_state true) let rewrite_transparent_state () = Hints.Hint_db.transparent_state (Hints.searchtable_map rewrite_db) let rewrite_core_unif_flags = { Unification.modulo_conv_on_closed_terms = None; Unification.use_metas_eagerly_in_conv_on_closed_terms = true; Unification.use_evars_eagerly_in_conv_on_closed_terms = true; Unification.modulo_delta = empty_transparent_state; Unification.modulo_delta_types = full_transparent_state; Unification.check_applied_meta_types = true; 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; } (* Flags used for the setoid variant of "rewrite" and for the strategies "hints"/"old_hints"/"terms" of "rewrite_strat", and for solving pre-existing evars in "rewrite" (see unify_abs) *) let rewrite_unif_flags = let flags = rewrite_core_unif_flags in { Unification.core_unify_flags = flags; Unification.merge_unify_flags = flags; Unification.subterm_unify_flags = flags; Unification.allow_K_in_toplevel_higher_order_unification = true; Unification.resolve_evars = true } let rewrite_core_conv_unif_flags = { rewrite_core_unif_flags with Unification.modulo_conv_on_closed_terms = Some conv_transparent_state; Unification.modulo_delta_types = conv_transparent_state; Unification.modulo_betaiota = true } (* Fallback flags for the setoid variant of "rewrite" *) let rewrite_conv_unif_flags = let flags = rewrite_core_conv_unif_flags in { Unification.core_unify_flags = flags; Unification.merge_unify_flags = flags; Unification.subterm_unify_flags = flags; Unification.allow_K_in_toplevel_higher_order_unification = true; Unification.resolve_evars = true } (* Flags for "setoid_rewrite c"/"rewrite_strat -> c" *) let general_rewrite_unif_flags () = let ts = rewrite_transparent_state () in let core_flags = { rewrite_core_unif_flags with Unification.modulo_conv_on_closed_terms = Some ts; Unification.use_evars_eagerly_in_conv_on_closed_terms = false; Unification.modulo_delta = ts; Unification.modulo_delta_types = ts; Unification.modulo_betaiota = true } in { Unification.core_unify_flags = core_flags; Unification.merge_unify_flags = core_flags; Unification.subterm_unify_flags = { core_flags with Unification.modulo_delta = empty_transparent_state }; Unification.allow_K_in_toplevel_higher_order_unification = true; Unification.resolve_evars = true } let refresh_hypinfo env sigma hypinfo c = let sigma, hypinfo = match hypinfo with | None -> decompose_applied_relation_expr env sigma c | Some hypinfo -> if hypinfo.env != env then (* If the lemma actually generates existential variables, we cannot use it here as it will polute the evar map with existential variables that might not ever get instantiated (e.g. if we rewrite under a binder and need to refresh [c] again) *) (* TODO: remove bindings in sigma corresponding to c *) decompose_applied_relation_expr env sigma c else sigma, hypinfo in let { c1; c2; car; rel; prf; sort; holes } = hypinfo in sigma, (car, rel, prf, c1, c2, holes, sort) (** FIXME: write this in the new monad interface *) let solve_remaining_by env sigma holes by = match by with | None -> sigma | Some tac -> let map h = if h.Clenv.hole_deps then None else let (evk, _) = destEvar (h.Clenv.hole_evar) in Some evk in (** Only solve independent holes *) let indep = List.map_filter map holes in let solve_tac = Tacticals.New.tclCOMPLETE (Tacinterp.eval_tactic tac) in let solve sigma evk = let evi = try Some (Evd.find_undefined sigma evk) with Not_found -> None in match evi with | None -> sigma (** Evar should not be defined, but just in case *) | Some evi -> let ctx = Evd.evar_universe_context sigma in let env = Environ.reset_with_named_context evi.evar_hyps env in let ty = evi.evar_concl in let c, _, ctx = Pfedit.build_by_tactic env ctx ty solve_tac in let sigma = Evd.set_universe_context sigma ctx in Evd.define evk c sigma in List.fold_left solve sigma indep 