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Diffstat (limited to 'plugins/ssr/ssrcommon.ml')
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diff --git a/plugins/ssr/ssrcommon.ml b/plugins/ssr/ssrcommon.ml new file mode 100644 index 00000000..82cae439 --- /dev/null +++ b/plugins/ssr/ssrcommon.ml @@ -0,0 +1,1572 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) +(************************************************************************) + +(* This file is (C) Copyright 2006-2015 Microsoft Corporation and Inria. *) + +open Util +open Names +open Evd +open Term +open Constr +open Termops +open Printer +open Locusops + +open Ltac_plugin +open Tacmach +open Refiner +open Libnames +open Ssrmatching_plugin +open Ssrmatching +open Ssrast +open Ssrprinters + +module RelDecl = Context.Rel.Declaration +module NamedDecl = Context.Named.Declaration + +(* Defining grammar rules with "xx" in it automatically declares keywords too, + * we thus save the lexer to restore it at the end of the file *) +let frozen_lexer = CLexer.get_keyword_state () ;; + +let errorstrm x = CErrors.user_err ~hdr:"ssreflect" x + +let allocc = Some(false,[]) + +(** Bound assumption argument *) + +(* The Ltac API does have a type for assumptions but it is level-dependent *) +(* and therefore impractical to use for complex arguments, so we substitute *) +(* our own to have a uniform representation. Also, we refuse to intern *) +(* idents that match global/section constants, since this would lead to *) +(* fragile Ltac scripts. *) + +let hyp_id (SsrHyp (_, id)) = id + +let hyp_err ?loc msg id = + CErrors.user_err ?loc ~hdr:"ssrhyp" Pp.(str msg ++ Id.print id) + +let not_section_id id = not (Termops.is_section_variable id) + +let hyps_ids = List.map hyp_id + +let rec check_hyps_uniq ids = function + | SsrHyp (loc, id) :: _ when List.mem id ids -> + hyp_err ?loc "Duplicate assumption " id + | SsrHyp (_, id) :: hyps -> check_hyps_uniq (id :: ids) hyps + | [] -> () + +let check_hyp_exists hyps (SsrHyp(_, id)) = + try ignore(Context.Named.lookup id hyps) + with Not_found -> errorstrm Pp.(str"No assumption is named " ++ Id.print id) + +let test_hypname_exists hyps id = + try ignore(Context.Named.lookup id hyps); true + with Not_found -> false + +let hoik f = function Hyp x -> f x | Id x -> f x +let hoi_id = hoik hyp_id + +let mk_hint tac = false, [Some tac] +let mk_orhint tacs = true, tacs +let nullhint = true, [] +let nohint = false, [] + +type 'a tac_a = (goal * 'a) sigma -> (goal * 'a) list sigma + +let push_ctx a gl = re_sig (sig_it gl, a) (project gl) +let push_ctxs a gl = + re_sig (List.map (fun x -> x,a) (sig_it gl)) (project gl) +let pull_ctx gl = let g, a = sig_it gl in re_sig g (project gl), a +let pull_ctxs gl = let g, a = List.split (sig_it gl) in re_sig g (project gl), a + +let with_ctx f gl = + let gl, ctx = pull_ctx gl in + let rc, ctx = f ctx in + rc, push_ctx ctx gl +let without_ctx f gl = + let gl, _ctx = pull_ctx gl in + f gl +let tac_ctx t gl = + let gl, a = pull_ctx gl in + let gl = t gl in + push_ctxs a gl + +let tclTHEN_ia t1 t2 gl = + let gal = t1 gl in + let goals, sigma = sig_it gal, project gal in + let _, opened, sigma = + List.fold_left (fun (i,opened,sigma) g -> + let gl = t2 i (re_sig g sigma) in + i+1, sig_it gl :: opened, project gl) + (1,[],sigma) goals in + re_sig (List.flatten (List.rev opened)) sigma + +let tclTHEN_a t1 t2 gl = tclTHEN_ia t1 (fun _ -> t2) gl + +let tclTHENS_a t1 tl gl = tclTHEN_ia t1 + (fun i -> List.nth tl (i-1)) gl + +let rec tclTHENLIST_a = function + | [] -> tac_ctx tclIDTAC + | t1::tacl -> tclTHEN_a t1 (tclTHENLIST_a tacl) + +(* like tclTHEN_i but passes to the tac "i of n" and not just i *) +let tclTHEN_i_max tac taci gl = + let maxi = ref 0 in + tclTHEN_ia (tclTHEN_ia tac (fun i -> maxi := max i !maxi; tac_ctx tclIDTAC)) + (fun i gl -> taci i !maxi gl) gl + +let tac_on_all gl tac = + let goals = sig_it gl in + let opened, sigma = + List.fold_left (fun (opened,sigma) g -> + let gl = tac (re_sig g sigma) in + sig_it gl :: opened, project gl) + ([],project gl) goals in + re_sig (List.flatten (List.rev opened)) sigma + +(* Used to thread data between intro patterns at run time *) +type tac_ctx = { + tmp_ids : (Id.t * Name.t ref) list; + wild_ids : Id.t list; + delayed_clears : Id.t list; +} + +let new_ctx () = + { tmp_ids = []; wild_ids = []; delayed_clears = [] } + +let with_fresh_ctx t gl = + let gl = push_ctx (new_ctx()) gl in + let gl = t gl in + fst (pull_ctxs gl) + +open Genarg +open Stdarg +open Pp + +let errorstrm x = CErrors.user_err ~hdr:"ssreflect" x +let anomaly s = CErrors.anomaly (str s) + +(* Tentative patch from util.ml *) + +let array_fold_right_from n f v a = + let rec fold n = + if n >= Array.length v then a else f v.(n) (fold (succ n)) + in + fold n + +let array_app_tl v l = + if Array.length v = 0 then invalid_arg "array_app_tl"; + array_fold_right_from 1 (fun e l -> e::l) v l + +let array_list_of_tl v = + if Array.length v = 0 then invalid_arg "array_list_of_tl"; + array_fold_right_from 1 (fun e l -> e::l) v [] + +(* end patch *) + +let option_assert_get o msg = + match o with + | None -> CErrors.anomaly msg + | Some x -> x + + +(** Constructors for rawconstr *) +open Glob_term +open Globnames +open Misctypes +open Decl_kinds + +let mkRHole = DAst.make @@ GHole (Evar_kinds.InternalHole, IntroAnonymous, None) + +let rec mkRHoles n = if n > 0 then mkRHole :: mkRHoles (n - 1) else [] +let rec isRHoles cl = match cl with +| [] -> true +| c :: l -> match DAst.get c with GHole _ -> isRHoles l | _ -> false +let mkRApp f args = if args = [] then f else DAst.make @@ GApp (f, args) +let mkRVar id = DAst.make @@ GRef (VarRef id,None) +let mkRltacVar id = DAst.make @@ GVar (id) +let mkRCast rc rt = DAst.make @@ GCast (rc, CastConv rt) +let mkRType = DAst.make @@ GSort (GType []) +let mkRProp = DAst.make @@ GSort (GProp) +let mkRArrow rt1 rt2 = DAst.make @@ GProd (Anonymous, Explicit, rt1, rt2) +let mkRConstruct c = DAst.make @@ GRef (ConstructRef c,None) +let mkRInd mind = DAst.make @@ GRef (IndRef mind,None) +let mkRLambda n s t = DAst.make @@ GLambda (n, Explicit, s, t) + +let rec mkRnat n = + if n <= 0 then DAst.make @@ GRef (Coqlib.glob_O, None) else + mkRApp (DAst.make @@ GRef (Coqlib.glob_S, None)) [mkRnat (n - 1)] + +let glob_constr ist genv = function + | _, Some ce -> + let vars = Id.Map.fold (fun x _ accu -> Id.Set.add x accu) ist.Tacinterp.lfun Id.Set.empty in + let ltacvars = { + Constrintern.empty_ltac_sign with Constrintern.ltac_vars = vars } in + Constrintern.intern_gen Pretyping.WithoutTypeConstraint ~ltacvars genv Evd.