(************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) (* eq_gr r1 r2 | GVar (_,v1), GVar (_,v2) -> on_true_do (Id.equal v1 v2) add (Name v1) | GApp (_,f1,l1), GApp (_,f2,l2) -> f f1 f2 && List.for_all2eq f l1 l2 | GLambda (_,na1,bk1,ty1,c1), GLambda (_,na2,bk2,ty2,c2) when Name.equal na1 na2 && Constrexpr_ops.binding_kind_eq bk1 bk2 -> on_true_do (f ty1 ty2 && f c1 c2) add na1 | GProd (_,na1,bk1,ty1,c1), GProd (_,na2,bk2,ty2,c2) when Name.equal na1 na2 && Constrexpr_ops.binding_kind_eq bk1 bk2 -> on_true_do (f ty1 ty2 && f c1 c2) add na1 | GHole _, GHole _ -> true | GSort (_,s1), GSort (_,s2) -> Miscops.glob_sort_eq s1 s2 | GLetIn (_,na1,b1,c1), GLetIn (_,na2,b2,c2) when Name.equal na1 na2 -> on_true_do (f b1 b2 && f c1 c2) add na1 | (GCases _ | GRec _ | GPatVar _ | GEvar _ | GLetTuple _ | GIf _ | GCast _),_ | _,(GCases _ | GRec _ | GPatVar _ | GEvar _ | GLetTuple _ | GIf _ | GCast _) -> error "Unsupported construction in recursive notations." | (GRef _ | GVar _ | GApp _ | GLambda _ | GProd _ | GHole _ | GSort _ | GLetIn _), _ -> false let rec eq_notation_constr (vars1,vars2 as vars) t1 t2 = match t1, t2 with | NRef gr1, NRef gr2 -> eq_gr gr1 gr2 | NVar id1, NVar id2 -> Int.equal (List.index Id.equal id1 vars1) (List.index Id.equal id2 vars2) | NApp (t1, a1), NApp (t2, a2) -> (eq_notation_constr vars) t1 t2 && List.equal (eq_notation_constr vars) a1 a2 | NHole (_, _, _), NHole (_, _, _) -> true (** FIXME? *) | NList (i1, j1, t1, u1, b1), NList (i2, j2, t2, u2, b2) -> Id.equal i1 i2 && Id.equal j1 j2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 && b1 == b2 | NLambda (na1, t1, u1), NLambda (na2, t2, u2) -> Name.equal na1 na2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 | NProd (na1, t1, u1), NProd (na2, t2, u2) -> Name.equal na1 na2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 | NBinderList (i1, j1, t1, u1), NBinderList (i2, j2, t2, u2) -> Id.equal i1 i2 && Id.equal j1 j2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 | NLetIn (na1, t1, u1), NLetIn (na2, t2, u2) -> Name.equal na1 na2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 | NCases (_, o1, r1, p1), NCases (_, o2, r2, p2) -> (** FIXME? *) let eqpat (p1, t1) (p2, t2) = List.equal cases_pattern_eq p1 p2 && (eq_notation_constr vars) t1 t2 in let eqf (t1, (na1, o1)) (t2, (na2, o2)) = let eq (i1, n1) (i2, n2) = eq_ind i1 i2 && List.equal Name.equal n1 n2 in (eq_notation_constr vars) t1 t2 && Name.equal na1 na2 && Option.equal eq o1 o2 in Option.equal (eq_notation_constr vars) o1 o2 && List.equal eqf r1 r2 && List.equal eqpat p1 p2 | NLetTuple (nas1, (na1, o1), t1, u1), NLetTuple (nas2, (na2, o2), t2, u2) -> List.equal Name.equal nas1 nas2 && Name.equal na1 na2 && Option.equal (eq_notation_constr vars) o1 o2 && (eq_notation_constr vars) t1 t2 && (eq_notation_constr vars) u1 u2 | NIf (t1, (na1, o1), u1, r1), NIf (t2, (na2, o2), u2, r2) -> (eq_notation_constr vars) t1 t2 && Name.equal na1 na2 && Option.equal (eq_notation_constr vars) o1 o2 && (eq_notation_constr vars) u1 u2 && (eq_notation_constr vars) r1 r2 | NRec (_, ids1, ts1, us1, rs1), NRec (_, ids2, ts2, us2, rs2) -> (** FIXME? *) let eq (na1, o1, t1) (na2, o2, t2) = Name.equal na1 na2 && Option.equal (eq_notation_constr vars) o1 o2 && (eq_notation_constr vars) t1 t2 in Array.equal Id.equal ids1 ids2 && Array.equal (List.equal eq) ts1 ts2 && Array.equal (eq_notation_constr vars) us1 us2 && Array.equal (eq_notation_constr vars) rs1 rs2 | NSort s1, NSort s2 -> Miscops.glob_sort_eq s1 s2 | NCast (t1, c1), NCast (t2, c2) -> (eq_notation_constr vars) t1 t2 && cast_type_eq (eq_notation_constr vars) c1 c2 | (NRef _ | NVar _ | NApp _ | NHole _ | NList _ | NLambda _ | NProd _ | NBinderList _ | NLetIn _ | NCases _ | NLetTuple _ | NIf _ | NRec _ | NSort _ | NCast _), _ -> false (**********************************************************************) (* Re-interpret a notation as a glob_constr, taking care of binders *) let name_to_ident = function | Anonymous -> CErrors.error "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 rec cases_pattern_fold_map loc g e = function | PatVar (_,na) -> let e',na' = g e na in e', PatVar (loc,na') | PatCstr (_,cstr,patl,na) -> let e',na' = g e na in let e',patl' = List.fold_map (cases_pattern_fold_map loc g) e patl in e', PatCstr (loc,cstr,patl',na') let subst_binder_type_vars l = function | Evar_kinds.BinderType (Name id) -> let id = try match Id.List.assoc id l with GVar(_,id') -> id' | _ -> id with Not_found -> id in Evar_kinds.BinderType (Name id) | e -> e let rec subst_glob_vars l = function | GVar (_,id) as r -> (try Id.List.assoc id l with Not_found -> r) | GProd (loc,Name id,bk,t,c) -> let id = try match Id.List.assoc id l with GVar(_,id') -> id' | _ -> id with Not_found -> id in GProd (loc,Name id,bk,subst_glob_vars l t,subst_glob_vars l c) | GLambda (loc,Name id,bk,t,c) -> let id = try