(************************************************************************) (* * The Rocq Prover / The Rocq Development Team *) (* v * Copyright INRIA, CNRS and contributors *) (* t" with "fun '(y,z) => t'", we accumulate y and z; used for avoiding collisions with global names *) actualvars : Id.Set.t; (* the matching between binders of the pattern unbound in the notation and actual binders of the term to match; e.g. when matching term "fun y => t" against pattern "fun x => u" where "x" is not a notation variable, we bind "y" to "x" and compare t and u up to this renaming (note that in this case, "x" is not bound to a notation variable and thus will not occur in any instance of a notation variable in "t"). *) staticbinders : (Name.t * Id.t) list; (* the renaming to do between binder variables bound several times; e.g. if "fun x => t" has to match pattern "fun y => u" and, either "fun z => v" is already known to match pattern "fun y => w" (for the same binder variable "y"), or "y" already occurs also as a term bound, say, to the variable "z", then, when matching "fun x => t" against "fun y => u", "t" is matched against "u" with the constraint that any "x" in "t" has to be renamed into "z" (and in particular any subterm bound by the notation and mentioning "x" must be renamed so as to use "z" instead). *) renaming : (Id.t * Id.t) list; } (* Check if [id1], in the actual term, matches [id2], in the pattern, up to the static alpha-renaming obtained by matching the context of the pattern with the actual names of the term *) let rec alpha_var id1 id2 = function | (Name i1,i2)::_ when Id.equal i1 id1 -> Id.equal i2 id2 | (i1,i2)::_ when Id.equal i2 id2 -> Name.equal i1 (Name id1) | _::idl -> alpha_var id1 id2 idl | [] -> Id.equal id1 id2 (* used to update the notation variable with the local variables used in NList and NBinderList, since the iterator has its own variable *) let replace_var i j var = j :: List.remove Id.equal i var let eq_rigid a b = let open UState in match a, b with | UnivRigid, UnivRigid -> true | UnivFlexible a, UnivFlexible b -> (a:bool) = b | (UnivRigid | UnivFlexible _), _ -> false (* compare_glob_universe_instances true strictly_lt us1 us2 computes us1 <= us2, compare_glob_universe_instances false strictly_lt us1 us2 computes us1 = us2. strictly_lt will be set to true if any part is strictly less. *) let compare_glob_universe_instances lt strictly_lt us1 us2 = match us1, us2 with | None, None -> true | Some _, None -> strictly_lt := true; lt | None, Some _ -> false | Some (ql1,ul1), Some (ql2,ul2) -> let is_anon = function | GLocalQVar {v=Anonymous} -> true | _ -> false in CList.for_all2eq (fun q1 q2 -> match is_anon q1, is_anon q2 with | true, true -> true | false, true -> strictly_lt := true; lt | true, false -> false | false, false -> glob_quality_eq q1 q2) ql1 ql2 && CList.for_all2eq (fun u1 u2 -> match u1, u2 with | UAnonymous {rigid}, UAnonymous {rigid=rigid'} -> eq_rigid rigid rigid' | UNamed _, UAnonymous _ -> strictly_lt := true; lt | UAnonymous _, UNamed _ -> false | UNamed _, UNamed _ -> glob_level_eq u1 u2) ul1 ul2 (* Compute us1 <= us2, as a boolean *) let compare_glob_universe_instances_le us1 us2 = compare_glob_universe_instances true (ref false) us1 us2 (* When [lt] is [true], tell if [t1] is a strict refinement of [t2] (this is a partial order, so returning [false] does not mean that [t2] is finer than [t1]); when [lt] is false, tell if [t1] is the same pattern as [t2] *) let compare_notation_constr lt var_eq_hole (vars1,vars2) t1 t2 = (* this is used to reason up to order of notation variables *) let alphameta = ref [] in (* this becomes true when at least one subterm is detected as strictly smaller *) let strictly_lt = ref false in (* this is the stack of inner of iter patterns for comparison with a new iteration or the tail of a recursive pattern *) let tail = ref [] in let check_alphameta id1 id2 = try if not (Id.equal (List.assoc id1 !alphameta) id2) then raise_notrace Exit with Not_found -> if (List.mem_assoc id1 !alphameta) then raise_notrace Exit; alphameta := (id1,id2) :: !alphameta in let check_eq_id (vars1,vars2) renaming id1 id2 = let ismeta1 = List.mem_f Id.equal id1 vars1 in let ismeta2 = List.mem_f Id.equal id2 vars2 in match ismeta1, ismeta2 with | true, true -> check_alphameta id1 id2 | false, false -> if not (alpha_var id1 id2 renaming) then raise_notrace Exit | false, true -> if not lt then raise_notrace Exit else (* a binder which is not bound in the notation can be considered as strictly more precise since it prevents the notation variables in its scope to be bound by this binder; i.e. it is strictly more precise in the sense that it covers strictly less patterns than a notation where the same binder is bound in the notation; this is hawever disputable *) strictly_lt := true | true, false -> if not lt then raise_notrace Exit in let check_eq_name vars renaming na1 na2 = match na1, na2 with | Name id1, Name id2 -> check_eq_id vars renaming id1 id2; (Name id1,id2)::renaming | Anonymous, Anonymous -> renaming | Anonymous, Name _ when lt -> renaming | _ -> raise_notrace Exit in let rec aux (vars1,vars2 as vars) renaming t1 t2 = match t1, t2 with | NVar id1, NVar id2 when id1 = ldots_var && id2 = ldots_var -> () | _, NVar id2 when lt && id2 = ldots_var -> tail := t1 :: !tail | NVar id1, _ when lt && id1 = ldots_var -> tail := t2 :: !tail | NVar id1, NVar id2 -> check_eq_id vars renaming id1 id2 | NHole _, NVar id2 when lt && List.mem_f Id.equal id2 vars2 -> () | NVar id1, NHole _ when lt && List.mem_f Id.equal id1 vars1 -> () | _, NVar id2 when lt && List.mem_f Id.equal id2 vars2 -> strictly_lt := true | NRef (gr1,u1), NRef (gr2,u2) when GlobRef.CanOrd.equal gr1 gr2 && compare_glob_universe_instances lt strictly_lt u1 u2 -> () | NHole _, NHole _ -> () (* FIXME? *) | _, NHole _ when lt -> strictly_lt := true | NGenarg _, NGenarg _ -> () (* FIXME? *) | NList (i1, j1, iter1, tail1, b1), NList (i2, j2, iter2, tail2, b2) | NBinderList (i1, j1, iter1, tail1, b1), NBinderList (i2, j2, iter2, tail2, b2) -> if b1 <> b2 then raise_notrace Exit; let vars1 = replace_var i1 j1 vars1 in let vars2 = replace_var i2 j2 vars2 in check_alphameta i1 i2; aux (vars1,vars2) renaming iter1 iter2; aux vars renaming tail1 tail2; | NBinderList (i1, j1, iter1, tail1, b1), NList (i2, j2, iter2, tail2, b2) | NList (i1, j1, iter1, tail1, b1), NBinderList (i2, j2, iter2, tail2, b2) -> (* They may overlap on a unique iteration of them *) let vars1 = replace_var i1 j1 vars1 in let vars2 = replace_var i2 j2 vars2 in aux (vars1,vars2) renaming iter1 iter2; aux vars renaming tail1 tail2 | t1, NList (i2, j2, iter2, tail2, b2) | t1, NBinderList (i2, j2, iter2, tail2, b2) when lt -> (* checking if t1 is a finite iteration of the pattern *) let vars2 = replace_var i2 j2 vars2 in aux (vars1,vars2) renaming t1 iter2; let t1 = List.hd !tail in tail := List.tl !tail; (* either matching a new iteration, or matching the tail *) (try aux vars renaming t1 tail2 with Exit -> aux vars renaming t1 t2) | NList (i1, j1, iter1, tail1, b1), t2 | NBinderList (i1, j1, iter1, tail1, b1), t2 when lt -> (* we see the NList as a single iteration *) let vars1 = replace_var i1 j1 vars1 in aux (vars1,vars2) renaming iter1 t2; let t2 = match !tail with | t::rest -> tail := rest; t | _ -> (* ".." is in a discarded fine-grained position *) raise_notrace Exit in (* it had to be a single iteration of iter1 *) aux vars renaming tail1 t2 | NApp (t1, a1), NApp (t2, a2) -> aux vars renaming t1 t2; List.iter2 (aux vars renaming) a1 a2 | NProj ((cst1,u1), l1, a1), NProj ((cst2,u2), l2, a2) when GlobRef.CanOrd.equal (GlobRef.ConstRef cst1) (GlobRef.ConstRef cst2) && compare_glob_universe_instances lt strictly_lt u1 u2 -> List.iter2 (aux vars renaming) l1 l2; aux vars renaming a1 a2 | NLambda (na1, t1, u1), NLambda (na2, t2, u2) | NProd (na1, t1, u1), NProd (na2, t2, u2) -> (match t1, t2 with | None, None -> () | Some _, None -> if lt then strictly_lt := true | Some t1, Some t2 -> aux vars renaming t1 t2 | None, Some _ -> raise_notrace Exit); let renaming = check_eq_name vars renaming na1 na2 in aux vars renaming u1 u2 | NLetIn (na1, b1, t1, u1), NLetIn (na2, b2, t2, u2) -> aux vars renaming b1 b2; Option.iter2 (aux vars renaming) t1 t2;(* TODO : subtyping? *) let renaming = check_eq_name vars renaming na1 na2 in aux vars renaming u1 u2 | NCases (_, o1, r1, p1), NCases (_, o2, r2, p2) -> (* FIXME? *) let check_pat (p1, t1) (p2, t2) = if not (List.equal cases_pattern_eq p1 p2) then raise_notrace Exit; (* TODO: subtyping and renaming *) aux vars renaming t1 t2 in let eqf renaming (t1, (na1, o1)) (t2, (na2, o2)) = aux vars renaming t1 t2; let renaming = check_eq_name vars renaming na1 na2 in let eq renaming (i1, n1) (i2, n2) = if not (Ind.CanOrd.equal i1 i2) then raise_notrace Exit; List.fold_left2 (check_eq_name vars) renaming n1 n2 in Option.fold_left2 eq renaming o1 o2 in let renaming = List.fold_left2 eqf renaming r1 r2 in Option.iter2 (aux vars renaming) o1 o2; List.iter2 check_pat p1 p2 | NLetTuple (nas1, (na1, o1), t1, u1), NLetTuple (nas2, (na2, o2), t2, u2) -> aux vars renaming