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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 *)
(************************************************************************)
(*i*)
open Pp
open Util
open Names
open Nameops
open Libnames
open Glob_term
open Term
open Mod_subst
(*i*)
(**********************************************************************)
(* This is the subtype of glob_constr allowed in syntactic extensions *)
(* For AList: first constr is iterator, second is terminator;
first id is where each argument of the list has to be substituted
in iterator and snd id is alternative name just for printing;
boolean is associativity *)
type aconstr =
(* Part common to glob_constr and cases_pattern *)
| ARef of global_reference
| AVar of identifier
| AApp of aconstr * aconstr list
| AList of identifier * identifier * aconstr * aconstr * bool
(* Part only in glob_constr *)
| ALambda of name * aconstr * aconstr
| AProd of name * aconstr * aconstr
| ABinderList of identifier * identifier * aconstr * aconstr
| ALetIn of name * aconstr * aconstr
| ACases of case_style * aconstr option *
(aconstr * (name * (inductive * int * name list) option)) list *
(cases_pattern list * aconstr) list
| ALetTuple of name list * (name * aconstr option) * aconstr * aconstr
| AIf of aconstr * (name * aconstr option) * aconstr * aconstr
| ARec of fix_kind * identifier array *
(name * aconstr option * aconstr) list array * aconstr array *
aconstr array
| ASort of glob_sort
| AHole of Evd.hole_kind
| APatVar of patvar
| ACast of aconstr * aconstr cast_type
type scope_name = string
type tmp_scope_name = scope_name
type subscopes = tmp_scope_name option * scope_name list
type notation_var_instance_type =
| NtnTypeConstr | NtnTypeConstrList | NtnTypeBinderList
type notation_var_internalization_type =
| NtnInternTypeConstr | NtnInternTypeBinder | NtnInternTypeIdent
type interpretation =
(identifier * (subscopes * notation_var_instance_type)) list * aconstr
(**********************************************************************)
(* Re-interpret a notation as a glob_constr, taking care of binders *)
let name_to_ident = function
| Anonymous -> 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_aconstr_with_binders loc g f e = function
| AVar id -> GVar (loc,id)
| AApp (a,args) -> GApp (loc,f e a, List.map (f e) args)
| AList (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
| ABinderList (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
| ALambda (na,ty,c) ->
let e',na = g e na in GLambda (loc,na,Explicit,f e ty,f e' c)
| AProd (na,ty,c) ->
let e',na = g e na in GProd (loc,na,Explicit,f e ty,f e' c)
| ALetIn (na,b,c) ->
let e',na = g e na in GLetIn (loc,na,f e b,f e' c)
| ACases (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,npar,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,npar,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')
| ALetTuple (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)
| AIf (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)
| ARec (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)
| ACast (c,k) -> GCast (loc,f e c,
match k with
| CastConv (k,t) -> CastConv (k,f e t)
| CastCoerce -> CastCoerce)
| ASort x -> GSort (loc,x)
| AHole x -> GHole (loc,x)
| APatVar n -> GPatVar (loc,(false,n))
| ARef x -> GRef (loc,x)
let rec glob_constr_of_aconstr loc x =
let rec aux () x =
glob_constr_of_aconstr_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 = make_loc (fst (unloc loc1),fst (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(dummy_loc,x)] iterator
else iterator) in
(* found have been collected by compare_constr *)
found := newfound;
AList (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;
ABinderList (x,y,iterator,f (Option.get !terminator))
else
raise Not_found
let aconstr_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; AVar id
| GApp (_,g,args) -> AApp (aux g, List.map aux args)
| GLambda (_,na,bk,ty,c) -> add_name found na; ALambda (na,aux ty,aux c)
| GProd (_,na,bk,ty,c) -> add_name found na; AProd (na,aux ty,aux c)