match Id.List.assoc id l with GVar(_,id') -> id' | _ -> id with Not_found -> id in GLambda (loc,Name id,bk,subst_glob_vars l t,subst_glob_vars l c) | GHole (loc,x,naming,arg) -> GHole (loc,subst_binder_type_vars l x,naming,arg) | r -> map_glob_constr (subst_glob_vars l) r (* assume: id is not binding *) let ldots_var = Id.of_string ".." let glob_constr_of_notation_constr_with_binders loc g f e = function | NVar id -> GVar (loc,id) | NApp (a,args) -> GApp (loc,f e a, List.map (f e) args) | 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 [] else [x,GVar(loc,y)]) in let inner = GApp (loc,GVar (loc,ldots_var),[subst_glob_vars innerl it]) in let outerl = (ldots_var,inner)::(if swap then [x,GVar(loc,y)] else []) in subst_glob_vars outerl it | NBinderList (x,y,iter,tail) -> let t = f e tail in let it = f e iter in let innerl = [(ldots_var,t);(x,GVar(loc,y))] in let inner = GApp (loc,GVar (loc,ldots_var),[subst_glob_vars innerl it]) in let outerl = [(ldots_var,inner)] in subst_glob_vars outerl it | NLambda (na,ty,c) -> let e',na = g e na in GLambda (loc,na,Explicit,f e ty,f e' c) | NProd (na,ty,c) -> let e',na = g e na in GProd (loc,na,Explicit,f e ty,f e' c) | NLetIn (na,b,c) -> let e',na = g e na in GLetIn (loc,na,f e b,f e' c) | NCases (sty,rtntypopt,tml,eqnl) -> 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' = g e' na in e',na'::nal) nal (e',[]) in e',Some (loc,ind,nal') in let e',na' = g e' na in (e',(f e tm,(na',t'))::tml')) tml (e,[]) in let fold (idl,e) na = let (e,na) = g e na in ((name_cons na idl,e),na) in let eqnl' = List.map (fun (patl,rhs) -> let ((idl,e),patl) = List.fold_map (cases_pattern_fold_map loc fold) ([],e) patl in (loc,idl,patl,f e rhs)) eqnl in GCases (loc,sty,Option.map (f e') rtntypopt,tml',eqnl') | NLetTuple (nal,(na,po),b,c) -> let e',nal = List.fold_map g e nal in let e'',na = g e na in GLetTuple (loc,nal,(na,Option.map (f e'') po),f e b,f e' c) | NIf (c,(na,po),b1,b2) -> let e',na = g e na in GIf (loc,f e c,(na,Option.map (f e') po),f e b1,f e b2) | NRec (fk,idl,dll,tl,bl) -> let e,dll = Array.fold_map (List.fold_map (fun e (na,oc,b) -> let e,na = g e na in (e,(na,Explicit,Option.map (f e) oc,f e b)))) e dll in let e',idl = Array.fold_map (to_id g) e idl in GRec (loc,fk,idl,dll,Array.map (f e) tl,Array.map (f e') bl) | NCast (c,k) -> GCast (loc,f e c,Miscops.map_cast_type (f e) k) | NSort x -> GSort (loc,x) | NHole (x, naming, arg) -> GHole (loc, x, naming, arg) | NRef x -> GRef (loc,x,None) let glob_constr_of_notation_constr loc x = let rec aux () x = glob_constr_of_notation_constr_with_binders loc (fun () id -> ((),id)) aux () x in aux () x (******************************************************************************) (* Translating a glob_constr into a notation, interpreting recursive patterns *) let add_id r id = r := (id :: pi1 !r, pi2 !r, pi3 !r) let add_name r = function Anonymous -> () | Name id -> add_id r id let split_at_recursive_part c = let sub = ref None in let rec aux = function | GApp (loc0,GVar(loc,v),c::l) when Id.equal v ldots_var -> begin match !sub with | None -> let () = sub := Some c in begin match l with | [] -> GVar (loc, ldots_var) | _ :: _ -> GApp (loc0, GVar (loc, ldots_var), l) end | Some _ -> (* Not narrowed enough to find only one recursive part *) raise Not_found end | c -> 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 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 = Loc.make_loc (fst (Loc.unloc loc1),fst (Loc.unloc loc2)-1) let check_is_hole id = function GHole _ -> () | t -> user_err_loc (loc_of_glob_constr t,"", strbrk "In recursive notation with binders, " ++ pr_id id ++ strbrk " is expected to come without type.") let pair_equal eq1 eq2 (a,b) (a',b') = eq1 a a' && eq2 b b' type recursive_pattern_kind = | RecursiveTerms of bool (* associativity *) | RecursiveBinders of glob_constr * glob_constr let compare_recursive_parts found f f' (iterator,subc) = let diff = ref None in let terminator = ref None in let rec aux c1 c2 = match c1,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 term; true | GApp (_,GVar(_,v),l1), GApp (_,term,l2) 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 | GVar (_,x), GVar (_,y) when not (Id.equal x y) -> (* We found the position where it differs *) let lassoc = match !terminator with None -> false | Some _ -> true in let x,y = if lassoc then y,x else x,y in begin match !diff with | None -> let () = diff := Some (x, y, RecursiveTerms lassoc) in true | Some _ -> false end | GLambda (_,Name x,_,t_x,c), GLambda (_,Name y,_,t_y,term) | GProd (_,Name x,_,t_x,c), GProd (_,Name y,_,t_y,term) -> (* We found a binding position where it differs *) begin match !diff with | None -> let () = diff := Some (x, y, RecursiveBinders (t_x,t_y)) in aux c term | Some _ -> false end | _ -> compare_glob_constr aux (add_name found) 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 