(************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* = 2 -> let head = if isApp c then fst (destApp c) else c in if eq_constr (Lazy.force coq_eq) 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 evd, evar = Evarutil.new_evar sigma env' (new_Type ()) in let inst = mkApp (Lazy.force rewrite_relation_class, [| evar; mkApp (c, params) |]) in let _ = Typeclasses.resolve_one_typeclass env' evd inst in Some (it_mkProd_or_LetIn t rels) with _ -> None) | _ -> None let _ = Equality.register_is_applied_rewrite_relation is_applied_rewrite_relation let split_head = function hd :: tl -> hd, tl | [] -> assert(false) let new_goal_evar (goal,cstr) env t = let goal', t = Evarutil.new_evar goal env t in (goal', cstr), t let new_cstr_evar (goal,cstr) env t = let cstr', t = Evarutil.new_evar cstr env t in (goal, cstr'), t let build_signature evars env m (cstrs : 'a option list) (finalcstr : 'a option) (f : 'a -> constr) = let new_evar evars env t = new_cstr_evar evars env (* ~src:(dummy_loc, ImplicitArg (ConstRef (Lazy.force respectful), (n, Some na))) *) t in let mk_relty evars env ty obj = match obj with | None -> let relty = mk_relation ty in new_evar evars env relty | Some x -> evars, f x in let rec aux env evars ty l = let t = Reductionops.whd_betadeltaiota env (fst 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 (fst 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 newarg = mkApp (Lazy.force 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 (fst evars) ty in let pred = mkLambda (na, ty, b) in let liftarg = mkLambda (na, ty, arg) in let arg' = mkApp (Lazy.force forall_relation, [| ty ; pred ; liftarg |]) in if obj = None then evars, mkProd(na, ty, b), arg', (ty, None) :: cstrs else error "build_signature: no constraint can apply on a dependent argument" | _, obj :: _ -> anomaly "build_signature: not enough products" | _, [] -> (match finalcstr with | 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 codom -> let (t, rel) = codom in evars, t, rel, [t, Some rel]) in aux env evars m cstrs let proper_proof env evars carrier relation x = let goal = mkApp (Lazy.force proper_proxy_type, [| carrier ; relation; x |]) in new_cstr_evar evars env goal let find_class_proof proof_type proof_method env evars carrier relation = try let goal = mkApp (Lazy.force proof_type, [| carrier ; relation |]) in let evars, c = Typeclasses.resolve_one_typeclass env evars goal in mkApp (Lazy.force proof_method, [| carrier; relation; c |]) with e when Logic.catchable_exception e -> raise Not_found 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 exception FoundInt of int let array_find (arr: 'a array) (pred: int -> 'a -> bool): int = try for i=0 to Array.length arr - 1 do if pred i (arr.(i)) then raise (FoundInt i) done; raise Not_found with FoundInt i -> i type hypinfo = { cl : clausenv; prf : constr; car : constr; rel : constr; l2r : bool; c1 : constr; c2 : constr; c : constr option; abs : (constr * types) option; } let evd_convertible env evd x y = try ignore(Evarconv.the_conv_x env x y evd); true with _ -> false let decompose_applied_relation env sigma c left2right = let ctype = Typing.type_of env sigma c in let find_rel ty = let eqclause = Clenv.mk_clenv_from_env env sigma None (c,ty) in let (equiv, args) = decompose_app (Clenv.clenv_type eqclause) 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 applied relation." in let others,(c1,c2) = split_last_two args in let ty1, ty2 = Typing.type_of env eqclause.evd c1, Typing.type_of env eqclause.evd c2 in if not (evd_convertible env eqclause.evd ty1 ty2) then None else Some { cl=eqclause; prf=(Clenv.clenv_value eqclause); car=ty1; rel=mkApp (equiv, Array.of_list others); l2r=left2right; c1=c1; c2=c2; c=Some c; abs=None } in match find_rel ctype with | Some c -> c | None -> let ctx,t' = Reductionops.splay_prod_assum env sigma ctype in (* Search for underlying eq *) match find_rel (it_mkProd_or_LetIn t' ctx) with | Some c -> c | None -> error "The term does not end with an applied homogeneous relation." let rewrite_unif_flags = { Unification.modulo_conv_on_closed_terms = None; Unification.use_metas_eagerly = true; Unification.modulo_delta = empty_transparent_state; Unification.resolve_evars = true; Unification.use_evars_pattern_unification = true; } let conv_transparent_state = (Idpred.empty, Cpred.full) let rewrite2_unif_flags = { Unification.modulo_conv_on_closed_terms = Some conv_transparent_state; Unification.use_metas_eagerly = true; Unification.modulo_delta = empty_transparent_state; Unification.resolve_evars = true; Unification.use_evars_pattern_unification = true; } let setoid_rewrite_unif_flags = { Unification.modulo_conv_on_closed_terms = Some conv_transparent_state; Unification.use_metas_eagerly = true; Unification.modulo_delta = conv_transparent_state; Unification.resolve_evars = true; Unification.use_evars_pattern_unification = true; } let convertible env evd x y = Reductionops.is_conv env evd x y let allowK = true let refresh_hypinfo env sigma hypinfo = if hypinfo.abs = None then let {l2r=l2r; c=c;cl=cl} = hypinfo