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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
(*i*)
open Pp
open Util
open Names
open Nameops
open Libnames
open Rawterm
open Term
(*i*)
(**********************************************************************)
(* This is the subtype of rawconstr allowed in syntactic extensions *)
type aconstr =
| ARef of global_reference
| AVar of identifier
| AApp of aconstr * aconstr list
| ALambda of name * aconstr * aconstr
| AProd of name * aconstr * aconstr
| ALetIn of name * aconstr * aconstr
| ACases of aconstr option * aconstr list *
(identifier list * cases_pattern list * aconstr) list
| AOrderedCase of case_style * aconstr option * aconstr * aconstr array
| ASort of rawsort
| AHole of hole_kind
| AMeta of int
| ACast of aconstr * aconstr
let name_app f e = function
| Name id -> let (id, e) = f id e in (Name id, e)
| Anonymous -> Anonymous, e
let map_aconstr_with_binders_loc loc g f e = function
| AVar id -> RVar (loc,id)
| AApp (a,args) -> RApp (loc,f e a, List.map (f e) args)
| ALambda (na,ty,c) ->
let na,e = name_app g e na in RLambda (loc,na,f e ty,f e c)
| AProd (na,ty,c) ->
let na,e = name_app g e na in RProd (loc,na,f e ty,f e c)
| ALetIn (na,b,c) ->
let na,e = name_app g e na in RLetIn (loc,na,f e b,f e c)
| ACases (tyopt,tml,eqnl) ->
let fold id (idl,e) = let (id,e) = g id e in (id::idl,e) in
let eqnl = List.map (fun (idl,pat,rhs) ->
let (idl,e) = List.fold_right fold idl ([],e) in (loc,idl,pat,f e rhs)) eqnl in
RCases (loc,option_app (f e) tyopt,List.map (f e) tml,eqnl)
| AOrderedCase (b,tyopt,tm,bv) ->
ROrderedCase (loc,b,option_app (f e) tyopt,f e tm,Array.map (f e) bv)
| ACast (c,t) -> RCast (loc,f e c,f e t)
| ASort x -> RSort (loc,x)
| AHole x -> RHole (loc,x)
| AMeta n -> RMeta (loc,n)
| ARef x -> RRef (loc,x)
let rec subst_pat subst pat =
match pat with
| PatVar _ -> pat
| PatCstr (loc,((kn,i),j),cpl,n) ->
let kn' = subst_kn 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 raw =
match raw with
| ARef ref ->
let ref' = subst_global subst ref in
if ref' == ref then raw else
ARef ref'
| AVar _ -> raw
| AApp (r,rl) ->
let r' = subst_aconstr subst r
and rl' = list_smartmap (subst_aconstr subst) rl in
if r' == r && rl' == rl then raw else
AApp(r',rl')
| ALambda (n,r1,r2) ->
let r1' = subst_aconstr subst r1 and r2' = subst_aconstr subst r2 in
if r1' == r1 && r2' == r2 then raw else
ALambda (n,r1',r2')
| AProd (n,r1,r2) ->
let r1' = subst_aconstr subst r1 and r2' = subst_aconstr subst r2 in
if r1' == r1 && r2' == r2 then raw else
AProd (n,r1',r2')
| ALetIn (n,r1,r2) ->
let r1' = subst_aconstr subst r1 and r2' = subst_aconstr subst r2 in
if r1' == r1 && r2' == r2 then raw else
ALetIn (n,r1',r2')
| ACases (ro,rl,branches) ->
let ro' = option_smartmap (subst_aconstr subst) ro
and rl' = list_smartmap (subst_aconstr subst) rl
and branches' = list_smartmap
(fun (idl,cpl,r as branch) ->
let cpl' = list_smartmap (subst_pat subst) cpl
and r' = subst_aconstr subst r in
if cpl' == cpl && r' == r then branch else
(idl,cpl',r'))
branches
in
if ro' == ro && rl' == rl && branches' == branches then raw else
ACases (ro',rl',branches')
| AOrderedCase (b,ro,r,ra) ->
let ro' = option_smartmap (subst_aconstr subst) ro
and r' = subst_aconstr subst r
and ra' = array_smartmap (subst_aconstr subst) ra in
