Source file notation_ops.ml
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open Pp
open CErrors
open Util
open Names
open Nameops
open Constr
open Globnames
open Namegen
open Glob_term
open Glob_ops
open Mod_subst
open Notation_term
let ldots_var = Id.of_string ".."
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 replace_var i j var = j :: List.remove Id.equal i var
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 l1, Some l2 ->
CList.for_all2eq (fun u1 u2 ->
match u1, u2 with
| UAnonymous {rigid=true}, UAnonymous {rigid=true} -> true
| UAnonymous {rigid=false}, UAnonymous {rigid=false} -> true
| UAnonymous _, UAnonymous _ -> false
| UNamed _, UAnonymous _ -> strictly_lt := true; lt
| UAnonymous _, UNamed _ -> false
| UNamed _, UNamed _ -> glob_level_eq u1 u2) l1 l2
let compare_glob_universe_instances_le us1 us2 =
compare_glob_universe_instances true (ref false) us1 us2
let compare_notation_constr lt (vars1,vars2) t1 t2 =
let alphameta = ref [] in
let strictly_lt = ref false in
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
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; (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.equal gr1 gr2 && compare_glob_universe_instances lt strictly_lt u1 u2 -> ()
| NHole (_, _, _), NHole (_, _, _) -> ()
| _, NHole (_, _, _) when lt -> strictly_lt := true
| 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) ->
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 ->
let vars2 = replace_var i2 j2 vars2 in
aux (vars1,vars2) renaming t1 iter2;
let t1 = List.hd !tail in
tail := List.tl !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 ->
let vars1 = replace_var i1 j1 vars1 in
aux (vars1,vars2) renaming iter1 t2;
let t2 = match !tail with
| t::rest -> tail := rest; t
| _ -> raise_notrace Exit in
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.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;
let renaming = check_eq_name vars renaming na1 na2 in
aux vars renaming u1 u2
| NCases (_, o1, r1, p1), NCases (_, o2, r2, p2) ->
let check_pat (p1, t1) (p2, t2) =
if not (List.equal cases_pattern_eq p1 p2) then raise_notrace Exit;
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) ->
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; (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 (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 _ | NList _ | NLambda _ | NProd _
| NBinderList _ | NLetIn _ | NCases _ | NLetTuple _ | NIf _
| NRec _ | NSort _ | NCast _ | NInt _ | NFloat _ | NArray _), _ -> raise_notrace Exit in
try
let _ = aux (vars1,vars2) [] t1 t2 in
if not lt then
List.iter2 check_alphameta vars1 vars2;
not lt || !strictly_lt
with Exit | Option.Heterogeneous | Invalid_argument _ -> false
let eq_notation_constr vars t1 t2 = t1 == t2 || compare_notation_constr false vars t1 t2
let strictly_finer_notation_constr vars t1 t2 = compare_notation_constr true vars t1 t2
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
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
| Evar_kinds.BinderType (Name id) ->
let id =
try match DAst.get (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 gc = DAst.map (function
| GVar id as r -> (try DAst.get (Id.List.assoc id l) with Not_found -> r)
| GProd (Name id,bk,t,c) ->
let id =
try match DAst.get (Id.List.assoc id l) with GVar id' -> id' | _ -> id
with Not_found -> id in
GProd (Name id,bk,subst_glob_vars l t,subst_glob_vars l c)
| GLambda (Name id,bk,t,c) ->
let id =
try match DAst.get (Id.List.assoc id l) with GVar id' -> id' | _ -> id
with Not_found -> id in
GLambda (Name id,bk,subst_glob_vars l t,subst_glob_vars l c)
| GHole (x,naming,arg) -> GHole (subst_binder_type_vars l x,naming,arg)
| _ -> DAst.get (map_glob_constr (subst_glob_vars l) gc)
) 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 (Evar_kinds.BinderType na, IntroAnonymous, None)
| 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',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',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,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,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, naming, arg) -> GHole (x, naming, arg)