in match c with | Some c -> (* Refresh the clausenv to not get the same meta twice in the goal. *) decompose_applied_relation env cl.evd c l2r; | _ -> hypinfo else hypinfo let unify_eqn env sigma hypinfo 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 env', prf, c1, c2, car, rel = match abs with | Some (absprf, absprfty) -> let env' = clenv_unify allowK ~flags:rewrite_unif_flags CONV left t cl in env', prf, c1, c2, car, rel | None -> let env' = try clenv_unify allowK ~flags:rewrite_unif_flags CONV left t cl with Pretype_errors.PretypeError _ -> (* For Ring essentially, only when doing setoid_rewrite *) clenv_unify allowK ~flags:rewrite2_unif_flags CONV left t cl in let env' = let mvs = clenv_dependent false env' in clenv_pose_metas_as_evars env' mvs in let evd' = Typeclasses.resolve_typeclasses ~fail:true env'.env env'.evd in let env' = { env' with evd = evd' } in let nf c = Evarutil.nf_evar 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 (Clenv.clenv_value env') in let ty1 = Typing.type_of env'.env env'.evd c1 and ty2 = Typing.type_of env'.env env'.evd c2 in if convertible env env'.evd ty1 ty2 then ( if occur_meta prf then hypinfo := refresh_hypinfo env sigma !hypinfo; env', prf, c1, c2, car, rel) else raise Reduction.NotConvertible in let res = if l2r then (prf, (car, rel, c1, c2)) else try (mkApp (get_symmetric_proof env Evd.empty car rel, [| c1 ; c2 ; prf |]), (car, rel, c2, c1)) with Not_found -> (prf, (car, inverse car rel, c2, c1)) in Some (env', res) with e when Class_tactics.catchable e -> None 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_id t = match kind_of_term t with | App (id, [| a; b |]) (* when eq_constr id (Lazy.force coq_id) *) -> 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 decomp_prod env evm n c = snd (Reductionops.splay_prod_n env evm n c) let rec decomp_pointwise n c = if n = 0 then c else match kind_of_term c with | App (pointwise, [| a; b; relb |]) -> decomp_pointwise (pred n) relb | _ -> raise Not_found let lift_cstr env sigma evars args cstr = let cstr = let start = match cstr with | Some codom -> codom | None -> let car = Evarutil.e_new_evar evars env (new_Type ()) in let rel = Evarutil.e_new_evar evars env (mk_relation car) in (car, rel) in Array.fold_right (fun arg (car, rel) -> let ty = Typing.type_of env sigma arg in let car' = mkProd (Anonymous, ty, car) in let rel' = mkApp (Lazy.force pointwise_relation, [| ty; car; rel |]) in (car', rel')) args start in Some cstr let unlift_cstr env sigma = function | None -> None | Some codom -> Some (decomp_pointwise 1 codom) type rewrite_flags = { under_lambdas : bool; on_morphisms : bool } let default_flags = { under_lambdas = true; on_morphisms = true; } type evars = evar_map * evar_map (* goal evars, constraint evars *) type rewrite_result_info = { rew_car : constr; rew_rel : constr; rew_from : constr; rew_to : constr; rew_prf : constr; rew_evars : evars; } type rewrite_result = rewrite_result_info option type strategy = Environ.env -> evar_map -> constr -> types -> constr option -> evars -> rewrite_result option let resolve_subrelation env sigma car rel rel' res = if eq_constr rel rel' then res else (* try let evd' = Evarconv.the_conv_x env rel rel' res.rew_evars in *) (* { res with rew_evars = evd' } *) (* with NotConvertible -> *) let app = mkApp (Lazy.force subrelation, [|car; rel; rel'|]) in let evars, subrel = new_cstr_evar res.rew_evars env app in { res with rew_prf = mkApp (subrel, [| res.rew_from ; res.rew_to ; res.rew_prf |]); rew_rel = rel'; rew_evars = evars } let resolve_morphism env sigma oldt m ?(fnewt=fun x -> x) args args' cstr evars = let evars, morph_instance, proj, sigargs, m', args, args' = let first = try (array_find args' (fun i b -> b <> None)) with Not_found -> raise (Invalid_argument "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 sigma appm in let cstrs = List.map (Option.map (fun r -> r.rew_car, r.rew_rel)) (Array.to_list morphobjs') in (* Desired signature *) let evars, appmtype', signature, sigargs = build_signature evars env appmtype cstrs cstr (fun (a,r) -> r) in (* Actual signature found *) let cl_args = [| appmtype' ; signature ; appm |] in let app = mkApp (Lazy.force proper_type, cl_args) in let env' = Environ.push_named (id_of_string "do_subrelation", Some (Lazy.force do_subrelation), Lazy.force apply_subrelation) 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 = proper_proof env evars carrier relation x in [ proof ; x ; x ] @ acc, subst, evars, sigargs, x :: typeargs' | Some r -> [ r.rew_prf; r.rew_to; x ] @ acc, subst, evars, sigargs, r.rew_to :: typeargs') | None -> if y <> None 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 sigma car rel cstr res = match cstr with | None -> res | Some r -> resolve_subrelation env sigma car rel r res let eq_env x y = x == y let apply_rule hypinfo loccs : strategy = let (nowhere_except_in,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 sigma t ty cstr evars -> if not (eq_env !hypinfo.cl.env env) then hypinfo := refresh_hypinfo env sigma !hypinfo; let unif = unify_eqn env sigma hypinfo t in if unif <> None then incr occ; match unif with | Some (env', (prf, (car, rel, c1, c2))) when is_occ !occ -> begin let goalevars = Evd.evar_merge (fst evars) (Evd.undefined_evars (Evarutil.nf_evar_map env'.evd)) in let res = { rew_car = ty; rew_rel = rel; rew_from = c1; rew_to = c2; rew_prf = prf; rew_evars = goalevars, snd evars } in Some (Some (apply_constraint env sigma car rel cstr res)) end | _ -> None let apply_lemma (evm,c) left2right loccs : strategy = fun env sigma -> let evars = Evd.merge sigma evm in let hypinfo = ref (decompose_applied_relation env evars c left2right) in apply_rule hypinfo loccs env sigma let make_leibniz_proof c ty r = let prf = mkApp (Lazy.force coq_f_equal, [| r.rew_car; ty; mkLambda (Anonymous, r.rew_car, c (mkRel 1)); r.rew_from; r.rew_to; r.rew_prf |]) in { r with rew_car = ty; rew_rel = mkApp (Lazy.force coq_eq, [| ty |]); rew_from = c r.rew_from; rew_to = c r.rew_to; rew_prf = prf } let pointwise_or_dep_relation n t car rel = if noccurn 1 car then mkApp (Lazy.force pointwise_relation, [| t; lift (-1) car; lift (-1) rel |]) else mkApp (Lazy.force forall_relation, [| t; mkLambda (n, t, car); mkLambda (n, t, rel) |]) let subterm all flags (s : strategy) : strategy = let rec aux env sigma t ty cstr evars = let cstr' = Option.map (fun c -> (ty, 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 progress <> None && not all then (None :: acc, evars, progress) else let res = s env sigma arg (Typing.type_of env sigma arg) None evars in match res with | Some None -> (None :: acc, evars, if progress = None 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 let evars', prf, car, rel, c1, c2 = resolve_morphism env sigma t m args args' cstr' evars' in let res = { rew_car = ty; rew_rel = rel; rew_from = c1; rew_to = c2; rew_prf = prf; rew_evars = evars' } in Some (Some res) in if flags.on_morphisms then let evarsref = ref (snd evars) in let cstr' = lift_cstr env sigma evarsref args cstr' in let m' = s env sigma m (Typing.type_of env sigma m) (Option.map snd cstr') (fst evars, !evarsref) 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 nargs = Array.length args in let res = { rew_car = decomp_prod env (fst r.rew_evars) nargs r.rew_car; rew_rel = decomp_pointwise nargs r.rew_rel; rew_from = mkApp(r.rew_from, args); rew_to = mkApp(r.rew_to, args); rew_prf = mkApp (r.rew_prf, args); rew_evars = r.rew_evars } in Some (Some res) else rewrite_args None | Prod (n, x, b) when noccurn 1 b -> let b = subst1 mkProp b in let tx = Typing.type_of env sigma x and tb = Typing.type_of env sigma b in let res = aux env sigma (mkApp (arrow_morphism tx tb, [| x; b |])) ty cstr evars in (match res with | Some (Some r) -> Some (Some { r with rew_to = unfold_impl 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) when eq_constr ty mkProp -> let lam = mkLambda (n, dom, codom) in let res = aux env sigma (mkApp (Lazy.force coq_all, [| dom; lam |])) ty cstr evars in (match res with | Some (Some r) -> Some (Some { r with rew_to = unfold_all r.rew_to }) | _ -> res) | Lambda (n, t, b) when flags.under_lambdas -> let env' = Environ.push_rel (n, None, t) env in let b' = s env' sigma b (Typing.type_of env' sigma b) (unlift_cstr env sigma cstr) evars in (match b' with | Some (Some r) -> Some (Some { r with rew_prf = mkLambda (n, t, r.rew_prf); rew_car = mkProd (n, t, r.rew_car); rew_rel = pointwise_or_dep_relation n t r.rew_car r.rew_rel; rew_from = mkLambda(n, t, r.rew_from); rew_to = mkLambda (n, t, r.rew_to) }) | _ -> b') | Case (ci, p, c, brs) -> let cty = Typing.type_of env sigma c in let cstr = Some (mkApp (Lazy.force coq_eq, [| cty |])) in let c' = s env sigma c cty cstr evars in (match c' with | Some (Some r) -> Some (Some (make_leibniz_proof (fun x -> mkCase (ci, p, x, brs)) ty r)) | x -> if array_for_all ((=) 0) ci.ci_cstr_nargs then let cstr = Some (mkApp (Lazy.force coq_eq, [| ty |])) in let found, brs' = Array.fold_left (fun (found, acc) br -> if found <> None then (found, fun x -> br :: acc x) else match s env sigma br ty cstr evars with | Some (Some r) -> (Some r, fun x -> x :: acc x) | _ -> (None, fun x -> br :: acc x)) (None, fun x -> []) brs in match found with | Some r -> let ctxc x = mkCase (ci, p, c, Array.of_list (List.rev (brs' x))) in Some (Some (make_leibniz_proof ctxc ty r)) | None -> x else x) | _ -> if all then Some None else None in aux let all_subterms = subterm true default_flags let one_subterm = subterm false default_flags (** Requires transitivity of the rewrite step, not tail-recursive. *) let transitivity env sigma (res : rewrite_result_info) (next : strategy) : rewrite_result option = match next env sigma res.rew_to res.rew_car (Some res.rew_rel) res.rew_evars with | None -> None | Some None -> Some (Some res) | Some (Some res') -> let prfty = mkApp (Lazy.force transitive_type, [| res.rew_car ; res.rew_rel |]) in let evars, prf = new_cstr_evar res'.rew_evars env prfty in let prf = mkApp (prf, [|res.rew_from; res'.rew_from; res'.rew_to; res.rew_prf; res'.rew_prf |]) in Some (Some { res' with