lassoc) -> let newfound,x,y,lassoc = if List.mem_f (pair_equal Id.equal Id.equal) (x,y) (pi2 !found) || List.mem_f (pair_equal Id.equal Id.equal) (x,y) (pi3 !found) then !found,x,y,lassoc else if List.mem_f (pair_equal Id.equal Id.equal) (y,x) (pi2 !found) || List.mem_f (pair_equal Id.equal Id.equal) (y,x) (pi3 !found) then !found,y,x,not lassoc else (pi1 !found, (x,y) :: pi2 !found, pi3 !found),x,y,lassoc in let iterator = f' (if lassoc then iterator else subst_glob_vars [x,GVar(Loc.ghost,y)] iterator) in (* found have been collected by compare_constr *) found := newfound; NList (x,y,iterator,f (Option.get !terminator),lassoc) | Some (x,y,RecursiveBinders (t_x,t_y)) -> let newfound = (pi1 !found, pi2 !found, (x,y) :: pi3 !found) in let iterator = f' (subst_glob_vars [x,GVar(Loc.ghost,y)] iterator) in (* found have been collected by compare_constr *) found := newfound; check_is_hole x t_x; check_is_hole y t_y; NBinderList (x,y,iterator,f (Option.get !terminator)) else raise Not_found let notation_constr_and_vars_of_glob_constr a = let found = ref ([],[],[]) in let has_ltac = ref false in let rec aux c = let keepfound = !found in (* n^2 complexity but small and done only once per notation *) try compare_recursive_parts found aux aux' (split_at_recursive_part c) with Not_found -> found := keepfound; match c with | GApp (_,GVar (loc,f),[c]) when Id.equal f ldots_var -> (* Fall on the second part of the recursive pattern w/o having found the first part *) user_err_loc (loc,"", str "Cannot find where the recursive pattern starts.") | c -> aux' c and aux' = function | GVar (_,id) -> add_id found id; NVar id | GApp (_,g,args) -> NApp (aux g, List.map aux args) | GLambda (_,na,bk,ty,c) -> add_name found na; NLambda (na,aux ty,aux c) | GProd (_,na,bk,ty,c) -> add_name found na; NProd (na,aux ty,aux c) | GLetIn (_,na,b,c) -> add_name found na; NLetIn (na,aux b,aux c) | GCases (_,sty,rtntypopt,tml,eqnl) -> let f (_,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 (_,_,nl) -> List.iter (add_name found) nl) x; (aux tm,(na,Option.map (fun (_,ind,nal) -> (ind,nal)) x))) tml, List.map f eqnl) | GLetTuple (loc,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 (loc,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 error "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) -> NCast (aux c,Miscops.map_cast_type aux k) | GSort (_,s) -> NSort s | GHole (_,w,naming,arg) -> if arg != None then has_ltac := true; NHole (w, naming, arg) | GRef (_,r,_) -> NRef r | GEvar _ | GPatVar _ -> error "Existential variables not allowed in notations." in let t = aux a in (* Side effect *) t, !found, !has_ltac let check_variables_and_reversibility nenv (found,foundrec,foundrecbinding) = let injective = ref true in let recvars = nenv.ninterp_rec_vars in let fold _ y accu = Id.Set.add y accu in let useless_vars = Id.Map.fold 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 errorlabstrm "" (pr_id 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 error (Id.to_string x ^ " should not be bound in a recursive pattern of the right-hand side.") else injective := false in let check_pair s x y where = if not (List.mem_f (pair_equal Id.equal Id.equal) (x,y) where) then errorlabstrm "" (strbrk "in the right-hand side, " ++ pr_id x ++ str " and " ++ pr_id y ++ strbrk " should appear in " ++ str s ++ str " position as part of a recursive pattern.") in let check_type x typ = match typ with | NtnInternTypeConstr -> begin try check_pair "term" x (Id.Map.find x recvars) foundrec with Not_found -> check_bound x end | NtnInternTypeBinder -> begin try check_pair "binding" x (Id.Map.find x recvars) foundrecbinding with Not_found -> check_bound x end | NtnInternTypeIdent -> check_bound x in Id.Map.iter check_type vars; !injective let notation_constr_of_glob_constr nenv a = let a, found, has_ltac = notation_constr_and_vars_of_glob_constr a in let injective = check_variables_and_reversibility nenv found in a, not has_ltac && injective (**********************************************************************) (* Substitution of kernel names, avoiding a list of bound identifiers *) let notation_constr_of_constr avoiding t = let t = Detyping.detype false avoiding (Global.env()) Evd.empty t in let nenv = { ninterp_var_type = Id.Map.empty; ninterp_rec_vars = Id.Map.empty; } in notation_constr_of_glob_constr nenv t let rec subst_pat subst pat = match pat with | PatVar _ -> pat | PatCstr (loc,((kn,i),j),cpl,n) -> let kn' = subst_mind subst kn and cpl' = List.smartmap (subst_pat subst) cpl in if kn' == kn && cpl' == cpl then pat else PatCstr (loc,((kn',i),j),cpl',n) let rec subst_notation_constr subst bound raw = match raw with | NRef ref -> let ref',t = subst_global subst ref in if ref' == ref then raw else fst (notation_constr_of_constr bound t) | NVar _ -> raw | NApp (r,rl) -> let r' = subst_notation_constr