| NRef (x,u) -> GRef (x,u)
| NInt i -> GInt i
| NFloat f -> GFloat f
| 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 print_parentheses = ref false
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
| 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 _ ->
raise Not_found
end
| _ -> map_glob_constr aux c in
let outer_iterator = aux c in
match !sub with
| None -> raise Not_found
| Some c ->
match DAst.get outer_iterator with
| GVar v when Id.equal v ldots_var -> 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 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
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 pair_equal eq1 eq2 (a,b) (a',b') = eq1 a a' && eq2 b b'
let mem_recursive_pair (x,y) l = List.mem_f (pair_equal Id.equal Id.equal) (x,y) l
type recursive_pattern_kind =
| RecursiveTerms of bool
| RecursiveBinders of bool
let compare_recursive_parts recvars found f f' (iterator,subc) =
let diff = ref None in
let terminator = ref None in
let rec aux c1 c2 = match DAst.get c1, DAst.get c2 with
| GVar v, term when Id.equal v ldots_var ->
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 ->
assert (match !terminator with None -> true | Some _ -> false);
terminator := Some term;
List.for_all2eq aux l1 l2
| _ -> mk_glob_constr_eq aux c1 c2
end
| GVar x, GVar y
when mem_recursive_pair (x,y) recvars || mem_recursive_pair (y,x) recvars ->
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
| GLambda (Name x,_,t_x,c), GLambda (Name y,_,t_y,term)
| GProd (Name x,_,t_x,c), GProd (Name y,_,t_y,term)
when mem_recursive_pair (x,y) recvars || mem_recursive_pair (y,x) recvars ->
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 ->
let () = diff := Some (x, y, RecursiveBinders revert) in
aux c term
| Some (x', y', RecursiveBinders revert') ->
check_pair_matching ?loc:c1.CAst.loc x y x' y' revert revert';
true
| Some (x', y', RecursiveTerms revert') ->
check_pair_matching ?loc:c1.CAst.loc x y x' y' revert revert';
let () = diff := Some (x, y, RecursiveBinders revert) in
true
end
| _ ->
mk_glob_constr_eq aux 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
user_err ?loc:(subtract_loc loc1 loc2)
(str "Both ends of the recursive pattern are the same.")
| Some (x,y,RecursiveTerms revert) ->
let iterator =
f' (if revert then iterator else subst_glob_vars [x, DAst.make @@ GVar y] iterator) in
found := { !found with vars = List.remove Id.equal y (!found).vars;
recursive_term_vars = List.add_set (pair_equal 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 := { !found with vars = List.remove Id.equal y (!found).vars;
recursive_binders_vars = List.add_set (pair_equal 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 has_ltac = ref false in
let rec aux c =
let keepfound = !found in
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 ->
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,[])
| GApp (g,args) ->
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) -> NCast (aux c, k, aux t)
| GSort s -> NSort s
| GInt i -> NInt i
| GFloat f -> NFloat f
| GHole (w,naming,arg) ->
if arg != None then has_ltac := true;
NHole (w, naming, 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 (Evar_kinds.BinderType _,IntroAnonymous,None) -> None
| _ -> Some (aux t)) t
in
let t = aux a in
t, !found, !has_ltac
let check_variables_and_reversibility nenv
{ vars = found; recursive_term_vars = foundrec; recursive_binders_vars = foundrecbinding } =
let injective = ref [] 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
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
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 notation_constr_of_glob_constr nenv a =
let recvars = Id.Map.bindings nenv.ninterp_rec_vars in
let a, found, has_ltac = notation_constr_and_vars_of_glob_constr recvars a in
let injective = check_variables_and_reversibility nenv found in
let status = if has_ltac then HasLtac else match injective with
| [] -> APrioriReversible
| l -> NonInjective l in
a, status
let notation_constr_of_constr avoiding 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 false avoiding env evd 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 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 ->