| GLetIn (_,na,b,c) -> add_name found na; ALetIn (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
ACases (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,n,nal) -> (ind,n,nal)) x))) tml,
List.map f eqnl)
| GLetTuple (loc,nal,(na,po),b,c) ->
add_name found na;
List.iter (add_name found) nal;
ALetTuple (nal,(na,Option.map aux po),aux b,aux c)
| GIf (loc,c,(na,po),b1,b2) ->
add_name found na;
AIf (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
ARec (fk,idl,dll,Array.map aux tl,Array.map aux bl)
| GCast (_,c,k) -> ACast (aux c,
match k with CastConv (k,t) -> CastConv (k,aux t)
| CastCoerce -> CastCoerce)
| GSort (_,s) -> ASort s
| GHole (_,w) -> AHole w
| GRef (_,r) -> ARef r
| GPatVar (_,(_,n)) -> APatVar 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 aconstr_of_glob_constr vars recvars a =
let a,found = aconstr_and_vars_of_glob_constr a in
check_variables vars recvars found;
a
(* Substitution of kernel names, avoiding a list of bound identifiers *)
let aconstr_of_constr avoiding t =
aconstr_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_aconstr subst bound raw =
match raw with
| ARef ref ->
let ref',t = subst_global subst ref in
if ref' == ref then raw else
aconstr_of_constr bound t
| AVar _ -> raw
| AApp (r,rl) ->
let r' = subst_aconstr subst bound r
and rl' = list_smartmap (subst_aconstr subst bound) rl in
if r' == r && rl' == rl then raw else
AApp(r',rl')
| AList (id1,id2,r1,r2,b) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
AList (id1,id2,r1',r2',b)
| ALambda (n,r1,r2) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
ALambda (n,r1',r2')
| AProd (n,r1,r2) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
AProd (n,r1',r2')
| ABinderList (id1,id2,r1,r2) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
ABinderList (id1,id2,r1',r2')
| ALetIn (n,r1,r2) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
ALetIn (n,r1',r2')
| ACases (sty,rtntypopt,rl,branches) ->
let rtntypopt' = Option.smartmap (subst_aconstr subst bound) rtntypopt
and rl' = list_smartmap
(fun (a,(n,signopt) as x) ->
let a' = subst_aconstr subst bound a in
let signopt' = Option.map (fun ((indkn,i),n,nal as z) ->
let indkn' = subst_ind subst indkn in
if indkn == indkn' then z else ((indkn',i),n,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_aconstr 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
ACases (sty,rtntypopt',rl',branches')
| ALetTuple (nal,(na,po),b,c) ->
let po' = Option.smartmap (subst_aconstr subst bound) po
and b' = subst_aconstr subst bound b
and c' = subst_aconstr subst bound c in
if po' == po && b' == b && c' == c then raw else
ALetTuple (nal,(na,po'),b',c')
| AIf (c,(na,po),b1,b2) ->
let po' = Option.smartmap (subst_aconstr subst bound) po
and b1' = subst_aconstr subst bound b1
and b2' = subst_aconstr subst bound b2
and c' = subst_aconstr subst bound c in
if po' == po && b1' == b1 && b2' == b2 && c' == c then raw else
AIf (c',(na,po'),b1',b2')
| ARec (fk,idl,dll,tl,bl) ->
let dll' =
array_smartmap (list_smartmap (fun (na,oc,b as x) ->
let oc' = Option.smartmap (subst_aconstr subst bound) oc in
let b' = subst_aconstr subst bound b in
if oc' == oc && b' == b then x else (na,oc',b'))) dll in
let tl' = array_smartmap (subst_aconstr subst bound) tl in
let bl' = array_smartmap (subst_aconstr subst bound) bl in
if dll' == dll && tl' == tl && bl' == bl then raw else
ARec (fk,idl,dll',tl',bl')
| APatVar _ | ASort _ -> raw
| AHole (Evd.ImplicitArg (ref,i,b)) ->
let ref',t = subst_global subst ref in
if ref' == ref then raw else
AHole (Evd.InternalHole)
| AHole (Evd.BinderType _ | Evd.QuestionMark _ | Evd.CasesType
| Evd.InternalHole | Evd.TomatchTypeParameter _ | Evd.GoalEvar
| Evd.ImpossibleCase | Evd.MatchingVar _) -> raw
| ACast (r1,k) ->
match k with
CastConv (k, r2) ->
let r1' = subst_aconstr subst bound r1
and r2' = subst_aconstr subst bound r2 in
if r1' == r1 && r2' == r2 then raw else
ACast (r1',CastConv (k,r2'))
| CastCoerce ->
let r1' = subst_aconstr subst bound r1 in
if r1' == r1 then raw else
ACast (r1',CastCoerce)
let subst_interpretation subst (metas,pat) =