(from_env genv) ce + | rc, None -> rc + +let pf_intern_term ist gl (_, c) = glob_constr ist (pf_env gl) c +let intern_term ist env (_, c) = glob_constr ist env c + +(* Estimate a bound on the number of arguments of a raw constr. *) +(* This is not perfect, because the unifier may fail to *) +(* typecheck the partial application, so we use a minimum of 5. *) +(* Also, we don't handle delayed or iterated coercions to *) +(* FUNCLASS, which is probably just as well since these can *) +(* lead to infinite arities. *) + +let splay_open_constr gl (sigma, c) = + let env = pf_env gl in let t = Retyping.get_type_of env sigma c in + Reductionops.splay_prod env sigma t + +let isAppInd env sigma c = + let c = Reductionops.clos_whd_flags CClosure.all env sigma c in + let c, _ = decompose_app_vect sigma c in + EConstr.isInd sigma c + +(** Generic argument-based globbing/typing utilities *) + +let interp_refine ist gl rc = + let constrvars = Tacinterp.extract_ltac_constr_values ist (pf_env gl) in + let vars = { Glob_ops.empty_lvar with + Ltac_pretype.ltac_constrs = constrvars; ltac_genargs = ist.Tacinterp.lfun + } in + let kind = Pretyping.OfType (pf_concl gl) in + let flags = { + Pretyping.use_typeclasses = true; + solve_unification_constraints = true; + use_hook = None; + fail_evar = false; + expand_evars = true } + in + let sigma, c = Pretyping.understand_ltac flags (pf_env gl) (project gl) vars kind rc in +(* ppdebug(lazy(str"sigma@interp_refine=" ++ pr_evar_map None sigma)); *) + ppdebug(lazy(str"c@interp_refine=" ++ Printer.pr_econstr_env (pf_env gl) sigma c)); + (sigma, (sigma, c)) + + +let interp_open_constr ist gl gc = + let (sigma, (c, _)) = Tacinterp.interp_open_constr_with_bindings ist (pf_env gl) (project gl) (gc, Misctypes.NoBindings) in + (project gl, (sigma, c)) + +let interp_term ist gl (_, c) = snd (interp_open_constr ist gl c) + +let of_ftactic ftac gl = + let r = ref None in + let tac = Ftactic.run ftac (fun ans -> r := Some ans; Proofview.tclUNIT ()) in + let tac = Proofview.V82.of_tactic tac in + let { sigma = sigma } = tac gl in + let ans = match !r with + | None -> assert false (** If the tactic failed we should not reach this point *) + | Some ans -> ans + in + (sigma, ans) + +let interp_wit wit ist gl x = + let globarg = in_gen (glbwit wit) x in + let arg = Tacinterp.interp_genarg ist globarg in + let (sigma, arg) = of_ftactic arg gl in + sigma, Tacinterp.Value.cast (topwit wit) arg + +let interp_hyp ist gl (SsrHyp (loc, id)) = + let s, id' = interp_wit wit_var ist gl CAst.(make ?loc id) in + if not_section_id id' then s, SsrHyp (loc, id') else + hyp_err ?loc "Can't clear section hypothesis " id' + +let interp_hyps ist gl ghyps = + let hyps = List.map snd (List.map (interp_hyp ist gl) ghyps) in + check_hyps_uniq [] hyps; Tacmach.project gl, hyps + +(* Old terms *) +let mk_term k c = k, (mkRHole, Some c) +let mk_lterm c = mk_term xNoFlag c + +(* New terms *) + +let mk_ast_closure_term a t = { + annotation = a; + body = t; + interp_env = None; + glob_env = None; +} + +let glob_ast_closure_term (ist : Genintern.glob_sign) t = + { t with glob_env = Some ist } +let subst_ast_closure_term (_s : Mod_subst.substitution) t = + (* _s makes sense only for glob constr *) + t +let interp_ast_closure_term (ist : Geninterp.interp_sign) (gl : 'goal Evd.sigma) t = + (* gl is only useful if we want to interp *now*, later we have + * a potentially different gl.sigma *) + Tacmach.project gl, { t with interp_env = Some ist } + +let ssrterm_of_ast_closure_term { body; annotation } = + let c = match annotation with + | `Parens -> xInParens + | `At -> xWithAt + | _ -> xNoFlag in + mk_term c body + +let ssrdgens_of_parsed_dgens = function + | [], clr -> { dgens = []; gens = []; clr } + | [gens], clr -> { dgens = []; gens; clr } + | [dgens;gens], clr -> { dgens; gens; clr } + | _ -> assert false + + +let nbargs_open_constr gl oc = + let pl, _ = splay_open_constr gl oc in List.length pl + +let pf_nbargs gl c = nbargs_open_constr gl (project gl, c) + +let internal_names = ref [] +let add_internal_name pt = internal_names := pt :: !internal_names +let is_internal_name s = List.exists (fun p -> p s) !internal_names + +let tmp_tag = "_the_" +let tmp_post = "_tmp_" +let mk_tmp_id i = + Id.of_string (Printf.sprintf "%s%s%s" tmp_tag (CString.ordinal i) tmp_post) +let new_tmp_id ctx = + let id = mk_tmp_id (1 + List.length ctx.tmp_ids) in + let orig = ref Anonymous in + (id, orig), { ctx with tmp_ids = (id, orig) :: ctx.tmp_ids } +;; + +let mk_internal_id s = + let s' = Printf.sprintf "_%s_" s in + let s' = String.map (fun c -> if c = ' ' then '_' else c) s' in + add_internal_name ((=) s'); Id.of_string s' + +let same_prefix s t n = + let rec loop i = i = n || s.[i] = t.[i] && loop (i + 1) in loop 0 + +let skip_digits s = + let n = String.length s in + let rec loop i = if i < n && is_digit s.[i] then loop (i + 1) else i in loop + +let mk_tagged_id t i = Id.of_string (Printf.sprintf "%s%d_" t i) +let is_tagged t s = + let n = String.length s - 1 and m = String.length t in + m < n && s.[n] = '_' && same_prefix s t m && skip_digits s m = n + +let evar_tag = "_evar_" +let _ = add_internal_name (is_tagged evar_tag) +let mk_evar_name n = Name (mk_tagged_id evar_tag n) + +let ssr_anon_hyp = "Hyp" + +let wildcard_tag = "_the_" +let wildcard_post = "_wildcard_" +let mk_wildcard_id i = + Id.of_string (Printf.sprintf "%s%s%s" wildcard_tag (CString.ordinal i) wildcard_post) +let has_wildcard_tag s = + let n = String.length s in let m = String.length wildcard_tag in + let m' = String.length wildcard_post in + n < m + m' + 2 && same_prefix s wildcard_tag m && + String.sub s (n - m') m' = wildcard_post && + skip_digits s m = n - m' - 2 +let _ = add_internal_name has_wildcard_tag + +let new_wild_id ctx = + let i = 1 + List.length ctx.wild_ids in + let id = mk_wildcard_id i in + id, { ctx with wild_ids = id :: ctx.wild_ids } + +let discharged_tag = "_discharged_" +let mk_discharged_id id = + Id.of_string (Printf.sprintf "%s%s_" discharged_tag (Id.to_string id)) +let has_discharged_tag s = + let m = String.length discharged_tag and n = String.length s - 1 in + m < n && s.[n] = '_' && same_prefix s discharged_tag m +let _ = add_internal_name has_discharged_tag +let is_discharged_id id = has_discharged_tag (Id.to_string id) + +let max_suffix m (t, j0 as tj0) id = + let s = Id.to_string id in let n = String.length s - 1 in + let dn = String.length t - 1 - n in let i0 = j0 - dn in + if not (i0 >= m && s.[n] = '_' && same_prefix s t m) then tj0 else + let rec loop i = + if i < i0 && s.[i] = '0' then loop (i + 1) else + if (if i < i0 then skip_digits s i = n else le_s_t i) then s, i else tj0 + and le_s_t i = + let ds = s.[i] and dt = t.[i + dn] in + if ds = dt then i = n || le_s_t (i + 1) else + dt < ds && skip_digits s i = n in + loop m + +let mk_anon_id t gl_ids = + let m, si0, id0 = + let s = ref (Printf.sprintf "_%s_" t) in + if is_internal_name !s then s := "_" ^ !s; + let n = String.length !s - 1 in + let rec loop i j = + let d = !s.[i] in if not (is_digit d) then i + 1, j else + loop (i - 1) (if d = '0' then j else i) in + let m, j = loop (n - 1) n in m, (!s, j), Id.of_string !s in + if not (List.mem id0 gl_ids) then id0 else + let s, i = List.fold_left (max_suffix m) si0 gl_ids in + let open Bytes in + let s = of_string s in + let n = length s - 1 in + let rec loop i = + if get s i = '9' then (set s i '0'; loop (i - 1)) else + if i < m then (set s n '0'; set s m '1'; cat s (of_string "_")) else + (set s i (Char.chr (Char.code (get s i) + 1)); s) in + Id.of_bytes (loop (n - 1)) + +let convert_concl_no_check t = Tactics.convert_concl_no_check t Term.DEFAULTcast +let convert_concl t = Tactics.convert_concl t Term.DEFAULTcast + +let rename_hd_prod orig_name_ref gl = + match EConstr.kind (project gl) (pf_concl gl) with + | Term.Prod(_,src,tgt) -> + Proofview.V82.of_tactic (convert_concl_no_check (EConstr.mkProd (!orig_name_ref,src,tgt))) gl + | _ -> CErrors.anomaly (str "gentac creates no product") + +(* Reduction that preserves the Prod/Let spine of the "in" tactical. *) + +let inc_safe n = if n = 0 then n else n + 1 +let rec safe_depth s c = match EConstr.kind s c with +| LetIn (Name x, _, _, c') when is_discharged_id x -> safe_depth s c' + 1 +| LetIn (_, _, _, c') | Prod (_, _, c') -> inc_safe (safe_depth s c') +| _ -> 0 + +let red_safe (r : Reductionops.reduction_function) e s c0 = + let rec red_to e c n = match EConstr.kind s c with + | Prod (x, t, c') when n > 0 -> + let t' = r e s t in let e' = EConstr.push_rel (RelDecl.LocalAssum (x, t')) e in + EConstr.mkProd (x, t', red_to e' c' (n - 1)) + | LetIn (x, b, t, c') when n > 0 -> + let t' = r e s t in let e' = EConstr.push_rel (RelDecl.LocalAssum (x, t')) e in + EConstr.mkLetIn (x, r e s b, t', red_to e' c' (n - 1)) + | _ -> r e s c in + red_to e c0 (safe_depth s c0) + +let is_id_constr sigma c = match EConstr.kind sigma c with + | Lambda(_,_,c) when EConstr.isRel sigma c -> 1 = EConstr.destRel sigma c + | _ -> false + +let red_product_skip_id env sigma c = match EConstr.kind sigma c with + | App(hd,args) when Array.length args = 1 && is_id_constr sigma hd -> args.