fst (notation_constr_of_constr bound t.Univ.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
| 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.Smart.map (Genintern.generic_substitute subst) solve in
if nsolve == solve && nknd == knd then raw
else NHole (nknd, naming, nsolve)
| 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, _) -> Id.Set.add id accu) Id.Set.empty metas in
(metas,subst_notation_constr subst bound pat)
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,Explicit,DAst.make @@ GHole(Evar_kinds.InternalHole,IntroAnonymous,None),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 id metas =
try match Id.List.assoc id metas with _,(NtnTypeConstr | NtnTypeConstrList) -> true | _ -> false
with Not_found -> false
let is_onlybinding_strict_meta id metas =
try match Id.List.assoc id metas with _,NtnTypeBinder (NtnParsedAsPattern true) -> true | _ -> false
with Not_found -> false
let is_onlybinding_meta id metas =
try match Id.List.assoc id metas with _,NtnTypeBinder _ -> true | _ -> false
with Not_found -> false
let is_onlybinding_pattern_like_meta isvar id metas =
try match Id.List.assoc id metas with
| _,NtnTypeBinder (NtnBinderParsedAsConstr
(AsNameOrPattern | AsStrictPattern)) -> true
| _,NtnTypeBinder (NtnParsedAsPattern strict) -> not (strict && isvar)
| _,NtnTypeBinder NtnParsedAsBinder -> not isvar
| _ -> 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 alpha_rename alpmetas v =
if alpmetas == [] then v
else try rename_glob_vars alpmetas v with UnsoundRenaming -> raise No_match
let add_env (vars,(alp,alpmetas)) (terms,termlists,binders,binderlists) var v =
if not (Id.equal ldots_var var) &&
List.exists (fun (id,_) -> occur_glob_constr id v) alp then raise No_match;
let v = alpha_rename alpmetas v in
((var,(vars,v))::terms,termlists,binders,binderlists)
let add_termlist_env (vars,(alp,alpmetas)) (terms,termlists,binders,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,(var,(vars,vl))::termlists,binders,binderlists)
let add_binding_env (vars,alp) (terms,termlists,binders,binderlists) var v =
(terms,termlists,(var,(vars,v))::binders,binderlists)
let add_bindinglist_env (vars,alp) (terms,termlists,binders,binderlists) var bl =
(terms,termlists,binders,(var,(vars,bl))::binderlists)
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 (vars,alp) na na' =
match na, na' with
| Anonymous, na' -> (Termops.add_vname vars na',alp), na'
| na, Anonymous -> (Termops.add_vname vars na,alp), na
| Name id, Name id' ->
let vars = Termops.add_vname vars na' in
if Id.equal id id' then (vars,alp), na'
else (vars,(fst alp,(id,id')::snd alp)), 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 (_,alp) v v' =
match DAst.get v, DAst.get v' with
| GHole _, _ -> v'
| _, GHole _ -> v
| _, _ -> if glob_constr_eq (alpha_rename (snd alp) 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_binder_upto alp b b' =
let loc, loc' = CAst.(b.loc, b'.loc) in
match DAst.get b, DAst.get b' with
| GLocalAssum (na,bk,t), GLocalAssum (na',bk',t') ->
let alp, na = unify_name_upto alp na na' in
alp, DAst.make ?loc @@ GLocalAssum (na, unify_binding_kind bk bk', unify_term alp t t')
| GLocalDef (na,c,t), GLocalDef (na',c',t') ->
let alp, na = unify_name_upto alp na na' in
alp, DAst.make ?loc @@ GLocalDef (na, unify_term alp c c', unify_opt_term alp 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 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 (_,alp) 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
let unify_pat (_,alp) p p' =
if cases_pattern_eq (map_cases_pattern_name_left (Name.map (rename_var (snd alp))) p) p' then p'
else raise No_match
let unify_term_binder alp c = DAst.(map (fun b' ->
match DAst.get c, b' with
| GVar id, GLocalAssum (na', bk', t') ->
GLocalAssum (unify_id alp id na', bk', t')
| _, GLocalPattern (([p'],ids), id, bk', t') ->
let p = pat_binder_of_term c in
GLocalPattern (([unify_pat alp p p'],ids), id, bk', t')
| _ -> raise No_match))
let rec unify_terms_binders alp cl bl' =
match cl, bl' with
| [], [] -> []
| c :: cl, b' :: bl' ->
begin match DAst.get b' with
| GLocalDef (_, _, t) -> unify_terms_binders alp cl bl'
