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Diffstat (limited to 'interp/notation_ops.ml')
| -rw-r--r-- | interp/notation_ops.ml | 856 |
1 files changed, 856 insertions, 0 deletions
diff --git a/interp/notation_ops.ml b/interp/notation_ops.ml new file mode 100644 index 00000000..c91c7815 --- /dev/null +++ b/interp/notation_ops.ml @@ -0,0 +1,856 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +open Pp +open Errors +open Util +open Names +open Nameops +open Globnames +open Misctypes +open Glob_term +open Glob_ops +open Mod_subst +open Notation_term +open Decl_kinds + +(**********************************************************************) +(* Re-interpret a notation as a glob_constr, taking care of binders *) + +let name_to_ident = function + | Anonymous -> Errors.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 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) + | 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) + | NPatVar n -> GPatVar (loc,(false,n)) + | 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 on_true_do b f c = if b then (f c; b) else b + +let compare_glob_constr f add t1 t2 = match t1,t2 with + | GRef (_,r1,_), GRef (_,r2,_) -> 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_glob_constr t1 t2 = compare_glob_constr eq_glob_constr (fun _ -> ()) t1 t2 + +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 compare_recursive_parts found 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, Some 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 *) + check_is_hole x t_x; + check_is_hole y t_y; + begin match !diff with + | None -> + let () = diff := Some (x, y, None) 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,Some lassoc) -> + let newfound = (pi1 !found, (x,y) :: pi2 !found, pi3 !found) in + let iterator = + f (if lassoc then subst_glob_vars [y,GVar(Loc.ghost,x)] iterator + else iterator) in + (* found have been collected by compare_constr *) + found := newfound; + NList (x,y,iterator,f (Option.get !terminator),lassoc) + | Some (x,y,None) -> + let newfound = (pi1 !found, pi2 !found, (x,y) :: pi3 !found) in + let iterator = f iterator in + (* found have been collected by compare_constr *) + found := newfound; + 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 rec aux c = + let keepfound = !found in + (* n^2 complexity but small and done only once per notation *) + try compare_recursive_parts found 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) -> NHole (w, naming, arg) + | GRef (_,r,_) -> NRef r + | GPatVar (_,(_,n)) -> NPatVar n + | GEvar _ -> + error "Existential variables not allowed in notations." + + in + let t = aux a in + (* Side effect *) + t, !found + +let pair_equal eq1 eq2 (a,b) (a',b') = eq1 a a' && eq2 b b' + +let check_variables nenv (found,foundrec,foundrecbinding) = + 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 nenv.ninterp_only_parse <- true + 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 + +let notation_constr_of_glob_constr nenv a = + let a, found = notation_constr_and_vars_of_glob_constr a in + let () = check_variables nenv found in + a + +(* 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; + ninterp_only_parse = false; + } 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 + 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') + + | NPatVar _ | 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 glob_constr and 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)) + +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 add_env alp (sigma,sigmalist,sigmabinders) var v = + (* Check that no capture of binding variables occur *) + if List.exists (fun (id,_) ->occur_glob_constr id v) alp then raise No_match; + (* TODO: handle the case of multiple occs in different scopes *) + ((var,v)::sigma,sigmalist,sigmabinders) + +let bind_env alp (sigma,sigmalist,sigmabinders as fullsigma) var v = + try + let v' = Id.List.assoc var sigma in + match v, v' with + | GHole _, _ -> fullsigma + | _, GHole _ -> + add_env alp (Id.List.remove_assoc var sigma,sigmalist,sigmabinders) var v + | _, _ -> + if glob_constr_eq v v' then fullsigma + else raise No_match + with Not_found -> add_env alp fullsigma var v + +let bind_binder (sigma,sigmalist,sigmabinders) x bl = + (sigma,sigmalist,(x,List.rev bl)::sigmabinders) + +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 + | (_,Name id2) when Id.List.mem id2 (fst metas) -> + let rhs = match na1 with + | Name id1 -> GVar (Loc.ghost,id1) + | Anonymous -> GHole (Loc.ghost,Evar_kinds.InternalHole,Misctypes.IntroAnonymous,None) in + alp, bind_env alp sigma id2 rhs + | (Name id1,Name id2) -> (id1,id2)::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 (_,na,bk,t,b) when islambda -> + match_iterated_binders islambda ((na,bk,None,t)::decls) b + | GProd (_,(Name _ as na),bk,t,b) when not islambda -> + match_iterated_binders islambda ((na,bk,None,t)::decls) b + | GLetIn (loc,na,c,b) when glue_letin_with_decls -> + match_iterated_binders islambda + ((na,Explicit (*?