subst bound r and rl' = List.smartmap (subst_notation_constr subst bound) rl in if r' == r && rl' == rl then raw else NApp(r',rl') | 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' = 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' = 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) -> 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') | NLetIn (n,r1,r2) -> 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 NLetIn (n,r1',r2') | NCases (sty,rtntypopt,rl,branches) -> let rtntypopt' = Option.smartmap (subst_notation_constr subst bound) rtntypopt and rl' = List.smartmap (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.smartmap (fun (cpl,r as branch) -> let cpl' = List.smartmap (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.smartmap (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.smartmap (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.smartmap (List.smartmap (fun (na,oc,b as x) -> let oc' = Option.smartmap (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.smartmap (subst_notation_constr subst bound) tl in let bl' = Array.smartmap (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 | NHole (knd, naming, solve) -> let nknd = match knd with | Evar_kinds.ImplicitArg (ref, i, b) -> let nref, _ = subst_global subst ref in if nref == ref then knd else Evar_kinds.ImplicitArg (nref, i, b) | _ -> knd in let nsolve = Option.smartmap (Genintern.generic_substitute subst) solve in if nsolve == solve && nknd == knd then raw else NHole (nknd, naming, nsolve) | NCast (r1,k) -> let r1' = subst_notation_constr subst bound r1 in let k' = Miscops.smartmap_cast_type (subst_notation_constr subst bound) k in if r1' == r1 && k' == k then raw else NCast(r1',k') let subst_interpretation subst (metas,pat) = let bound = List.map fst metas in (metas,subst_notation_constr subst 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 = abstract_return_type_context (fun (_,_,nal) -> nal) (fun na c -> GLambda(Loc.ghost,na,Explicit,GHole(Loc.ghost,Evar_kinds.InternalHole,Misctypes.IntroAnonymous,None),c)) let abstract_return_type_context_notation_constr = abstract_return_type_context snd (fun na c -> NLambda(na,NHole (Evar_kinds.InternalHole, Misctypes.IntroAnonymous, None),c)) let is_term_meta id metas = try match Id.List.assoc id metas with _,(NtnTypeConstr | NtnTypeConstrList) -> true | _ -> false with Not_found -> false let is_onlybinding_meta id metas = try match Id.List.assoc id metas with _,NtnTypeOnlyBinder -> true | _ -> false with Not_found -> false let is_bindinglist_meta id metas = try match Id.List.assoc id metas with _,NtnTypeBinderList -> true | _ -> false with Not_found -> false exception No_match let rec alpha_var id1 id2 = function | (i1,i2)::_ when Id.equal i1 id1 -> Id.equal i2 id2 | (i1,i2)::_ when Id.equal i2 id2 -> Id.equal i1 id1 | _::idl -> alpha_var id1 id2 idl | [] -> Id.equal id1 id2 let alpha_rename alpmetas v = if alpmetas == [] then v else try rename_glob_vars alpmetas v with UnsoundRenaming -> raise No_match let add_env (alp,alpmetas) (terms,onlybinders,termlists,binderlists) var v = (* Check that no capture of binding variables occur *) (* [alp] 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 alp, 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) && List.exists (fun (id,_) -> occur_glob_constr id v) alp then raise No_match; (* [alpmetas] 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 alpmetas, 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 alpmetas v in (* TODO: handle the case of multiple occs in different scopes *) ((var,v)::terms,onlybinders,termlists,binderlists) let add_termlist_env (alp,alpmetas) (terms,onlybinders,termlists,binderlists) var vl = if List.exists (fun (id,_) -> List.exists (occur_glob_constr id) vl) alp then raise No_match; let vl = List.map (alpha_rename alpmetas) vl in (terms,onlybinders,(var,vl)::termlists,binderlists) let add_binding_env alp (terms,onlybinders,termlists,binderlists) var v = (* TODO: handle the case of multiple occs in different scopes *) (terms,(var,v)::onlybinders,termlists,binderlists) let add_bindinglist_env (terms,onlybinders,termlists,binderlists) x bl = (terms,onlybinders,termlists,(x,bl)::binderlists) let rec pat_binder_of_term = function | GVar (loc, id) -> PatVar (loc, Name id) | GApp (loc, GRef (_,ConstructRef cstr,_), l) -> let nparams = Inductiveops.inductive_nparams (fst cstr) in let _,l = List.chop nparams l in PatCstr (loc, cstr, List.map pat_binder_of_term l, Anonymous) | _ -> raise No_match let bind_term_env alp (terms,onlybinders,termlists,binderlists as sigma) var v = try let v' = Id.List.assoc var terms in match v, v' with | GHole _, _ -> sigma | _, GHole _ -> let sigma = Id.List.remove_assoc var terms,onlybinders,termlists,binderlists in add_env alp sigma var v | _, _ -> if glob_constr_eq (alpha_rename (snd alp) v) v' then sigma else