(0) + | _ -> try Tacred.red_product env sigma c with _ -> c + +let ssrevaltac ist gtac = Tacinterp.tactic_of_value ist gtac + +(** Open term to lambda-term coercion *)(* {{{ ************************************) + +(* This operation takes a goal gl and an open term (sigma, t), and *) +(* returns a term t' where all the new evars in sigma are abstracted *) +(* with the mkAbs argument, i.e., for mkAbs = mkLambda then there is *) +(* some duplicate-free array args of evars of sigma such that the *) +(* term mkApp (t', args) is convertible to t. *) +(* This makes a useful shorthand for local definitions in proofs, *) +(* i.e., pose succ := _ + 1 means pose succ := fun n : nat => n + 1, *) +(* and, in context of the 4CT library, pose mid := maps id means *) +(* pose mid := fun d : detaSet => @maps d d (@id (datum d)) *) +(* Note that this facility does not extend to set, which tries *) +(* instead to fill holes by matching a goal subterm. *) +(* The argument to "have" et al. uses product abstraction, e.g. *) +(* have Hmid: forall s, (maps id s) = s. *) +(* stands for *) +(* have Hmid: forall (d : dataSet) (s : seq d), (maps id s) = s. *) +(* We also use this feature for rewrite rules, so that, e.g., *) +(* rewrite: (plus_assoc _ 3). *) +(* will execute as *) +(* rewrite (fun n => plus_assoc n 3) *) +(* i.e., it will rewrite some subterm .. + (3 + ..) to .. + 3 + ... *) +(* The convention is also used for the argument of the congr tactic, *) +(* e.g., congr (x + _ * 1). *) + +(* Replace new evars with lambda variables, retaining local dependencies *) +(* but stripping global ones. We use the variable names to encode the *) +(* the number of dependencies, so that the transformation is reversible. *) + +let env_size env = List.length (Environ.named_context env) + +let pf_concl gl = EConstr.Unsafe.to_constr (pf_concl gl) +let pf_get_hyp gl x = EConstr.Unsafe.to_named_decl (pf_get_hyp gl x) + +let pf_e_type_of gl t = + let sigma, env, it = project gl, pf_env gl, sig_it gl in + let sigma, ty = Typing.type_of env sigma t in + re_sig it sigma, ty + +let nf_evar sigma t = + EConstr.Unsafe.to_constr (Evarutil.nf_evar sigma (EConstr.of_constr t)) + +let pf_abs_evars2 gl rigid (sigma, c0) = + let c0 = EConstr.to_constr sigma c0 in + let sigma0, ucst = project gl, Evd.evar_universe_context sigma in + let nenv = env_size (pf_env gl) in + let abs_evar n k = + let evi = Evd.find sigma k in + let dc = CList.firstn n (evar_filtered_context evi) in + let abs_dc c = function + | NamedDecl.LocalDef (x,b,t) -> mkNamedLetIn x b t (mkArrow t c) + | NamedDecl.LocalAssum (x,t) -> mkNamedProd x t c in + let t = Context.Named.fold_inside abs_dc ~init:evi.evar_concl dc in + nf_evar sigma t in + let rec put evlist c = match Constr.kind c with + | Evar (k, a) -> + if List.mem_assoc k evlist || Evd.mem sigma0 k || List.mem k rigid then evlist else + let n = max 0 (Array.length a - nenv) in + let t = abs_evar n k in (k, (n, t)) :: put evlist t + | _ -> Constr.fold put evlist c in + let evlist = put [] c0 in + if evlist = [] then 0, EConstr.of_constr c0,[], ucst else + let rec lookup k i = function + | [] -> 0, 0 + | (k', (n, _)) :: evl -> if k = k' then i, n else lookup k (i + 1) evl in + let rec get i c = match Constr.kind c with + | Evar (ev, a) -> + let j, n = lookup ev i evlist in + if j = 0 then Constr.map (get i) c else if n = 0 then mkRel j else + mkApp (mkRel j, Array.init n (fun k -> get i a.(n - 1 - k))) + | _ -> Constr.map_with_binders ((+) 1) get i c in + let rec loop c i = function + | (_, (n, t)) :: evl -> + loop (mkLambda (mk_evar_name n, get (i - 1) t, c)) (i - 1) evl + | [] -> c in + List.length evlist, EConstr.of_constr (loop (get 1 c0) 1 evlist), List.map fst evlist, ucst + +let pf_abs_evars gl t = pf_abs_evars2 gl [] t + + +(* As before but if (?i : T(?j)) and (?j : P : Prop), then the lambda for i + * looks like (fun evar_i : (forall pi : P. T(pi))) thanks to "loopP" and all + * occurrences of evar_i are replaced by (evar_i evar_j) thanks to "app". + * + * If P can be solved by ssrautoprop (that defaults to trivial), then + * the corresponding lambda looks like (fun evar_i : T(c)) where c is + * the solution found by ssrautoprop. + *) +let ssrautoprop_tac = ref (fun gl -> assert false) + +(* Thanks to Arnaud Spiwack for this snippet *) +let call_on_evar tac e s = + let { it = gs ; sigma = s } = + tac { it = e ; sigma = s; } in + gs, s + +open Pp +let pp _ = () (* FIXME *) +module Intset = Evar.Set + +let pf_abs_evars_pirrel gl (sigma, c0) = + pp(lazy(str"==PF_ABS_EVARS_PIRREL==")); + pp(lazy(str"c0= " ++ Printer.pr_constr_env (pf_env gl) sigma c0)); + let sigma0 = project gl in + let c0 = nf_evar sigma0 (nf_evar sigma c0) in + let nenv = env_size (pf_env gl) in + let abs_evar n k = + let evi = Evd.find sigma k in + let dc = CList.firstn n (evar_filtered_context evi) in + let abs_dc c = function + | NamedDecl.LocalDef (x,b,t) -> mkNamedLetIn x b t (mkArrow t c) + | NamedDecl.LocalAssum (x,t) -> mkNamedProd x t c in + let t = Context.Named.fold_inside abs_dc ~init:evi.evar_concl dc in + nf_evar sigma0 (nf_evar sigma t) in + let rec put evlist c = match Constr.kind c with + | Evar (k, a) -> + if List.mem_assoc k evlist || Evd.mem sigma0 k then evlist else + let n = max 0 (Array.length a - nenv) in + let k_ty = + Retyping.get_sort_family_of + (pf_env gl) sigma (EConstr.of_constr (Evd.evar_concl (Evd.find sigma k))) in + let is_prop = k_ty = InProp in + let t = abs_evar n k in (k, (n, t, is_prop)) :: put evlist t + | _ -> Constr.fold put evlist c in + let evlist = put [] c0 in + if evlist = [] then 0, c0 else + let pr_constr t = Printer.pr_econstr_env (pf_env gl) sigma (Reductionops.nf_beta (pf_env gl) (project gl) (EConstr.of_constr t)) in + pp(lazy(str"evlist=" ++ pr_list (fun () -> str";") + (fun (k,_) -> Evar.print k) evlist)); + let evplist = + let depev = List.fold_left (fun evs (_,(_,t,_)) -> + let t = EConstr.of_constr t in + Intset.union evs (Evarutil.undefined_evars_of_term sigma t)) Intset.empty evlist in + List.filter (fun (i,(_,_,b)) -> b && Intset.mem i depev) evlist in + let evlist, evplist, sigma = + if evplist = [] then evlist, [], sigma else + List.fold_left (fun (ev, evp, sigma) (i, (_,t,_) as p) -> + try + let ng, sigma = call_on_evar !ssrautoprop_tac i sigma in + if (ng <> []) then errorstrm (str "Should we tell the user?"); + List.filter (fun (j,_) -> j <> i) ev, evp, sigma + with _ -> ev, p::evp, sigma) (evlist, [], sigma) (List.rev evplist) in + let c0 = nf_evar sigma c0 in + let evlist = + List.map (fun (x,(y,t,z)) -> x,(y,nf_evar sigma t,z)) evlist in + let evplist = + List.map (fun (x,(y,t,z)) -> x,(y,nf_evar sigma t,z)) evplist in + pp(lazy(str"c0= " ++ pr_constr c0)); + let rec lookup k i = function + | [] -> 0, 0 + | (k', (n,_,_)) :: evl -> if k = k' then i,n else lookup k (i + 1) evl in + let rec get evlist i c = match Constr.kind c with + | Evar (ev, a) -> + let j, n = lookup ev i evlist in + if j = 0 then Constr.map (get evlist i) c else if n = 0 then mkRel j else + mkApp (mkRel j, Array.init n (fun k -> get evlist i a.