open Util open Names open Cic open Term (** Substitutions, code imported from kernel/mod_subst *) module Deltamap = struct type t = delta_resolver let empty = MPmap.empty, KNmap.empty let is_empty (mm, km) = MPmap.is_empty mm && KNmap.is_empty km let add_kn kn hint (mm,km) = (mm,KNmap.add kn hint km) let add_mp mp mp' (mm,km) = (MPmap.add mp mp' mm, km) let remove_mp mp (mm,km) = (MPmap.remove mp mm, km) let find_mp mp map = MPmap.find mp (fst map) let find_kn kn map = KNmap.find kn (snd map) let mem_mp mp map = MPmap.mem mp (fst map) let mem_kn kn map = KNmap.mem kn (snd map) let fold_kn f map i = KNmap.fold f (snd map) i let fold fmp fkn (mm,km) i = MPmap.fold fmp mm (KNmap.fold fkn km i) let join map1 map2 = fold add_mp add_kn map1 map2 end let empty_delta_resolver = Deltamap.empty module Umap = struct type 'a t = 'a umap_t let empty = MPmap.empty, MBImap.empty let is_empty (m1,m2) = MPmap.is_empty m1 && MBImap.is_empty m2 let add_mbi mbi x (m1,m2) = (m1,MBImap.add mbi x m2) let add_mp mp x (m1,m2) = (MPmap.add mp x m1, m2) let find_mp mp map = MPmap.find mp (fst map) let find_mbi mbi map = MBImap.find mbi (snd map) let mem_mp mp map = MPmap.mem mp (fst map) let mem_mbi mbi map = MBImap.mem mbi (snd map) let iter_mbi f map = MBImap.iter f (snd map) let fold fmp fmbi (m1,m2) i = MPmap.fold fmp m1 (MBImap.fold fmbi m2 i) let join map1 map2 = fold add_mp add_mbi map1 map2 end type 'a subst_fun = substitution -> 'a -> 'a let empty_subst = Umap.empty let is_empty_subst = Umap.is_empty let add_mbid mbid mp = Umap.add_mbi mbid (mp,empty_delta_resolver) let add_mp mp1 mp2 = Umap.add_mp mp1 (mp2,empty_delta_resolver) let map_mbid mbid mp = add_mbid mbid mp empty_subst let map_mp mp1 mp2 = add_mp mp1 mp2 empty_subst let mp_in_delta mp = Deltamap.mem_mp mp let find_prefix resolve mp = let rec sub_mp = function | MPdot(mp,l) as mp_sup -> (try Deltamap.find_mp mp_sup resolve with Not_found -> MPdot(sub_mp mp,l)) | p -> Deltamap.find_mp p resolve in try sub_mp mp with Not_found -> mp (** Nota: the following function is slightly different in mod_subst PL: Is it on purpose ? *) let solve_delta_kn resolve kn = try match Deltamap.find_kn kn resolve with | Equiv kn1 -> kn1 | Inline _ -> raise Not_found with Not_found -> let mp,dir,l = repr_kn kn in let new_mp = find_prefix resolve mp in if mp == new_mp then kn else make_kn new_mp dir l let gen_of_delta resolve x kn fix_can = let new_kn = solve_delta_kn resolve kn in if kn == new_kn then x else fix_can new_kn let constant_of_delta resolve con = let kn = user_con con in gen_of_delta resolve con kn (constant_of_kn_equiv kn) let constant_of_delta2 resolve con = let kn, kn' = canonical_con con, user_con con in gen_of_delta resolve con kn (constant_of_kn_equiv kn') let mind_of_delta resolve mind = let kn = user_mind mind in gen_of_delta resolve mind kn (mind_of_kn_equiv kn) let mind_of_delta2 resolve mind = let kn, kn' = canonical_mind mind, user_mind mind in gen_of_delta resolve mind kn (mind_of_kn_equiv kn') let find_inline_of_delta kn resolve = match Deltamap.find_kn kn resolve with | Inline (_,o) -> o | _ -> raise Not_found let constant_of_delta_with_inline resolve con = let kn1,kn2 = canonical_con con,user_con con in try find_inline_of_delta kn2 resolve