raise No_match with Not_found -> add_env alp sigma var v let bind_termlist_env alp (terms,onlybinders,termlists,binderlists as sigma) var vl = try let vl' = Id.List.assoc var termlists in let unify_term v v' = match v, v' with | GHole _, _ -> v' | _, GHole _ -> v | _, _ -> if glob_constr_eq (alpha_rename (snd alp) v) v' then v' else raise No_match in let rec unify vl vl' = match vl, vl' with | [], [] -> [] | v :: vl, v' :: vl' -> unify_term v v' :: unify vl vl' | _ -> raise No_match in let vl = unify vl vl' in let sigma = (terms,onlybinders,Id.List.remove_assoc var termlists,binderlists) in add_termlist_env alp sigma var vl with Not_found -> add_termlist_env alp sigma var vl let bind_term_as_binding_env alp (terms,onlybinders,termlists,binderlists as sigma) var id = try match Id.List.assoc var terms with | GVar (_,id') -> (if not (Id.equal id id') then (fst alp,(id,id')::snd alp) else alp), sigma | _ -> anomaly (str "A term which can be a binder has to be a variable") with Not_found -> (* The matching against a term allowing to find the instance has not been found yet *) (* If it will be a different name, we shall unfortunately fail *) (* TODO: look at the consequences for alp *) alp, add_env alp sigma var (GVar (Loc.ghost,id)) let bind_binding_as_term_env alp (terms,onlybinders,termlists,binderlists as sigma) var id = try let v' = Id.List.assoc var onlybinders in match v' with | Anonymous -> (* Should not occur, since the term has to be bound upwards *) let sigma = (terms,Id.List.remove_assoc var onlybinders,termlists,binderlists) in add_binding_env alp sigma var (Name id) | Name id' -> if Id.equal (rename_var (snd alp) id) id' then sigma else raise No_match with Not_found -> add_binding_env alp sigma var (Name id) let bind_binding_env alp (terms,onlybinders,termlists,binderlists as sigma) var v = try let v' = Id.List.assoc var onlybinders in match v, v' with | Anonymous, _ -> alp, sigma | _, Anonymous -> let sigma = (terms,Id.List.remove_assoc var onlybinders,termlists,binderlists) in alp, add_binding_env alp sigma var v | Name id1, Name id2 -> if Id.equal id1 id2 then alp,sigma else (fst alp,(id1,id2)::snd alp),sigma with Not_found -> alp, add_binding_env alp sigma var v let rec map_cases_pattern_name_left f = function | PatVar (loc,na) -> PatVar (loc,f na) | PatCstr (loc,c,l,na) -> PatCstr (loc,c,List.map_left (map_cases_pattern_name_left f) l,f na) let rec fold_cases_pattern_eq f x p p' = match p, p' with | PatVar (loc,na), PatVar (_,na') -> let x,na = f x na na' in x, PatVar (loc,na) | PatCstr (loc,c,l,na), PatCstr (_,c',l',na') when eq_constructor c c' -> let x,l = fold_cases_pattern_list_eq f x l l' in let x,na = f x na na' in x, PatCstr (loc,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 p1, p2 with | PatVar (_, na1), PatVar (_, na2) -> Name.equal na1 na2 | PatCstr (_, c1, pl1, na1), PatCstr (_, c2, pl2, na2) -> eq_constructor c1 c2 && List.equal cases_pattern_eq pl1 pl2 && Name.equal na1 na2 | _ -> false let bind_bindinglist_env alp (terms,onlybinders,termlists,binderlists as sigma) var bl = let bl = List.rev bl in try let bl' = Id.List.assoc var binderlists in let unify_name alp na na' = match na, na' with | Anonymous, na' -> alp, na' | na, Anonymous -> alp, na | Name id, Name id' -> if Id.equal id id' then alp, na' else (fst alp,(id,id')::snd alp), na' in let unify_pat alp p p' = try fold_cases_pattern_eq unify_name alp p p' with Failure _ -> raise No_match in let unify_term alp v v' = match v, v' with | GHole _, _ -> v' | _, GHole _ -> v | _, _ -> if glob_constr_eq (alpha_rename (snd alp) v) v' then v else raise No_match in let unify_binding_kind bk bk' = if bk == bk' then bk' else raise No_match in let unify_binder alp b b' = match b, b' with | (Inl na, bk, None, t), (Inl na', bk', None, t') (* assum *) -> let alp, na = unify_name alp na na' in alp, (Inl na, unify_binding_kind bk bk', None, unify_term alp t t') | (Inl na, bk, Some c, t), (Inl na', bk', Some c', t') (* let *) -> let alp, na = unify_name alp na na' in alp, (Inl na, unify_binding_kind bk bk', Some (unify_term alp c c'), unify_term alp t t') | (Inr p, bk, None, t), (Inr p', bk', None, t') (* pattern *) -> let alp, p = unify_pat alp p p' in alp, (Inr p, unify_binding_kind bk bk', None, unify_term alp t t') | _ -> raise No_match in let rec unify alp bl bl' = match bl, bl' with | [], [] -> alp, [] | b :: bl, b' :: bl' -> let alp,b = unify_binder alp b b' in let alp,bl = unify alp bl bl' in alp, b :: bl | _ -> raise No_match in let alp, bl = unify alp bl bl' in let sigma = (terms,Id.List.remove_assoc var onlybinders,termlists,binderlists) in alp, add_bindinglist_env sigma var bl with Not_found -> alp, add_bindinglist_env sigma var bl let bind_bindinglist_as_term_env alp (terms,onlybinders,termlists,binderlists) var cl = try let bl' = Id.List.assoc var binderlists in let unify_id id na' = match