t1 t2; let renaming = check_eq_name vars renaming na1 na2 in Option.iter2 (aux vars renaming) o1 o2; let renaming' = List.fold_left2 (check_eq_name vars) renaming nas1 nas2 in aux vars renaming' u1 u2 | NIf (t1, (na1, o1), u1, r1), NIf (t2, (na2, o2), u2, r2) -> aux vars renaming t1 t2; aux vars renaming u1 u2; aux vars renaming r1 r2; let renaming = check_eq_name vars renaming na1 na2 in Option.iter2 (aux vars renaming) o1 o2 | NRec (_, ids1, ts1, us1, rs1), NRec (_, ids2, ts2, us2, rs2) -> (* FIXME? *) let eq renaming (na1, o1, t1) (na2, o2, t2) = Option.iter2 (aux vars renaming) o1 o2; aux vars renaming t1 t2; check_eq_name vars renaming na1 na2 in let renaming = Array.fold_left2 (fun r id1 id2 -> check_eq_id vars r id1 id2; (Name id1,id2)::r) renaming ids1 ids2 in let renamings = Array.map2 (List.fold_left2 eq renaming) ts1 ts2 in Array.iter3 (aux vars) renamings us1 us2; Array.iter3 (aux vars) (Array.map ((@) renaming) renamings) rs1 rs2 | NSort s1, NSort s2 when glob_sort_eq s1 s2 -> () | NCast (c1, k1, t1), NCast (c2, k2, t2) -> aux vars renaming c1 c2; if not (Option.equal cast_kind_eq k1 k2) then raise_notrace Exit; aux vars renaming t1 t2 | NInt i1, NInt i2 when Uint63.equal i1 i2 -> () | NFloat f1, NFloat f2 when Float64.equal f1 f2 -> () | NArray(t1,def1,ty1), NArray(t2,def2,ty2) -> Array.iter2 (aux vars renaming) t1 t2; aux vars renaming def1 def2; aux vars renaming ty1 ty2 | (NRef _ | NVar _ | NApp _ | NProj _ | NHole _ | NGenarg _ | NList _ | NLambda _ | NProd _ | NBinderList _ | NLetIn _ | NCases _ | NLetTuple _ | NIf _ | NRec _ | NSort _ | NCast _ | NInt _ | NFloat _ | NString _ | NArray _), _ -> raise_notrace Exit in try let _ = aux (vars1,vars2) [] t1 t2 in if not lt then (* Check that order of notation metavariables does not matter *) List.iter2 check_alphameta vars1 vars2; not lt || var_eq_hole || !strictly_lt with Exit | (* Option.iter2: *) Option.Heterogeneous | Invalid_argument _ -> false let eq_notation_constr vars t1 t2 = t1 == t2 || compare_notation_constr false false vars t1 t2 (* "strictly finer" is the order generated by constructed-node <= var/hole *) let strictly_finer_notation_constr vars t1 t2 = compare_notation_constr true false vars t1 t2 (* "finer" is the order also including var = hole and hole = var *) let finer_notation_constr vars t1 t2 = compare_notation_constr true true vars t1 t2 let adjust_application c1 c2 = match c1, c2 with | NApp (t1, a1), (NList (_,_,NApp (_, a2),_,_) | NBinderList (_,_,NApp (_, a2),_,_) | NApp (_, a2)) when List.length a1 >= List.length a2 -> NApp (t1, List.firstn (List.length a2) a1) | NApp (t1, a1), _ -> t1 | _ -> c1 let strictly_finer_interpretation_than (vars1,c1) (vars2,c2) = let c1 = adjust_application c1 c2 in strictly_finer_notation_constr (List.map fst vars1, List.map fst vars2) c1 c2 let finer_interpretation_than (vars1,c1) (vars2,c2) = let c1 = adjust_application c1 c2 in finer_notation_constr (List.map fst vars1, List.map fst vars2) c1 c2 (**********************************************************************) (* Re-interpret a notation as a glob_constr, taking care of binders *) let name_to_ident = function | Anonymous -> CErrors.user_err Pp.(str "This expression should be a simple identifier.") | Name id -> id let to_id g e id = let e,na = g e (Name id) in e,name_to_ident na let product_of_cases_patterns patl = List.fold_right (fun patl restl -> List.flatten (List.map (fun p -> List.map (fun rest -> p::rest) restl) patl)) patl [[]] let rec cases_pattern_fold_map ?loc g e = DAst.with_val (function | PatVar na -> let e',disjpat,na' = g e na in e', (match disjpat with | None -> [DAst.make ?loc @@ PatVar na'] | Some ((_,disjpat),_) -> disjpat) | PatCstr (cstr,patl,na) -> let e',disjpat,na' = g e na in if disjpat <> None then user_err (Pp.str "Unable to instantiate an \"as\" clause with a pattern."); let e',patl' = List.fold_left_map (cases_pattern_fold_map ?loc g) e patl in (* Distribute outwards the inner disjunctive patterns *) let disjpatl' = product_of_cases_patterns patl' in e', List.map (fun patl' -> DAst.make ?loc @@ PatCstr (cstr,patl',na')) disjpatl' ) let subst_binder_type_vars l = function | GBinderType (Name id) -> let id = try match DAst.get (Id.List.assoc id l) with GVar id' -> id' | _ -> id with Not_found -> id in GBinderType (Name id) | e -> e let rec subst_glob_vars l gc = DAst.map (function | GVar id as r -> (try DAst.get (Id.List.assoc id l) with Not_found -> r) | GHole x -> GHole (subst_binder_type_vars l x) | _ -> let g = Name.map (fun id -> try match DAst.get (Id.List.assoc id l) with GVar id' -> id' | _ -> id with Not_found -> id) in DAst.get (map_glob_constr_left_to_right_with_names (subst_glob_vars l) g gc) (* assume: id is not binding *) ) gc type 'a binder_status_fun = { no : 'a -> 'a; restart_prod : 'a -> 'a; restart_lambda : 'a -> 'a; switch_prod : 'a -> 'a; switch_lambda : 'a -> 'a; slide : 'a -> 'a; } let default_binder_status_fun = { no = (fun x -> x); restart_prod = (fun x -> x); restart_lambda = (fun x -> x); switch_prod = (fun x -> x); switch_lambda = (fun x -> x); slide = (fun x -> x); } let test_implicit_argument_mark bk = if not (Glob_ops.binding_kind_eq bk Explicit) then user_err (Pp.str "Unexpected implicit argument mark.") let test_pattern_cast = function | None -> () | Some t -> user_err ?loc:t.CAst.loc (Pp.str "Unsupported pattern cast.") let protect g e na = let e',disjpat,na,bk,t = g e na None in if disjpat <> None then user_err (Pp.str "Unsupported substitution of an arbitrary pattern."); test_implicit_argument_mark bk; test_pattern_cast t; e',na let set_anonymous_type na = function | None -> DAst.make @@ GHole (GBinderType na) | Some t -> t let apply_cases_pattern_term ?loc (ids,disjpat) tm c = let eqns = List.map (fun pat -> (CAst.make ?loc (ids,[pat],c))) disjpat in DAst.make ?loc @@ GCases (Constr.LetPatternStyle, None, [tm,(Anonymous,None)], eqns) let apply_cases_pattern ?loc (ids_disjpat,id) c = apply_cases_pattern_term ?loc ids_disjpat (DAst.make ?loc (GVar id)) c let glob_constr_of_notation_constr_with_binders ?loc g f ?(h=default_binder_status_fun) e nc = let lt x = DAst.make ?loc x in lt @@ match nc with | NVar id -> GVar id | NApp (a,args) -> let e = h.no e in DAst.get (mkGApp (f e a) (List.map (f e) args)) | NProj (p,args,c) -> let e = h.no e in GProj (p, List.map (f e) args, f e c) | NList (x,y,iter,tail,swap) -> let t = f e tail in let it = f e iter in let innerl = (ldots_var,t)::(if swap then [y, lt @@ GVar x] else []) in let inner = lt @@ GApp (lt @@ GVar (ldots_var),[subst_glob_vars innerl it]) in let outerl = (ldots_var,inner)::(if swap then [] else [y, lt @@ GVar x]) in DAst.get (subst_glob_vars outerl it) | NBinderList (x,y,iter,tail,swap) -> let t = f e tail in let it = f e iter in let innerl = (ldots_var,t)::(if swap then [y, lt @@ GVar x] else []) in let inner = lt @@ GApp (lt @@ GVar ldots_var,[subst_glob_vars innerl it]) in let outerl = (ldots_var,inner)::(if swap then [] else [y, lt @@ GVar x]) in DAst.get (subst_glob_vars outerl it) | NLambda (na,ty,c) -> let e = h.switch_lambda e in let ty = Option.map (f (h.restart_prod e)) ty in let e',disjpat,na',bk,ty = g e na ty in GLambda (na',None,bk,set_anonymous_type na ty,Option.fold_right (apply_cases_pattern ?loc) disjpat (f e' c)) | NProd (na,ty,c) -> let e = h.switch_prod e in let ty = Option.map (f (h.restart_prod e)) ty in let e',disjpat,na',bk,ty = g e na ty in GProd (na',None,bk,set_anonymous_type na ty,Option.fold_right (apply_cases_pattern ?loc) disjpat (f e' c)) | NLetIn (na,b,t,c) -> let t = Option.map (f (h.restart_prod e)) t in let e',disjpat,na,bk,t = g e na t in test_implicit_argument_mark bk; (match disjpat with | None -> GLetIn (na,None, f (h.restart_lambda e) b,t,f e' c) | Some (disjpat,_id) -> test_pattern_cast t; DAst.get (apply_cases_pattern_term ?loc disjpat (f e b) (f e' c))) | NCases (sty,rtntypopt,tml,eqnl) -> let e = h.no e in let e',tml' = List.fold_right (fun (tm,(na,t)) (e',tml') -> let e',t' = match t with | None -> e',None | Some (ind,nal) -> let e',nal' = List.fold_right (fun na (e',nal) -> let e',na' = protect g e' na in e',na'::nal) nal (e',[]) in e',Some (CAst.make ?loc (ind,nal')) in let e',na' = protect g e' na in (e',(f e tm,(na',t'))::tml')) tml (e,[]) in let fold (idl,e) na = let (e,disjpat,na,bk,t) = g e na None in test_implicit_argument_mark bk; test_pattern_cast t; ((Name.cons na idl,e),disjpat,na) in let eqnl' = List.map (fun (patl,rhs) -> let ((idl,e),patl) = List.fold_left_map (cases_pattern_fold_map ?loc fold) ([],e) patl in let disjpatl = product_of_cases_patterns patl in List.map (fun patl -> CAst.make (idl,patl,f e rhs)) disjpatl) eqnl in GCases (sty,Option.map (f e') rtntypopt,tml',List.flatten eqnl') | NLetTuple (nal,(na,po),b,c) -> let e = h.no e in let e',nal = List.fold_left_map (protect g) e nal in let e'',na = protect g e na in GLetTuple (nal,(na,Option.map (f e'') po),f e b,f e' c) | NIf (c,(na,po),b1,b2) -> let e = h.no e in let e',na = protect g e na in GIf (f e c,(na,Option.map (f e') po),f e b1,f e b2) | NRec (fk,idl,dll,tl,bl) -> let e = h.no e in let e,dll = Array.fold_left_map (List.fold_left_map (fun e (na,oc,b) -> let e,na = protect g e na in (e,(na,None,Explicit,Option.map (f e) oc,f e b)))) e dll in let e',idl = Array.fold_left_map (to_id (protect g)) e idl in GRec (fk,idl,dll,Array.map (f e) tl,Array.map (f e') bl) | NCast (c,k,t) -> GCast (f e c, k, f (h.slide e) t) | NSort x -> GSort x | NHole x -> GHole x | NGenarg arg -> GGenarg arg | NRef (x,u) -> GRef (x,u) | NInt i -> GInt i | NFloat f -> GFloat f | NString s -> GString s | NArray (t,def,ty) -> GArray(None, Array.map (f e) t, f e def, f e ty) let glob_constr_of_notation_constr ?loc x = let rec aux () x = glob_constr_of_notation_constr_with_binders ?loc (fun () id t -> ((),None,id,Explicit,t)) aux () x in aux () x let pr_notation_info prglob ntn c = str (String.quote_coq_string ntn) ++ str " :=" ++ spc() ++ prglob (glob_constr_of_notation_constr c) (******************************************************************************) (* Translating a glob_constr into a notation, interpreting recursive patterns *) type found_variables = { vars : Id.t list; recursive_term_vars : (Id.t * Id.t) list; recursive_binders_vars : (Id.t * Id.t) list; } let add_id r id = r := { !r with vars = id :: (!r).vars } let add_name r = function Anonymous -> () | Name id -> add_id r id let mkNApp1 (g,a) = match g with (* Ensure flattening of nested applicative nodes *) | NApp (g,args') -> NApp (g,args'@[a]) | _ -> NApp (g,[a]) let is_gvar id c = match DAst.get c with | GVar id' -> Id.equal id id' | _ -> false let split_at_recursive_part c = let sub = ref None in let rec aux c = let loc0 = c.CAst.loc in match DAst.get c with | GApp (f, c::l) when is_gvar ldots_var f -> (* *) let loc = f.CAst.loc in begin match !sub with | None -> let () = sub := Some c in begin match l with | [] -> DAst.make ?loc @@ GVar ldots_var | _ :: _ -> DAst.make ?loc:loc0 @@ GApp (DAst.make ?loc @@ GVar ldots_var, l) end | Some _ -> (* Not narrowed enough to find only one recursive part *) raise Not_found end | _ -> map_glob_constr aux c in let outer_iterator = aux c in match !sub with | None -> (* No recursive pattern found *) raise Not_found | Some c -> match DAst.get outer_iterator with | GVar v when Id.equal v ldots_var -> (* Not enough context *) raise Not_found | _ -> outer_iterator, c let subtract_loc loc1 loc2 = let l1 = fst (Option.cata Loc.unloc (0,0) loc1) in let l2 = fst (Option.cata Loc.unloc (0,0) loc2) in Some (Loc.make_loc (l1,l2-1)) let check_is_hole id = function | None -> () | Some t -> match DAst.get t with GHole _ -> () | _ -> user_err ?loc:(loc_of_glob_constr t) (strbrk "In recursive notation with binders, " ++ Id.print id ++ strbrk " is expected to come without type.") let check_pair_matching ?loc x y x' y' revert revert' = if not (Id.equal x x' && Id.equal y y' && revert = revert') then let x,y = if revert then y,x else x,y in let x',y' = if revert' then y',x' else x',y' in (* This is a case where one would like to highlight two locations! *) user_err ?loc (strbrk "Found " ++ Id.print x ++ strbrk " matching " ++ Id.print y ++ strbrk " while " ++ Id.print x' ++ strbrk " matching " ++ Id.print y' ++ strbrk " was first found.") let mem_recursive_pair (x,y) l = List.mem_f (eq_pair Id.equal Id.equal) (x,y) l type recursive_pattern_kind = | RecursiveTerms of bool (* in reverse order *) | RecursiveBinders of bool (* in reverse order *) let compare_recursive_parts recvars found f f' (iterator,subc) = let diff = ref None in let terminator = ref None in let treat_binder ?loc x y t_x t_y = match x, y with | Name x, Name y when mem_recursive_pair (x,y) recvars || mem_recursive_pair (y,x) recvars -> (* We found a binding position where it differs *) check_is_hole x t_x; check_is_hole y t_y; let revert = mem_recursive_pair (y,x) recvars in let x,y = if revert then y,x else x,y in begin match !diff with | None -> diff := Some (x, y, RecursiveBinders revert) | Some (x', y', RecursiveBinders revert') -> check_pair_matching ?loc x y x' y' revert revert' | Some (x', y', RecursiveTerms revert') -> (* Recursive binders have precedence: they can be coerced to terms but not reciprocally *) check_pair_matching ?loc x y x' y' revert revert'; diff := Some (x, y, RecursiveBinders revert) end; true | _ -> Name.equal x y in let rec aux c1 c2 = match DAst.get c1, DAst.get c2 with | GVar v, term when Id.equal v ldots_var -> (* We found the pattern *) assert (match !terminator with None -> true | Some _ -> false); terminator := Some c2; true | GApp (f,l1), GApp (term, l2) -> begin match DAst.get f with | GVar v when Id.equal v ldots_var -> (* We found the pattern, but there are extra arguments *) (* (this allows e.g. alternative (recursive) notation of application) *) assert (match !terminator with None -> true | Some _ -> false); terminator := Some term; List.for_all2eq aux l1 l2 | _ -> mk_glob_constr_eq aux (treat_binder ?loc:c1.CAst.loc) c1 c2 end | GVar x, GVar y when mem_recursive_pair (x,y) recvars || mem_recursive_pair (y,x) recvars -> (* We found the position where it differs *) let revert = mem_recursive_pair (y,x) recvars in let x,y = if revert then y,x else x,y in begin match !diff with | None -> let () = diff := Some (x, y, RecursiveTerms revert) in true | Some (x', y', RecursiveTerms revert') | Some (x', y', RecursiveBinders revert') -> check_pair_matching ?loc:c1.CAst.loc x y x' y' revert revert'; true end | _ -> mk_glob_constr_eq aux (treat_binder ?loc:c1.CAst.loc) c1 c2 in if aux iterator subc then match !diff with | None -> let loc1 = loc_of_glob_constr iterator in let loc2 = loc_of_glob_constr (Option.get !terminator) in (* Here, we would need a loc made of several parts ... *) user_err ?loc:(subtract_loc loc1 loc2) (str "Both ends of the recursive pattern are the same.") | Some (x,y,RecursiveTerms revert) -> (* By arbitrary convention, we use the second variable of the pair as the place-holder for the iterator *) let iterator = f' (if revert then iterator else subst_glob_vars [x, DAst.make @@ GVar y] iterator) in (* found variables have been collected by compare_constr *) found := { !found with vars = List.remove Id.equal y (!found).vars; recursive_term_vars = List.add_set (eq_pair Id.equal Id.equal) (x,y) (!found).recursive_term_vars }; NList (x,y,iterator,f (Option.get !terminator),revert) | Some (x,y,RecursiveBinders revert) -> let iterator = f' (if revert then iterator else subst_glob_vars [x, DAst.make @@ GVar y] iterator) in (* found have been collected by compare_constr *) found := { !found with vars = List.remove Id.equal y (!found).vars; recursive_binders_vars = List.add_set (eq_pair Id.equal Id.equal) (x,y) (!found).recursive_binders_vars }; NBinderList (x,y,iterator,f (Option.get !terminator),revert) else raise Not_found let notation_constr_and_vars_of_glob_constr recvars a = let found = ref { vars = []; recursive_term_vars = []; recursive_binders_vars = [] } in let forgetful = ref { forget_ltac = false; forget_volatile_cast = false } in (* Turn a glob_constr into a notation_constr by first trying to find a recursive pattern *) let rec aux c = let keepfound = !found in (* n^2 complexity but small and done only once per notation *) try compare_recursive_parts recvars found aux aux' (split_at_recursive_part c) with Not_found -> found := keepfound; match DAst.get c with | GApp (t, [_]) -> begin match DAst.get t with | GVar f when Id.equal f ldots_var -> (* Fall on the second part of the recursive pattern w/o having found the first part *) let loc = t.CAst.loc in user_err ?loc (str "Cannot find where the recursive pattern starts.") | _ -> aux' c end | _c -> aux' c and aux' x = DAst.with_val (function | GVar id -> if not (Id.equal id ldots_var) then add_id found id; NVar id | GApp (g,[]) -> NApp (aux g,[]) (* Encoding @foo *) | GApp (g,args) -> (* Treat applicative notes as binary nodes *) let a,args = List.sep_last args in mkNApp1 (aux (DAst.make (GApp (g, args))), aux a) | GProj (p,args,c) -> NProj (p, List.map aux args, aux c) | GLambda (na,_,bk,ty,c) -> add_name found na; NLambda (na,aux_type ty,aux c) | GProd (na,_,bk,ty,c) -> add_name found na; NProd (na,aux_type ty,aux c) | GLetIn (na,_,b,t,c) -> add_name found na; NLetIn (na,aux b,Option.map aux t, aux c) | GCases (sty,rtntypopt,tml,eqnl) -> let f {CAst.v=(idl,pat,rhs)} = List.iter (add_id found) idl; (pat,aux rhs) in NCases (sty,Option.map aux rtntypopt, List.map (fun (tm,(na,x)) -> add_name found na; Option.iter (fun {CAst.v=(_,nl)} -> List.iter (add_name found) nl) x; (aux tm,(na,Option.map (fun {CAst.v=(ind,nal)} -> (ind,nal)) x))) tml, List.map f eqnl) | GLetTuple (nal,(na,po),b,c) -> add_name found na; List.iter (add_name found) nal; NLetTuple (nal,(na,Option.map aux po),aux b,aux c) | GIf (c,(na,po),b1,b2) -> add_name found na; NIf (aux c,(na,Option.map aux po),aux b1,aux b2) | GRec (fk,idl,dll,tl,bl) -> Array.iter (add_id found) idl; let dll = Array.map (List.map (fun (na,_,bk,oc,b) -> if bk != Explicit then user_err Pp.