with Not_found -> try find_inline_of_delta kn1 resolve with Not_found -> None let subst_mp0 sub mp = (* 's like subst *) let rec aux mp = match mp with | MPfile sid -> Umap.find_mp mp sub | MPbound bid -> begin try Umap.find_mbi bid sub with Not_found -> Umap.find_mp mp sub end | MPdot (mp1,l) as mp2 -> begin try Umap.find_mp mp2 sub with Not_found -> let mp1',resolve = aux mp1 in MPdot (mp1',l),resolve end in try Some (aux mp) with Not_found -> None let subst_mp sub mp = match subst_mp0 sub mp with None -> mp | Some (mp',_) -> mp' let subst_kn_delta sub kn = let mp,dir,l = repr_kn kn in match subst_mp0 sub mp with Some (mp',resolve) -> solve_delta_kn resolve (make_kn mp' dir l) | None -> kn let subst_kn sub kn = let mp,dir,l = repr_kn kn in match subst_mp0 sub mp with Some (mp',_) -> make_kn mp' dir l | None -> kn exception No_subst type sideconstantsubst = | User | Canonical let gen_subst_mp f sub mp1 mp2 = match subst_mp0 sub mp1, subst_mp0 sub mp2 with | None, None -> raise No_subst | Some (mp',resolve), None -> User, (f mp' mp2), resolve | None, Some (mp',resolve) -> Canonical, (f mp1 mp'), resolve | Some (mp1',_), Some (mp2',resolve2) -> Canonical, (f mp1' mp2'), resolve2 let make_mind_equiv mpu mpc dir l = let knu = make_kn mpu dir l in if mpu == mpc then mind_of_kn knu else mind_of_kn_equiv knu (make_kn mpc dir l) let subst_ind sub mind = let kn1,kn2 = user_mind mind, canonical_mind mind in let mp1,dir,l = repr_kn kn1 in let mp2,_,_ = repr_kn kn2 in let rebuild_mind mp1 mp2 = make_mind_equiv mp1 mp2 dir l in try let side,mind',resolve = gen_subst_mp rebuild_mind sub mp1 mp2 in match side with | User -> mind_of_delta resolve mind' | Canonical -> mind_of_delta2 resolve mind' with No_subst -> mind let make_con_equiv mpu mpc dir l = let knu = make_kn mpu dir l in if mpu == mpc then constant_of_kn knu else constant_of_kn_equiv knu (make_kn mpc dir l) let subst_con0 sub con u = let kn1,kn2 = user_con con,canonical_con con in let mp1,dir,l = repr_kn kn1 in let mp2,_,_ = repr_kn kn2 in let rebuild_con mp1 mp2 = make_con_equiv mp1 mp2 dir l in let dup con = con, Const (con, u) in let side,con',resolve = gen_subst_mp rebuild_con sub mp1 mp2 in match constant_of_delta_with_inline resolve con' with | Some t -> con', t | None -> let con'' = match side with | User -> constant_of_delta resolve con' | Canonical -> constant_of_delta2 resolve con' in if con'' == con then raise No_subst else dup con'' let rec map_kn f f' c = let func = map_kn f f' in match c with | Const (kn, u) -> (try snd (f' kn u) with No_subst -> c) | Proj (p,t) -> let p' = Projection.map (fun kn -> try fst (f' kn Univ.Instance.empty) with No_subst -> kn) p in let t' = func t in if p' == p && t' == t then c else Proj (p', t') | Ind ((kn,i),u) -> let kn' = f kn in if kn'==kn then c else Ind ((kn',i),u) | Construct (((kn,i),j),u) -> let kn' = f kn in if kn'==kn then c else Construct (((kn',i),j),u) | Case (ci,p,ct,l) -> let ci_ind = let (kn,i) = ci.ci_ind in let kn' = f kn in if kn'==kn then ci.ci_ind else kn',i in let p' = func p in let ct' = func ct in let l' = Array.smartmap func l in if (ci.ci_ind==ci_ind && p'==p && l'==l && ct'==ct)then c else Case ({ci with ci_ind = ci_ind}, p',ct', l') | Cast (ct,k,t) -> let ct' = func ct in