let bound = List.map fst metas in
(metas,subst_aconstr subst bound pat)
(* Pattern-matching glob_constr and aconstr *)
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(dummy_loc,na,Explicit,GHole(dummy_loc,Evd.InternalHole),c))
let abstract_return_type_context_aconstr =
abstract_return_type_context pi3
(fun na c -> ALambda(na,AHole Evd.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 (dummy_loc,id1)
| Anonymous -> GHole (dummy_loc,Evd.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,Evd.BinderType na))::decls) b
| b -> (decls,b)
let remove_sigma x (sigmavar,sigmalist,sigmabinders) =
(List.remove_assoc x sigmavar,sigmalist,sigmabinders)
let rec 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, AVar id2 when List.mem id2 tmetas -> bind_env alp sigma id2 r1
(* Matching recursive notations for terms *)
| r1, AList (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), ABinderList (x,_,ALambda (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), ABinderList (x,_,AProd (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, ABinderList (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), ALambda (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), AProd (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), AVar id2 when alpha_var id1 id2 alp -> sigma
| GRef (_,r1), ARef r2 when (eq_gr r1 r2) -> sigma
| GPatVar (_,(_,n1)), APatVar n2 when n1=n2 -> sigma
| GApp (loc,f1,l1), AApp (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, AApp (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), ALambda (na2,t2,b2) ->
match_binders u alp metas na1 na2 (match_in u alp metas sigma t1 t2) b1 b2
| GProd (_,na1,_,t1,b1), AProd (na2,t2,b2) ->
match_binders u alp metas na1 na2 (match_in u alp metas sigma t1 t2) b1 b2
| GLetIn (_,na1,t1,b1), ALetIn (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), ACases (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_aconstr 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), ALetTuple (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), AIf (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), ARec (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)), ACast(c2, CastConv (_,t2)) ->
match_in u alp metas (match_in u alp metas sigma c1 c2) t1 t2
| GCast(_,c1, CastCoerce), ACast(c2, CastCoerce) ->
match_in u alp metas sigma c1 c2
| GSort (_,GType _), ASort (GType None) when not u -> sigma
| GSort (_,s1), ASort s2 when s1 = s2 -> sigma
| GPatVar _, AHole _ -> (*Don't hide Metas, they bind in ltac*) raise No_match
| a, AHole _ -> 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, ALambda (Name id,AHole _,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(dummy_loc,Evd.BinderType (Name id')))])
(mkGApp dummy_loc b1 (GVar (dummy_loc,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_aconstr u c (metas,pat) =
let vars = list_split_by (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 (dummy_loc,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 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, AVar id2 when List.mem id2 metas -> bind_env_cases_pattern sigma id2 r1
| PatVar (_,Anonymous), AHole _ -> sigma
| PatCstr (loc,(ind,_ as r1),[],_), ARef (ConstructRef r2) when r1 = r2 ->
sigma
| PatCstr (loc,(ind,_ as r1),args1,_), AApp (ARef (ConstructRef r2),l2)
when r1 = r2 ->
let nparams = Inductive.inductive_params (Global.lookup_inductive ind) in
if List.length l2 <> nparams + List.length args1
then
(* TODO: revert partially applied notations of the form
"Notation P := (@pair)." *)
raise No_match
else
let (p2,args2) = list_chop nparams l2 in
(* All parameters must be _ *)
List.iter (function AHole _ -> () | _ -> raise No_match) p2;
List.fold_left2 (match_cases_pattern metas) sigma args1 args2
| r1, AList (x,_,iter,termin,lassoc) ->
match_alist (fun (metas,_) -> match_cases_pattern metas)
(metas,[]) (pi1 sigma,pi2 sigma,()) r1 x iter termin lassoc
| _ -> raise No_match
let match_aconstr_cases_pattern c (metas,pat) =
let vars = List.map fst metas in
let terms,termlists,() = match_cases_pattern vars ([],[],()) c pat in