(n - 1 - k))) + | _ -> Constr.map_with_binders ((+) 1) (get evlist) i c in + let rec app extra_args i c = match decompose_app c with + | hd, args when isRel hd && destRel hd = i -> + let j = destRel hd in + mkApp (mkRel j, Array.of_list (List.map (Vars.lift (i-1)) extra_args @ args)) + | _ -> Constr.map_with_binders ((+) 1) (app extra_args) i c in + let rec loopP evlist c i = function + | (_, (n, t, _)) :: evl -> + let t = get evlist (i - 1) t in + let n = Name (Id.of_string (ssr_anon_hyp ^ string_of_int n)) in + loopP evlist (mkProd (n, t, c)) (i - 1) evl + | [] -> c in + let rec loop c i = function + | (_, (n, t, _)) :: evl -> + let evs = Evarutil.undefined_evars_of_term sigma (EConstr.of_constr t) in + let t_evplist = List.filter (fun (k,_) -> Intset.mem k evs) evplist in + let t = loopP t_evplist (get t_evplist 1 t) 1 t_evplist in + let t = get evlist (i - 1) t in + let extra_args = + List.map (fun (k,_) -> mkRel (fst (lookup k i evlist))) + (List.rev t_evplist) in + let c = if extra_args = [] then c else app extra_args 1 c in + loop (mkLambda (mk_evar_name n, t, c)) (i - 1) evl + | [] -> c in + let res = loop (get evlist 1 c0) 1 evlist in + pp(lazy(str"res= " ++ pr_constr res)); + List.length evlist, res + +(* Strip all non-essential dependencies from an abstracted term, generating *) +(* standard names for the abstracted holes. *) + +let nb_evar_deps = function + | Name id -> + let s = Id.to_string id in + if not (is_tagged evar_tag s) then 0 else + let m = String.length evar_tag in + (try int_of_string (String.sub s m (String.length s - 1 - m)) with _ -> 0) + | _ -> 0 + +let pf_type_id gl t = Id.of_string (Namegen.hdchar (pf_env gl) (project gl) t) +let pfe_type_of gl t = + let sigma, ty = pf_type_of gl t in + re_sig (sig_it gl) sigma, ty +let pf_type_of gl t = + let sigma, ty = pf_type_of gl (EConstr.of_constr t) in + re_sig (sig_it gl) sigma, EConstr.Unsafe.to_constr ty + +let pf_abs_cterm gl n c0 = + if n <= 0 then c0 else + let c0 = EConstr.Unsafe.to_constr c0 in + let noargs = [|0|] in + let eva = Array.make n noargs in + let rec strip i c = match Constr.kind c with + | App (f, a) when isRel f -> + let j = i - destRel f in + if j >= n || eva.(j) = noargs then mkApp (f, Array.map (strip i) a) else + let dp = eva.(j) in + let nd = Array.length dp - 1 in + let mkarg k = strip i a.(if k < nd then dp.(k + 1) - j else k + dp.(0)) in + mkApp (f, Array.init (Array.length a - dp.(0)) mkarg) + | _ -> Constr.map_with_binders ((+) 1) strip i c in + let rec strip_ndeps j i c = match Constr.kind c with + | Prod (x, t, c1) when i < j -> + let dl, c2 = strip_ndeps j (i + 1) c1 in + if Vars.noccurn 1 c2 then dl, Vars.lift (-1) c2 else + i :: dl, mkProd (x, strip i t, c2) + | LetIn (x, b, t, c1) when i < j -> + let _, _, c1' = destProd c1 in + let dl, c2 = strip_ndeps j (i + 1) c1' in + if Vars.noccurn 1 c2 then dl, Vars.lift (-1) c2 else + i :: dl, mkLetIn (x, strip i b, strip i t, c2) + | _ -> [], strip i c in + let rec strip_evars i c = match Constr.kind c with + | Lambda (x, t1, c1) when i < n -> + let na = nb_evar_deps x in + let dl, t2 = strip_ndeps (i + na) i t1 in + let na' = List.length dl in + eva.(i) <- Array.of_list (na - na' :: dl); + let x' = + if na' = 0 then Name (pf_type_id gl (EConstr.of_constr t2)) else mk_evar_name na' in + mkLambda (x', t2, strip_evars (i + 1) c1) +(* if noccurn 1 c2 then lift (-1) c2 else + mkLambda (Name (pf_type_id gl t2), t2, c2) *) + | _ -> strip i c in + EConstr.of_constr (strip_evars 0 c0) + +(* }}} *) + +let pf_merge_uc uc gl = + re_sig (sig_it gl) (Evd.merge_universe_context (Refiner.project gl) uc) +let pf_merge_uc_of sigma gl = + let ucst = Evd.evar_universe_context sigma in + pf_merge_uc ucst gl + + +let rec constr_name sigma c = match EConstr.kind sigma c with + | Var id -> Name id + | Cast (c', _, _) -> constr_name sigma c' + | Const (cn,_) -> Name (Label.to_id (Constant.label cn)) + | App (c', _) -> constr_name sigma c' + | _ -> Anonymous + +let pf_mkprod gl c ?(name=constr_name (project gl) c) cl = + let gl, t = pfe_type_of gl c in + if name <> Anonymous || EConstr.Vars.noccurn (project gl) 1 cl then gl, EConstr.mkProd (name, t, cl) else + gl, EConstr.mkProd (Name (pf_type_id gl t), t, cl) + +let pf_abs_prod name gl c cl = pf_mkprod gl c ~name (Termops.subst_term (project gl) c cl) + +(** look up a name in the ssreflect internals module *) +let ssrdirpath = DirPath.make [Id.of_string "ssreflect"] +let ssrqid name = Libnames.make_qualid ssrdirpath (Id.of_string name) +let ssrtopqid name = Libnames.qualid_of_ident (Id.of_string name) +let locate_reference qid = + Smartlocate.global_of_extended_global (Nametab.locate_extended qid) +let mkSsrRef name = + try locate_reference (ssrqid name) with Not_found -> + try locate_reference (ssrtopqid name) with Not_found -> + CErrors.user_err (Pp.str "Small scale reflection library not loaded") +let mkSsrRRef name = (DAst.make @@ GRef (mkSsrRef name,None)), None +let mkSsrConst name env sigma = + EConstr.fresh_global env sigma (mkSsrRef name) +let pf_mkSsrConst name gl = + let sigma, env, it = project gl, pf_env gl, sig_it gl in + let (sigma, t) = mkSsrConst name env sigma in + t, re_sig it sigma +let pf_fresh_global name gl = + let sigma, env, it = project gl, pf_env gl, sig_it gl in + let sigma,t = Evd.fresh_global env sigma name in + t, re_sig it sigma + +let mkProt t c gl = + let prot, gl = pf_mkSsrConst "protect_term" gl in + EConstr.mkApp (prot, [|t; c|]), gl + +let mkEtaApp c n imin = + let open EConstr in + if n = 0 then c else + let nargs, mkarg = + if n < 0 then -n, (fun i -> mkRel (imin + i)) else + let imax = imin + n - 1 in n, (fun i -> mkRel (imax - i)) in + mkApp (c, Array.init nargs mkarg) + +let mkRefl t c gl = + let sigma = project gl in + let (sigma, refl) = EConstr.fresh_global (pf_env gl) sigma Coqlib.((build_coq_eq_data()).refl) in + EConstr.mkApp (refl, [|t; c|]), { gl with sigma } + +let discharge_hyp (id', (id, mode)) gl = + let cl' = Vars.subst_var id (pf_concl gl) in + match pf_get_hyp gl id, mode with + | NamedDecl.LocalAssum (_, t), _ | NamedDecl.LocalDef (_, _, t), "(" -> + Proofview.V82.of_tactic (Tactics.apply_type ~typecheck:true (EConstr.of_constr (mkProd (Name id', t, cl'))) + [EConstr.of_constr (mkVar id)]) gl + | NamedDecl.LocalDef (_, v, t), _ -> + Proofview.V82.of_tactic + (convert_concl (EConstr.of_constr (mkLetIn (Name id', v, t, cl')))) gl + +(* wildcard names *) +let clear_wilds wilds gl = + Proofview.V82.of_tactic (Tactics.clear (List.filter (fun id -> List.mem id wilds) (pf_ids_of_hyps gl))) gl + +let clear_with_wilds wilds clr0 gl = + let extend_clr clr nd = + let id = NamedDecl.get_id nd in + if List.mem id clr || not (List.mem id wilds) then clr else + let vars = Termops.global_vars_set_of_decl (pf_env gl) (project gl) nd in + let occurs id' = Id.Set.mem id' vars in + if List.exists occurs clr then id :: clr else clr in + Proofview.V82.of_tactic (Tactics.clear (Context.Named.fold_inside extend_clr ~init:clr0 (Tacmach.pf_hyps