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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \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 List.assoc id l with Not_found -> r)
| GProd (loc,Name id,bk,t,c) ->
let id =
try match 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 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 -> GHole (loc,x)
| NPatVar n -> GPatVar (loc,(false,n))
| NRef x -> GRef (loc,x)
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 v = ldots_var ->
if !sub <> None then
(* Not narrowed enough to find only one recursive part *)
raise Not_found
else
(sub := Some c;
if l = [] then GVar (loc,ldots_var)
else GApp (loc0,GVar (loc,ldots_var),l))
| 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 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 (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 na1 = na2 && bk1 = bk2 -> on_true_do (f ty1 ty2 & f c1 c2) add na1
| GProd (_,na1,bk1,ty1,c1), GProd (_,na2,bk2,ty2,c2) when na1 = na2 && bk1 = bk2 ->
on_true_do (f ty1 ty2 & f c1 c2) add na1
| GHole _, GHole _ -> true
| GSort (_,s1), GSort (_,s2) -> s1 = s2
| GLetIn (_,na1,b1,c1), GLetIn (_,na2,b2,c2) when 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 v = ldots_var ->
(* We found the pattern *)
assert (!terminator = None); terminator := Some term;
true
| GApp (_,GVar(_,v),l1), GApp (_,term,l2) when v = ldots_var ->
(* We found the pattern, but there are extra arguments *)
(* (this allows e.g. alternative (recursive) notation of application) *)
assert (!terminator = None); terminator := Some term;
List.for_all2eq aux l1 l2
| GVar (_,x), GVar (_,y) when x<>y ->
(* We found the position where it differs *)
let lassoc = (!terminator <> None) in
let x,y = if lassoc then y,x else x,y in
!diff = None && (diff := Some (x,y,Some lassoc); true)
| 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;
!diff = None && (diff := Some (x,y,None); aux c term)
| _ ->
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 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) -> NHole w
| 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 rec list_rev_mem_assoc x = function
| [] -> false
| (_,x')::l -> x = x' || list_rev_mem_assoc x l
let check_variables vars recvars (found,foundrec,foundrecbinding) =
let useless_vars = List.map snd recvars in
let vars = List.filter (fun (y,_) -> not (List.mem y useless_vars)) vars in
let check_recvar x =
if List.mem x found then
errorlabstrm "" (pr_id x ++
strbrk " should only be used in the recursive part of a pattern.") in
List.iter (fun (x,y) -> check_recvar x; check_recvar y)
(foundrec@foundrecbinding);
let check_bound x =
if not (List.mem x found) then
if List.mem_assoc x foundrec or List.mem_assoc x foundrecbinding
or list_rev_mem_assoc x foundrec or list_rev_mem_assoc x foundrecbinding
then
error ((string_of_id x)^" should not be bound in a recursive pattern of the right-hand side.")
else
error ((string_of_id x)^" is unbound in the right-hand side.") in
let check_pair s x y where =
if not (List.mem (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 (List.assoc x recvars) foundrec
with Not_found -> check_bound x
end
| NtnInternTypeBinder ->
begin
try check_pair "binding" x (List.assoc x recvars) foundrecbinding
with Not_found -> check_bound x
end
| NtnInternTypeIdent -> check_bound x in
List.iter check_type vars
let notation_constr_of_glob_constr vars recvars a =
let a,found = notation_constr_and_vars_of_glob_constr a in
check_variables vars recvars found;
a
(* Substitution of kernel names, avoiding a list of bound identifiers *)
let notation_constr_of_constr avoiding t =
notation_constr_of_glob_constr [] [] (Detyping.detype false avoiding [] t)
let rec subst_pat subst pat =
match pat with
| PatVar _ -> pat
| PatCstr (loc,((kn,i),j),cpl,n) ->
let kn' = subst_ind 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_ind 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 (Evar_kinds.ImplicitArg (ref,i,b)) ->
let ref',t = subst_global subst ref in
if ref' == ref then raw else
NHole (Evar_kinds.InternalHole)
| NHole (Evar_kinds.BinderType _ |Evar_kinds.QuestionMark _
|Evar_kinds.CasesType |Evar_kinds.InternalHole
|Evar_kinds.TomatchTypeParameter _ |Evar_kinds.GoalEvar
|Evar_kinds.ImpossibleCase |Evar_kinds.MatchingVar _) -> raw
| 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),c))
let abstract_return_type_context_notation_constr =
abstract_return_type_context snd
(fun na c -> NLambda(na,NHole Evar_kinds.InternalHole,c))
exception No_match
let rec alpha_var id1 id2 = function
| (i1,i2)::_ when i1=id1 -> i2 = id2
| (i1,i2)::_ when i2=id2 -> i1 = id1
| _::idl -> alpha_var id1 id2 idl
| [] -> id1 = id2
let alpha_eq_val (x,y) = x = y
let bind_env alp (sigma,sigmalist,sigmabinders as fullsigma) var v =
try
let vvar = List.assoc var sigma in
if alpha_eq_val (v,vvar) then fullsigma
else raise No_match
with Not_found ->
(* 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_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 -> n1 = n2
| GFix (nl1,n1), GFix (nl2,n2) ->
n1 = n2 &&
Array.for_all2 (fun (n1,_) (n2,_) -> n2 = None || n1 = n2) 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 List.mem id2 (fst metas) ->
let rhs = match na1 with
| Name id1 -> GVar (Loc.ghost,id1)
| Anonymous -> GHole (Loc.ghost,Evar_kinds.InternalHole) 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 c1 = c2 & 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))::decls) b
| b -> (decls,b)
let remove_sigma x (sigmavar,sigmalist,sigmabinders) =
(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 = List.assoc ldots_var (pi1 sigma) in
let b = match 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 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 = List.assoc ldots_var (pi1 sigma) in
let t = 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 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 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 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 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 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
& List.length tml1 = List.length tml2
& 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 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 & Array.length idl1 = Array.length idl2 &
Array.for_all2 (fun l1 l2 -> 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 None) when not u -> sigma
| GSort (_,s1), NSort s2 when 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"; expects type not given because don't know
otherwise how to ensure it corresponds to a well-typed eta-expansion;
ensure at least one constructor is consumed to avoid looping *)
| b1, NLambda (Name id,NHole _,b2) when inner ->
let id' = Namegen.next_ident_away id (free_glob_vars b1) in
match_in u alp metas (bind_binder sigma id
[(Name id',Explicit,None,GHole(Loc.ghost,Evar_kinds.BinderType (Name id')))])
(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 vars = List.partition (fun (_,(_,x)) -> x <> NtnTypeBinderList) 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 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',(List.assoc x termlists,scl)::termlists',binders')
| NtnTypeBinderList ->
(terms',termlists',(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 = List.assoc var sigma in
if 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 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 r1 = r2 ->
sigma,(0,largs)
| PatCstr (loc,(ind,_ as r1),args1,_), NApp (NRef (ConstructRef r2),l2)
when r1 = r2 ->
let l1 = add_patterns_for_params (fst r1) args1 in
let le2 = List.length l2 in
if 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 ind = r2 ->
sigma,(0,pats)
| NApp (NRef (IndRef r2),l2)
when ind = r2 ->
let le2 = List.length l2 in
if 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 -> ((List.assoc x terms, scl)::terms',termlists')
| NtnTypeConstrList -> (terms',(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
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