(* Reorder canonically the substitution *)
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 ([],[])
(**********************************************************************)
(*s Concrete syntax for terms *)
type notation = string
type explicitation = ExplByPos of int * identifier option | ExplByName of identifier
type binder_kind = Default of binding_kind | Generalized of binding_kind * binding_kind * bool
type abstraction_kind = AbsLambda | AbsPi
type proj_flag = int option (* [Some n] = proj of the n-th visible argument *)
type prim_token = Numeral of Bigint.bigint | String of string
type cases_pattern_expr =
| CPatAlias of loc * cases_pattern_expr * identifier
| CPatCstr of loc * reference * cases_pattern_expr list
| CPatCstrExpl of loc * reference * cases_pattern_expr list
| CPatAtom of loc * reference option
| CPatOr of loc * cases_pattern_expr list
| CPatNotation of loc * notation * cases_pattern_notation_substitution
| CPatPrim of loc * prim_token
| CPatRecord of Util.loc * (reference * cases_pattern_expr) list
| CPatDelimiters of loc * string * cases_pattern_expr
and cases_pattern_notation_substitution =
cases_pattern_expr list * (** for constr subterms *)
cases_pattern_expr list list (** for recursive notations *)
type constr_expr =
| CRef of reference
| CFix of loc * identifier located * fix_expr list
| CCoFix of loc * identifier located * cofix_expr list
| CArrow of loc * constr_expr * constr_expr
| CProdN of loc * (name located list * binder_kind * constr_expr) list * constr_expr
| CLambdaN of loc * (name located list * binder_kind * constr_expr) list * constr_expr
| CLetIn of loc * name located * constr_expr * constr_expr
| CAppExpl of loc * (proj_flag * reference) * constr_expr list
| CApp of loc * (proj_flag * constr_expr) *
(constr_expr * explicitation located option) list
| CRecord of loc * constr_expr option * (reference * constr_expr) list
| CCases of loc * case_style * constr_expr option *
(constr_expr * (name located option * constr_expr option)) list *
(loc * cases_pattern_expr list located list * constr_expr) list
| CLetTuple of loc * name located list * (name located option * constr_expr option) *
constr_expr * constr_expr
| CIf of loc * constr_expr * (name located option * constr_expr option)
* constr_expr * constr_expr
| CHole of loc * Evd.hole_kind option
| CPatVar of loc * (bool * patvar)
| CEvar of loc * existential_key * constr_expr list option
| CSort of loc * glob_sort
| CCast of loc * constr_expr * constr_expr cast_type
| CNotation of loc * notation * constr_notation_substitution
| CGeneralization of loc * binding_kind * abstraction_kind option * constr_expr
| CPrim of loc * prim_token
| CDelimiters of loc * string * constr_expr
and fix_expr =
identifier located * (identifier located option * recursion_order_expr) * local_binder list * constr_expr * constr_expr
and cofix_expr =
identifier located * local_binder list * constr_expr * constr_expr
and recursion_order_expr =
| CStructRec
| CWfRec of constr_expr
| CMeasureRec of constr_expr * constr_expr option (* measure, relation *)
and local_binder =
| LocalRawDef of name located * constr_expr
| LocalRawAssum of name located list * binder_kind * constr_expr
and constr_notation_substitution =
constr_expr list * (* for constr subterms *)
constr_expr list list * (* for recursive notations *)
local_binder list list (* for binders subexpressions *)
type typeclass_constraint = name located * binding_kind * constr_expr
and typeclass_context = typeclass_constraint list
type constr_pattern_expr = constr_expr
(***********************)
(* For binders parsing *)
let default_binder_kind = Default Explicit
let names_of_local_assums bl =
List.flatten (List.map (function LocalRawAssum(l,_,_)->l|_->[]) bl)
let names_of_local_binders bl =
List.flatten (List.map (function LocalRawAssum(l,_,_)->l|LocalRawDef(l,_)->[l]) bl)
(**********************************************************************)
(* Miscellaneous *)
let error_invalid_pattern_notation loc =
user_err_loc (loc,"",str "Invalid notation for pattern.")