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 type rewrite_proof = | RewPrf of constr * constr | RewCast of cast_kind type rewrite_result_info = { rew_car : constr; rew_from : constr; rew_to : constr; rew_prf : rewrite_proof; rew_evars : evars; } type rewrite_result = | Fail | Identity | Success of rewrite_result_info type 'a pure_strategy = 'a -> Environ.env -> Id.t list -> constr -> types -> (bool (* prop *) * constr option) -> evars -> 'a * rewrite_result type strategy = unit pure_strategy let symmetry env sort rew = let { rew_evars = evars; rew_car = car; } = rew in let (rew_evars, rew_prf) = match rew.rew_prf with | RewCast _ -> (rew.rew_evars, rew.rew_prf) | RewPrf (rel, prf) -> try let evars, symprf = get_symmetric_proof sort env evars car rel in let prf = mkApp (symprf, [| rew.rew_from ; rew.rew_to ; prf |]) in (evars, RewPrf (rel, prf)) with Not_found -> let evars, rel = poly_inverse sort env evars car rel in (evars, RewPrf (rel, prf)) in { rew with rew_from = rew.rew_to; rew_to = rew.rew_from; rew_prf; rew_evars; } (* Matching/unifying the rewriting rule against [t] *) let unify_eqn (car, rel, prf, c1, c2, holes, sort) l2r flags env (sigma, cstrs) by t = try let left = if l2r then c1 else c2 in let sigma = Unification.w_unify ~flags env sigma CONV left t in let sigma = Typeclasses.resolve_typeclasses ~filter:(no_constraints cstrs) ~fail:true env sigma in let evd = solve_remaining_by env sigma holes by in let nf c = Evarutil.nf_evar evd (Reductionops.nf_meta evd c) in let c1 = nf c1 and c2 = nf c2 and rew_car = nf car and rel = nf rel and prf = nf prf in let ty1 = Retyping.get_type_of env evd c1 in let ty2 = Retyping.get_type_of env evd c2 in let () = if not (convertible env evd ty2 ty1) then raise Reduction.NotConvertible in let rew_evars = evd, cstrs in let rew_prf = RewPrf (rel, prf) in let rew = { rew_evars; rew_prf; rew_car; rew_from = c1; rew_to = c2; } in let rew = if l2r then rew else symmetry env sort rew in Some rew with | e when Class_tactics.catchable e -> None | Reduction.NotConvertible -> None let unify_abs (car, rel, prf, c1, c2) l2r sort env (sigma, cstrs) t = try let left = if l2r then c1 else c2 in (* The pattern is already instantiated, so the next w_unify is basically an eq_constr, except when preexisting evars occur in either the lemma or the goal, in which case the eq_constr also solved this evars *) let sigma = Unification.w_unify ~flags:rewrite_unif_flags env sigma CONV left t in let rew_evars = sigma, cstrs in let rew_prf = RewPrf (rel, prf) in let rew = { rew_car = car; rew_from = c1; rew_to = c2; rew_prf; rew_evars; } in let rew = if l2r then rew else symmetry env sort rew in Some ((), rew) with | e when Class_tactics.catchable e -> None | Reduction.NotConvertible -> None type rewrite_flags = { under_lambdas : bool; on_morphisms : bool } let default_flags = { under_lambdas = true; on_morphisms = true; } let get_opt_rew_rel = function RewPrf (rel, prf) -> Some rel | _ -> None 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_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 inside dependent arguments of a 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, substl subst a, substl subst 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 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 apply_rule unify loccs : ('a * int) pure_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 fun (hypinfo, occ) env avoid t ty cstr evars -> let unif = if isEvar t then None else unify hypinfo env evars t in match unif with | None -> ((hypinfo, occ), Fail) | Some (hypinfo', rew) -> let occ = succ occ in if not (is_occ occ) then ((hypinfo, occ), Fail) else if eq_constr t rew.rew_to then ((hypinfo, occ), Identity) else let res = { rew with rew_car = ty } in let rel, prf = get_rew_prf res in let res = Success (apply_constraint env