na' with | Anonymous -> Name (rename_var (snd alp) id) | Name id' -> if Id.equal (rename_var (snd alp) id) id' then na' else raise No_match in let unify_pat p p' = if cases_pattern_eq (map_cases_pattern_name_left (name_app (rename_var (snd alp))) p) p' then p' else raise No_match in let unify_term_binder c b' = match c, b' with | GVar (_, id), (Inl na', bk', None, t') (* assum *) -> (Inl (unify_id id na'), bk', None, t') | c, (Inr p', bk', None, t') (* pattern *) -> let p = pat_binder_of_term c in (Inr (unify_pat p p'), bk', None, t') | _ -> raise No_match in let rec unify cl bl' = match cl, bl' with | [], [] -> [] | c :: cl, (Inl _, _, Some _,t) :: bl' -> unify cl bl' | c :: cl, b' :: bl' -> unify_term_binder c b' :: unify cl bl' | _ -> raise No_match in let bl = unify cl bl' in let sigma = (terms,onlybinders,termlists,Id.List.remove_assoc var binderlists) in add_bindinglist_env 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 match_names metas (alp,sigma) na1 na2 = match (na1,na2) with | (na1,Name id2) when is_onlybinding_meta id2 metas -> bind_binding_env alp sigma id2 na1 | (Name id1,Name id2) when is_term_meta id2 metas -> (* We let the non-binding occurrence define the rhs and hence reason up to *) (* alpha-conversion for the given occurrence of the name (see #4592)) *) bind_term_as_binding_env alp sigma id2 id1 | (Anonymous,Name id2) when is_term_meta id2 metas -> (* We let the non-binding occurrence define the rhs *) alp, sigma | (Name id1,Name id2) -> ((id1,id2)::fst alp, snd alp),sigma | (Anonymous,Anonymous) -> alp,sigma | _ -> raise No_match let rec match_cases_pattern_binders metas acc pat1 pat2 = match (pat1,pat2) with | PatVar (_,na1), PatVar (_,na2) -> match_names metas acc na1 na2 | PatCstr (_,c1,patl1,na1), PatCstr (_,c2,patl2,na2) when eq_constructor c1 c2 && Int.equal (List.length patl1) (List.length patl2) -> List.fold_left2 (match_cases_pattern_binders metas) (match_names metas acc na1 na2) patl1 patl2 | _ -> raise No_match let glue_letin_with_decls = true let rec match_iterated_binders islambda decls = function | GLambda (_,Name p,bk,t,GCases (_,LetPatternStyle,None,[(GVar(_,e),_)],[(_,_,[cp],b)])) when islambda && Id.equal p e -> match_iterated_binders islambda ((Inr cp,bk,None,t)::decls) b | GLambda (_,na,bk,t,b) when islambda -> match_iterated_binders islambda ((Inl na,bk,None,t)::decls) b | GProd (_,Name p,bk,t,GCases (_,LetPatternStyle,None,[(GVar(_,e),_)],[(_,_,[cp],b)])) when not islambda && Id.equal p e -> match_iterated_binders islambda ((Inr cp,bk,None,t)::decls) b | GProd (_,(Name _ as na),bk,t,b) when not islambda -> match_iterated_binders islambda ((Inl na,bk,None,t)::decls) b | GLetIn (loc,na,c,b) when glue_letin_with_decls -> match_iterated_binders islambda ((Inl na,Explicit (*?*), Some c,GHole(loc,Evar_kinds.BinderType na,Misctypes.IntroAnonymous,None))::decls) b | b -> (decls,b) let remove_sigma x (terms,onlybinders,termlists,binderlists) = (Id.List.remove_assoc x terms,onlybinders,termlists,binderlists) let remove_bindinglist_sigma x (terms,onlybinders,termlists,binderlists) = (terms,onlybinders,termlists,Id.List.remove_assoc x binderlists) let add_ldots_var metas = (ldots_var,((None,[]),NtnTypeConstr))::metas let add_meta_bindinglist x metas = (x,((None,[]),NtnTypeBinderList))::metas let match_binderlist_with_app match_fun alp metas sigma rest x y iter termin = let rec aux sigma bl rest = try let metas = add_ldots_var (add_meta_bindinglist y metas) in let (terms,_,_,binderlists as sigma) = match_fun alp metas sigma rest iter in let rest = Id.List.assoc ldots_var terms in let b = match Id.List.assoc y binderlists with [b] -> b | _ ->assert false in let sigma = remove_bindinglist_sigma y (remove_sigma ldots_var sigma) in aux sigma (b::bl) rest with No_match when not (List.is_empty bl) -> bl, rest, sigma in let bl,rest,sigma = aux sigma [] rest in let alp,sigma = bind_bindinglist_env alp sigma x bl in match_fun alp metas sigma rest termin let add_meta_term x metas = (x,((None,[]),NtnTypeConstr))::metas let match_termlist match_fun alp metas sigma rest x y iter termin lassoc = let rec aux sigma acc rest = try let metas = add_ldots_var (add_meta_term y metas) in let (terms,_,_,_ as sigma) = match_fun metas sigma rest iter in let rest = Id.List.assoc ldots_var terms in let t = Id.List.assoc y terms in let sigma = remove_sigma y (remove_sigma 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,(terms,onlybinders,termlists,binderlists as sigma) = aux sigma [] rest in let l = if lassoc then l else List.rev l in if is_bindinglist_meta x metas then (* This is a recursive pattern for both bindings and terms; it is *) (* registered for binders *) bind_bindinglist_as_term_env alp sigma x l else bind_termlist_env alp sigma x l let does_not_come_from_already_eta_expanded_var = (* 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). *) function