(str "Binders marked as implicit not allowed in notations."); add_name found na; (na,Option.map aux oc,aux b))) dll in NRec (fk,idl,dll,Array.map aux tl,Array.map aux bl) | GCast (c,k,t) -> if Option.is_empty k then forgetful := { !forgetful with forget_volatile_cast = true }; NCast (aux c, k, aux t) | GSort s -> NSort s | GInt i -> NInt i | GFloat f -> NFloat f | GString s -> NString s | GHole w -> NHole w | GGenarg arg -> forgetful := { !forgetful with forget_ltac = true }; NGenarg arg | GRef (r,u) -> NRef (r,u) | GArray (_u,t,def,ty) -> NArray (Array.map aux t, aux def, aux ty) | GEvar _ | GPatVar _ -> user_err Pp.(str "Existential variables not allowed in notations.") ) x and aux_type t = DAst.with_val (function | GHole (GBinderType _) -> None | _ -> Some (aux t)) t in let t = aux a in (* Side effect *) t, !found, !forgetful let rec make_iterated_pairs : type s. (s -> Id.t list) -> s notation_raw_type -> Id.t list = fun f -> function | NtnRawTypeVar x -> f x | NtnRawTypeVarList typ -> make_iterated_pairs (fun (x,y) -> f x @ f y) typ | NtnRawTypeVarTuple typs -> List.map_append (make_iterated_pairs f) typs let rec pairs_of_notation = function | NtnRawTypeVar _ -> [] | NtnRawTypeVarList typ -> make_iterated_pairs (fun (x,y) -> [x;y]) typ | NtnRawTypeVarTuple l -> List.map_append pairs_of_notation l let check_variables_and_reversibility nenv { vars = found; recursive_term_vars = foundrec; recursive_binders_vars = foundrecbinding } = let injective = ref [] in let recvars = List.map pairs_of_notation nenv.ninterp_raw_types in (* We have iterated tuples (pairs, pairs of pairs, etc.) where the first name is the reference *) let recvars = List.filter (fun l -> not (List.is_empty l)) recvars in let fold l accu = List.fold_right Id.Set.add (List.tl l) accu in let useless_vars = List.fold_right fold recvars Id.Set.empty in let filter y _ = not (Id.Set.mem y useless_vars) in let vars = Id.Map.filter filter nenv.ninterp_var_type in let check_recvar x = if Id.List.mem x found then user_err (Id.print x ++ strbrk " should only be used in the recursive part of a pattern.") in let check (x, y) = check_recvar x; check_recvar y in let () = List.iter check foundrec in let () = List.iter check foundrecbinding in let check_bound x = if not (Id.List.mem x found) then if Id.List.mem_assoc x foundrec || Id.List.mem_assoc x foundrecbinding || Id.List.mem_assoc_sym x foundrec || Id.List.mem_assoc_sym x foundrecbinding then user_err Pp.(str (Id.to_string x ^ " should not be bound in a recursive pattern of the right-hand side.")) else injective := x :: !injective in let check_pair s x y where = if not (mem_recursive_pair (x,y) where) then user_err (strbrk "in the right-hand side, " ++ Id.print x ++ str " and " ++ Id.print y ++ strbrk " should appear in " ++ str s ++ str " position as part of a recursive pattern.") in (* TEMPORARY : no iteration *) let recvars = Id.Map.of_list (List.map (fun l -> (List.hd l, List.hd (List.tl l))) recvars) in let check_type x typ = match typ with | NtnInternTypeAny _ -> begin try check_pair "term" x (Id.Map.find x recvars) foundrec with Not_found -> check_bound x end | NtnInternTypeOnlyBinder -> begin try check_pair "binding" x (Id.Map.find x recvars) foundrecbinding with Not_found -> check_bound x end in Id.Map.iter check_type vars; List.rev !injective let[@warning "+9"] is_forgetful { forget_ltac; forget_volatile_cast } = forget_ltac || forget_volatile_cast let notation_constr_of_glob_constr nenv a = let recvars = List.map pairs_of_notation nenv.ninterp_raw_types in (* TEMPORARY : no iteration *) let recvars = List.map (fun l -> (List.hd l, List.hd (List.tl l))) (List.filter (fun l -> not (List.is_empty l)) recvars) in let a, found, forgetful = notation_constr_and_vars_of_glob_constr recvars a in let injective = check_variables_and_reversibility nenv found in let status = if is_forgetful forgetful then Forgetful forgetful else match injective with | [] -> APrioriReversible | l -> NonInjective l in a, status (**********************************************************************) (* Substitution of kernel names, avoiding a list of bound identifiers *) let notation_constr_of_constr ~flags avoid t = let t = EConstr.of_constr t in let env = Global.env () in let evd = Evd.from_env env in let t = Detyping.detype Detyping.Now ~flags ~avoid env evd t in let nenv = { ninterp_var_type = Id.Map.empty; ninterp_raw_types = []; } in notation_constr_of_glob_constr nenv t let rec subst_pat subst pat = match DAst.get pat with | PatVar _ -> pat | PatCstr (((kn,i),j),cpl,n) -> let kn' = subst_mind subst kn and cpl' = List.Smart.map (subst_pat subst) cpl in if kn' == kn && cpl' == cpl then pat else DAst.make ?loc:pat.CAst.loc @@ PatCstr (((kn',i),j),cpl',n) let rec subst_notation_constr subst bound raw = match raw with | NRef (ref,u) -> let ref',t = subst_global subst ref in if ref' == ref then raw else (match t with | None -> NRef (ref',u) | Some t -> let flags = PrintingFlags.Detype.current() in fst (notation_constr_of_constr ~flags bound t.UVars.univ_abstracted_value)) | NVar _ -> raw | NApp (r,rl) -> let r' = subst_notation_constr subst bound r and rl' = List.Smart.map (subst_notation_constr subst bound) rl in if r' == r && rl' == rl then raw else NApp(r',rl') | NProj ((cst,u),rl,r) -> let ref = GlobRef.ConstRef cst in let ref',t = subst_global subst ref in assert (t = None); let rl' = List.Smart.map (subst_notation_constr subst bound) rl and r' = subst_notation_constr subst bound r in if ref' == ref && rl' == rl && r' == r then raw else NProj ((destConstRef ref',u),rl',r') | NList (id1,id2,r1,r2,b) -> let r1' = subst_notation_constr subst bound r1 and r2' = subst_notation_constr subst bound r2 in if r1' == r1 && r2' == r2 then raw else NList (id1,id2,r1',r2',b) | NLambda (n,r1,r2) -> let r1' = Option.Smart.map (subst_notation_constr subst bound) r1 and r2' = subst_notation_constr subst bound r2 in if r1' == r1 && r2' == r2 then raw else NLambda (n,r1',r2') | NProd (n,r1,r2) -> let r1' = Option.Smart.map (subst_notation_constr subst bound) r1 and r2' = subst_notation_constr subst bound r2 in if r1' == r1 && r2' == r2 then raw else NProd (n,r1',r2') | NBinderList (id1,id2,r1,r2,b) -> let r1' = subst_notation_constr subst bound r1 and r2' = subst_notation_constr subst bound r2 in if r1' == r1 && r2' == r2 then raw else NBinderList (id1,id2,r1',r2',b) | NLetIn (n,r1,t,r2) -> let r1' = subst_notation_constr subst bound r1 in let t' = Option.Smart.map (subst_notation_constr subst bound) t in let r2' = subst_notation_constr subst bound r2 in if r1' == r1 && t == t' && r2' == r2 then raw else NLetIn (n,r1',t',r2') | NCases (sty,rtntypopt,rl,branches) -> let rtntypopt' = Option.Smart.map (subst_notation_constr subst bound) rtntypopt and rl' = List.Smart.map (fun (a,(n,signopt) as x) -> let a' = subst_notation_constr subst bound a in let signopt' = Option.map (fun ((indkn,i),nal as z) -> let indkn' = subst_mind subst indkn in if indkn == indkn' then z else ((indkn',i),nal)) signopt in if a' == a && signopt' == signopt then x else (a',(n,signopt'))) rl and branches' = List.Smart.map (fun (cpl,r as branch) -> let cpl' = List.Smart.map (subst_pat subst) cpl and r' = subst_notation_constr subst bound r in if cpl' == cpl && r' == r then branch else (cpl',r')) branches in if rtntypopt' == rtntypopt && rtntypopt == rtntypopt' && rl' == rl && branches' == branches then raw else NCases (sty,rtntypopt',rl',branches') | NLetTuple (nal,(na,po),b,c) -> let po' = Option.Smart.map (subst_notation_constr subst bound) po and b' = subst_notation_constr subst bound b and c' = subst_notation_constr subst bound c in if po' == po && b' == b && c' == c then raw else NLetTuple (nal,(na,po'),b',c') | NIf (c,(na,po),b1,b2) -> let po' = Option.Smart.map (subst_notation_constr subst bound) po and b1' = subst_notation_constr subst bound b1 and b2' = subst_notation_constr subst bound b2 and c' = subst_notation_constr subst bound c in if po' == po && b1' == b1 && b2' == b2 && c' == c then raw else NIf (c',(na,po'),b1',b2') | NRec (fk,idl,dll,tl,bl) -> let dll' = Array.Smart.map (List.Smart.map (fun (na,oc,b as x) -> let oc' = Option.Smart.map (subst_notation_constr subst bound) oc in let b' = subst_notation_constr subst bound b in if oc' == oc && b' == b then x else (na,oc',b'))) dll in let tl' = Array.Smart.map (subst_notation_constr subst bound) tl in let bl' = Array.Smart.map (subst_notation_constr subst bound) bl in if dll' == dll && tl' == tl && bl' == bl then raw else NRec (fk,idl,dll',tl',bl') | NSort _ -> raw | NInt _ -> raw | NFloat _ -> raw | NString _ -> raw | NHole knd -> let nknd = match knd with | GImplicitArg (ref, i, b) -> let nref, _ = subst_global subst ref in if nref == ref then knd else GImplicitArg (nref, i, b) | _ -> knd in if nknd == knd then raw else NHole nknd | NGenarg arg -> let arg' = Gensubst.constr_subst subst arg in if arg' == arg then raw else NGenarg arg' | NCast (r1,k,t) -> let r1' = subst_notation_constr subst bound r1 in let t' = subst_notation_constr subst bound t in if r1' == r1 && t' == t then raw else NCast(r1',k,t') | NArray (t,def,ty) -> let def' = subst_notation_constr subst bound def and t' = Array.Smart.map (subst_notation_constr subst bound) t and ty' = subst_notation_constr subst bound ty in if def' == def && t' == t && ty' == ty then raw else NArray(t',def',ty') let subst_interpretation