if ro' == ro && r' == r && ra' == ra then raw else
AOrderedCase (b,ro',r',ra')
| AMeta _ | ASort _ -> raw
| AHole (ImplicitArg (ref,i)) ->
let ref' = subst_global subst ref in
if ref' == ref then raw else
AHole (ImplicitArg (ref',i))
| AHole ( (AbstractionType _ | QuestionMark | CasesType |
InternalHole | TomatchTypeParameter _)) -> raw
| ACast (r1,r2) ->
let r1' = subst_aconstr subst r1 and r2' = subst_aconstr subst r2 in
if r1' == r1 && r2' == r2 then raw else
ACast (r1',r2')
let add_name r = function
| Anonymous -> ()
| Name id -> r := id :: !r
let aconstr_of_rawconstr vars a =
let found = ref [] in
let bound_binders = ref [] in
let rec aux = function
| RVar (_,id) ->
if not (List.mem id !bound_binders) then found := id::!found;
AVar id
| RApp (_,g,args) -> AApp (aux g, List.map aux args)
| RLambda (_,na,ty,c) -> add_name bound_binders na; ALambda (na,aux ty,aux c)
| RProd (_,na,ty,c) -> add_name bound_binders na; AProd (na,aux ty,aux c)
| RLetIn (_,na,b,c) -> add_name bound_binders na; ALetIn (na,aux b,aux c)
| RCases (_,tyopt,tml,eqnl) ->
let f (_,idl,pat,rhs) =
bound_binders := idl@(!bound_binders);
(idl,pat,aux rhs) in
ACases (option_app aux tyopt,List.map aux tml, List.map f eqnl)
| ROrderedCase (_,b,tyopt,tm,bv) ->
AOrderedCase (b,option_app aux tyopt,aux tm, Array.map aux bv)
| RCast (_,c,t) -> ACast (aux c,aux t)
| RSort (_,s) -> ASort s
| RHole (_,w) -> AHole w
| RRef (_,r) -> ARef r
| RMeta (_,n) -> AMeta n
| RDynamic _ | RRec _ | REvar _ ->
error "Fixpoints, cofixpoints, existential variables and pattern-matching not \
allowed in abbreviatable expressions"
in
let a = aux a in
let check_type x =
if not (List.mem x !found or List.mem x !bound_binders) then
error ((string_of_id x)^" is unbound in the right-hand-side") in
List.iter check_type vars;
a
(* Pattern-matching rawconstr and aconstr *)
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 sigma var v =
try
let vvar = List.assoc var sigma in
if alpha_eq_val (v,vvar) then sigma
else raise No_match
with Not_found ->
(var,v)::sigma
let rec match_ alp metas sigma a1 a2 = match (a1,a2) with
| r1, AVar id2 when List.mem id2 metas -> bind_env sigma id2 r1
| RVar (_,id1), AVar id2 when alpha_var id1 id2 alp -> sigma
| RRef (_,r1), ARef r2 when r1 = r2 -> sigma
| RMeta (_,n1), AMeta n2 when n1=n2 -> sigma
| RApp (_,f1,l1), AApp (f2,l2) when List.length l1 = List.length l2 ->
List.fold_left2 (match_ alp metas) (match_ alp metas sigma f1 f2) l1 l2
| RLambda (_,na1,t1,b1), ALambda (na2,t2,b2) ->
match_binders alp metas (match_ alp metas sigma t1 t2) b1 b2 na1 na2
| RProd (_,na1,t1,b1), AProd (na2,t2,b2) ->
match_binders alp metas (match_ alp metas sigma t1 t2) b1 b2 na1 na2
| RLetIn (_,na1,t1,b1), AProd (na2,t2,b2) ->
match_binders alp metas (match_ alp metas sigma t1 t2) b1 b2 na1 na2
| RCases (_,po1,tml1,eqnl1), ACases (po2,tml2,eqnl2) ->
let sigma = option_fold_left2 (match_ alp metas) sigma po1 po2 in
let sigma = List.fold_left2 (match_ alp metas) sigma tml1 tml2 in
List.fold_left2 (match_equations alp metas) sigma eqnl1 eqnl2
| ROrderedCase (_,st,po1,c1,bl1), AOrderedCase (st2,po2,c2,bl2) ->
let sigma = option_fold_left2 (match_ alp metas) sigma po1 po2 in
array_fold_left2 (match_ alp metas) (match_ alp metas sigma c1 c2) bl1 bl2
| RCast(_,c1,t1), ACast(c2,t2) ->
match_ alp metas (match_ alp metas sigma c1 c2) t1 t2