avoid rew.rew_car rel prf cstr res) in ((hypinfo', occ), res) let apply_lemma l2r flags oc by loccs : strategy = fun () env avoid t ty cstr (sigma, cstrs) -> let sigma, c = oc sigma in let sigma, hypinfo = decompose_applied_relation env sigma c in let { c1; c2; car; rel; prf; sort; holes } = hypinfo in let rew = (car, rel, prf, c1, c2, holes, sort) in let evars = (sigma, cstrs) in let unify () env evars t = let rew = unify_eqn rew l2r flags env evars by t in match rew with | None -> None | Some rew -> Some ((), rew) in let _, res = apply_rule unify loccs ((), 0) env avoid t ty cstr evars in (), res 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 subterm all flags (s : 'a pure_strategy) : 'a pure_strategy = let rec aux state 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 state success = let state, (args', evars', progress) = Array.fold_left (fun (state, (acc, evars, progress)) arg -> if not (Option.is_empty progress) && not all then state, (None :: acc, evars, progress) else let argty = Retyping.get_type_of env (goalevars evars) arg in let state, res = s state env avoid arg argty (prop,None) evars in let res' = match res with | Identity -> let progress = if Option.is_empty progress then Some false else progress in (None :: acc, evars, progress) | Success r -> (Some r :: acc, r.rew_evars, Some true) | Fail -> (None :: acc, evars, progress) in state, res') (state, ([], evars, success)) args in let res = match progress with | None -> Fail | Some false -> Identity | 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 Success 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 Success res in state, 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 state, m' = s state env avoid m mty (prop, cstr') evars in match m' with | Fail -> rewrite_args state None (* Standard path, try rewrite on arguments *) | Identity -> rewrite_args state (Some false) | Success 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 let res = match prf with | RewPrf (rel, prf) -> Success (apply_constraint env avoid res.rew_car rel prf (prop,cstr) res) | _ -> Success res in state, res else rewrite_args state 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 state, res = aux state env avoid mor ty (prop,cstr) evars' in let res = match res with | Success r -> Success { r with rew_to = unfold r.rew_to } | Fail | Identity -> res in state, 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 state, res = aux state env avoid app ty (prop,cstr) evars' in let res = match res with | Success r -> Success { r with rew_to = unfold r.rew_to } | Fail | Identity -> res in state, 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 state, b' = s state env' avoid b bty (prop, unlift env evars cstr) evars in let res = match b' with | Success 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 Success { 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) } | Fail | Identity -> b' in state, res | 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 state, c' = s state env avoid c cty (prop, cstr') evars' in let state, res = match c' with | Success 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 state, Success (coerce env avoid (prop,cstr) res) | Fail | Identity -> 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 state, found, brs' = Array.fold_left (fun (state, found, acc) br -> if not (Option.is_empty found) then (state, found, fun x -> lift 1 br :: acc x) else let state, res = s state env avoid br ty (prop,cstr) evars in match res with | Success r -> (state, Some r, fun x -> mkRel 1 :: acc x) | Fail | Identity -> (state, None, fun x -> lift 1 br :: acc x)) (state, 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' c'))) in state, Success (make_leibniz_proof env ctxc ty r) | None -> state, c' else match try Some (fold_match env (goalevars evars) t) with Not_found -> None