gl))) gl + +let clear_wilds_and_tmp_and_delayed_ids gl = + let _, ctx = pull_ctx gl in + tac_ctx + (tclTHEN + (clear_with_wilds ctx.wild_ids ctx.delayed_clears) + (clear_wilds (List.map fst ctx.tmp_ids @ ctx.wild_ids))) gl + +let rec is_name_in_ipats name = function + | IPatClear clr :: tl -> + List.exists (function SsrHyp(_,id) -> id = name) clr + || is_name_in_ipats name tl + | IPatId id :: tl -> id = name || is_name_in_ipats name tl + | IPatAbstractVars ids :: tl -> + CList.mem_f Id.equal name ids || is_name_in_ipats name tl + | (IPatCase l | IPatDispatch l | IPatInj l) :: tl -> + List.exists (is_name_in_ipats name) l || is_name_in_ipats name tl + | (IPatView _ | IPatAnon _ | IPatSimpl _ | IPatRewrite _ | IPatTac _ | IPatNoop) :: tl -> is_name_in_ipats name tl + | [] -> false + +let view_error s gv = + errorstrm (str ("Cannot " ^ s ^ " view ") ++ pr_term gv) + + +open Locus +(****************************** tactics ***********************************) + +let rewritetac dir c = + (* Due to the new optional arg ?tac, application shouldn't be too partial *) + Proofview.V82.of_tactic begin + Equality.general_rewrite (dir = L2R) AllOccurrences true false c + end + +(**********************`:********* hooks ************************************) + +type name_hint = (int * EConstr.types array) option ref + +let pf_abs_ssrterm ?(resolve_typeclasses=false) ist gl t = + let sigma, ct as t = interp_term ist gl t in + let sigma, _ as t = + let env = pf_env gl in + if not resolve_typeclasses then t + else + let sigma = Typeclasses.resolve_typeclasses ~fail:false env sigma in + sigma, Evarutil.nf_evar sigma ct in + let n, c, abstracted_away, ucst = pf_abs_evars gl t in + List.fold_left Evd.remove sigma abstracted_away, pf_abs_cterm gl n c, ucst, n + +let top_id = mk_internal_id "top assumption" + +let ssr_n_tac seed n gl = + let name = if n = -1 then seed else ("ssr" ^ seed ^ string_of_int n) in + let fail msg = CErrors.user_err (Pp.str msg) in + let tacname = + try Tacenv.locate_tactic (Libnames.qualid_of_ident (Id.of_string name)) + with Not_found -> try Tacenv.locate_tactic (ssrqid name) + with Not_found -> + if n = -1 then fail "The ssreflect library was not loaded" + else fail ("The tactic "^name^" was not found") in + let tacexpr = Loc.tag @@ Tacexpr.Reference (ArgArg (Loc.tag @@ tacname)) in + Proofview.V82.of_tactic (Tacinterp.eval_tactic (Tacexpr.TacArg tacexpr)) gl + +let donetac n gl = ssr_n_tac "done" n gl + +open Constrexpr +open Util + +(** Constructors for constr_expr *) +let mkCProp loc = CAst.make ?loc @@ CSort GProp +let mkCType loc = CAst.make ?loc @@ CSort (GType []) +let mkCVar ?loc id = CAst.make ?loc @@ CRef (CAst.make ?loc @@ Ident id, None) +let rec mkCHoles ?loc n = + if n <= 0 then [] else (CAst.make ?loc @@ CHole (None, IntroAnonymous, None)) :: mkCHoles ?loc (n - 1) +let mkCHole loc = CAst.make ?loc @@ CHole (None, IntroAnonymous, None) +let mkCLambda ?loc name ty t = CAst.make ?loc @@ + CLambdaN ([CLocalAssum([CAst.make ?loc name], Default Explicit, ty)], t) +let mkCArrow ?loc ty t = CAst.make ?loc @@ + CProdN ([CLocalAssum([CAst.make Anonymous], Default Explicit, ty)], t) +let mkCCast ?loc t ty = CAst.make ?loc @@ CCast (t, CastConv ty) + +let rec isCHoles = function { CAst.v = CHole _ } :: cl -> isCHoles cl | cl -> cl = [] +let rec isCxHoles = function ({ CAst.v = CHole _ }, None) :: ch -> isCxHoles ch | _ -> false + +let pf_interp_ty ?(resolve_typeclasses=false) ist gl ty = + let n_binders = ref 0 in + let ty = match ty with + | a, (t, None) -> + let rec force_type ty = DAst.(map (function + | GProd (x, k, s, t) -> incr n_binders; GProd (x, k, s, force_type t) + | GLetIn (x, v, oty, t) -> incr n_binders; GLetIn (x, v, oty, force_type t) + | _ -> DAst.get (mkRCast ty mkRType))) ty in + a, (force_type t, None) + | _, (_, Some ty) -> + let rec force_type ty = CAst.(map (function + | CProdN (abs, t) -> + n_binders := !n_binders + List.length (List.flatten (List.map (function CLocalAssum (nal,_,_) -> nal | CLocalDef (na,_,_) -> [na] | CLocalPattern _ -> (* We count a 'pat for 1; TO BE CHECKED *) [CAst.make Name.Anonymous]) abs)); + CProdN (abs, force_type t) + | CLetIn (n, v, oty, t) -> incr n_binders; CLetIn (n, v, oty, force_type t) + | _ -> (mkCCast ty (mkCType None)).v)) ty in + mk_term ' ' (force_type ty) in + let strip_cast (sigma, t) = + let rec aux t = match EConstr.kind_of_type sigma t with + | CastType (t, ty) when !n_binders = 0 && EConstr.isSort sigma ty -> t + | ProdType(n,s,t) -> decr n_binders; EConstr.mkProd (n, s, aux t) + | LetInType(n,v,ty,t) -> decr n_binders; EConstr.mkLetIn (n, v, ty, aux t) + | _ -> anomaly "pf_interp_ty: ssr Type cast deleted by typecheck" in + sigma, aux t in + let sigma, cty as ty = strip_cast (interp_term ist gl ty) in + let ty = + let env = pf_env gl in + if not resolve_typeclasses then ty + else + let sigma = Typeclasses.resolve_typeclasses ~fail:false env sigma in + sigma, Evarutil.nf_evar sigma cty in + let n, c, _, ucst = pf_abs_evars gl ty in + let lam_c = pf_abs_cterm gl n c in + let ctx, c = EConstr.decompose_lam_n_assum sigma n lam_c in + n, EConstr.it_mkProd_or_LetIn c ctx, lam_c, ucst +;; + +(* TASSI: given (c : ty), generates (c ??? : ty[???/...]) with m evars *) +exception NotEnoughProducts +let saturate ?(beta=false) ?(bi_types=false) env sigma c ?(ty=Retyping.get_type_of env sigma c) m += + let rec loop ty args sigma n = + if n = 0 then + let args = List.rev args in + (if beta then Reductionops.whd_beta sigma else fun x -> x) + (EConstr.mkApp (c, Array.of_list (List.map snd args))), ty, args, sigma + else match EConstr.kind_of_type sigma ty with + | ProdType (_, src, tgt) -> + let sigma = create_evar_defs sigma in + let (sigma, x) = + Evarutil.new_evar env sigma + (if bi_types then Reductionops.nf_betaiota env sigma src else src) in + loop (EConstr.Vars.subst1 x tgt) ((m - n,x) :: args) sigma (n-1) + | CastType (t, _) -> loop t args sigma n + | LetInType (_, v, _, t) -> loop (EConstr.Vars.subst1 v t) args sigma n + | SortType _ -> assert false + | AtomicType _ -> + let ty = (* FIXME *) + (Reductionops.whd_all env sigma) ty in + match EConstr.kind_of_type sigma ty with + | ProdType _ -> loop ty args sigma n + | _ -> raise NotEnoughProducts + in + loop ty [] sigma m + +let pf_saturate ?beta ?bi_types gl c ?ty m = + let env, sigma, si = pf_env gl, project gl, sig_it gl in + let t, ty, args, sigma = saturate ?beta ?bi_types env sigma c ?ty m in + t, ty, args, re_sig si sigma + +let pf_partial_solution gl t evl = + let sigma, g = project gl, sig_it gl in + let sigma = Goal.V82.partial_solution sigma g t in + re_sig (List.map (fun x -> (fst (EConstr.destEvar sigma x))) evl) sigma + +let dependent_apply_error = + try CErrors.user_err (Pp.str "Could not fill dependent hole in \"apply\"") + with err -> err + +(* TASSI: Sometimes Coq's apply fails. According to my experience it may be + * related to goals that are products and with beta redexes. In that case it + * guesses the wrong number of implicit arguments for your lemma. What follows + * is just like apply, but with a user-provided number n of implicits. + * + * Refine.refine function that handles type classes and evars but fails to + * handle "dependently typed higher order evars". + * + * Refiner.refiner that does not handle metas with a non ground type but works + * with dependently typed higher order metas. *) +let applyn ~with_evars ?beta ?