rew_from = res.rew_from; rew_evars = evars; rew_prf = 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 sigma t ty cstr evars -> None let id : strategy = fun env sigma t ty cstr evars -> Some None let refl : strategy = fun env sigma t ty cstr evars -> let evars, rel = match cstr with | None -> new_cstr_evar evars env (mk_relation ty) | Some r -> evars, r in let evars, proof = let mty = mkApp (Lazy.force proper_proxy_type, [| ty ; rel; t |]) in new_cstr_evar evars env mty in Some (Some { rew_car = ty; rew_rel = rel; rew_from = t; rew_to = t; rew_prf = proof; rew_evars = evars }) let progress (s : strategy) : strategy = fun env sigma t ty cstr evars -> match s env sigma t ty cstr evars with | None -> None | Some None -> None | r -> r let seq fst snd : strategy = fun env sigma t ty cstr evars -> match fst env sigma t ty cstr evars with | None -> None | Some None -> snd env sigma t ty cstr evars | Some (Some res) -> transitivity env sigma res snd let choice fst snd : strategy = fun env sigma t ty cstr evars -> match fst env sigma t ty cstr evars with | None -> snd env sigma 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 cs : strategy = List.fold_left (fun tac (l,l2r) -> choice tac (apply_lemma l l2r (false,[]))) fail cs let inj_open c = (Evd.empty,c) let old_hints (db : string) : strategy = let rules = Autorewrite.find_rewrites db in lemmas (List.map (fun hint -> (inj_open hint.Autorewrite.rew_lemma, hint.Autorewrite.rew_l2r)) rules) let hints (db : string) : strategy = fun env sigma t ty cstr evars -> let rules = Autorewrite.find_matches db t in lemmas (List.map (fun hint -> (inj_open hint.Autorewrite.rew_lemma, hint.Autorewrite.rew_l2r)) rules) env sigma t ty cstr evars end (** The strategy for a single rewrite, dealing with occurences. *) let rewrite_strat flags occs hyp = let app = apply_rule hyp occs in let rec aux () = Strategies.choice app (subterm true flags (fun env -> aux () env)) in aux () let rewrite_with (evm,c) left2right loccs : strategy = fun env sigma -> let evars = Evd.merge sigma evm in let hypinfo = ref (decompose_applied_relation env evars c left2right) in rewrite_strat default_flags loccs hypinfo env sigma let apply_strategy (s : strategy) env sigma concl cstr evars = let res = s env sigma concl (Typing.type_of env sigma concl) (Option.map snd cstr) !evars in match res with | None -> None | Some None -> Some None | Some (Some res) -> evars := res.rew_evars; Some (Some (res.rew_prf, (res.rew_car, res.rew_rel, res.rew_from, res.rew_to))) let split_evars_once sigma evd = Evd.fold (fun ev evi deps -> if Intset.mem ev deps then Intset.union (Class_tactics.evars_of_evi evi) deps else deps) evd sigma let existentials_of_evd evd = Evd.fold (fun ev evi acc -> Intset.add ev acc) evd Intset.empty let evd_of_existentials evd exs = Intset.fold (fun i acc -> let evi = Evd.find evd i in Evd.add acc i evi) exs Evd.empty let split_evars sigma evd = let rec aux deps = let deps' = split_evars_once deps evd in if Intset.equal deps' deps then evd_of_existentials evd deps else aux deps' in aux (existentials_of_evd sigma) let merge_evars (goal,cstr) = Evd.merge goal cstr let solve_constraints env evars = Typeclasses.resolve_typeclasses env ~split:false ~fail:true (merge_evars evars) let nf_zeta = Reductionops.clos_norm_flags (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA]) let cl_rewrite_clause_aux ?(abs=None) strat goal_meta clause gl = let concl, is_hyp = match clause with Some id -> pf_get_hyp_typ gl id, Some id | None -> pf_concl gl, None in let cstr = let sort = mkProp in let impl = Lazy.force impl in match is_hyp with | None -> (sort, inverse sort impl) | Some _ -> (sort, impl) in let sigma = project gl in let evars = ref (Evd.create_evar_defs sigma, Evd.empty) in let env = pf_env gl in let eq = apply_strategy strat env sigma concl (Some cstr) evars in match eq with | Some (Some (p, (_, _, oldt, newt))) -> (try let cstrevars = !evars in let evars = solve_constraints env cstrevars in let p = Evarutil.nf_evar evars p in let p = nf_zeta env evars 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 undef = split_evars (fst cstrevars) evars in let rewtac = match is_hyp with | Some id -> let term = match abs with | None -> p | Some (t, ty) -> mkApp (mkLambda (Name (id_of_string "lemma"), ty, p), [| t |]) in cut_replacing id newt (Tacmach.refine_no_check (mkApp (term, [| mkVar id |]))) | None -> (match abs with | None -> let name = next_name_away_with_default "H" Anonymous (pf_ids_of_hyps gl) in tclTHENLAST (Tacmach.internal_cut_no_check false name newt) (tclTHEN (Tactics.revert [name]) (Tacmach.refine_no_check p)) | Some (t, ty) -> Tacmach.refine_no_check (mkApp (mkLambda (Name (id_of_string "newt"), newt, mkLambda (Name (id_of_string "lemma"), ty, mkApp (p, [| mkRel 2 |]))), [| mkMeta goal_meta; t |]))) in let evartac = if not (undef = Evd.empty) then Refiner.tclEVARS undef else tclIDTAC in tclTHENLIST [evartac; rewtac] gl with | Stdpp.Exc_located (_, TypeClassError (env, (UnsatisfiableConstraints _ as e))) | TypeClassError (env, (UnsatisfiableConstraints _ as e)) -> Refiner.tclFAIL_lazy 0 (lazy (str"setoid rewrite failed: unable to satisfy the rewriting constraints." ++ fnl () ++ Himsg.explain_typeclass_error env e)) gl) | Some None -> tclFAIL 0 (str"setoid rewrite failed: no progress made") gl | None -> raise Not_found let cl_rewrite_clause_strat strat clause gl = init_setoid (); let meta = Evarutil.new_meta() in let gl = { gl with sigma = Typeclasses.mark_unresolvables gl.sigma } in try cl_rewrite_clause_aux strat meta clause gl with Not_found -> tclFAIL 0 (str"setoid rewrite failed: strategy failed") gl let cl_rewrite_clause l left2right occs clause gl = cl_rewrite_clause_strat (rewrite_with l left2right occs) clause gl open Pp open Pcoq open Names open Tacexpr open Tacinterp open Termops open Genarg open Extraargs 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) let pr_gen_strategy pr_id = Pp.mt () let pr_loc_strategy _ _ _ = Pp.mt () let pr_strategy _ _ _ (s : strategy) = Pp.str "" let intern_strategy ist gl c = c let interp_strategy ist gl c = c let glob_strategy ist l = l let subst_strategy evm l = l let apply_constr_expr c l2r occs = fun env sigma -> let c = Constrintern.interp_open_constr sigma env c in apply_lemma c l2r occs env sigma let interp_constr_list env sigma cs = List.map (fun c -> Constrintern.interp_open_constr sigma env c, true) cs open Pcoq let (wit_strategy, globwit_strategy, rawwit_strategy) = (Genarg.create_arg "strategy" : ((strategy, Genarg.tlevel) Genarg.abstract_argument_type * (strategy, Genarg.glevel) Genarg.abstract_argument_type * (strategy, Genarg.rlevel) Genarg.abstract_argument_type)) ARGUMENT EXTEND rewstrategy TYPED AS strategy PRINTED BY pr_strategy INTERPRETED BY interp_strategy GLOBALIZED BY glob_strategy SUBSTITUTED BY subst_strategy [ constr(c) ] -> [ apply_constr_expr c true all_occurrences ] | [ "<-" constr(c) ] -> [ apply_constr_expr c false all_occurrences ] | [ "subterms" rewstrategy(h) ] -> [ all_subterms h ] | [ "subterm" rewstrategy(h) ] -> [ one_subterm h ] | [ "innermost" rewstrategy(h) ] -> [ Strategies.innermost h ] | [ "outermost" rewstrategy(h) ] -> [ Strategies.outermost h ] | [ "bottomup" rewstrategy(h) ] -> [ Strategies.bu h ] | [ "topdown" rewstrategy(h) ] -> [ Strategies.td h ] | [ "id" ] -> [ Strategies.id ] | [ "refl" ] -> [ Strategies.refl ] | [ "progress" rewstrategy(h) ] -> [ Strategies.progress h ] | [ "fail" ] -> [ Strategies.fail ] | [ "try" rewstrategy(h) ] -> [ Strategies.try_ h ] | [ "any" rewstrategy(h) ] -> [ Strategies.any h ] | [ "repeat" rewstrategy(h) ] -> [ Strategies.repeat h ] | [ rewstrategy(h) ";" rewstrategy(h') ] -> [ Strategies.seq h h' ] | [ "(" rewstrategy(h) ")" ] -> [ h ] | [ "choice" rewstrategy(h) rewstrategy(h') ] -> [ Strategies.choice h h' ] | [ "old_hints" preident(h) ] -> [ Strategies.old_hints h ] | [ "hints" preident(h) ] -> [ Strategies.hints h ] | [ "terms" constr_list(h) ] -> [ fun env sigma -> Strategies.lemmas (interp_constr_list env sigma h) env sigma ] END TACTIC EXTEND class_rewrite | [ "clrewrite" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some id) ] | [ "clrewrite" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some id) ] | [ "clrewrite" orient(o) open_constr(c) "in" hyp(id) ] -> [ cl_rewrite_clause c o all_occurrences (Some id) ] | [ "clrewrite" orient(o) open_constr(c) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) None ] | [ "clrewrite" orient(o) open_constr(c) ] -> [ cl_rewrite_clause c o all_occurrences None ] END TACTIC EXTEND class_rewrite_strat | [ "clrewrite_strat" rewstrategy(s) ] -> [ cl_rewrite_clause_strat s None ] (* | [ "clrewrite_strat" strategy(s) "in" hyp(id) ] -> [ cl_rewrite_clause_strat s (Some id) ] *) END let clsubstitute o c = let is_tac id = match kind_of_term (snd c) with Var id' when id' = id -> true | _ -> false in Tacticals.onAllHypsAndConcl (fun cl -> match cl with | Some id when is_tac id -> tclIDTAC | _ -> tclTRY (cl_rewrite_clause c o all_occurrences cl)) TACTIC EXTEND substitute | [ "substitute" orient(o) open_constr(c) ] -> [ clsubstitute o c ] END (* Compatibility with old Setoids *) TACTIC EXTEND setoid_rewrite [ "setoid_rewrite" orient(o) open_constr(c) ] -> [ cl_rewrite_clause c o all_occurrences None ] | [ "setoid_rewrite" orient(o) open_constr(c) "in" hyp(id) ] -> [ cl_rewrite_clause c o all_occurrences (Some id)] | [ "setoid_rewrite" orient(o) open_constr(c) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) None] | [ "setoid_rewrite" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id)] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some id)] | [ "setoid_rewrite" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ)] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some id)] END (* let solve_obligation lemma = *) (* tclTHEN (Tacinterp.interp (Tacexpr.TacAtom (dummy_loc, Tacexpr.TacAnyConstructor None))) *) (* (eapply_with_bindings (Constrintern.interp_constr Evd.empty (Global.env()) lemma, NoBindings)) *) let mkappc s l = CAppExpl (dummy_loc,(None,(Libnames.Ident (dummy_loc,id_of_string s))),l) let declare_an_instance n