(**********************************************************************)
(* Functions on constr_expr *)
let constr_loc = function
| CRef (Ident (loc,_)) -> loc
| CRef (Qualid (loc,_)) -> loc
| CFix (loc,_,_) -> loc
| CCoFix (loc,_,_) -> loc
| CArrow (loc,_,_) -> loc
| CProdN (loc,_,_) -> loc
| CLambdaN (loc,_,_) -> loc
| CLetIn (loc,_,_,_) -> loc
| CAppExpl (loc,_,_) -> loc
| CApp (loc,_,_) -> loc
| CRecord (loc,_,_) -> loc
| CCases (loc,_,_,_,_) -> loc
| CLetTuple (loc,_,_,_,_) -> loc
| CIf (loc,_,_,_,_) -> loc
| CHole (loc, _) -> loc
| CPatVar (loc,_) -> loc
| CEvar (loc,_,_) -> loc
| CSort (loc,_) -> loc
| CCast (loc,_,_) -> loc
| CNotation (loc,_,_) -> loc
| CGeneralization (loc,_,_,_) -> loc
| CPrim (loc,_) -> loc
| CDelimiters (loc,_,_) -> loc
let cases_pattern_expr_loc = function
| CPatAlias (loc,_,_) -> loc
| CPatCstr (loc,_,_) -> loc
| CPatCstrExpl (loc,_,_) -> loc
| CPatAtom (loc,_) -> loc
| CPatOr (loc,_) -> loc
| CPatNotation (loc,_,_) -> loc
| CPatRecord (loc, _) -> loc
| CPatPrim (loc,_) -> loc
| CPatDelimiters (loc,_,_) -> loc
let local_binder_loc = function
| LocalRawAssum ((loc,_)::_,_,t)
| LocalRawDef ((loc,_),t) -> join_loc loc (constr_loc t)
| LocalRawAssum ([],_,_) -> assert false
let local_binders_loc bll =
if bll = [] then dummy_loc else
join_loc (local_binder_loc (List.hd bll)) (local_binder_loc (list_last bll))
let ids_of_cases_indtype =
let add_var ids = function CRef (Ident (_,id)) -> id::ids | _ -> ids in
let rec vars_of = function
(* We deal only with the regular cases *)
| CApp (_,_,l) -> List.fold_left add_var [] (List.map fst l)
| CNotation (_,_,(l,[],[]))
(* assume the ntn is applicative and does not instantiate the head !! *)
| CAppExpl (_,_,l) -> List.fold_left add_var [] l
| CDelimiters(_,_,c) -> vars_of c
| _ -> [] in
vars_of
let ids_of_cases_tomatch tms =
List.fold_right
(fun (_,(ona,indnal)) l ->
Option.fold_right (fun t -> (@) (ids_of_cases_indtype t))
indnal (Option.fold_right (down_located name_cons) ona l))
tms []
let is_constructor id =
try ignore (Nametab.locate_extended (qualid_of_ident id)); true
with Not_found -> true
let rec cases_pattern_fold_names f a = function
| CPatRecord (_, l) ->
List.fold_left (fun acc (r, cp) -> cases_pattern_fold_names f acc cp) a l
| CPatAlias (_,pat,id) -> f id a
| CPatCstr (_,_,patl) | CPatCstrExpl (_,_,patl) | CPatOr (_,patl) ->
List.fold_left (cases_pattern_fold_names f) a patl
| CPatNotation (_,_,(patl,patll)) ->
List.fold_left (cases_pattern_fold_names f) a (patl@List.flatten patll)
| CPatDelimiters (_,_,pat) -> cases_pattern_fold_names f a pat
| CPatAtom (_,Some (Ident (_,id))) when not (is_constructor id) -> f id a
| CPatPrim _ | CPatAtom _ -> a
let ids_of_pattern_list =
List.fold_left
(located_fold_left
(List.fold_left (cases_pattern_fold_names Idset.add)))
Idset.empty
let rec fold_constr_expr_binders g f n acc b = function
| (nal,bk,t)::l ->
let nal = snd (List.split nal) in
let n' = List.fold_right (name_fold g) nal n in
f n (fold_constr_expr_binders g f n' acc b l) t
| [] ->
f n acc b
let rec fold_local_binders g f n acc b = function
| LocalRawAssum (nal,bk,t)::l ->
let nal = snd (List.split nal) in
let n' = List.fold_right (name_fold g) nal n in