(with_shelve=false) n t gl = + if with_evars then + let refine gl = + let t, ty, args, gl = pf_saturate ?beta ~bi_types:true gl t n in +(* pp(lazy(str"sigma@saturate=" ++ pr_evar_map None (project gl))); *) + let gl = pf_unify_HO gl ty (Tacmach.pf_concl gl) in + let gs = CList.map_filter (fun (_, e) -> + if EConstr.isEvar (project gl) e then Some e else None) + args in + pf_partial_solution gl t gs + in + Proofview.(V82.of_tactic + (tclTHEN (V82.tactic refine) + (if with_shelve then shelve_unifiable else tclUNIT ()))) gl + else + let t, gl = if n = 0 then t, gl else + let sigma, si = project gl, sig_it gl in + let rec loop sigma bo args = function (* saturate with metas *) + | 0 -> EConstr.mkApp (t, Array.of_list (List.rev args)), re_sig si sigma + | n -> match EConstr.kind sigma bo with + | Lambda (_, ty, bo) -> + if not (EConstr.Vars.closed0 sigma ty) then + raise dependent_apply_error; + let m = Evarutil.new_meta () in + loop (meta_declare m (EConstr.Unsafe.to_constr ty) sigma) bo ((EConstr.mkMeta m)::args) (n-1) + | _ -> assert false + in loop sigma t [] n in + pp(lazy(str"Refiner.refiner " ++ Printer.pr_econstr_env (pf_env gl) (project gl) t)); + Tacmach.refine_no_check t gl + +let refine_with ?(first_goes_last=false) ?beta ?(with_evars=true) oc gl = + let rec mkRels = function 1 -> [] | n -> mkRel n :: mkRels (n-1) in + let uct = Evd.evar_universe_context (fst oc) in + let n, oc = pf_abs_evars_pirrel gl (fst oc, EConstr.Unsafe.to_constr (snd oc)) in + let gl = pf_unsafe_merge_uc uct gl in + let oc = if not first_goes_last || n <= 1 then oc else + let l, c = decompose_lam oc in + if not (List.for_all_i (fun i (_,t) -> Vars.closedn ~-i t) (1-n) l) then oc else + compose_lam (let xs,y = List.chop (n-1) l in y @ xs) + (mkApp (compose_lam l c, Array.of_list (mkRel 1 :: mkRels n))) + in + pp(lazy(str"after: " ++ Printer.pr_constr_env (pf_env gl) (project gl) oc)); + try applyn ~with_evars ~with_shelve:true ?beta n (EConstr.of_constr oc) gl + with e when CErrors.noncritical e -> raise dependent_apply_error + +(** Profiling *)(* {{{ *************************************************************) +type profiler = { + profile : 'a 'b. ('a -> 'b) -> 'a -> 'b; + reset : unit -> unit; + print : unit -> unit } +let profile_now = ref false +let something_profiled = ref false +let profilers = ref [] +let add_profiler f = profilers := f :: !profilers;; +let _ = + Goptions.declare_bool_option + { Goptions.optname = "ssreflect profiling"; + Goptions.optkey = ["SsrProfiling"]; + Goptions.optread = (fun _ -> !profile_now); + Goptions.optdepr = false; + Goptions.optwrite = (fun b -> + Ssrmatching.profile b; + profile_now := b; + if b then List.iter (fun f -> f.reset ()) !profilers; + if not b then List.iter (fun f -> f.print ()) !profilers) } +let () = + let prof_total = + let init = ref 0.0 in { + profile = (fun f x -> assert false); + reset = (fun () -> init := Unix.gettimeofday ()); + print = (fun () -> if !something_profiled then + prerr_endline + (Printf.sprintf "!! %-39s %10d %9.4f %9.4f %9.4f" + "total" 0 (Unix.gettimeofday() -. !init) 0.0 0.0)) } in + let prof_legenda = { + profile = (fun f x -> assert false); + reset = (fun () -> ()); + print = (fun () -> if !something_profiled then begin + prerr_endline + (Printf.sprintf "!! %39s ---------- --------- --------- ---------" + (String.make 39 '-')); + prerr_endline + (Printf.sprintf "!! %-39s %10s %9s %9s %9s" + "function" "#calls" "total" "max" "average") end) } in + add_profiler prof_legenda; + add_profiler prof_total +;; + +let mk_profiler s = + let total, calls, max = ref 0.0, ref 0, ref 0.0 in + let reset () = total := 0.0; calls := 0; max := 0.0 in + let profile f x = + if not !profile_now then f x else + let before = Unix.gettimeofday () in + try + incr calls; + let res = f x in + let after = Unix.gettimeofday () in + let delta = after -. before in + total := !total +. delta; + if delta > !max then max := delta; + res + with exc -> + let after = Unix.gettimeofday () in + let delta = after -. before in + total := !total +. delta; + if delta > !max then max := delta; + raise exc in + let print () = + if !calls <> 0 then begin + something_profiled := true; + prerr_endline + (Printf.sprintf "!! %-39s %10d %9.4f %9.4f %9.4f" + s !calls !total !max (!total /. (float_of_int !calls))) end in + let prof = { profile = profile; reset = reset; print = print } in + add_profiler prof; + prof +;; +(* }}} *) + +(* We wipe out all the keywords generated by the grammar rules we defined. *) +(* The user is supposed to Require Import ssreflect or Require ssreflect *) +(* and Import ssreflect.SsrSyntax to obtain these keywords and as a *) +(* consequence the extended ssreflect grammar. *) +let () = CLexer.set_keyword_state frozen_lexer ;; + +(** Basic tactics *) + +let rec fst_prod red tac = Proofview.Goal.nf_enter begin fun gl -> + let concl = Proofview.Goal.concl gl in + match EConstr.kind (Proofview.Goal.sigma gl) concl with + | Prod (id,_,tgt) | LetIn(id,_,_,tgt) -> tac id + | _ -> if red then Tacticals.New.tclZEROMSG (str"No product even after head-reduction.") + else Tacticals.New.tclTHEN Tactics.hnf_in_concl (fst_prod true tac) +end + +let introid ?(orig=ref Anonymous) name = tclTHEN (fun gl -> + let g, env = Tacmach.pf_concl gl, pf_env gl in + let sigma = project gl in + match EConstr.kind sigma g with + | App (hd, _) when EConstr.isLambda sigma hd -> + Proofview.V82.of_tactic (convert_concl_no_check (Reductionops.whd_beta sigma g)) gl + | _ -> tclIDTAC gl) + (Proofview.V82.of_tactic + (fst_prod false (fun id -> orig := id; Tactics.intro_mustbe_force name))) +;; + +let anontac decl gl = + let id = match RelDecl.get_name decl with + | Name id -> + if is_discharged_id id then id else mk_anon_id (Id.to_string id) (Tacmach.pf_ids_of_hyps gl) + | _ -> mk_anon_id ssr_anon_hyp (Tacmach.pf_ids_of_hyps gl) in + introid id gl + +let rec intro_anon gl = + try anontac (List.hd (fst (EConstr.decompose_prod_n_assum (project gl) 1 (Tacmach.pf_concl gl)))) gl + with err0 -> try tclTHEN (Proofview.V82.of_tactic Tactics.red_in_concl) intro_anon gl with e when CErrors.noncritical e -> raise err0 + (* with _ -> CErrors.error "No product even after reduction" *) + +let is_pf_var sigma c = + EConstr.isVar sigma c && not_section_id (EConstr.destVar sigma c) + +let hyp_of_var sigma v = SsrHyp (Loc.tag @@ EConstr.destVar sigma v) + +let interp_clr sigma = function +| Some clr, (k, c) + when (k = xNoFlag || k = xWithAt) && is_pf_var sigma c -> + hyp_of_var sigma c :: clr +| Some clr, _ -> clr +| None, _ -> [] + +(** Basic tacticals *) + +(** Multipliers *)(* {{{ ***********************************************************) + +(* tactical *) + +let tclID tac = tac + +let tclDOTRY n tac = + if n <= 0 then tclIDTAC else + let rec loop i gl = + if i = n then tclTRY tac gl else + tclTRY (tclTHEN tac (loop (i + 1))) gl in + loop 1 + +let tclDO n tac = + let prefix i = str"At iteration " ++ int i ++ str": " in + let tac_err_at i gl = + try tac gl + with + | CErrors.UserError (l, s) as e -> + let _, info = CErrors.push e in + let e' = CErrors.UserError (l, prefix i ++ s) in + Util.iraise (e', info) + | Ploc.Exc(loc, CErrors.UserError (l, s)) -> + raise (Ploc.Exc(loc, CErrors.UserError (l, prefix i ++ s))) in + let rec loop i gl = + if i = n then tac_err_at i gl else + (tclTHEN (tac_err_at i) (loop (i + 1))) gl in + loop 1 + +let tclMULT = function + | 0, May -> tclREPEAT + | 1, May -> tclTRY + | n, May -> tclDOTRY n + | 0, Must -> tclAT_LEAST_ONCE + | n, Must when n > 1 -> tclDO n + | _ -> tclID + +let old_cleartac clr = check_hyps_uniq [] clr; Proofview.V82.of_tactic (Tactics.clear (hyps_ids clr)) +let cleartac clr = check_hyps_uniq [] clr; Tactics.clear (hyps_ids clr) + +(* }}} *) + +(** Generalize tactic *) + +(* XXX the k of the redex should percolate out *) +let pf_interp_gen_aux gl to_ind ((oclr, occ), t) = + let pat = interp_cpattern gl t None in (* UGLY API *) + let cl, env, sigma = Tacmach.pf_concl gl, pf_env gl, project gl in + let (c, ucst), cl = + try fill_occ_pattern ~raise_NoMatch:true env sigma (EConstr.Unsafe.to_constr cl) pat occ 1 + with NoMatch -> redex_of_pattern env pat, (EConstr.Unsafe.to_constr cl) in + let gl = pf_merge_uc ucst gl in + let c = EConstr.of_constr c in + let cl = EConstr.of_constr cl in + let clr = interp_clr sigma (oclr, (tag_of_cpattern t, c)) in + if not(occur_existential sigma c) then + if tag_of_cpattern t = xWithAt then + if not (EConstr.isVar sigma c) then + errorstrm (str "@ can be used with variables only") + else match Tacmach.pf_get_hyp gl (EConstr.destVar sigma c) with + | NamedDecl.LocalAssum _ -> errorstrm (str "@ can be used with let-ins only") + | NamedDecl.LocalDef (name, b, ty) -> true, pat, EConstr.mkLetIn (Name name,b,ty,cl),c,clr,ucst,gl + else let gl, ccl = pf_mkprod gl c cl in false, pat, ccl, c, clr,ucst,gl + else if to_ind && occ = None then + let nv, p, _, ucst' = pf_abs_evars gl (fst pat, c) in + let ucst = UState.union ucst ucst' in + if nv = 0 then anomaly "occur_existential but no evars" else + let gl, pty = pfe_type_of gl p in + false, pat, EConstr.mkProd (constr_name (project gl) c, pty, Tacmach.pf_concl gl), p, clr,ucst,gl + else CErrors.user_err ?loc:(loc_of_cpattern t) (str "generalized term didn't match") + +let apply_type x xs = Proofview.V82.of_tactic (Tactics.apply_type ~typecheck:true x xs) + +let genclrtac cl cs clr = + let tclmyORELSE tac1 tac2 gl = + try tac1 gl + with e when CErrors.noncritical e -> tac2 e gl in + (* apply_type may give a type error, but the useful message is + * the one of clear. You type "move: x" and you get + * "x is used in hyp H" instead of + * "The term H has type T x but is expected to have type T x0". *) + tclTHEN + (tclmyORELSE + (apply_type cl cs) + (fun type_err gl -> + tclTHEN + (tclTHEN (Proofview.V82.of_tactic (Tactics.elim_type (EConstr.of_constr + (Universes.constr_of_global @@ Coqlib.build_coq_False ())))) (old_cleartac clr)) + (fun gl -> raise type_err) + gl)) + (old_cleartac clr) + +let gentac gen gl = +(* ppdebug(lazy(str"sigma@gentac=" ++ pr_evar_map None (project gl))); *) + let conv, _, cl, c, clr, ucst,gl = pf_interp_gen_aux gl false gen in + ppdebug(lazy(str"c@gentac=" ++ pr_econstr_env (pf_env gl) (project gl) c)); + let gl = pf_merge_uc ucst gl in + if conv + then tclTHEN (Proofview.V82.of_tactic (convert_concl cl)) (old_cleartac clr) gl + else genclrtac cl [c] clr gl + +let genstac (gens, clr) = + tclTHENLIST (old_cleartac clr :: List.rev_map gentac gens) + +let gen_tmp_ids + ?(ist=Geninterp.({ lfun = Id.Map.empty; extra = Tacinterp.TacStore.empty })) gl += + let gl, ctx = pull_ctx gl in + push_ctxs ctx + (tclTHENLIST + (List.map (fun (id,orig_ref) -> + tclTHEN + (gentac ((None,Some(false,[])),cpattern_of_id id)) + (rename_hd_prod orig_ref)) + ctx.tmp_ids) gl) +;; + +let pf_interp_gen gl to_ind gen = + let _, _, a, b, c, ucst,gl = pf_interp_gen_aux gl to_ind gen in + a, b ,c, pf_merge_uc ucst gl + +(* TASSI: This version of unprotects inlines the unfold tactic definition, + * since we don't want to wipe out let-ins, and it seems there is no flag + * to change that behaviour in the standard unfold code *) +let unprotecttac gl = + let c, gl = pf_mkSsrConst "protect_term" gl in + let prot, _ = EConstr.destConst (project gl) c in + Tacticals.onClause (fun idopt -> + let hyploc = Option.map (fun id -> id, InHyp) idopt in + Proofview.V82.of_tactic (Tactics.reduct_option + (Reductionops.clos_norm_flags + (CClosure.RedFlags.mkflags + [CClosure.RedFlags.fBETA; + CClosure.RedFlags.fCONST prot; + CClosure.RedFlags.fMATCH; + CClosure.RedFlags.fFIX; + CClosure.RedFlags.fCOFIX]), DEFAULTcast) hyploc)) + allHypsAndConcl gl + +let is_protect hd env sigma = + let _, protectC = mkSsrConst "protect_term" env sigma in + EConstr.eq_constr_nounivs sigma hd protectC + +let abs_wgen keep_let f gen (gl,args,c) = + let sigma, env = project gl, pf_env gl in + let evar_closed t p = + if occur_existential sigma t then + CErrors.user_err ?loc:(loc_of_cpattern p) ~hdr:"ssreflect" + (pr_constr_pat (EConstr.Unsafe.to_constr t) ++ + str" contains holes and matches no subterm of the goal") in + match gen with + | _, Some ((x, mode), None) when mode = "@" || (mode = " " && keep_let) -> + let x = hoi_id x in + let decl = Tacmach.pf_get_hyp gl x in + gl, + (if NamedDecl.is_local_def decl then args else EConstr.mkVar x :: args), + EConstr.mkProd_or_LetIn (decl |> NamedDecl.to_rel_decl |> RelDecl.set_name (Name (f x))) + (EConstr.Vars.subst_var x c) + | _, Some ((x, _), None) -> + let x = hoi_id x in + gl, EConstr.mkVar x :: args, EConstr.mkProd (Name (f x),Tacmach.pf_get_hyp_typ gl x, EConstr.Vars.subst_var x c) + | _, Some ((x, "@"), Some p) -> + let x = hoi_id x in + let cp = interp_cpattern gl p None in + let (t, ucst), c = + try fill_occ_pattern ~raise_NoMatch:true env sigma (EConstr.Unsafe.to_constr c) cp None 1 + with NoMatch -> redex_of_pattern env cp, (EConstr.Unsafe.to_constr c) in + let c = EConstr.of_constr c in + let t = EConstr.of_constr t in + evar_closed t p; + let ut = red_product_skip_id env sigma t in + let gl, ty = pfe_type_of gl t in + pf_merge_uc ucst gl, args, EConstr.mkLetIn(Name (f x), ut, ty, c) + | _, Some ((x, _), Some p) -> + let x = hoi_id x in + let cp = interp_cpattern gl p None in + let (t, ucst), c = + try fill_occ_pattern ~raise_NoMatch:true env sigma (EConstr.Unsafe.to_constr c) cp None 1 + with NoMatch -> redex_of_pattern env cp, (EConstr.Unsafe.to_constr c) in + let c = EConstr.of_constr c in + let t = EConstr.of_constr t in + evar_closed t p; + let gl, ty = pfe_type_of gl t in + pf_merge_uc ucst gl, t :: args, EConstr.mkProd(Name (f x), ty, c) + | _ -> gl, args, c + +let clr_of_wgen gen clrs = match gen with + | clr, Some ((x, _), None) -> + let x = hoi_id x in + old_cleartac clr :: old_cleartac [SsrHyp(Loc.tag x)] :: clrs + | clr, _ -> old_cleartac clr :: clrs + + +let reduct_in_concl t = Tactics.reduct_in_concl (t, DEFAULTcast) +let unfold cl = + let module R = Reductionops in let module F = CClosure.RedFlags in + reduct_in_concl (R.clos_norm_flags (F.mkflags + (List.map (fun c -> F.fCONST (fst (destConst (EConstr.Unsafe.to_constr c)))) cl @ + [F.fBETA; F.fMATCH; F.fFIX; F.fCOFIX]))) + +open Proofview +open Notations + +let tacSIGMA = Goal.enter_one begin fun g -> + let k = Goal.goal g in + let sigma = Goal.sigma g in + tclUNIT (Tacmach.re_sig k sigma) +end + +let tclINTERP_AST_CLOSURE_TERM_AS_CONSTR c = + tclINDEPENDENTL begin tacSIGMA >>= fun gl -> + let old_ssrterm = mkRHole, Some c.Ssrast.body in + let ist = + option_assert_get c.Ssrast.interp_env + Pp.