| _ -> unify_term_binder alp c b' :: unify_terms_binders alp cl bl'
end
| _ -> raise No_match
let bind_term_env alp (terms,termlists,binders,binderlists as sigma) var v =
try
let vars,v' = Id.List.assoc var terms in
let v'' = unify_term alp v v' in
if v'' == v' then sigma else
let sigma = (Id.List.remove_assoc var terms,termlists,binders,binderlists) in
add_env (Id.Set.union vars (fst alp),snd alp) sigma var v
with Not_found -> add_env alp sigma var v
let bind_termlist_env alp (terms,termlists,binders,binderlists as sigma) var vl =
try
let vars,vl' = Id.List.assoc var termlists in
let vl = unify_terms alp vl vl' in
let sigma = (terms,Id.List.remove_assoc var termlists,binders,binderlists) in
add_termlist_env (Id.Set.union vars (fst alp),snd alp) sigma var vl
with Not_found -> add_termlist_env alp sigma var vl
let bind_term_as_binding_env alp (terms,termlists,binders,binderlists as sigma) var id =
try
let vars',v' = Id.List.assoc var terms in
match DAst.get v' with
| GVar id' | GRef (GlobRef.VarRef id',None) ->
let (vars,(alpha,alpmetas)) = alp in
let vars = Id.Set.add id' vars in
let alpmetas = if not (Id.equal id id') then (id,id')::alpmetas else alpmetas in
(Id.Set.union vars' vars,(alpha,alpmetas)), sigma
| t ->
raise No_match
with Not_found ->
let alp = (Id.Set.add id (fst alp), snd alp) in
alp, add_env alp sigma var (DAst.make @@ GVar id)
let bind_binding_as_term_env alp (terms,termlists,binders,binderlists as 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
let vars,patl' = Id.List.assoc var binders in
let patl'' = List.map2 (unify_pat alp) [pat] patl' in
if patl' == patl'' then sigma
else
let sigma = (terms,termlists,Id.List.remove_assoc var binders,binderlists) in
add_binding_env (Id.Set.union vars (fst alp),snd alp) sigma var patl''
with Not_found -> add_binding_env alp sigma var [pat]
let bind_binding_env alp (terms,termlists,binders,binderlists as sigma) var disjpat =
try
let vars,disjpat' = Id.List.assoc var binders in
let alp' = (Id.Set.union vars (fst alp),snd alp) in
let alp, disjpat = List.fold_left2_map unify_pat_upto alp disjpat disjpat' in
let sigma = (terms,termlists,Id.List.remove_assoc var binders,binderlists) in
alp, add_binding_env alp' sigma var disjpat
with Not_found ->
let alp = (push_pattern_binders (fst alp) (List.hd disjpat), snd alp) in
alp, add_binding_env alp sigma var disjpat
let bind_bindinglist_env alp (terms,termlists,binders,binderlists as sigma) var bl =
let bl = List.rev bl in
try
let vars, bl' = Id.List.assoc var binderlists in
let alp' = (Id.Set.union vars (fst alp),snd alp) in
let alp, bl = unify_binders_upto alp bl bl' in
let sigma = (terms,termlists,binders,Id.List.remove_assoc var binderlists) in
alp, add_bindinglist_env alp' sigma var bl
with Not_found ->
let alp = (push_context_binders (fst alp) bl, snd alp) in
alp, add_bindinglist_env alp sigma var bl
let bind_bindinglist_as_termlist_env alp (terms,termlists,binders,binderlists) var cl =
try
let vars,bl' = Id.List.assoc var binderlists in
let bl = unify_terms_binders alp cl bl' in
let alp = (Id.Set.union vars (fst alp),snd alp) in
let sigma = (terms,termlists,binders,Id.List.remove_assoc var binderlists) in
add_bindinglist_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 match_names metas (alp,sigma) na1 na2 = match (na1,na2) with
| (na1,Name id2) when is_onlybinding_strict_meta id2 metas ->
raise No_match
| (na1,Name id2) when is_onlybinding_meta id2 metas ->
bind_binding_env alp sigma id2 [DAst.make (PatVar na1)]
| (Name id1,Name id2) when is_term_meta id2 metas ->
bind_term_as_binding_env alp sigma id2 id1
| (Anonymous,Name id2) when is_term_meta id2 metas ->
alp, sigma
| (Name id1,Name id2) ->
let (vars,(alp,alpmetas)) = alp in
(vars,((id1,id2)::alp,alpmetas)),sigma
| (Anonymous,Anonymous) -> alp,sigma
| _ -> raise No_match
let rec match_cases_pattern_binders allow_catchall metas (alp,sigma as acc) pat1 pat2 =
match DAst.get pat1, DAst.get pat2 with
| PatVar _, PatVar (Name id2) when is_onlybinding_pattern_like_meta true id2 metas ->
bind_binding_env alp sigma id2 [pat1]
| _, PatVar (Name id2) when is_onlybinding_pattern_like_meta false id2 metas ->
bind_binding_env alp sigma id2 [pat1]