f n (fold_local_binders g f n' acc b l) t
| LocalRawDef ((_,na),t)::l ->
f n (fold_local_binders g f (name_fold g na n) acc b l) t
| [] ->
f n acc b
let fold_constr_expr_with_binders g f n acc = function
| CArrow (loc,a,b) -> f n (f n acc a) b
| CAppExpl (loc,(_,_),l) -> List.fold_left (f n) acc l
| CApp (loc,(_,t),l) -> List.fold_left (f n) (f n acc t) (List.map fst l)
| CProdN (_,l,b) | CLambdaN (_,l,b) -> fold_constr_expr_binders g f n acc b l
| CLetIn (_,na,a,b) -> fold_constr_expr_binders g f n acc b [[na],default_binder_kind,a]
| CCast (loc,a,CastConv(_,b)) -> f n (f n acc a) b
| CCast (loc,a,CastCoerce) -> f n acc a
| CNotation (_,_,(l,ll,bll)) ->
(* The following is an approximation: we don't know exactly if
an ident is binding nor to which subterms bindings apply *)
let acc = List.fold_left (f n) acc (l@List.flatten ll) in
List.fold_left (fun acc bl -> fold_local_binders g f n acc (CHole (dummy_loc,None)) bl) acc bll
| CGeneralization (_,_,_,c) -> f n acc c
| CDelimiters (loc,_,a) -> f n acc a
| CHole _ | CEvar _ | CPatVar _ | CSort _ | CPrim _ | CRef _ ->
acc
| CRecord (loc,_,l) -> List.fold_left (fun acc (id, c) -> f n acc c) acc l
| CCases (loc,sty,rtnpo,al,bl) ->
let ids = ids_of_cases_tomatch al in
let acc = Option.fold_left (f (List.fold_right g ids n)) acc rtnpo in
let acc = List.fold_left (f n) acc (List.map fst al) in
List.fold_right (fun (loc,patl,rhs) acc ->
let ids = ids_of_pattern_list patl in
f (Idset.fold g ids n) acc rhs) bl acc
| CLetTuple (loc,nal,(ona,po),b,c) ->
let n' = List.fold_right (down_located (name_fold g)) nal n in
f (Option.fold_right (down_located (name_fold g)) ona n') (f n acc b) c
| CIf (_,c,(ona,po),b1,b2) ->
let acc = f n (f n (f n acc b1) b2) c in
Option.fold_left
(f (Option.fold_right (down_located (name_fold g)) ona n)) acc po
| CFix (loc,_,l) ->
let n' = List.fold_right (fun ((_,id),_,_,_,_) -> g id) l n in
List.fold_right (fun (_,(_,o),lb,t,c) acc ->
fold_local_binders g f n'
(fold_local_binders g f n acc t lb) c lb) l acc
| CCoFix (loc,_,_) ->
Pp.warning "Capture check in multiple binders not done"; acc
let free_vars_of_constr_expr c =
let rec aux bdvars l = function
| CRef (Ident (_,id)) -> if List.mem id bdvars then l else Idset.add id l
| c -> fold_constr_expr_with_binders (fun a l -> a::l) aux bdvars l c
in aux [] Idset.empty c
let occur_var_constr_expr id c = Idset.mem id (free_vars_of_constr_expr c)
let mkIdentC id = CRef (Ident (dummy_loc, id))
let mkRefC r = CRef r
let mkCastC (a,k) = CCast (dummy_loc,a,k)
let mkLambdaC (idl,bk,a,b) = CLambdaN (dummy_loc,[idl,bk,a],b)
let mkLetInC (id,a,b) = CLetIn (dummy_loc,id,a,b)
let mkProdC (idl,bk,a,b) = CProdN (dummy_loc,[idl,bk,a],b)
let mkAppC (f,l) =
let l = List.map (fun x -> (x,None)) l in
match f with
| CApp (_,g,l') -> CApp (dummy_loc, g, l' @ l)
| _ -> CApp (dummy_loc, (None, f), l)
let rec mkCProdN loc bll c =
match bll with
| LocalRawAssum ((loc1,_)::_ as idl,bk,t) :: bll ->
CProdN (loc,[idl,bk,t],mkCProdN (join_loc loc1 loc) bll c)
| LocalRawDef ((loc1,_) as id,b) :: bll ->
CLetIn (loc,id,b,mkCProdN (join_loc loc1 loc) bll c)
| [] -> c
| LocalRawAssum ([],_,_) :: bll -> mkCProdN loc bll c
let rec mkCLambdaN loc bll c =
match bll with