let t'= func t in if (t'==t && ct'==ct) then c else Cast (ct', k, t') | Prod (na,t,ct) -> let ct' = func ct in let t'= func t in if (t'==t && ct'==ct) then c else Prod (na, t', ct') | Lambda (na,t,ct) -> let ct' = func ct in let t'= func t in if (t'==t && ct'==ct) then c else Lambda (na, t', ct') | LetIn (na,b,t,ct) -> let ct' = func ct in let t'= func t in let b'= func b in if (t'==t && ct'==ct && b==b') then c else LetIn (na, b', t', ct') | App (ct,l) -> let ct' = func ct in let l' = Array.smartmap func l in if (ct'== ct && l'==l) then c else App (ct',l') | Evar (e,l) -> let l' = Array.smartmap func l in if (l'==l) then c else Evar (e,l') | Fix (ln,(lna,tl,bl)) -> let tl' = Array.smartmap func tl in let bl' = Array.smartmap func bl in if (bl == bl'&& tl == tl') then c else Fix (ln,(lna,tl',bl')) | CoFix(ln,(lna,tl,bl)) -> let tl' = Array.smartmap func tl in let bl' = Array.smartmap func bl in if (bl == bl'&& tl == tl') then c else CoFix (ln,(lna,tl',bl')) | _ -> c let subst_mps sub c = if is_empty_subst sub then c else map_kn (subst_ind sub) (subst_con0 sub) c let rec replace_mp_in_mp mpfrom mpto mp = match mp with | _ when ModPath.equal mp mpfrom -> mpto | MPdot (mp1,l) -> let mp1' = replace_mp_in_mp mpfrom mpto mp1 in if mp1==mp1' then mp else MPdot (mp1',l) | _ -> mp let rec mp_in_mp mp mp1 = match mp1 with | _ when ModPath.equal mp1 mp -> true | MPdot (mp2,l) -> mp_in_mp mp mp2 | _ -> false let subset_prefixed_by mp resolver = let mp_prefix mkey mequ rslv = if mp_in_mp mp mkey then Deltamap.add_mp mkey mequ rslv else rslv in let kn_prefix kn hint rslv = match hint with | Inline _ -> rslv | Equiv _ -> if mp_in_mp mp (modpath kn) then Deltamap.add_kn kn hint rslv else rslv in Deltamap.fold mp_prefix kn_prefix resolver empty_delta_resolver let subst_dom_delta_resolver subst resolver = let mp_apply_subst mkey mequ rslv = Deltamap.add_mp (subst_mp subst mkey) mequ rslv in let kn_apply_subst kkey hint rslv = Deltamap.add_kn (subst_kn subst kkey) hint rslv in Deltamap.fold mp_apply_subst kn_apply_subst resolver empty_delta_resolver let subst_mp_delta sub mp mkey = match subst_mp0 sub mp with None -> empty_delta_resolver,mp | Some (mp',resolve) -> let mp1 = find_prefix resolve mp' in let resolve1 = subset_prefixed_by mp1 resolve in (subst_dom_delta_resolver (map_mp mp1 mkey) resolve1),mp1 let gen_subst_delta_resolver dom subst resolver = let mp_apply_subst mkey mequ rslv = let mkey' = if dom then subst_mp subst mkey else mkey in let rslv',mequ' = subst_mp_delta subst mequ mkey in Deltamap.join rslv' (Deltamap.add_mp mkey' mequ' rslv) in let kn_apply_subst kkey hint rslv = let kkey' = if dom then subst_kn subst kkey else kkey in let hint' = match hint with | Equiv kequ -> Equiv (subst_kn_delta subst kequ) | Inline (lev,Some t) -> Inline (lev,Some (subst_mps subst t)) | Inline (_,None) -> hint in Deltamap.add_kn kkey' hint' rslv in Deltamap.fold mp_apply_subst kn_apply_subst resolver empty_delta_resolver let subst_codom_delta_resolver = gen_subst_delta_resolver false let subst_dom_codom_delta_resolver = gen_subst_delta_resolver true let update_delta_resolver resolver1 resolver2 = let mp_apply_rslv mkey mequ rslv = if Deltamap.mem_mp mkey resolver2 then rslv else Deltamap.add_mp mkey (find_prefix