with | None -> state, c' | Some (cst, _, t', eff (*FIXME*)) -> let state, res = aux state env avoid t' ty (prop,cstr) evars in let res = match res with | Success prf -> Success { prf with rew_from = t; rew_to = unfold_match env (goalevars evars) cst prf.rew_to } | x' -> c' in state, res in let res = match res with | Success r -> let rel, prf = get_rew_prf r in Success (apply_constraint env avoid r.rew_car rel prf (prop,cstr) r) | Fail | Identity -> res in state, res | _ -> state, Fail 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 state env avoid prop (res : rewrite_result_info) (next : 'a pure_strategy) : 'a * rewrite_result = let state, nextres = next state env avoid res.rew_to res.rew_car (prop, get_opt_rew_rel res.rew_prf) res.rew_evars in let res = match nextres with | Fail -> Fail | Identity -> Success res | Success res' -> match res.rew_prf with | RewCast c -> Success { res' with rew_from = res.rew_from } | RewPrf (rew_rel, rew_prf) -> match res'.rew_prf with | RewCast _ -> Success { 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 Success { res' with rew_from = res.rew_from; rew_evars = evars; rew_prf = RewPrf (res'_rel, prf) } in state, res (** 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 : 'a pure_strategy = fun state env avoid t ty cstr evars -> state, Fail let id : 'a pure_strategy = fun state env avoid t ty cstr evars -> state, Identity let refl : 'a pure_strategy = fun state 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 let res = Success { rew_car = ty; rew_from = t; rew_to = t; rew_prf = RewPrf (rel, proof); rew_evars = evars } in state, res let progress (s : 'a pure_strategy) : 'a pure_strategy = fun state env avoid t ty cstr evars -> let state, res = s state env avoid t ty cstr evars in match res with | Fail -> state, Fail | Identity -> state, Fail | Success r -> state, Success r let seq first snd : 'a pure_strategy = fun state env avoid t ty cstr evars -> let state, res = first state env avoid t ty cstr evars in match res with | Fail -> state, Fail | Identity -> snd state env avoid t ty cstr evars | Success res -> transitivity state env avoid (fst cstr) res snd let choice fst snd : 'a pure_strategy = fun state env avoid t ty cstr evars -> let state, res = fst state env avoid t ty cstr evars in match res with | Fail -> snd state env avoid t ty cstr evars | Identity | Success _ -> state, res let try_ str : 'a pure_strategy = choice str id let check_interrupt str s e l c t r ev = Control.check_for_interrupt (); str s e l c t r ev let fix (f : 'a pure_strategy -> 'a pure_strategy) : 'a pure_strategy = let rec aux state = f (fun state -> check_interrupt aux state) state in aux let any (s : 'a pure_strategy) : 'a pure_strategy = fix (fun any -> try_ (seq s any)) let repeat (s : 'a pure_strategy) : 'a pure_strategy = seq s (any s) let bu (s : 'a pure_strategy) : 'a pure_strategy = fix (fun s' -> seq (choice (progress (all_subterms s')) s) (try_ s')) let td (s : 'a pure_strategy) : 'a pure_strategy = fix (fun s' -> seq (choice s (progress (all_subterms s'))) (try_ s')) let innermost (s : 'a pure_strategy) : 'a pure_strategy = fix (fun ins -> choice (one_subterm ins) s) let outermost (s : 'a pure_strategy) : 'a pure_strategy = fix (fun out -> choice s (one_subterm out)) let lemmas cs : 'a pure_strategy = List.fold_left (fun tac (l,l2r,by) -> choice tac (apply_lemma l2r rewrite_unif_flags l by AllOccurrences)) fail cs let inj_open hint = (); fun sigma -> let ctx = Evd.evar_universe_context_of hint.Autorewrite.rew_ctx in let sigma = Evd.merge_universe_context sigma ctx in (sigma, (hint.Autorewrite.rew_lemma, NoBindings)) let old_hints (db : string) : 'a pure_strategy = let rules = Autorewrite.find_rewrites db in lemmas (List.map (fun hint -> (inj_open hint, hint.Autorewrite.rew_l2r, hint.Autorewrite.rew_tac)) rules) let hints (db : string) : 'a pure_strategy = fun state 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 lems state env avoid t ty cstr evars let reduce (r : Redexpr.red_expr) : 'a pure_strategy = fun state env avoid t ty cstr evars -> let rfn, ckind = Redexpr.reduction_of_red_expr env r in let evars', t' = rfn env (goalevars evars) t in if eq_constr t' t then state, Identity else state, Success { rew_car = ty; rew_from = t; rew_to = t'; rew_prf = RewCast ckind; rew_evars = evars', cstrevars evars } let fold_glob c : 'a pure_strategy = fun state 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 env (goalevars evars) 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 state, Success { rew_car = ty; rew_from = t; rew_to = c'; rew_prf = RewCast DEFAULTcast; rew_evars = (sigma, snd evars) } with e when Errors.noncritical e -> state, Fail end (** The strategy for a single rewrite, dealing with occurences. *) (** A dummy initial clauseenv to avoid generating initial evars before even finding a first application of the rewriting lemma, in setoid_rewrite mode *) let rewrite_with l2r flags c occs : strategy = fun () env avoid t ty cstr (sigma, cstrs) -> let hypinfo = None in let unify hypinfo env evars t = let (sigma, cstrs) = evars in let ans = try Some (refresh_hypinfo env sigma hypinfo c) with e when Class_tactics.catchable e -> None in match ans with | None -> None | Some (sigma, rew) -> let rew = unify_eqn rew l2r flags env (sigma, cstrs) None t in match rew with | None -> None | Some rew -> Some (None, rew) (** reset the hypinfo cache *) in let app = apply_rule unify occs in let strat = Strategies.fix (fun aux -> Strategies.choice app (subterm true default_flags aux)) in let _, res = strat (hypinfo, 0) env avoid t ty cstr (sigma, cstrs) in ((), res) let apply_strategy (s : strategy) env avoid concl (prop, cstr) evars = let ty = Retyping.get_type_of env (goalevars evars) concl in let _, res = s () env avoid concl ty (prop, Some cstr) evars in res let solve_constraints env (evars,cstrs) = let filter = all_constraints cstrs in Typeclasses.resolve_typeclasses env ~filter ~split:false ~fail:true (Typeclasses.mark_resolvables ~filter 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 evdref = ref sigma in let sort = Typing.sort_of env evdref concl in let evars = (!evdref, Evar.Set.empty) in let evars, cstr = 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 | Fail -> None | Identity -> Some None | Success res -> let (_, cstrs) = res.rew_evars in let evars' = solve_constraints env res.rew_evars in let newt = Evarutil.nf_evar evars' res.rew_to 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 res.rew_prf with | RewCast c -> None | RewPrf (rel, p) -> let p = nf_zeta env evars' (Evarutil.nf_evar evars' p) in let term = match abs with | None -> p | Some (t, ty) -> let t = Evarutil.nf_evar evars' t in let ty = Evarutil.nf_evar evars' ty in mkApp (mkLambda (Name (Id.of_string "lemma"), ty, p), [| t |]) in let proof = match is_hyp with | None -> term | Some id -> mkApp (term, [| mkVar id |]) in Some proof in Some (Some (evars, res, newt)) let assert_replacing id newt tac = let prf = Proofview.Goal.nf_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 ~unsafe:false begin fun sigma -> let env' = Environ.reset_with_named_context (val_of_named_context nc') env in let sigma, ev = Evarutil.new_evar env' sigma concl in let sigma, ev' = Evarutil.new_evar env sigma newt in let fold _ (n, b, t) inst = if Id.equal n id then ev' :: inst else mkVar n :: inst in let inst = fold_named_context fold env ~init:[] in let (e, args) = destEvar ev in sigma, 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 ?origsigma strat clause = let open Proofview.Notations in let treat sigma (res, is_hyp) = match res with | None -> newfail 0 (str "Nothing to rewrite") | Some None -> Proofview.tclUNIT () | Some (Some res) -> let (undef, prf, newt) = res in let fold ev _ accu = if Evd.mem sigma ev then accu else ev :: accu in let gls = List.rev (Evd.fold_undefined fold undef []) in match is_hyp, prf with | Some id, Some p -> let tac = Proofview.Refine.refine ~unsafe:false (fun h -> (h, p)) <*> Proofview.Unsafe.tclNEWGOALS gls in Proofview.Unsafe.tclEVARS undef <*> assert_replacing id newt tac | Some id, None -> Proofview.Unsafe.tclEVARS undef <*> convert_hyp_no_check (id, None, newt) | None, Some p -> Proofview.Unsafe.tclEVARS undef <*> Proofview.Goal.enter begin fun gl -> let env = Proofview.Goal.env gl in let make sigma = let (sigma, ev) = Evarutil.new_evar env sigma newt in sigma, mkApp (p, [| ev |]) in Proofview.Refine.refine ~unsafe:false make <*> Proofview.Unsafe.tclNEWGOALS gls end | None, None -> Proofview.Unsafe.tclEVARS undef <*> convert_concl_no_check newt DEFAULTcast in let beta_red _ sigma c = Reductionops.nf_betaiota sigma c in let beta = Proofview.V82.tactic (Tactics.reduct_in_concl (beta_red, DEFAULTcast)) in let opt_beta = match clause with | None -> Proofview.tclUNIT () | Some id -> Proofview.V82.tactic (Tactics.reduct_in_hyp beta_red (id, InHyp)) in Proofview.Goal.nf_enter begin fun gl -> let concl = Proofview.Goal.concl gl in let env = Proofview.Goal.env gl in let sigma = Proofview.Goal.sigma gl in 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 let sigma = match origsigma with None -> sigma | Some sigma -> sigma in treat sigma (res, is_hyp) <*> (** For compatibility *) beta <*> opt_beta <*> Proofview.shelve_unifiable with | PretypeError (env, evd, (UnsatisfiableConstraints _ as e)) -> raise (RewriteFailure (Himsg.explain_pretype_error env evd e)) end let tactic_init_setoid () = try init_setoid (); tclIDTAC with e when Errors.noncritical e -> tclFAIL 0 (str"Setoid library not loaded") (** Setoid rewriting when called with "rewrite_strat" *) let cl_rewrite_clause_strat strat clause = tclTHEN (tactic_init_setoid ()) (fun gl -> try Proofview.V82.of_tactic (cl_rewrite_clause_newtac strat clause) gl with RewriteFailure e -> errorlabstrm "" (str"setoid rewrite failed: " ++ e) | Refiner.FailError (n, pp) -> tclFAIL n (str"setoid rewrite failed: " ++ Lazy.force pp) gl) (** Setoid rewriting when called with "setoid_rewrite" *) let cl_rewrite_clause l left2right occs clause gl = let strat = rewrite_with left2right (general_rewrite_unif_flags ()) l occs in cl_rewrite_clause_strat strat clause gl let apply_glob_constr c l2r occs = (); fun () env avoid t ty cstr evars -> let c sigma = let (sigma, c) = Pretyping.understand_tcc env sigma c in (sigma, (c, NoBindings)) in let flags = general_rewrite_unif_flags () in apply_lemma l2r flags c None occs () env avoid t ty cstr evars let interp_glob_constr_list env = let make c = (); fun sigma -> let sigma, c = Pretyping.understand_tcc env sigma c in (sigma, (c, NoBindings)) in List.map (fun c -> make c, true, None) (* Syntax for rewriting with strategies *) type unary_strategy = Subterms | Subterm | Innermost | Outermost | Bottomup | Topdown | Progress | Try | Any | Repeat type binary_strategy = | Compose | Choice type ('constr,'redexpr) strategy_ast = | StratId | StratFail | StratRefl | StratUnary of unary_strategy * ('constr,'redexpr) strategy_ast | StratBinary of binary_strategy * ('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 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 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 (List.map fst l) in Strategies.lemmas 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, Misctypes.IntroAnonymous, 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 env Evd.empty m in let sigma = Evd.from_env ~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 env evd 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 evd = Evd.