s args = ((dummy_loc,Name n), Explicit, CAppExpl (dummy_loc, (None, Qualid (dummy_loc, qualid_of_string s)), args)) let declare_instance a aeq n s = declare_an_instance n s [a;aeq] let anew_instance binders instance fields = new_instance binders instance (CRecord (dummy_loc,None,fields)) ~generalize:false None let require_library dirpath = let qualid = (dummy_loc, Libnames.qualid_of_dirpath (Libnames.dirpath_of_string dirpath)) in Library.require_library [qualid] (Some false) let declare_instance_refl binders a aeq n lemma = let instance = declare_instance a aeq (add_suffix n "_Reflexive") "Coq.Classes.RelationClasses.Reflexive" in anew_instance binders instance [(Ident (dummy_loc,id_of_string "reflexivity"),lemma)] let declare_instance_sym binders a aeq n lemma = let instance = declare_instance a aeq (add_suffix n "_Symmetric") "Coq.Classes.RelationClasses.Symmetric" in anew_instance binders instance [(Ident (dummy_loc,id_of_string "symmetry"),lemma)] let declare_instance_trans binders a aeq n lemma = let instance = declare_instance a aeq (add_suffix n "_Transitive") "Coq.Classes.RelationClasses.Transitive" in anew_instance binders instance [(Ident (dummy_loc,id_of_string "transitivity"),lemma)] let constr_tac = Tacinterp.interp (Tacexpr.TacAtom (dummy_loc, Tacexpr.TacAnyConstructor (false,None))) let declare_relation ?(binders=[]) a aeq n refl symm trans = init_setoid (); let instance = declare_instance a aeq (add_suffix n "_relation") "Coq.Classes.RelationClasses.RewriteRelation" in ignore(anew_instance binders instance []); match (refl,symm,trans) with (None, None, None) -> () | (Some lemma1, None, None) -> ignore (declare_instance_refl binders a aeq n lemma1) | (None, Some lemma2, None) -> ignore (declare_instance_sym binders a aeq n lemma2) | (None, None, Some lemma3) -> ignore (declare_instance_trans binders a aeq n lemma3) | (Some lemma1, Some lemma2, None) -> ignore (declare_instance_refl binders a aeq n lemma1); ignore (declare_instance_sym binders a aeq n lemma2) | (Some lemma1, None, Some lemma3) -> let _lemma_refl = declare_instance_refl binders a aeq n lemma1 in let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PreOrder" in ignore( anew_instance binders instance [(Ident (dummy_loc,id_of_string "PreOrder_Reflexive"), lemma1); (Ident (dummy_loc,id_of_string "PreOrder_Transitive"),lemma3)]) | (None, Some lemma2, Some lemma3) -> let _lemma_sym = declare_instance_sym binders a aeq n lemma2 in let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.PER" in ignore( anew_instance binders instance [(Ident (dummy_loc,id_of_string "PER_Symmetric"), lemma2); (Ident (dummy_loc,id_of_string "PER_Transitive"),lemma3)]) | (Some lemma1, Some lemma2, Some lemma3) -> let _lemma_refl = declare_instance_refl binders a aeq n lemma1 in let _lemma_sym = declare_instance_sym binders a aeq n lemma2 in let _lemma_trans = declare_instance_trans binders a aeq n lemma3 in let instance = declare_instance a aeq n "Coq.Classes.RelationClasses.Equivalence" in ignore( anew_instance binders instance [(Ident (dummy_loc,id_of_string "Equivalence_Reflexive"), lemma1); (Ident (dummy_loc,id_of_string "Equivalence_Symmetric"), lemma2); (Ident (dummy_loc,id_of_string "Equivalence_Transitive"), lemma3)]) type 'a binders_let_argtype = (local_binder list, 'a) Genarg.abstract_argument_type let (wit_binders_let : Genarg.tlevel binders_let_argtype), (globwit_binders_let : Genarg.glevel binders_let_argtype), (rawwit_binders_let : Genarg.rlevel binders_let_argtype) = Genarg.create_arg "binders_let" open Pcoq.Constr VERNAC COMMAND EXTEND AddRelation | [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] -> [ declare_relation a aeq n (Some lemma1) (Some lemma2) None ] | [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "as" ident(n) ] -> [ declare_relation a aeq n (Some lemma1) None None ] | [ "Add" "Relation" constr(a) constr(aeq) "as" ident(n) ] -> [ declare_relation a aeq n None None None ] END VERNAC COMMAND EXTEND AddRelation2 [ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] -> [ declare_relation a aeq n None (Some lemma2) None ] | [ "Add" "Relation" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation a aeq n None (Some lemma2) (Some lemma3) ] END VERNAC COMMAND EXTEND AddRelation3 [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation a aeq n (Some lemma1) None (Some lemma3) ] | [ "Add" "Relation" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ] | [ "Add" "Relation" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation a aeq n None None (Some lemma3) ] END VERNAC COMMAND EXTEND AddParametricRelation | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) None ] | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n (Some lemma1) None None ] | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n None None None ] END VERNAC COMMAND EXTEND AddParametricRelation2 [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n None (Some lemma2) None ] | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n None (Some lemma2) (Some lemma3) ] END VERNAC COMMAND EXTEND