| RSort (_,s1), ASort s2 when s1 = s2 -> sigma
| RHole _, a -> sigma
| RMeta _, AHole _ -> (*Don't hide Metas, they bind in ltac*) raise No_match
| a, AHole _ -> sigma
| (RDynamic _ | RRec _ | REvar _), _
| _,_ -> raise No_match
and match_binders alp metas sigma b1 b2 na1 na2 = match (na1,na2) with
| (na1,Name id2) when List.mem id2 metas ->
let sigma =
name_fold
(fun id sigma -> bind_env sigma id2 (RVar (dummy_loc,id))) na1 sigma
in
match_ alp metas sigma b1 b2
| (na1,na2) ->
let alp =
name_fold
(fun id1 -> name_fold (fun id2 alp -> (id1,id2)::alp) na2) na1 alp in
match_ alp metas sigma b1 b2
and match_equations alp metas sigma (_,idl1,pat1,rhs1) (idl2,pat2,rhs2) =
if idl1 = idl2 & pat1 = pat2 (* Useful to reason up to alpha ?? *) then
match_ alp metas sigma rhs1 rhs2
else raise No_match
type scope_name = string
type interpretation = (identifier * scope_name list) list * aconstr
let match_aconstr c (metas_scl,pat) =
let subst = match_ [] (List.map fst metas_scl) [] c pat in
(* Reorder canonically the substitution *)
let find x subst =
try List.assoc x subst
with Not_found ->
(* Happens for binders bound to Anonymous *)
(* Find a better way to propagate Anonymous... *)
RVar (dummy_loc,x) in
List.map (fun (x,scl) -> (find x subst,scl)) metas_scl
(**********************************************************************)
(*s Concrete syntax for terms *)
type notation = string
type explicitation = int
type cases_pattern_expr =
| CPatAlias of loc * cases_pattern_expr * identifier
| CPatCstr of loc * reference * cases_pattern_expr list
| CPatAtom of loc * reference option
| CPatNumeral of loc * Bignat.bigint
| CPatDelimiters of loc * string * cases_pattern_expr
type constr_expr =
| CRef of reference
| CFix of loc * identifier located * fixpoint_expr list
| CCoFix of loc * identifier located * cofixpoint_expr list
| CArrow of loc * constr_expr * constr_expr
| CProdN of loc * (name located list * constr_expr) list * constr_expr
| CLambdaN of loc * (name located list * constr_expr) list * constr_expr
| CLetIn of loc * name located * constr_expr * constr_expr
| CAppExpl of loc * reference * constr_expr list
| CApp of loc * constr_expr * (constr_expr * explicitation option) list
| CCases of loc * constr_expr option * constr_expr list *
(loc * cases_pattern_expr list * constr_expr) list
| COrderedCase of loc * case_style * constr_expr option * constr_expr
* constr_expr list
| CHole of loc
| CMeta of loc * int
| CSort of loc * rawsort
| CCast of loc * constr_expr * constr_expr
| CNotation of loc * notation * constr_expr list
| CNumeral of loc * Bignat.bigint
| CDelimiters of loc * string * constr_expr
| CDynamic of loc * Dyn.t
and fixpoint_expr = identifier * int * constr_expr * constr_expr
and cofixpoint_expr = identifier * constr_expr * constr_expr
(***********************)
(* For binders parsing *)
type local_binder =
| LocalRawDef of name located * constr_expr
| LocalRawAssum of name located list * constr_expr
(**********************************************************************)
(* 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
| CCases (loc,_,_,_) -> loc
| COrderedCase (loc,_,_,_,_) -> loc
| CHole loc -> loc
| CMeta (loc,_) -> loc
| CSort (loc,_) -> loc
| CCast (loc,_,_) -> loc
| CNotation (loc,_,_) -> loc
| CNumeral (loc,_) -> loc
| CDelimiters (loc,_,_) -> loc
| CDynamic _ -> dummy_loc