*), Some c,GHole(loc,Evar_kinds.BinderType na,Misctypes.IntroAnonymous,None))::decls) b + | b -> (decls,b) + +let remove_sigma x (sigmavar,sigmalist,sigmabinders) = + (Id.List.remove_assoc x sigmavar,sigmalist,sigmabinders) + +let match_abinderlist_with_app match_fun metas sigma rest x iter termin = + let rec aux sigma acc rest = + try + let sigma = match_fun (ldots_var::fst metas,snd metas) sigma rest iter in + let rest = Id.List.assoc ldots_var (pi1 sigma) in + let b = + match Id.List.assoc x (pi3 sigma) with [b] -> b | _ ->assert false + in + let sigma = remove_sigma x (remove_sigma ldots_var sigma) in + aux sigma (b::acc) rest + with No_match when not (List.is_empty acc) -> + acc, match_fun metas sigma rest termin in + let bl,sigma = aux sigma [] rest in + bind_binder sigma x bl + +let match_alist match_fun metas sigma rest x iter termin lassoc = + let rec aux sigma acc rest = + try + let sigma = match_fun (ldots_var::fst metas,snd metas) sigma rest iter in + let rest = Id.List.assoc ldots_var (pi1 sigma) in + let t = Id.List.assoc x (pi1 sigma) in + let sigma = remove_sigma x (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,sigma = aux sigma [] rest in + (pi1 sigma, (x,if lassoc then l else List.rev l)::pi2 sigma, pi3 sigma) + +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 (tmetas,blmetas as metas) sigma a1 a2 = + match (a1,a2) with + + (* Matching notation variable *) + | r1, NVar id2 when Id.List.mem id2 tmetas -> bind_env alp sigma id2 r1 + + (* Matching recursive notations for terms *) + | r1, NList (x,_,iter,termin,lassoc) -> + match_alist (match_hd u alp) metas sigma r1 x iter termin lassoc + + (* 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 [(na1,bk,None,t1)] b1 in + (* TODO: address the possibility that termin is a Lambda itself *) + match_in u alp metas (bind_binder sigma x decls) b termin + | GProd (_,na1,bk,t1,b1), NBinderList (x,_,NProd (Name id2,_,b2),termin) + when na1 != Anonymous -> + let (decls,b) = match_iterated_binders false [(na1,bk,None,t1)] b1 in + (* TODO: address the possibility that termin is a Prod itself *) + match_in u alp metas (bind_binder sigma x decls) b termin + (* Matching recursive notations for binders: general case *) + | r, NBinderList (x,_,iter,termin) -> + match_abinderlist_with_app (match_hd u alp) metas sigma r x iter termin + + (* Matching individual binders as part of a recursive pattern *) + | GLambda (_,na,bk,t,b1), NLambda (Name id,_,b2) when Id.List.mem id blmetas -> + match_in u alp metas (bind_binder sigma id [(na,bk,None,t)]) b1 b2 + | GProd (_,na,bk,t,b1), NProd (Name id,_,b2) + when Id.List.mem id blmetas && na != Anonymous -> + match_in u alp metas (bind_binder sigma id [(na,bk,None,t)]) b1 b2 + + (* Matching compositionally *) + | GVar (_,id1), NVar id2 when alpha_var id1 id2 alp -> sigma + | GRef (_,r1,_), NRef r2 when (eq_gr r1 r2) -> sigma + | GPatVar (_,(_,n1)), NPatVar n2 when Id.equal n1 n2 -> 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,(NHole _ | NVar _ as t2),b2) when inner -> + let id' = Namegen.next_ident_away id (free_glob_vars b1) 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_env alp sigma id2 t1 + | _ -> assert false in + match_in u alp metas (bind_binder sigma id [(Name id',Explicit,None,t1)]) + (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 match_notation_constr u c (metas,pat) = + let test (_, (_, x)) = match x with NtnTypeBinderList -> false | _ -> true in + let vars = List.partition test metas in + let vars = (List.map fst (fst vars), List.map fst (snd vars)) in + let terms,termlists,binders = match_ false u [] vars ([],[],[]) c pat in + (* Reorder canonically the substitution *) + let find x = + try Id.List.assoc x terms + 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 -> + ((find x, scl)::terms',termlists',binders') + | NtnTypeConstrList -> + (terms',(Id.List.assoc x termlists,scl)::termlists',binders') + | NtnTypeBinderList -> + (terms',termlists',(Id.List.assoc x binders,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 (sigma,sigmalist,x as fullsigma) var v = + try + let vvar = Id.List.assoc var sigma in + if cases_pattern_eq v vvar then fullsigma else raise No_match + with Not_found -> + (* TODO: handle the case of multiple occs in different scopes *) + (var,v)::sigma,sigmalist,x + +let rec match_cases_pattern metas sigma a1 a2 = + match (a1,a2) with + | r1, NVar id2 when Id.List.mem 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,_,iter,termin,lassoc) -> + (match_alist (fun (metas,_) -> match_cases_pattern_no_more_args metas) + (metas,[]) (pi1 sigma,pi2 sigma,()) r1 x 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') + | NtnTypeConstrList -> (terms',(Id.List.assoc x termlists,scl)::termlists') + | NtnTypeBinderList -> assert false) + metas ([],[]) + +let match_notation_constr_cases_pattern c (metas,pat) = + let vars = List.map fst metas in + let (terms,termlists,()),more_args = match_cases_pattern vars ([],[],()) c pat in + reorder_canonically_substitution terms termlists metas, more_args + +let match_notation_constr_ind_pattern ind args (metas,pat) = + let vars = List.map fst metas in + let (terms,termlists,()),more_args = match_ind_pattern vars ([],[],()) ind args pat in + reorder_canonically_substitution terms termlists metas, more_args |