AddParametricRelation3 [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n (Some lemma1) None (Some lemma3) ] | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "reflexivity" "proved" "by" constr(lemma1) "symmetry" "proved" "by" constr(lemma2) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n (Some lemma1) (Some lemma2) (Some lemma3) ] | [ "Add" "Parametric" "Relation" binders_let(b) ":" constr(a) constr(aeq) "transitivity" "proved" "by" constr(lemma3) "as" ident(n) ] -> [ declare_relation ~binders:b a aeq n None None (Some lemma3) ] END let mk_qualid s = Libnames.Qualid (dummy_loc, Libnames.qualid_of_string s) let cHole = CHole (dummy_loc, None) open Entries open Libnames 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 proper_proj, Array.append args [| instarg |]) in it_mkLambda_or_LetIn app ctx let declare_projection n instance_id r = let ty = Global.type_of_global r in let c = constr_of_global r 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 eq_constr f (Lazy.force respectful) -> succ (aux rel') | _ -> 0 in let init = match kind_of_term typ with App (f, args) when eq_constr f (Lazy.force respectful) -> 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 = { const_entry_body = term; const_entry_type = Some typ; const_entry_opaque = false; const_entry_boxed = false } 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 = Constrintern.interp_constr Evd.empty env m in let t = Typing.type_of env Evd.empty m in let isevars = ref (Evd.empty, Evd.empty) 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 = build_signature !isevars env t cstrs None snd in let _ = isevars := evars in let _ = List.iter (fun (ty, rel) -> Option.iter (fun rel -> let default = mkApp (Lazy.force default_relation, [| ty; rel |]) in let evars,c = new_cstr_evar !isevars env default in isevars := evars) rel) cstrs in let morph = mkApp (Lazy.force proper_type, [| t; sig_; m |]) in let evd = solve_constraints env !isevars 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 = build_signature (Evd.empty,Evd.empty) env t (fst sign) (snd sign) (fun (ty, rel) -> rel) in let morph = mkApp (Lazy.force proper_type, [| t; sign; m |]) in let evars, mor = resolve_one_typeclass env (merge_evars evars) morph in mor, proper_projection mor morph let add_setoid binders a aeq t n = init_setoid (); let _lemma_refl = declare_instance_refl binders a aeq n (mkappc "Seq_refl" [a;aeq;t]) in let _lemma_sym = declare_instance_sym binders a aeq n (mkappc "Seq_sym" [a;aeq;t]) in let _lemma_trans = declare_instance_trans 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 binders instance [(Ident (dummy_loc,id_of_string "Equivalence_Reflexive"), mkappc "Seq_refl" [a;aeq;t]); (Ident (dummy_loc,id_of_string "Equivalence_Symmetric"), mkappc "Seq_sym" [a;aeq;t]); (Ident (dummy_loc,id_of_string "Equivalence_Transitive"), mkappc "Seq_trans" [a;aeq;t])]) let add_morphism_infer glob m n = init_setoid (); let instance_id = add_suffix n "_Proper" in let instance = build_morphism_signature m in if Lib.is_modtype () then let cst = Declare.declare_internal_constant instance_id (Entries.ParameterEntry (instance,false), Decl_kinds.IsAssumption Decl_kinds.Logical) in add_instance (Typeclasses.new_instance (Lazy.force proper_class) None glob (ConstRef cst)); declare_projection n instance_id (ConstRef cst) else let kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Instance in Flags.silently (fun () -> Lemmas.start_proof instance_id kind instance (fun _ -> function Libnames.ConstRef cst -> add_instance (Typeclasses.new_instance (Lazy.force proper_class) None glob (ConstRef cst)); declare_projection n instance_id (ConstRef cst) | _ -> assert false); Pfedit.by (Tacinterp.interp <:tactic< Coq.Classes.SetoidTactics.add_morphism_tactic>>)) (); Flags.if_verbose (fun x -> msg (Printer.pr_open_subgoals x)) () let add_morphism glob binders m s n = init_setoid (); let instance_id = add_suffix n "_Proper" in let instance = ((dummy_loc,Name instance_id), Explicit, CAppExpl (dummy_loc, (None, Qualid (dummy_loc, Libnames.qualid_of_string "Coq.Classes.Morphisms.Proper")), [cHole; s; m])) in let tac = Tacinterp.interp <:tactic> in ignore(new_instance ~global:glob binders instance (CRecord (dummy_loc,None,[])) ~generalize:false ~tac ~hook:(declare_projection n instance_id) None) VERNAC COMMAND EXTEND AddSetoid1 [ "Add" "Setoid" constr(a) constr(aeq) constr(t) "as" ident(n) ] -> [ add_setoid [] a aeq t n ] | [ "Add" "Parametric" "Setoid" binders_let(binders) ":" constr(a) constr(aeq) constr(t) "as" ident(n) ] -> [ add_setoid binders a aeq t n ] | [ "Add" "Morphism" constr(m) ":" ident(n) ] -> [ add_morphism_infer (not (Vernacexpr.use_section_locality ())) m n ] | [ "Add" "Morphism" constr(m) "with" "signature" lconstr(s) "as" ident(n) ] -> [ add_morphism (not (Vernacexpr.use_section_locality ())) [] m s n ] | [ "Add" "Parametric" "Morphism" binders_let(binders) ":" constr(m) "with" "signature" lconstr(s) "as" ident(n) ] -> [ add_morphism (not (Vernacexpr.use_section_locality ())) binders m s n ] END (** 