GVar _ -> false | _ -> true let rec match_ inner u alp metas sigma a1 a2 = match (a1,a2) with (* Matching notation variable *) | r1, NVar id2 when is_term_meta id2 metas -> bind_term_env alp sigma id2 r1 | GVar (_,id1), NVar id2 when is_onlybinding_meta id2 metas -> bind_binding_as_term_env alp sigma id2 id1 | r1, NVar id2 when is_bindinglist_meta id2 metas -> bind_term_env alp sigma id2 r1 (* Matching recursive notations for terms *) | r1, NList (x,y,iter,termin,lassoc) -> match_termlist (match_hd u alp) alp metas sigma r1 x y iter termin lassoc (* "λ p, let 'cp = p in t" -> "λ 'cp, t" *) | GLambda (_,Name p,bk,t1,GCases (_,LetPatternStyle,None,[(GVar(_,e),_)],[(_,_,[cp],b1)])), NBinderList (x,_,NLambda (Name _id2,_,b2),termin) when Id.equal p e -> let (decls,b) = match_iterated_binders true [(Inr cp,bk,None,t1)] b1 in let alp,sigma = bind_bindinglist_env alp sigma x decls in match_in u alp metas sigma b termin (* Matching recursive notations for binders: ad hoc cases supporting let-in *) | GLambda (_,na1,bk,t1,b1), NBinderList (x,_,NLambda (Name _id2,_,b2),termin)-> let (decls,b) = match_iterated_binders true [(Inl na1,bk,None,t1)] b1 in (* TODO: address the possibility that termin is a Lambda itself *) let alp,sigma = bind_bindinglist_env alp sigma x decls in match_in u alp metas sigma b termin (* "∀ p, let 'cp = p in t" -> "∀ 'cp, t" *) | GProd (_,Name p,bk,t1,GCases (_,LetPatternStyle,None,[(GVar(_,e),_)],[(_,_,[cp],b1)])), NBinderList (x,_,NProd (Name _id2,_,b2),(NVar v as termin)) when Id.equal p e -> let (decls,b) = match_iterated_binders true [(Inr cp,bk,None,t1)] b1 in let alp,sigma = bind_bindinglist_env alp sigma x decls in match_in u alp metas sigma b termin | GProd (_,na1,bk,t1,b1), NBinderList (x,_,NProd (Name _id2,_,b2),termin) when na1 != Anonymous -> let (decls,b) = match_iterated_binders false [(Inl na1,bk,None,t1)] b1 in (* TODO: address the possibility that termin is a Prod itself *) let alp,sigma = bind_bindinglist_env alp sigma x decls in match_in u alp metas sigma b termin (* Matching recursive notations for binders: general case *) | r, NBinderList (x,y,iter,termin) -> match_binderlist_with_app (match_hd u) alp metas sigma r x y iter termin (* Matching individual binders as part of a recursive pattern *) | GLambda (_,Name p,bk,t,GCases (_,LetPatternStyle,None,[(GVar(_,e),_)],[(_,_,[cp],b1)])), NLambda (Name id,_,b2) when is_bindinglist_meta id metas -> let alp,sigma = bind_bindinglist_env alp sigma id [(Inr cp,bk,None,t)] in match_in u alp metas sigma b1 b2 | GLambda (_,na,bk,t,b1), NLambda (Name id,_,b2) when is_bindinglist_meta id metas -> let alp,sigma = bind_bindinglist_env alp sigma id [(Inl na,bk,None,t)] in match_in u alp metas sigma b1 b2 | GProd (_,na,bk,t,b1), NProd (Name id,_,b2) when is_bindinglist_meta id metas && na != Anonymous -> let alp,sigma = bind_bindinglist_env alp sigma id [(Inl na,bk,None,t)] in match_in u alp metas sigma b1 b2 (* Matching compositionally *) | GVar (_,id1), NVar id2 when alpha_var id1 id2 (fst alp) -> sigma | GRef (_,r1,_), NRef r2 when (eq_gr r1 r2) -> sigma | GApp (loc,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 GApp (loc,f1,l11),l12, f2,l2 else f1,l1, f2, l2 in let may_use_eta = does_not_come_from_already_eta_expanded_var f1 in List.fold_left2 (match_ may_use_eta u alp metas) (match_in u alp metas sigma f1 f2) l1 l2 | GLambda (_,na1,_,t1,b1), NLambda (na2,t2,b2) -> match_binders u alp metas na1 na2 (match_in u alp metas sigma t1 t2) b1 b2 | GProd (_,na1,_,t1,b1), NProd (na2,t2,b2) -> match_binders u alp metas na1 na2 (match_in u alp metas sigma t1 t2) b1 b2 | GLetIn (_,na1,t1,b1), NLetIn (na2,t2,b2) -> match_binders u alp metas na1 na2 (match_in u alp metas sigma t1 t2) b1 b2 | GCases (_,sty1,rtno1,tml1,eqnl1), NCases (sty2,rtno2,tml2,eqnl2) when sty1 == sty2 && Int.equal (List.length tml1) (List.length tml2) && Int.equal (List.length eqnl1) (List.length eqnl2) -> 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 List.fold_left2 (match_equations u alp metas) sigma eqnl1 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,CastConv t1), NCast (c2,CastConv t2) | GCast(_,c1,CastVM t1), NCast (c2,CastVM t2) -> match_in u alp metas (match_in u alp metas sigma c1 c2) t1 t2 | GCast(_,c1, CastCoerce), NCast(c2, CastCoerce) -> match_in u alp metas sigma c1 c2 | GSort (_,GType _), NSort (GType _) when not u -> sigma | GSort (_,s1), NSort s2 when Miscops.glob_sort_eq 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,(NHole _ | NVar _ as t2),b2) when inner -> let avoid = free_glob_vars b1 @ (* as in Namegen: *) glob_visible_short_qualid b1 in let id' = Namegen.next_ident_away id avoid in let t1 = GHole(Loc.ghost,Evar_kinds.BinderType (Name id'),Misctypes.IntroAnonymous,None) in let sigma = match t2 with | NHole _ -> sigma | NVar id2 -> bind_term_env alp sigma id2 t1 | _ -> assert false in let (alp,sigma) = if is_bindinglist_meta id metas then bind_bindinglist_env alp sigma id [(Inl (Name id'),Explicit,None,t1)] else match_names metas (alp,sigma) (Name id') na in match_in u alp metas sigma (mkGApp Loc.ghost b1 (GVar (Loc.ghost,id'))) b2 | (GRec _ | GEvar _), _ | _,_ -> raise No_match 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 = let (alp,sigma) = match_names metas (alp,sigma) na1 na2 in match_in u alp metas sigma b1 b2 and match_equations u alp metas sigma (_,_,patl1,rhs1) (patl2,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 (match_cases_pattern_binders metas) (alp,sigma) patl1 patl2 in match_in u alp metas sigma rhs1 rhs2 let term_of_binder = function | Name id -> GVar (Loc.ghost,id) | Anonymous -> GHole (Loc.ghost,Evar_kinds.InternalHole,Misctypes.IntroAnonymous,None) type glob_decl2 = (name, cases_pattern) Util.union * Decl_kinds.binding_kind * glob_constr option * glob_constr let match_notation_constr u c (metas,pat) = let terms,binders,termlists,binderlists = match_ false u ([],[]) metas ([],[],[],[]) c pat in (* Reorder canonically the substitution *) let find_binder x = try term_of_binder (Id.List.assoc x binders) with Not_found -> (* Happens for binders bound to Anonymous *) (* Find a better way to propagate Anonymous... *) GVar (Loc.ghost,x) in List.fold_right (fun (x,(scl,typ)) (terms',termlists',binders') -> match typ with | NtnTypeConstr -> let term = try Id.List.assoc x terms with Not_found -> raise No_match in ((term, scl)::terms',termlists',binders') | NtnTypeOnlyBinder -> ((find_binder x, scl)::terms',termlists',binders') | NtnTypeConstrList -> (terms',(Id.List.assoc x termlists,scl)::termlists',binders') | NtnTypeBinderList -> let bl = try Id.List.assoc x binderlists with Not_found -> raise No_match in (terms',termlists',(bl, scl)::binders')) metas ([],[],[]) (* Matching cases pattern *) let add_patterns_for_params ind l = let mib,_ = Global.lookup_inductive ind in let nparams = mib.Declarations.mind_nparams in Util.List.addn nparams (PatVar (Loc.ghost,Anonymous)) l let bind_env_cases_pattern (terms,x,termlists,y as sigma) var v = try let vvar = Id.List.assoc var terms 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 *) (var,v)::terms,x,termlists,y let match_cases_pattern_list match_fun metas sigma rest x y iter termin lassoc = let rec aux sigma acc rest = try let metas = add_ldots_var (add_meta_term y metas) in let (terms,_,_,_ as sigma) = match_fun metas sigma rest iter in let rest = Id.List.assoc ldots_var terms in let t = Id.List.assoc y terms in let sigma = remove_sigma y (remove_sigma 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,(terms,onlybinders,termlists,binderlists as sigma) = aux sigma [] rest in (terms,onlybinders,(x,if lassoc then l else List.rev l)::termlists, binderlists) let rec match_cases_pattern metas (terms,(),termlists,() as sigma) a1 a2 = match (a1,a2) with | r1, NVar id2 when Id.List.mem_assoc id2 metas -> (bind_env_cases_pattern sigma id2 r1),(0,[]) | PatVar (_,Anonymous), NHole _ -> sigma,(0,[]) | PatCstr (loc,(ind,_ as r1),largs,_), NRef (ConstructRef r2) when eq_constructor r1 r2 -> sigma,(0,add_patterns_for_params (fst r1) largs) | PatCstr (loc,(ind,_ as r1),args1,_), NApp (NRef (ConstructRef r2),l2) when eq_constructor r1 r2 -> let l1 = add_patterns_for_params (fst r1) args1 in let le2 = List.length l2 in if Int.equal le2 0 (* Special case of a notation for a @Cstr *) || le2 > List.length l1 then raise No_match else let l1',more_args = Util.List.chop le2 l1 in (List.fold_left2 (match_cases_pattern_no_more_args metas) sigma l1' l2),(le2,more_args) | r1, NList (x,y,iter,termin,lassoc) -> (match_cases_pattern_list (match_cases_pattern_no_more_args) metas (terms,(),termlists,()) r1 x y iter termin lassoc),(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 (IndRef r2) when eq_ind ind r2 -> sigma,(0,pats) | NApp (NRef (IndRef r2),l2) when eq_ind 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 (List.fold_left2 (match_cases_pattern_no_more_args metas) sigma l1' l2),(le2,more_args) |_ -> raise No_match let reorder_canonically_substitution terms termlists metas = List.fold_right (fun (x,(scl,typ)) (terms',termlists') -> match typ with | NtnTypeConstr -> ((Id.List.assoc x terms, scl)::terms',termlists') | NtnTypeOnlyBinder -> assert false | NtnTypeConstrList -> (terms',(Id.List.assoc x termlists,scl)::termlists') | NtnTypeBinderList -> assert false) metas ([],[]) let match_notation_constr_cases_pattern c (metas,pat) = let (terms,(),termlists,()),more_args = match_cases_pattern metas ([],(),[],()) c pat in reorder_canonically_substitution terms termlists metas, more_args let match_notation_constr_ind_pattern ind args (metas,pat) = let (terms,(),termlists,()),more_args = match_ind_pattern metas ([],(),[],()) ind args pat in reorder_canonically_substitution terms termlists metas, more_args