subst (metas,pat) = let bound = List.fold_left (fun accu (id, _) -> Fresh.add id accu) Fresh.empty metas in (metas,subst_notation_constr subst (Namegen.Generator.fresh, bound) pat) (**********************************************************************) (* Pattern-matching a [glob_constr] against a [notation_constr] *) let abstract_return_type_context pi mklam tml rtno = Option.map (fun rtn -> let nal = List.flatten (List.map (fun (_,(na,t)) -> match t with Some x -> (pi x)@[na] | None -> [na]) tml) in List.fold_right mklam nal rtn) rtno let abstract_return_type_context_glob_constr tml rtn = abstract_return_type_context (fun {CAst.v=(_,nal)} -> nal) (fun na c -> DAst.make @@ GLambda(na,None,Explicit,DAst.make @@ GHole (GInternalHole), c)) tml rtn let abstract_return_type_context_notation_constr tml rtn = abstract_return_type_context snd (fun na c -> NLambda(na,None,c)) tml rtn let rec push_pattern_binders vars pat = match DAst.get pat with | PatVar na -> Termops.add_vname vars na | PatCstr (c, pl, na) -> List.fold_left push_pattern_binders (Termops.add_vname vars na) pl let rec push_context_binders vars = function | [] -> vars | b :: bl -> let vars = match DAst.get b with | GLocalAssum (na,_,_,_) -> Termops.add_vname vars na | GLocalPattern ((disjpat,ids),p,bk,t) -> List.fold_right Id.Set.add ids vars | GLocalDef (na,_,_,_) -> Termops.add_vname vars na in push_context_binders vars bl let is_term_meta = function | NtnTypeVar (_, NtnTypeVarConstr _) -> true | _ -> false let is_pattern_meta ~strict ~binder ~isvar = function | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsConstr (AsAnyPattern | AsStrictPattern))) -> true | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsSomeBinderKind AsStrictPattern)) -> strict | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsBinder)) -> binder | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsSomeBinderKind AsAnyPattern)) -> true | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsSomeBinderKind (AsIdent | AsName))) -> isvar | NtnTypeVar (_, NtnTypeVarPattern (NtnBinderParsedAsConstr (AsIdent | AsName))) -> isvar | NtnTypeVar (_, (NtnTypeVarConstr _ | NtnTypeVarBinders _)) | NtnTypeVarList _ | NtnTypeVarTuple _ -> false let is_binders_meta = function | NtnTypeVar (_, NtnTypeVarBinders _) -> true | _ -> false let is_binders_meta_var id metas = try is_binders_meta (Id.List.assoc id metas) with Not_found -> false exception No_match let alpha_rename renaming v = if renaming == [] then (* shortcut: *) v else try rename_glob_vars renaming v with UnsoundRenaming -> raise No_match let static_binder_escape staticbinders v = List.exists (function (Name id,_) -> occur_glob_constr id v | (Anonymous,_) -> false) staticbinders let add_term_env {actualvars;staticbinders;renaming} sigma var v = (* Check that no capture of binding variables occur *) (* [staticbinders] is used when matching a pattern "fun x => ... x ... ?var ... x ..." with an actual term "fun z => ... z ..." when "x" is not bound in the notation, as in "Notation "'twice_upto' y" := (fun x => x + x + y)". Then we keep (z,x) in staticbinders, and we have to check that what the [v] which is bound to [var] does not contain z *) if not (Id.equal ldots_var var) && static_binder_escape staticbinders v then raise No_match; (* [renaming] is used when matching a pattern "fun x => ... x ... ?var ... x ..." with an actual term "fun z => ... z ..." when "x" is bound in the notation and the name "x" cannot be changed to "z", e.g. because used at another occurrence, as in "Notation "'lam' y , P & Q" := ((fun y => P),(fun y => Q))". Then, we keep (z,y) in renaming, and we have to check that "fun z => ... z ..." denotes the same term as "fun x => ... x ... ?var ... x" up to alpha-conversion when [var] is instantiated by [v]; Currently, we fail, but, eventually, [x] in [v] could be replaced by [x], and, in match_, when finding "x" in subterm, failing because of a capture, and, in match_, when finding "z" in subterm, replacing it with "x", and, in an even further step, being even more robust, independent of the order, so that e.g. the notation for ex2 works on "x y |- ex2 (fun x => y=x) (fun y => x=y)" by giving, say, "exists2 x0, y=x0 & x=x0", but this would typically require the glob_constr_eq in bind_term_env to be postponed in match_notation_constr, and the choice of exact variable be done there; but again, this would be a non-trivial refinement *) let v = alpha_rename renaming v in (* TODO: handle the case of multiple occs in different scopes *) Id.Map.add var (Constrexpr.NtnTypeArg (NtnTypeArgConstr (actualvars,staticbinders,v))) sigma let add_termlist_env {actualvars;staticbinders;renaming} sigma var vl = if List.exists (static_binder_escape staticbinders) vl then raise No_match; let vl = List.map (alpha_rename renaming) vl in let vl = List.map (fun c -> NtnTypeArg (NtnTypeArgConstr (actualvars,staticbinders,c))) vl in Id.Map.add var (NtnTypeArgList vl) sigma let add_pattern_env {actualvars;staticbinders} sigma var v = (* TODO: handle the case of multiple occs in different scopes *) Id.Map.add var (NtnTypeArg (NtnTypeArgPattern (actualvars,staticbinders,v))) sigma let add_binders_env {actualvars;staticbinders} sigma var bl = Id.Map.add var (NtnTypeArg (NtnTypeArgBinders (actualvars,staticbinders,bl))) sigma let rec map_cases_pattern_name_left f = DAst.map (function | PatVar na -> PatVar (f na) | PatCstr (c,l,na) -> PatCstr (c,List.map_left (map_cases_pattern_name_left f) l,f na) ) let rec fold_cases_pattern_eq f x p p' = let loc = p.CAst.loc in match DAst.get p, DAst.get p' with | PatVar na, PatVar na' -> let x,na = f x na na' in x, DAst.make ?loc @@ PatVar na | PatCstr (c,l,na), PatCstr (c',l',na') when Construct.CanOrd.equal c c' -> let x,l = fold_cases_pattern_list_eq f x l l' in let x,na = f x na na' in x, DAst.make ?loc @@ PatCstr (c,l,na) | _ -> failwith "Not equal" and fold_cases_pattern_list_eq f x pl pl' = match pl, pl' with | [], [] -> x, [] | p::pl, p'::pl' -> let x, p = fold_cases_pattern_eq f x p p' in let x, pl = fold_cases_pattern_list_eq f x pl pl' in x, p :: pl | _ -> assert false let rec cases_pattern_eq p1 p2 = match DAst.get p1, DAst.get p2 with | PatVar na1, PatVar na2 -> Name.equal na1 na2 | PatCstr (c1, pl1, na1), PatCstr (c2, pl2, na2) -> Construct.CanOrd.equal c1 c2 && List.equal cases_pattern_eq pl1 pl2 && Name.equal na1 na2 | _ -> false let rec pat_binder_of_term t = DAst.map (function | GVar id -> PatVar (Name id) | GApp (t, l) -> begin match DAst.get t with | GRef (GlobRef.ConstructRef cstr,_) -> let nparams = Inductiveops.inductive_nparams (Global.env()) (fst cstr) in let _,l = List.chop nparams l in PatCstr (cstr, List.map pat_binder_of_term l, Anonymous) | _ -> raise No_match end | _ -> raise No_match ) t let unify_name_upto ({actualvars;staticbinders;renaming} as alp) na na' = match na, na' with | Anonymous, na' -> {alp with actualvars = Termops.add_vname actualvars na'}, na' | na, Anonymous -> {alp with actualvars = Termops.add_vname actualvars na}, na | Name id, Name id' -> let vars = Termops.add_vname actualvars na' in if Id.equal id id' then {alp with actualvars = vars}, na' else {actualvars = vars; staticbinders; renaming = (id,id')::renaming}, na' let unify_pat_upto alp p p' = try fold_cases_pattern_eq unify_name_upto alp p p' with Failure _ -> raise No_match let unify_term renaming v v' = match DAst.get v, DAst.get v' with | GHole _, _ -> v' | _, GHole _ -> v | _, _ -> let v = alpha_rename renaming v in if glob_constr_eq v v' then v else raise No_match let unify_opt_term alp v v' = match v, v' with | Some t, Some t' -> Some (unify_term alp t t') | (Some _ as x), None | None, (Some _ as x) -> x | None, None -> None let unify_binding_kind bk bk' = if bk == bk' then bk' else raise No_match let unify_relevance_info r r' = if relevance_info_eq r r' then r else raise No_match let unify_binder_upto alp b b' = let loc, loc' = CAst.(b.loc, b'.loc) in match DAst.get b, DAst.get b' with | GLocalAssum (na,r,bk,t), GLocalAssum (na',r',bk',t') -> let alp', na = unify_name_upto alp na na' in alp', DAst.make ?loc @@ GLocalAssum (na, unify_relevance_info r r', unify_binding_kind bk bk', unify_term alp.renaming t t') | GLocalDef (na,r,c,t), GLocalDef (na',r',c',t') -> let alp', na = unify_name_upto alp na na' in alp', DAst.make ?loc @@ GLocalDef (na, unify_relevance_info r r', unify_term alp.renaming c c', unify_opt_term alp.renaming t t') | GLocalPattern ((disjpat,ids),id,bk,t), GLocalPattern ((disjpat',_),_,bk',t') when List.length disjpat = List.length disjpat' -> let alp', p = List.fold_left2_map unify_pat_upto alp disjpat disjpat' in alp', DAst.make ?loc @@ GLocalPattern ((p,ids), id, unify_binding_kind bk bk', unify_term alp.renaming t t') | _ -> raise No_match let rec unify_terms alp vl vl' = match vl, vl' with | [], [] -> [] | v :: vl, v' :: vl' -> unify_term alp v v' :: unify_terms alp vl vl' | _ -> raise No_match let rec unify_binders_upto alp bl bl' = match bl, bl' with | [], [] -> alp, [] | b :: bl, b' :: bl' -> let alp,b = unify_binder_upto alp b b' in let alp,bl = unify_binders_upto alp bl bl' in alp, b :: bl | _ -> raise No_match let unify_id renaming id na' = let id = rename_var renaming id in match na' with | Anonymous -> Name id | Name id' -> if Id.equal id id' then na' else raise No_match let unify_pat renaming p p' = if cases_pattern_eq (map_cases_pattern_name_left (Name.map (rename_var renaming)) p) p' then p' else raise No_match let unify_term_binder renaming c = DAst.