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 evd instance 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 (* Find a subterm which matches the pattern to rewrite for "rewrite" *) let unification_rewrite l2r c1 c2 sigma prf car rel but env = let (sigma,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 env sigma ((if l2r then c1 else c2),but) with | ex when Pretype_errors.precatchable_exception ex -> (* ~flags:(true,true) to make Ring work (since it really exploits conversion) *) Unification.w_unify_to_subterm ~flags:rewrite_conv_unif_flags env sigma ((if l2r then c1 else c2),but) in let nf c = Evarutil.nf_evar sigma 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 sigma; let prf = nf prf in let prfty = nf (Retyping.get_type_of env sigma prf) in let sort = sort_of_rel env sigma but in let abs = prf, prfty in let prf = mkRel 1 in let res = (car, rel, prf, c1, c2) in abs, sigma, res, Sorts.is_prop sort let get_hyp gl (c,l) clause l2r = let evars = project gl in let env = pf_env gl in let sigma, hi = decompose_applied_relation env evars (c,l) in let but = match clause with | Some id -> pf_get_hyp_typ gl id | None -> Evarutil.nf_evar evars (pf_concl gl) in unification_rewrite l2r hi.c1 hi.c2 sigma hi.prf hi.car hi.rel but env let general_rewrite_flags = { under_lambdas = false; on_morphisms = true } (* let rewriteclaustac_key = Profile.declare_profile "cl_rewrite_clause_tac";; *) (* let cl_rewrite_clause_tac = Profile.profile5 rewriteclaustac_key cl_rewrite_clause_tac *) (** Setoid rewriting when called with "rewrite" *) let general_s_rewrite cl l2r occs (c,l) ~new_goals gl = let abs, evd, res, sort = get_hyp gl (c,l) cl l2r in let unify () env evars t = unify_abs res l2r sort env evars t in let app = apply_rule unify occs in let recstrat aux = Strategies.choice app (subterm true general_rewrite_flags aux) in let substrat = Strategies.fix recstrat in let strat () env avoid t ty cstr evars = let _, res = substrat ((), 0) env avoid t ty cstr evars in (), res in let origsigma = project gl in init_setoid (); try tclWEAK_PROGRESS (tclTHEN (Refiner.tclEVARS evd) (Proofview.V82.of_tactic (cl_rewrite_clause_newtac ~abs:(Some abs) ~origsigma strat cl))) gl with RewriteFailure e -> tclFAIL 0 (str"setoid rewrite failed: " ++ e) gl 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 = Proofview.V82.tactic (general_s_rewrite_clause x y z w ~new_goals) let _ = Hook.set Equality.general_setoid_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 Evd.empty 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.nf_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, _, _ = 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 (try init_setoid () with _ -> raise Not_found); fn env sigma car rel with e -> Proofview.tclZERO e end begin function | e -> Proofview.tclORELSE fallback begin function (e', info) -> match e' with | Hipattern.NoEquationFound -> begin match e with | (Not_found, _) -> let rel, _, _ = decompose_app_rel env sigma concl in not_declared env ty rel | (e, info) -> Proofview.tclZERO ~info e end | e' -> Proofview.tclZERO ~info 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) (fun c -> Proofview.V82.of_tactic (apply c))) (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) (fun c -> Proofview.V82.of_tactic (apply c))) (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 -> Proofview.V82.of_tactic (eapply proof) | Some c -> Proofview.V82.of_tactic (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 "Cannot find an equivalence relation to rewrite." 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 Proofview.V82.of_tactic (Tacticals.New.tclTHENLAST (Tactics.assert_after_replacing id new_hyp) (Tacticals.New.tclTHENLIST [ intros; setoid_symmetry; apply (mkVar id); 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 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