| LocalRawAssum ((loc1,_)::_ as idl,bk,t) :: bll ->
CLambdaN (loc,[idl,bk,t],mkCLambdaN (join_loc loc1 loc) bll c)
| LocalRawDef ((loc1,_) as id,b) :: bll ->
CLetIn (loc,id,b,mkCLambdaN (join_loc loc1 loc) bll c)
| [] -> c
| LocalRawAssum ([],_,_) :: bll -> mkCLambdaN loc bll c
let rec abstract_constr_expr c = function
| [] -> c
| LocalRawDef (x,b)::bl -> mkLetInC(x,b,abstract_constr_expr c bl)
| LocalRawAssum (idl,bk,t)::bl ->
List.fold_right (fun x b -> mkLambdaC([x],bk,t,b)) idl
(abstract_constr_expr c bl)
let rec prod_constr_expr c = function
| [] -> c
| LocalRawDef (x,b)::bl -> mkLetInC(x,b,prod_constr_expr c bl)
| LocalRawAssum (idl,bk,t)::bl ->
List.fold_right (fun x b -> mkProdC([x],bk,t,b)) idl
(prod_constr_expr c bl)
let coerce_reference_to_id = function
| Ident (_,id) -> id
| Qualid (loc,_) ->
user_err_loc (loc, "coerce_reference_to_id",
str "This expression should be a simple identifier.")
let coerce_to_id = function
| CRef (Ident (loc,id)) -> (loc,id)
| a -> user_err_loc
(constr_loc a,"coerce_to_id",
str "This expression should be a simple identifier.")
let coerce_to_name = function
| CRef (Ident (loc,id)) -> (loc,Name id)
| CHole (loc,_) -> (loc,Anonymous)
| a -> user_err_loc
(constr_loc a,"coerce_to_name",
str "This expression should be a name.")
(* Interpret the index of a recursion order annotation *)
let split_at_annot bl na =
let names = List.map snd (names_of_local_assums bl) in
match na with
| None ->
if names = [] then error "A fixpoint needs at least one parameter."
else [], bl
| Some (loc, id) ->
let rec aux acc = function
| LocalRawAssum (bls, k, t) as x :: rest ->
let l, r = list_split_when (fun (loc, na) -> na = Name id) bls in
if r = [] then aux (x :: acc) rest
else
(List.rev (if l = [] then acc else LocalRawAssum (l, k, t) :: acc),
LocalRawAssum (r, k, t) :: rest)
| LocalRawDef _ as x :: rest -> aux (x :: acc) rest
| [] ->
user_err_loc(loc,"",
str "No parameter named " ++ Nameops.pr_id id ++ str".")
in aux [] bl
(* Used in correctness and interface *)
let map_binder g e nal = List.fold_right (down_located (name_fold g)) nal e
let map_binders f g e bl =
(* TODO: avoid variable capture in [t] by some [na] in [List.tl nal] *)
let h (e,bl) (nal,bk,t) = (map_binder g e nal,(nal,bk,f e t)::bl) in
let (e,rbl) = List.fold_left h (e,[]) bl in
(e, List.rev rbl)
let map_local_binders f g e bl =
(* TODO: avoid variable capture in [t] by some [na] in [List.tl nal] *)
let h (e,bl) = function
LocalRawAssum(nal,k,ty) ->
(map_binder g e nal, LocalRawAssum(nal,k,f e ty)::bl)
| LocalRawDef((loc,na),ty) ->
(name_fold g na e, LocalRawDef((loc,na),f e ty)::bl) in
let (e,rbl) = List.fold_left h (e,[]) bl in
(e, List.rev rbl)
let map_constr_expr_with_binders g f e = function
| CArrow (loc,a,b) -> CArrow (loc,f e a,f e b)
| CAppExpl (loc,r,l) -> CAppExpl (loc,r,List.map (f e) l)
| CApp (loc,(p,a),l) ->
CApp (loc,(p,f e a),List.map (fun (a,i) -> (f e a,i)) l)
| CProdN (loc,bl,b) ->
let (e,bl) = map_binders f g e bl in CProdN (loc,bl,f e b)
| CLambdaN (loc,bl,b) ->
let (e,bl) = map_binders f g e bl in CLambdaN (loc,bl,f e b)
| CLetIn (loc,na,a,b) -> CLetIn (loc,na,f e a,f (name_fold g (snd na) e) b)
| CCast (loc,a,CastConv (k,b)) -> CCast (loc,f e a,CastConv(k, f e b))