(map (fun b' -> match DAst.get c, b' with | GVar id, GLocalAssum (na', r', bk', t') -> GLocalAssum (unify_id renaming id na', r', bk', t') | _, GLocalPattern (([p'],ids), id, bk', t') -> let p = pat_binder_of_term c in GLocalPattern (([unify_pat renaming p p'],ids), id, bk', t') | _ -> raise No_match)) let rec unify_terms_binders renaming cl bl' = match cl, bl' with | [], [] -> [] | c :: cl', b' :: bl' -> begin match DAst.get b' with | GLocalDef (_, _, _, t) -> b' :: unify_terms_binders renaming cl bl' | _ -> unify_term_binder renaming c b' :: unify_terms_binders renaming cl' bl' end | _ -> raise No_match let get_term = function | Constrexpr.NtnTypeArg (NtnTypeArgConstr c) -> c | _ -> raise Not_found let get_list f = function | Constrexpr.NtnTypeArgList l -> List.map f l | _ -> raise Not_found let get_pattern = function | Constrexpr.NtnTypeArg (NtnTypeArgPattern b) -> b | _ -> raise Not_found let get_binders = function | Constrexpr.NtnTypeArg (NtnTypeArgBinders bl) -> bl | _ -> raise Not_found let bind_term_env alp sigma var v = try (* If already bound to a term, unify with the new term *) let vars, _ntnbinders', v' = get_term (Id.Map.find var sigma) in (* Note: at Notation definition time, it should have been checked that v and v' are in the same static context, i.e. alp.staticbinders = _alp'.staticbinders *) let v'' = unify_term alp.renaming v v' in if v'' == v' then sigma else let sigma = Id.Map.remove var sigma in let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in add_term_env alp' sigma var v with Not_found -> add_term_env alp sigma var v let bind_termlist_env alp sigma var vl = try (* If already bound to a list of term, unify with the new terms *) let vl' = get_list get_term (Id.Map.find var sigma) in let vars, varsl = List.sep_first (List.map pi1 vl') in assert (List.for_all (Id.Set.equal vars) varsl); let vl' = List.map pi3 vl' in let vl = unify_terms alp.renaming vl vl' in let sigma = Id.Map.remove var sigma in let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in add_termlist_env alp' sigma var vl with Not_found -> add_termlist_env alp sigma var vl let bind_singleton_binders_as_term_env alp sigma var c = try (* If already bound to a binder, unify the term and the binder *) let vars, _, patl' = get_binders (Id.Map.find var sigma) in let patl'' = unify_terms_binders alp.renaming [c] patl' in if patl' == patl'' then sigma else let sigma = Id.Map.remove var sigma in let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in add_binders_env alp' sigma var patl'' with Not_found -> (* A term-as-binder occurs in the scope of a binder which is already bound *) anomaly (Pp.str "Unbound term as binder.") let bind_pattern_as_term_env alp sigma var c = let env = Global.env () in let pat = try cases_pattern_of_glob_constr env Anonymous c with Not_found -> raise No_match in try (* If already bound to a binder, unify the term and the binder *) let vars, _, disjpatl' = get_pattern (Id.Map.find var sigma) in let disjpatl'' = List.map2 (unify_pat alp.renaming) [pat] disjpatl' in if disjpatl' == disjpatl'' then sigma else let sigma = Id.Map.remove var sigma in let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in add_pattern_env alp' sigma var disjpatl'' with Not_found -> add_pattern_env alp sigma var [pat] let bind_pattern_env alp sigma var disjpat = try (* If already bound to a binder possibly *) (* generating an alpha-renaming from unifying the new binder *) let vars, _, disjpat' = get_pattern (Id.Map.find var sigma) in (* if, maybe, there is eventually casts in patterns, the common types have *) (* to exclude the spine of variable from the two locations they occur *) let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in let alp, disjpat = List.fold_left2_map unify_pat_upto alp disjpat disjpat' in let sigma = Id.Map.remove var sigma in alp, add_pattern_env alp' sigma var disjpat with Not_found -> (* Note: all patterns of the disjunction are supposed to have the same variables, thus one is enough *) let alp = {alp with actualvars = push_pattern_binders alp.actualvars (List.hd disjpat)} in alp, add_pattern_env alp sigma var disjpat let bind_binders_env alp sigma var bl = let bl = List.rev bl in try (* If already bound to a list of binders possibly *) (* generating an alpha-renaming from unifying the new binders *) let vars, _, bl' = get_binders (Id.Map.find var sigma) in (* The shared subterm can be under two different spines of *) (* variables (themselves bound in the notation), so we take the *) (* union of both locations *) let alp' = {alp with actualvars = Id.Set.union vars alp.actualvars} in let alp, bl = unify_binders_upto alp bl bl' in let sigma = Id.Map.remove var sigma in alp, add_binders_env alp' sigma var bl with Not_found -> let alp = {alp with actualvars = push_context_binders alp.actualvars bl} in alp, add_binders_env alp sigma var bl let bind_binders_as_termlist_env alp sigma var cl = try (* If already bound to a list of binders, unify the terms and binders *) let vars, _, bl' = get_binders (Id.Map.find var sigma) in let bl = unify_terms_binders alp.renaming cl bl' in let alp = {alp with actualvars = Id.Set.union vars alp.actualvars} in let sigma = Id.Map.remove var sigma in add_binders_env alp sigma var bl with Not_found -> anomaly (str "There should be a binder list bindings this list of terms.") let match_fix_kind fk1 fk2 = match (fk1,fk2) with | GCoFix n1, GCoFix n2 -> Int.equal n1 n2 | GFix (nl1,n1), GFix (nl2,n2) -> let test n1 n2 = match n1, n2 with | _, None -> true | Some id1, Some id2 -> Int.equal id1 id2 | _ -> false in Int.equal n1 n2 && Array.for_all2 test nl1 nl2 | _ -> false let match_opt f sigma t1 t2 = match (t1,t2) with | None, None -> sigma | Some t1, Some t2 -> f sigma t1 t2 | _ -> raise No_match let is_meta_variable_name na metas = match na with | Name id -> (try Some (id, Id.List.assoc id metas) with Not_found -> None) | Anonymous -> None let is_meta_variable_pat pat metas = match pat with | PatVar (Name id) -> (try Some (id, Id.List.assoc id metas) with Not_found -> None) | _ -> None let is_meta_variable_term term metas = match term with | NVar id -> (try Some (id, Id.List.assoc id metas) with Not_found -> None) | _ -> None let match_names_var (alp,sigma) na1 id2 typ = if is_pattern_meta ~strict:false ~binder:true ~isvar:true typ then bind_pattern_env alp sigma id2 [DAst.make (PatVar na1)] else raise No_match let match_names_non_var (alp,sigma) na1 na2 = match na1, na2 with | (na1,Name id2) -> {alp with staticbinders = (na1,id2)::alp.staticbinders},sigma | (Anonymous,Anonymous) -> alp,sigma | _ -> raise No_match let match_names metas acc na1 na2 = match is_meta_variable_name na2 metas with | Some (id2, typ) -> match_names_var acc na1 id2 typ | None -> match_names_non_var acc na1 na2 let isPatVar = function PatVar _ -> true | _ -> false let rec match_cases_pattern_binders allow_catchall metas (alp,sigma as acc) pat1 pat2 = let pat = DAst.get pat1 in let pat2 = DAst.get pat2 in match is_meta_variable_pat pat2 metas with | Some (id2, typ) -> if is_pattern_meta ~strict:(not (isPatVar pat)) ~binder:false ~isvar:(isPatVar pat) typ then bind_pattern_env alp sigma id2 [pat1] else if is_binders_meta typ then match pat with | PatVar id1 -> let t1 = DAst.make @@ GHole(GBinderType id1) in bind_binders_env alp sigma id2 [DAst.make @@ GLocalAssum (id1,None,Explicit,t1)] | _ -> (* dummy data; should not be used anyway *) let id1 = Namegen.next_ident_away (Id.of_string "x") Id.Set.empty in let t1 = DAst.make @@ GHole(GBinderType (Name id1)) in let ids1 = [] in bind_binders_env alp sigma id2 [DAst.make @@ GLocalPattern (([pat1],ids1),id1,Explicit,t1)] else raise No_match | None -> match pat, pat2 with | PatVar na1, PatVar na2 -> match_names_non_var acc na1 na2 | _, PatVar Anonymous when allow_catchall -> acc | PatCstr (c1,patl1,na1), PatCstr (c2,patl2,na2) when Construct.CanOrd.equal c1 c2 && Int.equal (List.length patl1) (List.length patl2) -> List.fold_left2 (match_cases_pattern_binders false metas) (match_names metas acc na1 na2) patl1 patl2 | _ -> raise No_match let dummy_subscopes = ((constr_some_level,[]),Id.Set.empty) let add_ldots_var metas = (ldots_var,NtnTypeVar (dummy_subscopes, NtnTypeVarConstr (* Dummy: *) NtnConstrForConstrAndPatternForPattern))::metas let add_meta_binders x metas = (x,NtnTypeVar ((*arbitrary:*) dummy_subscopes, NtnTypeVarBinders NtnBinderParsedAsBinder))::metas (* This tells if letins in the middle of binders should be included in the sequence of binders *) let glue_inner_letin_with_decls = true (* This tells if trailing letins (with no further proper binders) should be included in sequence of binders *) let glue_trailing_letin_with_decls = false exception OnlyTrailingLetIns let match_binderlist match_iter_fun match_termin_fun alp