(str "tclINTERP_AST_CLOSURE_TERM_AS_CONSTR: term with no ist") in + let sigma, t = + interp_wit Stdarg.wit_constr ist gl old_ssrterm in + Unsafe.tclEVARS sigma <*> + tclUNIT t +end + +let tacREDUCE_TO_QUANTIFIED_IND ty = + tacSIGMA >>= fun gl -> + tclUNIT (Tacmach.pf_reduce_to_quantified_ind gl ty) + +let tacTYPEOF c = Goal.enter_one ~__LOC__ (fun g -> + let sigma, env = Goal.sigma g, Goal.env g in + let sigma, ty = Typing.type_of env sigma c in + Unsafe.tclEVARS sigma <*> tclUNIT ty) + +(** This tactic creates a partial proof realizing the introduction rule, but + does not check anything. *) +let unsafe_intro env store decl b = + let open Context.Named.Declaration in + Refine.refine ~typecheck:false begin fun sigma -> + let ctx = Environ.named_context_val env in + let nctx = EConstr.push_named_context_val decl ctx in + let inst = List.map (get_id %> EConstr.mkVar) (Environ.named_context env) in + let ninst = EConstr.mkRel 1 :: inst in + let nb = EConstr.Vars.subst1 (EConstr.mkVar (get_id decl)) b in + let sigma, ev = + Evarutil.new_evar_instance nctx sigma nb ~principal:true ~store ninst in + sigma, EConstr.mkNamedLambda_or_LetIn decl ev + end + +let set_decl_id id = let open Context in function + | Rel.Declaration.LocalAssum(name,ty) -> Named.Declaration.LocalAssum(id,ty) + | Rel.Declaration.LocalDef(name,ty,t) -> Named.Declaration.LocalDef(id,ty,t) + +let rec decompose_assum env sigma orig_goal = + let open Context in + match EConstr.kind sigma orig_goal with + | Prod(name,ty,t) -> + Rel.Declaration.LocalAssum(name,ty), t, true + | LetIn(name,ty,t1,t2) -> Rel.Declaration.LocalDef(name, ty, t1), t2, true + | _ -> + let goal = Reductionops.whd_allnolet env sigma orig_goal in + match EConstr.kind sigma goal with + | Prod(name,ty,t) -> Rel.Declaration.LocalAssum(name,ty), t, false + | LetIn(name,ty,t1,t2) -> Rel.Declaration.LocalDef(name,ty,t1), t2, false + | App(hd,args) when EConstr.isLetIn sigma hd -> (* hack *) + let _,v,_,b = EConstr.destLetIn sigma hd in + let ctx, t, _ = + decompose_assum env sigma + (EConstr.mkApp (EConstr.Vars.subst1 v b, args)) in + ctx, t, false + | _ -> CErrors.user_err + Pp.(str "No assumption in " ++ Printer.pr_econstr_env env sigma goal) + +let tclFULL_BETAIOTA = Goal.enter begin fun gl -> + let r, _ = Redexpr.reduction_of_red_expr (Goal.env gl) + Genredexpr.(Lazy { + rBeta=true; rMatch=true; rFix=true; rCofix=true; + rZeta=false; rDelta=false; rConst=[]}) in + Tactics.e_reduct_in_concl ~check:false (r,Constr.DEFAULTcast) +end + +(** [intro id k] introduces the first premise (product or let-in) of the goal + under the name [id], reducing the head of the goal (using beta, iota, delta + but not zeta) if necessary. If [id] is None, a name is generated, that will + not be user accessible. If the goal does not start with a product or a +let-in even after reduction, it fails. In case of success, the original name +and final id are passed to the continuation [k] which gets evaluated. *) +let tclINTRO ~id ~conclusion:k = Goal.enter begin fun gl -> + let open Context in + let env, sigma, extra, g = Goal.(env gl, sigma gl, extra gl, concl gl) in + let decl, t, no_red = decompose_assum env sigma g in + let original_name = Rel.Declaration.get_name decl in + let already_used = Tacmach.New.pf_ids_of_hyps gl in + let id = match id, original_name with + | Some id, _ -> id + | _, Name id -> + if is_discharged_id id then id + else mk_anon_id (Id.to_string id) already_used + | _, _ -> + let ids = Tacmach.New.pf_ids_of_hyps gl in + mk_anon_id ssr_anon_hyp ids + in + if List.mem id already_used then + errorstrm Pp.(Id.print id ++ str" already used"); + unsafe_intro env extra (set_decl_id id decl) t <*> + (if no_red then tclUNIT () else tclFULL_BETAIOTA) <*> + k ~orig_name:original_name ~new_name:id +end + +let return ~orig_name:_ ~new_name:_ = tclUNIT () + +let tclINTRO_ID id = tclINTRO ~id:(Some id) ~conclusion:return +let tclINTRO_ANON = tclINTRO ~id:None ~conclusion:return + +let tclRENAME_HD_PROD name = Goal.enter begin fun gl -> + let convert_concl_no_check t = + Tactics.convert_concl_no_check t Term.DEFAULTcast in + let concl = Goal.concl gl in + let sigma = Goal.sigma gl in + match EConstr.kind sigma concl with + | Prod(_,src,tgt) -> + convert_concl_no_check EConstr.(mkProd (name,src,tgt)) + | _ -> CErrors.anomaly (Pp.str "rename_hd_prod: no head product") +end + +let tcl0G tac = + numgoals >>= fun ng -> if ng = 0 then tclUNIT () else tac + +let rec tclFIRSTa = function + | [] -> Tacticals.New.tclZEROMSG Pp.(str"No applicable tactic.") + | tac :: rest -> tclORELSE tac (fun _ -> tclFIRSTa rest) + +let rec tclFIRSTi tac n = + if n < 0 then Tacticals.New.tclZEROMSG Pp.(str "tclFIRSTi") + else tclORELSE (tclFIRSTi tac (n-1)) (fun _ -> tac n) + +let tacCONSTR_NAME ?name c = + match name with + | Some n -> tclUNIT n + | None -> + Goal.enter_one ~__LOC__ (fun g -> + let sigma = Goal.sigma g in + tclUNIT (constr_name sigma c)) + +let tacMKPROD c ?name cl = + tacTYPEOF c >>= fun t -> + tacCONSTR_NAME ?name c >>= fun name -> + Goal.enter_one ~__LOC__ begin fun g -> + let sigma, env = Goal.sigma g, Goal.env g in + if name <> Names.Name.Anonymous || EConstr.Vars.noccurn sigma 1 cl + then tclUNIT (EConstr.mkProd (name, t, cl)) + else + let name = Names.Id.of_string (Namegen.hdchar env sigma t) in + tclUNIT (EConstr.mkProd (Names.Name.Name name, t, cl)) +end + +let tacINTERP_CPATTERN cp = + tacSIGMA >>= begin fun gl -> + tclUNIT (Ssrmatching.interp_cpattern gl cp None) +end + +let tacUNIFY a b = + tacSIGMA >>= begin fun gl -> + let gl = Ssrmatching.pf_unify_HO gl a b in + Unsafe.tclEVARS (Tacmach.project gl) +end + +let tclOPTION o d = + match o with + | None -> d >>= tclUNIT + | Some x -> tclUNIT x + +let tacIS_INJECTION_CASE ?ty t = begin + tclOPTION ty (tacTYPEOF t) >>= fun ty -> + tacREDUCE_TO_QUANTIFIED_IND ty >>= fun ((mind,_),_) -> + tclUNIT (Globnames.eq_gr (Globnames.IndRef mind) (Coqlib.build_coq_eq ())) +end + +let tclWITHTOP tac = Goal.enter begin fun gl -> + let top = + mk_anon_id "top_assumption" (Tacmach.New.pf_ids_of_hyps gl) in + tclINTRO_ID top <*> + tac (EConstr.mkVar top) <*> + Tactics.clear [top] +end + +let tacMK_SSR_CONST name = Goal.enter_one ~__LOC__ begin fun g -> + let sigma, env = Goal.(sigma g, env g) in + let sigma, c = mkSsrConst name env sigma in + Unsafe.tclEVARS sigma <*> + tclUNIT c +end + +module type StateType = sig + type state + val init : state +end + +module MakeState(S : StateType) = struct + +let state_field : S.state Proofview_monad.StateStore.field = + Proofview_monad.StateStore.field () + +(* FIXME: should not inject fresh_state, but initialize it at the beginning *) +let lift_upd_state upd s = + let open Proofview_monad.StateStore in + let old_state = Option.default S.init (get s state_field) in + upd old_state >>= fun new_state -> + tclUNIT (set s state_field new_state) + +let tacUPDATE upd = Goal.enter begin fun gl -> + let s0 = Goal.state gl in + Goal.enter_one ~__LOC__ (fun _ -> lift_upd_state upd s0) >>= fun s -> + Unsafe.tclGETGOALS >>= fun gls -> + let gls = List.map (fun gs -> + let g = Proofview_monad.drop_state gs in + Proofview_monad.goal_with_state g s) gls in + Unsafe.tclSETGOALS gls +end + +let tclGET k = Goal.enter begin fun gl -> + let open Proofview_monad.StateStore in + k (Option.default S.init (get (Goal.state gl) state_field)) +end + +let tclSET new_s = + let open Proofview_monad.StateStore in + Unsafe.tclGETGOALS >>= fun gls -> + let gls = List.map (fun gs -> + let g = Proofview_monad.drop_state gs in + let s = Proofview_monad.get_state gs in + Proofview_monad.goal_with_state g (set s state_field new_s)) gls in + Unsafe.tclSETGOALS gls + +let get g = + Option.default S.init + (Proofview_monad.StateStore.get (Goal.state g) state_field) + +end + + +(* vim: set filetype=ocaml foldmethod=marker: *) |