let cases_pattern_loc = function
| CPatAlias (loc,_,_) -> loc
| CPatCstr (loc,_,_) -> loc
| CPatAtom (loc,_) -> loc
| CPatNumeral (loc,_) -> loc
| CPatDelimiters (loc,_,_) -> loc
let occur_var_constr_ref id = function
| Ident (loc,id') -> id = id'
| Qualid _ -> false
let rec occur_var_constr_expr id = function
| CRef r -> occur_var_constr_ref id r
| CArrow (loc,a,b) -> occur_var_constr_expr id a or occur_var_constr_expr id b
| CAppExpl (loc,r,l) ->
occur_var_constr_ref id r or List.exists (occur_var_constr_expr id) l
| CApp (loc,f,l) ->
occur_var_constr_expr id f or
List.exists (fun (a,_) -> occur_var_constr_expr id a) l
| CProdN (_,l,b) -> occur_var_binders id b l
| CLambdaN (_,l,b) -> occur_var_binders id b l
| CLetIn (_,na,a,b) -> occur_var_binders id b [[na],a]
| CCast (loc,a,b) -> occur_var_constr_expr id a or occur_var_constr_expr id b
| CNotation (_,_,l) -> List.exists (occur_var_constr_expr id) l
| CDelimiters (loc,_,a) -> occur_var_constr_expr id a
| CHole _ | CMeta _ | CSort _ | CNumeral _ | CDynamic _ -> false
| CCases (loc,_,_,_)
| COrderedCase (loc,_,_,_,_)
| CFix (loc,_,_)
| CCoFix (loc,_,_) ->
Pp.warning "Capture check in multiple binders not done"; false
and occur_var_binders id b = function
| (idl,a)::l ->
occur_var_constr_expr id a or
(not (List.mem (Name id) (snd (List.split idl)))
& occur_var_binders id b l)
| [] -> occur_var_constr_expr id b
let mkIdentC id = CRef (Ident (dummy_loc, id))
let mkRefC r = CRef r
let mkAppC (f,l) = CApp (dummy_loc, f, List.map (fun x -> (x,None)) l)
let mkCastC (a,b) = CCast (dummy_loc,a,b)
let mkLambdaC (idl,a,b) = CLambdaN (dummy_loc,[idl,a],b)
let mkLetInC (id,a,b) = CLetIn (dummy_loc,id,a,b)
let mkProdC (idl,a,b) = CProdN (dummy_loc,[idl,a],b)
(* Used in correctness and interface *)
let map_binders f g e bl =
(* TODO: avoid variable capture in [t] by some [na] in [List.tl nal] *)
let h (nal,t) (e,bl) =
(List.fold_right (fun (_,na) -> name_fold g na) nal e,(nal,f e t)::bl) in
List.fold_right h bl (e,[])
let map_constr_expr_with_binders f g 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,a,l) -> CApp (loc,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,b) -> CCast (loc,f e a,f e b)
| CNotation (loc,n,l) -> CNotation (loc,n,List.map (f e) l)
| CDelimiters (loc,s,a) -> CDelimiters (loc,s,f e a)
| CHole _ | CMeta _ | CSort _ | CNumeral _ | CDynamic _ | CRef _ as x -> x
| CCases (loc,po,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
CCases (loc,option_app (f e) po,List.map (f e) a,bl)
| COrderedCase (loc,s,po,a,bl) ->
COrderedCase (loc,s,option_app (f e) po,f e a,List.map (f e) bl)
| CFix (loc,id,dl) ->
CFix (loc,id,List.map (fun (id,n,t,d) -> (id,n,f e t,f e d)) dl)
| CCoFix (loc,id,dl) ->
CCoFix (loc,id,List.map (fun (id,t,d) -> (id,f e t,f e 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 replace_vars_constr_expr
(fun id l -> List.remove_assoc id l) l c
(**********************************************************************)
(* Concrete syntax for modules and modules types *)
type with_declaration_ast =
| CWith_Module of identifier * qualid located
| CWith_Definition of identifier * constr_expr
type module_type_ast =
| CMTEident of qualid located
| CMTEwith of module_type_ast * with_declaration_ast
type module_ast =
| CMEident of qualid located
| CMEapply of module_ast * module_ast
|