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 l2r c1 c2 cl car rel but gl = let env = pf_env gl 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 env ((if l2r then c1 else c2),but) cl.evd with Pretype_errors.PretypeError _ -> (* ~flags:(true,true) to make Ring work (since it really exploits conversion) *) Unification.w_unify_to_subterm ~flags:rewrite2_unif_flags env ((if l2r then c1 else c2),but) cl.evd in let evd' = Typeclasses.resolve_typeclasses ~fail:false env evd' in let cl' = {cl with evd = evd'} in let cl' = let mvs = clenv_dependent false cl' in clenv_pose_metas_as_evars cl' mvs 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 cl' = { cl' with templval = mk_freelisted prf ; templtyp = mk_freelisted prfty } in {cl=cl'; prf=(mkRel 1); car=car; rel=rel; l2r=l2r; c1=c1; c2=c2; c=None; abs=Some (prf, prfty)} let get_hyp gl evars c clause l2r = let hi = decompose_applied_relation (pf_env gl) evars c l2r in let but = match clause with Some id -> pf_get_hyp_typ gl id | None -> pf_concl gl in unification_rewrite hi.l2r hi.c1 hi.c2 hi.cl hi.car hi.rel but gl let general_rewrite_flags = { under_lambdas = false; on_morphisms = false } let apply_lemma gl c cl l2r occs = let sigma = project gl in let hypinfo = ref (get_hyp gl sigma c cl l2r) in let app = apply_rule hypinfo occs in let rec aux () = Strategies.choice app (subterm true general_rewrite_flags (fun env -> aux () env)) in !hypinfo, aux () 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 cl l2r occs in try tclTHEN (Refiner.tclEVARS hypinfo.cl.evd) (cl_rewrite_clause_aux ~abs:hypinfo.abs strat meta cl) gl with Not_found -> let {l2r=l2r; c1=x; c2=y} = hypinfo in raise (Pretype_errors.PretypeError (pf_env gl, Pretype_errors.NoOccurrenceFound ((if l2r then x else y), cl))) let general_s_rewrite_clause x = init_setoid (); match x with | None -> general_s_rewrite None | Some id -> general_s_rewrite (Some id) let _ = Equality.register_general_rewrite_clause general_s_rewrite_clause let is_loaded d = let d' = List.map id_of_string d in let dir = make_dirpath (List.rev d') in Library.library_is_loaded dir let try_loaded f gl = if is_loaded ["Coq";"Classes";"RelationClasses"] then f gl else tclFAIL 0 (str"You need to require Coq.Classes.RelationClasses first") gl (** [setoid_]{reflexivity,symmetry,transitivity} tactics *) let not_declared env ty rel = 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 relation_of_constr env c = match kind_of_term c with | App (f, args) when Array.length args >= 2 -> let relargs, args = array_chop (Array.length args - 2) args in mkApp (f, relargs), args | _ -> errorlabstrm "relation_of_constr" (str "The term " ++ Printer.pr_constr_env env c ++ str" is not an applied relation.") let setoid_proof gl ty fn fallback = let env = pf_env gl in try let rel, args = relation_of_constr env (pf_concl gl) in let evm, car = project gl, pf_type_of gl args.(0) in fn env evm car rel gl with e -> try fallback gl with Hipattern.NoEquationFound -> match e with | Not_found -> let rel, args = relation_of_constr env (pf_concl gl) in not_declared env ty rel gl | _ -> raise e let setoid_reflexivity gl = setoid_proof gl "reflexive" (fun env evm car rel -> apply (get_reflexive_proof env evm car rel)) (reflexivity_red true) let setoid_symmetry gl = setoid_proof gl "symmetric" (fun env evm car rel -> apply (get_symmetric_proof env evm car rel)) (symmetry_red true) let setoid_transitivity c gl = setoid_proof gl "transitive" (fun env evm car rel -> let proof = get_transitive_proof env evm car rel in match c with | None -> eapply proof | Some c -> apply_with_bindings (proof,Rawterm.ExplicitBindings [ dummy_loc, Rawterm.NamedHyp (id_of_string "y"), c ])) (transitivity_red true c) let setoid_symmetry_in id 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 (Tactics.cut new_hyp) [ intro_replacing id; tclTHENLIST [ intros; setoid_symmetry; apply (mkVar id); Tactics.assumption ] ] gl let _ = Tactics.register_setoid_reflexivity setoid_reflexivity let _ = Tactics.register_setoid_symmetry setoid_symmetry let _ = Tactics.register_setoid_symmetry_in setoid_symmetry_in let _ = Tactics.register_setoid_transitivity setoid_transitivity TACTIC EXTEND setoid_symmetry [ "setoid_symmetry" ] -> [ setoid_symmetry ] | [ "setoid_symmetry" "in" hyp(n) ] -> [ setoid_symmetry_in n ] END TACTIC EXTEND setoid_reflexivity [ "setoid_reflexivity" ] -> [ setoid_reflexivity ] END TACTIC EXTEND setoid_transitivity [ "setoid_transitivity" constr(t) ] -> [ setoid_transitivity (Some t) ] | [ "setoid_etransitivity" ] -> [ setoid_transitivity None ] END let implify id gl = let (_, b, ctype) = pf_get_hyp gl id in let binders,concl = decompose_prod_assum ctype in let 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 = Typing.type_of env sigma ty and tyconcl = Typing.type_of (Environ.push_rel hd env) sigma concl in let app = mkApp (arrow_morphism tyhd (subst1 mkProp tyconcl), [| ty; (subst1 mkProp concl) |]) in it_mkProd_or_LetIn app tl | _ -> ctype in convert_hyp_no_check (id, b, ctype') gl TACTIC EXTEND implify [ "implify" hyp(n) ] -> [ implify n ] END