| PatVar na1, PatVar na2 -> match_names metas 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 remove_sigma x (terms,termlists,binders,binderlists) =
(Id.List.remove_assoc x terms,termlists,binders,binderlists)
let remove_bindinglist_sigma x (terms,termlists,binders,binderlists) =
(terms,termlists,binders,Id.List.remove_assoc x binderlists)
let add_ldots_var metas = (ldots_var,((Constrexpr.InConstrEntrySomeLevel,(None,[])),NtnTypeConstr))::metas
let add_meta_bindinglist x metas = (x,((Constrexpr.InConstrEntrySomeLevel,(None,[])),NtnTypeBinderList))::metas
let glue_inner_letin_with_decls = true
let glue_trailing_letin_with_decls = false
exception OnlyTrailingLetIns
let match_binderlist match_fun alp metas sigma rest x y iter termin revert =
let rec aux trailing_letins 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
let sigma = remove_sigma y sigma in
aux false sigma (b::bl) rest
with No_match ->
match DAst.get rest with
| GLetIn (na,c,t,rest') when glue_inner_letin_with_decls ->
let b = DAst.make ?loc:rest.CAst.loc @@ GLocalDef (na,c,t) in
(try aux true sigma (b::bl) rest'
with OnlyTrailingLetIns
when not (trailing_letins && not glue_trailing_letin_with_decls) ->
if not (List.is_empty bl) then bl, rest, sigma else raise No_match)
| _ ->
if trailing_letins && not glue_trailing_letin_with_decls then
raise OnlyTrailingLetIns;
if not (List.is_empty bl) then bl, rest, sigma else raise No_match in
let bl,rest,sigma = aux false sigma [] rest in
let bl = if revert then List.rev bl else bl 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,((Constrexpr.InConstrEntrySomeLevel,(None,[])),NtnTypeConstr))::metas
let match_termlist 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 (terms,_,_,_ as sigma) = match_fun metas sigma rest iter in
let _,rest = Id.List.assoc ldots_var terms in
let vars,t = Id.List.assoc y terms in
let sigma = remove_sigma y (remove_sigma ldots_var sigma) in
if !print_parentheses && not (List.is_empty acc) then raise No_match;
aux (Id.Set.union vars (fst alp),snd alp) sigma (t::acc) rest
with No_match when not (List.is_empty acc) ->
alp, acc, match_fun metas sigma rest termin in
let alp,l,(terms,termlists,binders,binderlists as sigma) = aux alp sigma [] rest in
let l = if revert then l else List.rev l in
if is_bindinglist_meta x metas then
bind_bindinglist_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 =
match DAst.get glob with GVar _ -> false | _ -> true
let is_var_term = function
| 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
match DAst.get a1, a2 with
| r1, NVar id2 when is_term_meta id2 metas -> bind_term_env alp sigma id2 a1
| r1, NVar id2 when is_var_term r1 && is_onlybinding_pattern_like_meta true id2 metas -> bind_binding_as_term_env alp sigma id2 a1
| r1, NVar id2 when is_onlybinding_pattern_like_meta false id2 metas -> bind_binding_as_term_env alp sigma id2 a1
| r1, NVar id2 when is_var_term r1 && is_onlybinding_strict_meta id2 metas -> raise No_match
| r1, NVar id2 when is_var_term r1 && is_onlybinding_meta id2 metas -> bind_binding_as_term_env alp sigma id2 a1
| r1, NVar id2 when is_bindinglist_meta id2 metas -> bind_term_env alp sigma id2 a1
| r1, NList (x,y,iter,termin,revert) ->
match_termlist (match_hd u alp) alp metas sigma a1 x y iter termin revert
| _r, NBinderList (x,y,iter,termin,revert) ->
match_binderlist (match_hd u) alp metas sigma a1 x y iter termin revert
| GVar id1, NVar id2 when alpha_var id1 id2 (fst (snd alp)) -> sigma
| GRef (r1,u1), NRef (r2,u2) when (GlobRef.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 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.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.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 true u alp metas na1 na2 bk1 t1 (match_in_type u alp metas sigma t1 t2) b1 b2
| GLetIn (na1,b1,_,c1), NLetIn (na2,b2,None,c2)
| GLetIn (na1,b1,None,c1), NLetIn (na2,b2,_,c2) ->
match_binders u alp metas na1 na2 (match_in u alp metas sigma b1 b2) c1 c2
| GLetIn (na1,b1,Some t1,c1), NLetIn (na2,b2,Some t2,c2) ->
match_binders u alp metas na1 na2
(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