metas sigma rest x y iter termin revert = let rec aux trailing_letins alp sigma bl rest = try let metas = add_ldots_var (add_meta_binders y metas) in let sigma = match_iter_fun alp metas sigma rest iter in let _,newstaticbinders,rest = get_term (Id.Map.find ldots_var sigma) in let _, _, b = get_binders (Id.Map.find y sigma) in let b = match b with [b] -> b | _ -> assert false in let sigma = Id.Map.remove y (Id.Map.remove ldots_var sigma) in let alp' = {alp with staticbinders = newstaticbinders} in aux false alp' sigma (b::bl) rest with No_match -> match DAst.get rest with | GLetIn (na,r,c,t,rest') when glue_inner_letin_with_decls -> let b = DAst.make ?loc:rest.CAst.loc @@ GLocalDef (na,r,c,t) in (* collect let-in *) (try aux true alp sigma (b::bl) rest' with OnlyTrailingLetIns when not (trailing_letins && not glue_trailing_letin_with_decls) -> (* renounce to take into account trailing let-ins *) if not (List.is_empty bl) then alp, bl, rest, sigma else raise No_match) | _ -> if trailing_letins && not glue_trailing_letin_with_decls then (* Backtrack to when we tried to glue letins *) raise OnlyTrailingLetIns; if not (List.is_empty bl) then alp, bl, rest, sigma else raise No_match in let alp,bl,rest,sigma = aux false alp sigma [] rest in let bl = if revert then List.rev bl else bl in let alp,sigma = bind_binders_env alp sigma x bl in match_termin_fun alp metas sigma rest termin let add_meta_term x metas = (x,NtnTypeVar (dummy_subscopes, NtnTypeVarConstr NtnConstrForConstrAndPatternForPattern))::metas type match_flags = { print_parentheses : bool; factorize_eqns : PrintingFlags.Extern.FactorizeEqns.t; } let match_termlist flags match_fun alp metas sigma rest x y iter termin revert = let rec aux alp sigma acc rest = try let metas = add_ldots_var (add_meta_term y metas) in let sigma = match_fun alp metas sigma rest iter in let _,newstaticbinders,rest = get_term (Id.Map.find ldots_var sigma) in let vars,_,t = get_term (Id.Map.find y sigma) in let sigma = Id.Map.remove y (Id.Map.remove ldots_var sigma) in if flags.print_parentheses && not (List.is_empty acc) then raise No_match; (* The union is overkill at the current time because each term matches *) (* at worst the same binder metavariable of the same pattern *) let alp' = {actualvars = Id.Set.union vars alp.actualvars; staticbinders = newstaticbinders; renaming = alp.renaming} in aux alp' sigma (t::acc) rest with No_match when not (List.is_empty acc) -> alp, acc, match_fun alp metas sigma rest termin in let alp,l,sigma = aux alp sigma [] rest in let l = if revert then l else List.rev l in if is_binders_meta_var x metas then (* This is a recursive pattern for both bindings and terms; it is *) (* registered for binders *) bind_binders_as_termlist_env alp sigma x l else bind_termlist_env alp sigma x l let does_not_come_from_already_eta_expanded_var glob = (* This is hack to avoid looping on a rule with rhs of the form *) (* "?f (fun ?x => ?g)" since otherwise, matching "F H" expands in *) (* "F (fun x => H x)" and "H x" is recursively matched against the same *) (* rule, giving "H (fun x' => x x')" and so on. *) (* Ideally, we would need the type of the expression to know which of *) (* the arguments applied to it can be eta-expanded without looping. *) (* The following test is then an approximation of what can be done *) (* optimally (whether other looping situations can occur remains to be *) (* checked). *) match DAst.get glob with GVar _ -> false | _ -> true let eta_well_typed pat = (* A criterion for well-typedness of the eta-expansion is that the head of the pattern is rigid (see #15221) *) match pat with NVar _ -> false | _ -> true let is_var_term = function (* The kind of expressions allowed to be both a term and a binding variable *) | GVar _ -> true | GRef (GlobRef.VarRef _,None) -> true | _ -> false let rec match_ inner u alp metas sigma a1 a2 = let open CAst in let loc = a1.loc in let r1 = DAst.get a1 in (* Matching notation variable *) match is_meta_variable_term a2 metas with | Some (id2, typ) -> if is_term_meta typ then bind_term_env alp sigma id2 a1 else if is_pattern_meta ~strict:true ~binder:true ~isvar:(is_var_term r1) typ then bind_pattern_as_term_env alp sigma id2 a1 else if is_binders_meta typ then bind_singleton_binders_as_term_env alp sigma id2 a1 else raise No_match | None -> match r1, a2 with (* Matching recursive notations for terms *) | r1, NList (x,y,iter,termin,revert) -> match_termlist u (match_hd u) alp metas sigma a1 x y iter termin revert (* Matching recursive notations for binders: general case *) | _r, NBinderList (x,y,iter,termin,revert) -> (* When revert=true, binders are considered "inner" and thus not cumulative, as e.g. in Notation "!! x .. y # A #" := (.. (A,(forall x, True)) ..,(forall y, True)) (at level 200, x binder). This has an impact on the heuristic of preferring using "A -> B" where a recursive Prod binder on a anonymous would otherwise also be possible *) match_binderlist (match_ revert u) (match_hd u) alp metas sigma a1 x y iter termin revert (* Matching a static variable (not bound in the notation) *) | GVar id1, NVar id2 when alpha_var id1 id2 alp.staticbinders -> sigma (* Matching compositionally *) | GRef (r1,u1), NRef (r2,u2) when (GlobRef.CanOrd.equal r1 r2) && compare_glob_universe_instances_le u1 u2 -> sigma | GApp (f1,l1), NApp (f2,l2) -> let n1 = List.length l1 and n2 = List.length l2 in let f1,l1,f2,l2 = if n1 < n2 then let l21,l22 = List.chop (n2-n1) l2 in f1,l1, NApp (f2,l21), l22 else if n1 > n2 then let l11,l12 = List.chop (n1-n2) l1 in DAst.make ?loc @@ GApp (f1,l11),l12, f2,l2 else f1,l1, f2, l2 in let may_use_eta = does_not_come_from_already_eta_expanded_var f1 && eta_well_typed f2 in List.fold_left2 (match_ may_use_eta u alp metas) (match_hd u alp metas sigma f1 f2) l1 l2 | GProj ((cst1,u1),l1,a1), NProj ((cst2,u2),l2,a2) when GlobRef.CanOrd.equal (GlobRef.ConstRef cst1) (GlobRef.ConstRef cst2) && compare_glob_universe_instances_le u1 u2 -> match_in u alp metas (List.fold_left2 (match_in u alp metas) sigma l1 l2) a1 a2 | GApp (f1,l1), NProj ((cst2,u2),l2,a2) -> (match DAst.get f1 with | GRef (r1,u1) when GlobRef.CanOrd.equal r1 (GlobRef.ConstRef cst2) && compare_glob_universe_instances_le u1 u2 && List.length l1 = List.length l2 + 1 -> List.fold_left2 (match_in u alp metas) sigma l1 (l2@[a2]) | _ -> raise No_match) | GLambda (na1,_,bk1,t1,b1), NLambda (na2,t2,b2) -> match_extended_binders false u alp metas na1 na2 bk1 t1 (match_in_type u alp metas sigma t1 t2) b1 b2 | GProd (na1,_,bk1,t1,b1), NProd (na2,t2,b2) -> match_extended_binders (not inner) u alp metas na1 na2 bk1 t1 (match_in_type u alp metas sigma t1 t2) b1 b2 | GLetIn (na1,_,b1,t1,c1), NLetIn (na2,b2,None,c2) | GLetIn (na1,_,b1,(None as t1),c1), NLetIn (na2,b2,_,c2) -> let t = match t1 with Some t -> t | None -> DAst.make @@ GHole(GBinderType na1) in match_extended_binders false u alp metas na1 na2 Explicit t (match_in u alp metas sigma b1 b2) c1 c2 | GLetIn (na1,_,b1,Some t1,c1), NLetIn (na2,b2,Some t2,c2) -> match_extended_binders false u alp metas na1 na2 Explicit t1 (match_in u alp metas (match_in u alp metas sigma b1 b2) t1 t2) c1 c2 | GCases (sty1,rtno1,tml1,eqnl1), NCases (sty2,rtno2,tml2,eqnl2) when sty1 == sty2 && Int.equal (List.length tml1) (List.length tml2) -> let rtno1' = abstract_return_type_context_glob_constr tml1 rtno1 in let rtno2' = abstract_return_type_context_notation_constr tml2 rtno2 in let sigma = try Option.fold_left2 (match_in u alp metas) sigma rtno1' rtno2' with Option.Heterogeneous -> raise No_match in let sigma = List.fold_left2 (fun s (tm1,_) (tm2,_) -> match_in u alp metas s tm1 tm2) sigma tml1 tml2 in (* Try two different strategies for matching clauses *) (try List.fold_left2_set No_match (match_equations u alp metas) sigma eqnl1 eqnl2 with No_match -> List.fold_left2_set No_match (match_disjunctive_equations u alp metas) sigma (Detyping.factorize_eqns ~flags:u.factorize_eqns eqnl1) (List.map (fun (patl,rhs) -> ([patl],rhs)) eqnl2)) | GLetTuple (nal1,(na1,to1),b1,c1), NLetTuple (nal2,(na2,to2),b2,c2) when Int.equal (List.length nal1) (List.length nal2) -> let sigma = match_opt (match_binders u alp metas na1 na2) sigma to1 to2 in let sigma = match_in u alp metas sigma b1 b2 in let (alp,sigma) = List.fold_left2 (match_names metas) (alp,sigma) nal1 nal2 in match_in u alp metas sigma c1 c2 | GIf (a1,(na1,to1),b1,c1), NIf (a2,(na2,to2),b2,c2) -> let sigma = match_opt (match_binders u alp metas na1 na2) sigma to1 to2 in List.fold_left2 (match_in u alp metas) sigma [a1;b1;c1] [a2;b2;c2] | GRec (fk1,idl1,dll1,tl1,bl1), NRec (fk2,idl2,dll2,tl2,bl2) when match_fix_kind fk1 fk2 && Int.equal (Array.length idl1) (Array.length idl2) && Array.for_all2 (fun l1 l2 -> Int.equal (List.length l1) (List.length l2)) dll1 dll2 -> let alp,sigma = Array.fold_left2 (List.fold_left2 (fun (alp,sigma) (na1,_,_,oc1,b1) (na2,oc2,b2) -> let sigma = match_in u alp metas (match_opt (match_in u alp metas) sigma oc1 oc2) b1 b2 in match_names metas (alp,sigma) na1 na2)) (alp,sigma) dll1 dll2 in let sigma = Array.fold_left2 (match_in u alp metas) sigma tl1 tl2 in let alp,sigma = Array.fold_right2 (fun id1 id2 alsig -> match_names metas alsig (Name id1) (Name id2)) idl1 idl2 (alp,sigma) in Array.fold_left2 (match_in u alp metas) sigma bl1 bl2 | GCast(c1, k1, t1), NCast(c2, k2, t2) -> let sigma = match_in u alp metas sigma c1 c2 in if not (Option.equal cast_kind_eq k1 k2) then raise No_match; match_in u alp metas sigma t1 t2 (* [NSort (None, UAnonymous _)] from "Type" only matches anonymous glob sorts. This means it never matches the result of detyping a sort when Printing Universes is on. Is that really what we want? (Behaviour deliberately introduced in a38fbefca61f3392efe0ba98adfbae138022cce4 AFAICT) *) | GSort s1, NSort s2 when glob_sort_eq s1 s2 -> sigma | GInt i1, NInt i2 when Uint63.equal i1 i2 -> sigma | GFloat f1, NFloat f2 when Float64.equal f1 f2 -> sigma | GString s1, NString s2 when Pstring.equal s1 s2 -> sigma | GPatVar _, NHole _ -> (*Don't hide Metas, they bind in ltac*) raise No_match | a, NHole _ -> sigma (* On the fly eta-expansion so as to use notations of the form "exists x, P x" for "ex P"; ensure at least one constructor is consumed to avoid looping; expects type not given because don't know otherwise how to ensure it corresponds to a well-typed eta-expansion; we make an exception for types which are metavariables: this is useful e.g. to print "{x:_ & P x}" knowing that notation "{x & P x}" is not defined. *) | _b1, NLambda (Name id as na,(None | Some (NVar _) as t2),b2) when inner -> let avoid = Id.Set.union (free_glob_vars a1) (* as in Namegen: *) (glob_visible_short_qualid a1) in let id' = Namegen.next_ident_away id avoid in let t1 = DAst.make @@ GHole (GBinderType (Name id')) in let sigma = match t2 with | None -> sigma | Some (NVar id2) -> bind_term_env alp sigma id2 t1 | _ -> assert false in let (alp,sigma) = if is_binders_meta_var id metas then bind_binders_env alp sigma id [DAst.make @@ GLocalAssum (Name id',None,Explicit,t1)] else match_names metas (alp,sigma) (Name id') na in match_in u alp metas sigma (mkGApp a1 [DAst.make @@ GVar id']) b2 | GArray(_u,t,def,ty), NArray(nt,ndef,nty) -> if Int.equal (Array.length t) (Array.length nt) then let sigma = match_in u alp metas sigma def ndef in let sigma = match_in u alp metas sigma ty nty in Array.fold_left2 (match_in u alp metas) sigma t nt else raise No_match | (GRef _ | GVar _ | GEvar _ | GPatVar _ | GApp _ | GProj _ | GLambda _ | GProd _ | GLetIn _ | GCases _ | GLetTuple _ | GIf _ | GRec _ | GSort _ | GHole _ | GGenarg _ | GCast _ | GInt _ | GFloat _ | GString _ | GArray _), _ -> raise No_match and match_in_type u alp metas sigma t = function | None -> sigma | Some t' -> match_in u alp metas sigma t t' and match_in u = match_ true u and match_hd u = match_ false u and match_binders u alp metas na1 na2 sigma b1 b2 = (* Match binders which cannot be substituted by a pattern *) let (alp,sigma) = match_names metas (alp,sigma) na1 na2 in match_in u alp metas sigma b1 b2 and match_extended_binders ?loc isprod u alp metas na1 na2 bk t sigma b1 b2 = (* Match binders which can be substituted by a pattern: *) (* that is, try to extract a pattern part in b2 that can be bound to na2 *) match is_meta_variable_name na2 metas with | Some (id2, typ) -> (let store, get = set_temporary_memory () in (* Matching individual binders as part of a recursive pattern *) match na1, DAst.get b1 with | Name p, GCases (Constr.LetPatternStyle,None,[(e,_)],(_::_ as eqns)) when is_gvar p e && (is_binders_meta typ || is_pattern_meta ~strict:true ~binder:true ~isvar:false typ) && List.length (store (Detyping.factorize_eqns ~flags:u.factorize_eqns eqns)) = 1 -> (match get () with | [{CAst.v=(ids,disj_of_patl,b1)}] -> let disjpat = List.map (function [pat] -> pat | _ -> assert false) disj_of_patl in let disjpat = if occur_glob_constr p b1 then List.map (set_pat_alias p) disjpat else disjpat in let alp,sigma = if is_binders_meta typ then bind_binders_env alp sigma id2 [DAst.make ?loc @@ GLocalPattern ((disjpat,ids),p,bk,t)] else (* bk, t? *) bind_pattern_env alp sigma id2 disjpat in match_in u alp metas sigma b1 b2 | _ -> assert false) | _ -> if is_binders_meta typ then begin if (isprod && na1 = Anonymous) then raise No_match (* prefer using "A -> B" for anonymous forall *); let alp,sigma = bind_binders_env alp sigma id2 [DAst.make ?loc @@ GLocalAssum (na1,None,bk,t)] in match_in u alp metas sigma b1 b2 end else let (alp,sigma) = match_names_var (alp,sigma) na1 id2 typ in match_in u alp metas sigma b1 b2) | None -> match_binders u alp metas na1 na2 sigma b1 b2 and match_equations u alp metas sigma {CAst.v=(ids,patl1,rhs1)} (patl2,rhs2) rest1 rest2 = (* patl1 and patl2 have the same length because they respectively correspond to some tml1 and tml2 that have the same length *) let allow_catchall = (rest2 = [] && ids = []) in let (alp,sigma) = List.fold_left2 (match_cases_pattern_binders allow_catchall metas) (alp,sigma) patl1 patl2 in match_in u alp metas sigma rhs1 rhs2 and match_disjunctive_equations u alp metas sigma {CAst.v=(ids,disjpatl1,rhs1)} (disjpatl2,rhs2) _ _ = (* patl1 and patl2 have the same length because they respectively correspond to some tml1 and tml2 that have the same length *) let (alp,sigma) = List.fold_left2_set No_match (fun alp_sigma patl1 patl2 _ _ -> List.fold_left2 (match_cases_pattern_binders false metas) alp_sigma patl1 patl2) (alp,sigma) disjpatl1 disjpatl2 in match_in u alp metas sigma rhs1 rhs2 type 'a with_vars = Id.Set.t * (Name.t * Id.t) list * 'a type 'a glob_constr_notation_substitution = ('a glob_constr_g with_vars, 'a cases_pattern_disjunction_g with_vars, 'a extended_glob_local_binder_g list with_vars) notation_arg_type Id.Map.t let match_notation_constr ~print_parentheses ~factorize_eqns c ~vars (metas,pat) = let flags = { print_parentheses; factorize_eqns } in match_ false flags {actualvars=vars;staticbinders=[];renaming=[]} metas Id.Map.empty c pat (* Matching cases pattern *) let bind_env_cases_pattern sigma var v = try let vvar = Id.Map.find var sigma in let vvar = get_pattern vvar in if cases_pattern_eq v vvar then sigma else raise No_match with Not_found -> (* TODO: handle the case of multiple occs in different scopes *) Id.Map.add var (Constrexpr.NtnTypeArg (NtnTypeArgPattern v)) sigma let match_cases_pattern_list match_fun metas sigma rest x y iter termin revert = let rec aux sigma acc rest = try let metas = add_ldots_var (add_meta_term y metas) in let sigma = match_fun metas sigma rest iter in let rest = get_pattern (Id.Map.find ldots_var sigma) in let t = get_pattern (Id.Map.find y sigma) in let sigma = Id.Map.remove y (Id.Map.remove ldots_var sigma) in aux sigma (t::acc) rest with No_match when not (List.is_empty acc) -> acc, match_fun metas sigma rest termin in let l,sigma = aux sigma [] rest in let l = List.map (fun c -> NtnTypeArg (NtnTypeArgPattern c)) (if revert then l else List.rev l) in Id.Map.add x (NtnTypeArgList l) sigma let rec match_cases_pattern metas sigma a1 a2 = match DAst.get a1, a2 with | r1, NVar id2 when Id.List.mem_assoc id2 metas -> (bind_env_cases_pattern sigma id2 a1),(false,0,[]) | PatVar Anonymous, NHole _ -> sigma,(false,0,[]) | PatCstr ((ind,_ as r1),largs,Anonymous), NRef (GlobRef.ConstructRef r2,None) when Construct.CanOrd.equal r1 r2 -> let l = try add_patterns_for_params_remove_local_defs (Global.env ()) r1 largs with Not_found -> raise No_match in sigma,(false,0,l) | PatCstr ((ind,_ as r1),args1,Anonymous), NApp (NRef (GlobRef.ConstructRef r2,None),l2) when Construct.CanOrd.equal r1 r2 -> let l1 = try add_patterns_for_params_remove_local_defs (Global.env()) r1 args1 with Not_found -> raise No_match in let le2 = List.length l2 in if le2 > List.length l1 then raise No_match else let l1',more_args = Util.List.chop le2 l1 in (* Convention: notations to @f don't keep implicit arguments *) let no_implicit = le2 = 0 in (List.fold_left2 (match_cases_pattern_no_more_args metas) sigma l1' l2),(no_implicit,le2,more_args) | r1, NList (x,y,iter,termin,revert) -> (match_cases_pattern_list (match_cases_pattern_no_more_args) metas sigma a1 x y iter termin revert),(false,0,[]) | _ -> raise No_match and match_cases_pattern_no_more_args metas sigma a1 a2 = match match_cases_pattern metas sigma a1 a2 with | out,(_,_,[]) -> out | _ -> raise No_match let match_ind_pattern metas sigma ind pats a2 = match a2 with | NRef (GlobRef.IndRef r2,None) when Ind.CanOrd.equal ind r2 -> sigma,(false,0,pats) | NApp (NRef (GlobRef.IndRef r2,None),l2) when Ind.CanOrd.equal ind r2 -> let le2 = List.length l2 in if Int.equal le2 0 (* Special case of a notation for a @Cstr *) || le2 > List.length pats then raise No_match else let l1',more_args = Util.List.chop le2 pats in let no_implicit = le2 = 0 in (List.fold_left2 (match_cases_pattern_no_more_args metas) sigma l1' l2),(no_implicit,le2,more_args) |_ -> raise No_match type 'a glob_cases_pattern_notation_substitution = ('a glob_constr_g, 'a cases_pattern_g, unit) notation_arg_type Id.Map.t let match_notation_constr_cases_pattern c (metas,pat) = (match_cases_pattern metas Id.Map.empty c pat) let match_notation_constr_ind_pattern ind args (metas,pat) = match_ind_pattern metas Id.Map.empty ind args pat