| CCast (loc,a,CastCoerce) -> CCast (loc,f e a,CastCoerce)
| CNotation (loc,n,(l,ll,bll)) ->
(* This is an approximation because we don't know what binds what *)
CNotation (loc,n,(List.map (f e) l,List.map (List.map (f e)) ll,
List.map (fun bl -> snd (map_local_binders f g e bl)) bll))
| CGeneralization (loc,b,a,c) -> CGeneralization (loc,b,a,f e c)
| CDelimiters (loc,s,a) -> CDelimiters (loc,s,f e a)
| CHole _ | CEvar _ | CPatVar _ | CSort _
| CPrim _ | CRef _ as x -> x
| CRecord (loc,p,l) -> CRecord (loc,p,List.map (fun (id, c) -> (id, f e c)) l)
| CCases (loc,sty,rtnpo,a,bl) ->
(* TODO: apply g on the binding variables in pat... *)
let bl = List.map (fun (loc,pat,rhs) -> (loc,pat,f e rhs)) bl in
let ids = ids_of_cases_tomatch a in
let po = Option.map (f (List.fold_right g ids e)) rtnpo in
CCases (loc, sty, po, List.map (fun (tm,x) -> (f e tm,x)) a,bl)
| CLetTuple (loc,nal,(ona,po),b,c) ->
let e' = List.fold_right (down_located (name_fold g)) nal e in
let e'' = Option.fold_right (down_located (name_fold g)) ona e in
CLetTuple (loc,nal,(ona,Option.map (f e'') po),f e b,f e' c)
| CIf (loc,c,(ona,po),b1,b2) ->
let e' = Option.fold_right (down_located (name_fold g)) ona e in
CIf (loc,f e c,(ona,Option.map (f e') po),f e b1,f e b2)
| CFix (loc,id,dl) ->
CFix (loc,id,List.map (fun (id,n,bl,t,d) ->
let (e',bl') = map_local_binders f g e bl in
let t' = f e' t in
(* Note: fix names should be inserted before the arguments... *)
let e'' = List.fold_left (fun e ((_,id),_,_,_,_) -> g id e) e' dl in
let d' = f e'' d in
(id,n,bl',t',d')) dl)
| CCoFix (loc,id,dl) ->
CCoFix (loc,id,List.map (fun (id,bl,t,d) ->
let (e',bl') = map_local_binders f g e bl in
let t' = f e' t in
let e'' = List.fold_left (fun e ((_,id),_,_,_) -> g id e) e' dl in
let d' = f e'' d in
(id,bl',t',d')) dl)
(* Used in constrintern *)
let rec replace_vars_constr_expr l = function
| CRef (Ident (loc,id)) as x ->
(try CRef (Ident (loc,List.assoc id l)) with Not_found -> x)
| c -> map_constr_expr_with_binders List.remove_assoc
replace_vars_constr_expr l c
(**********************************************************************)
(* Concrete syntax for modules and modules types *)
type with_declaration_ast =
| CWith_Module of identifier list located * qualid located
| CWith_Definition of identifier list located * constr_expr
type module_ast =
| CMident of qualid located
| CMapply of loc * module_ast * module_ast
| CMwith of loc * module_ast * with_declaration_ast
(* Returns the ranges of locs of the notation that are not occupied by args *)
(* and which are then occupied by proper symbols of the notation (or spaces) *)
let locs_of_notation loc locs ntn =
let (bl,el) = Util.unloc loc in
let locs = List.map Util.unloc locs in
let rec aux pos = function
| [] -> if pos = el then [] else [(pos,el-1)]
| (ba,ea)::l ->if pos = ba then aux ea l else (pos,ba-1)::aux ea l
in aux bl (Sort.list (fun l1 l2 -> fst l1 < fst l2) locs)
let ntn_loc loc (args,argslist,binderslist) =
locs_of_notation loc
(List.map constr_loc (args@List.flatten argslist)@
List.map local_binders_loc binderslist)
let patntn_loc loc (args,argslist) =
locs_of_notation loc
(List.map cases_pattern_expr_loc (args@List.flatten argslist))
|