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 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 (cast_kind_eq k1 k2) then raise No_match;
match_in u alp metas sigma t1 t2
| GSort (UNamed [(GProp|GSet),0]), NSort (UAnonymous _) -> raise No_match
| GSort _, NSort (UAnonymous _) when not u -> sigma
| 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
| GPatVar _, NHole _ -> raise No_match
| a, NHole _ -> sigma
| _b1, NLambda (Name id as na,(None | Some (NVar _) as t2),b2) when inner ->
let avoid =
Id.Set.union (free_glob_vars a1) (glob_visible_short_qualid a1) in
let id' = Namegen.next_ident_away id avoid in
let t1 = DAst.make @@ GHole(Evar_kinds.BinderType (Name id'),IntroAnonymous,None) 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_bindinglist_meta id metas then
bind_bindinglist_env alp sigma id [DAst.make @@ GLocalAssum (Name id',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 _
| GCast _ | GInt _ | GFloat _ | 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 =
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 =
let store, get = set_temporary_memory () in
match na1, DAst.get b1, na2 with
| Name p, GCases (Constr.LetPatternStyle,None,[(e,_)],(_::_ as eqns)), Name id
when is_gvar p e && is_bindinglist_meta id metas && List.length (store (Detyping.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 = bind_bindinglist_env alp sigma id [DAst.make ?loc @@ GLocalPattern ((disjpat,ids),p,bk,t)] in
match_in u alp metas sigma b1 b2
| _ -> assert false)
| Name p, GCases (LetPatternStyle,None,[(e,_)],(_::_ as eqns)), Name id
when is_gvar p e && is_onlybinding_pattern_like_meta false id metas && List.length (store (Detyping.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 = bind_binding_env alp sigma id disjpat in
match_in u alp metas sigma b1 b2
| _ -> assert false)
| _, _, Name id when is_bindinglist_meta id metas && (not isprod || na1 != Anonymous)->
let alp,sigma = bind_bindinglist_env alp sigma id [DAst.make ?loc @@ GLocalAssum (na1,bk,t)] in
match_in u alp metas 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 {CAst.v=(ids,patl1,rhs1)} (patl2,rhs2) rest1 rest2 =
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) _ _ =
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
let match_notation_constr ~print_univ c ~vars (metas,pat) =
let terms,termlists,binders,binderlists =
match_ false print_univ (vars,([],[])) metas ([],[],[],[]) c pat in
List.fold_right (fun (x,(scl,typ)) (terms',termlists',binders',binderlists') ->
match typ with
| NtnTypeConstr ->
let term = try Id.List.assoc x terms with Not_found -> raise No_match in
((term, scl)::terms',termlists',binders',binderlists')
| NtnTypeBinder (NtnBinderParsedAsConstr _) ->
(match Id.List.assoc x binders with
| vars,[pat] ->
let v = glob_constr_of_cases_pattern (Global.env()) pat in
(((vars,v),scl)::terms',termlists',binders',binderlists')
| _ -> raise No_match)
| NtnTypeBinder (NtnParsedAsIdent | NtnParsedAsName | NtnParsedAsPattern _ | NtnParsedAsBinder) ->
(terms',termlists',(Id.List.assoc x binders,scl)::binders',binderlists')
| NtnTypeConstrList ->
(terms',(Id.List.assoc x termlists,scl)::termlists',binders',binderlists')
| NtnTypeBinderList ->
let bl = try Id.List.assoc x binderlists with Not_found -> raise No_match in
(terms',termlists',binders',(bl, scl)::binderlists'))
metas ([],[],[],[])
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 ->
(var,v)::terms,x,termlists,y
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 (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,termlists,binders,binderlists as sigma) = aux sigma [] rest in
(terms,(x,if revert then l else List.rev l)::termlists,binders,binderlists)
let rec match_cases_pattern metas (terms,termlists,(),() as 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
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 (terms,termlists,(),()) 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 || 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
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')
| NtnTypeBinder _ | NtnTypeBinderList -> anomaly (str "Unexpected binder in pattern notation."))
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