resolver2 mequ) rslv in let kn_apply_rslv kkey hint rslv = if Deltamap.mem_kn kkey resolver2 then rslv else let hint' = match hint with | Equiv kequ -> Equiv (solve_delta_kn resolver2 kequ) | _ -> hint in Deltamap.add_kn kkey hint' rslv in Deltamap.fold mp_apply_rslv kn_apply_rslv resolver1 empty_delta_resolver let add_delta_resolver resolver1 resolver2 = if resolver1 == resolver2 then resolver2 else if Deltamap.is_empty resolver2 then resolver1 else Deltamap.join (update_delta_resolver resolver1 resolver2) resolver2 let substition_prefixed_by k mp subst = let mp_prefixmp kmp (mp_to,reso) sub = if mp_in_mp mp kmp && not (ModPath.equal mp kmp) then let new_key = replace_mp_in_mp mp k kmp in Umap.add_mp new_key (mp_to,reso) sub else sub in let mbi_prefixmp mbi _ sub = sub in Umap.fold mp_prefixmp mbi_prefixmp subst empty_subst let join subst1 subst2 = let apply_subst mpk add (mp,resolve) res = let mp',resolve' = match subst_mp0 subst2 mp with | None -> mp, None | Some (mp',resolve') -> mp', Some resolve' in let resolve'' = match resolve' with | Some res -> add_delta_resolver (subst_dom_codom_delta_resolver subst2 resolve) res | None -> subst_codom_delta_resolver subst2 resolve in let prefixed_subst = substition_prefixed_by mpk mp' subst2 in Umap.join prefixed_subst (add (mp',resolve'') res) in let mp_apply_subst mp = apply_subst mp (Umap.add_mp mp) in let mbi_apply_subst mbi = apply_subst (MPbound mbi) (Umap.add_mbi mbi) in let subst = Umap.fold mp_apply_subst mbi_apply_subst subst1 empty_subst in Umap.join subst2 subst let from_val x = { subst_value = x; subst_subst = []; } let force fsubst r = match r.subst_subst with | [] -> r.subst_value | s -> let subst = List.fold_left join empty_subst (List.rev s) in let x = fsubst subst r.subst_value in let () = r.subst_subst <- [] in let () = r.subst_value <- x in x let subst_substituted s r = { r with subst_subst = s :: r.subst_subst; } let force_constr = force subst_mps let subst_constr_subst = subst_substituted let subst_lazy_constr sub = function | Indirect (l,dp,i) -> Indirect (sub::l,dp,i) let indirect_opaque_access = ref ((fun dp i -> assert false) : DirPath.t -> int -> constr) let indirect_opaque_univ_access = ref ((fun dp i -> assert false) : DirPath.t -> int -> Univ.ContextSet.t) let force_lazy_constr = function | Indirect (l,dp,i) -> let c = !indirect_opaque_access dp i in force_constr (List.fold_right subst_constr_subst l (from_val c)) let force_lazy_constr_univs = function | OpaqueDef (Indirect (l,dp,i)) -> !indirect_opaque_univ_access dp i | _ -> Univ.ContextSet.empty let subst_constant_def sub = function | Undef inl -> Undef inl | Def c -> Def (subst_constr_subst sub c) | OpaqueDef lc -> OpaqueDef (subst_lazy_constr sub lc) (** Local variables and graph *) let body_of_constant cb = match cb.const_body with | Undef _ -> None | Def c -> Some (force_constr c) | OpaqueDef c -> Some (force_lazy_constr c) let constant_has_body cb = match cb.const_body with | Undef _ -> false | Def _ | OpaqueDef _ -> true let is_opaque cb = match cb.const_body with | OpaqueDef _ -> true | Def _ | Undef _ -> false let opaque_univ_context cb = force_lazy_constr_univs cb.const_body let subst_rel_declaration sub (id,copt,t as x) = let copt' = Option.smartmap (subst_mps sub) copt in let t' = subst_mps sub t in if copt == copt' && t == t' then x else (id,copt',t') let subst_rel_context sub = List.smartmap (subst_rel_declaration sub) let subst_recarg sub r = match r with | Norec -> r | (Mrec(kn,i)|Imbr (kn,i)) -> let kn' = subst_ind sub kn in if kn==kn' then r else Imbr (kn',i) let mk_norec = Rtree.mk_node Norec [||] let mk_paths r recargs = Rtree.mk_node r (Array.map (fun l -> Rtree.mk_node Norec (Array.of_list l)) recargs) let dest_recarg p = fst (Rtree.dest_node p) let dest_subterms p = let (_,cstrs) = Rtree.dest_node p in Array.map (fun t -> Array.to_list (snd (Rtree.dest_node t))) cstrs let subst_wf_paths sub p = Rtree.smartmap (subst_recarg sub) p let eq_recarg r1 r2 = match r1, r2 with | Norec, Norec -> true | Mrec i1, Mrec i2 -> Names.eq_ind i1 i2 | Imbr i1, Imbr i2 -> Names.eq_ind i1 i2 | _ -> false let eq_wf_paths = Rtree.equal eq_recarg (**********************************************************************) (* Representation of mutual inductive types in the kernel *) (* Inductive I1 (params) : U1 := c11 : T11 | ... | c1p1 : T1p1 ... with In (params) : Un := cn1 : Tn1 | ... | cnpn : Tnpn *) let subst_decl_arity f g sub ar = match ar with | RegularArity x -> let x' = f sub x in if x' == x then ar else RegularArity x' | TemplateArity x -> let x' = g sub x in if x' == x then ar else TemplateArity x' let map_decl_arity f g = function | RegularArity a -> RegularArity (f a) | TemplateArity a -> TemplateArity (g a) let subst_rel_declaration sub (id,copt,t as x) = let copt' = Option.smartmap (subst_mps sub) copt in let t' = subst_mps sub t in if copt == copt' && t == t' then x else (id,copt',t') let subst_rel_context sub = List.smartmap (subst_rel_declaration sub) let subst_template_cst_arity sub (ctx,s as arity) = let ctx' = subst_rel_context sub ctx in if ctx==ctx' then arity else (ctx',s) let subst_arity sub s = subst_decl_arity subst_mps subst_template_cst_arity sub s (* TODO: should be changed to non-coping after Term.subst_mps *) (* NB: we leave bytecode and native code fields untouched *) let subst_const_body sub cb = { cb with const_body = subst_constant_def sub cb.const_body; const_type = subst_arity sub cb.const_type } let subst_regular_ind_arity sub s = let uar' = subst_mps sub s.mind_user_arity in if uar' == s.mind_user_arity then s else { mind_user_arity = uar'; mind_sort = s.mind_sort } let subst_template_ind_arity sub s = s (* FIXME records *) let subst_ind_arity = subst_decl_arity subst_regular_ind_arity subst_template_ind_arity let subst_mind_packet sub mbp = { mind_consnames = mbp.mind_consnames; mind_consnrealdecls = mbp.mind_consnrealdecls; mind_consnrealargs = mbp.mind_consnrealargs; mind_typename = mbp.mind_typename; mind_nf_lc = Array.smartmap (subst_mps sub) mbp.mind_nf_lc; mind_arity_ctxt = subst_rel_context sub mbp.mind_arity_ctxt; mind_arity = subst_ind_arity sub mbp.mind_arity; mind_user_lc = Array.smartmap (subst_mps sub) mbp.mind_user_lc; mind_nrealargs = mbp.mind_nrealargs; mind_nrealdecls = mbp.mind_nrealdecls; mind_kelim = mbp.mind_kelim; mind_recargs = subst_wf_paths sub mbp.mind_recargs (*wf_paths*); mind_nb_constant = mbp.mind_nb_constant; mind_nb_args = mbp.mind_nb_args; mind_reloc_tbl = mbp.mind_reloc_tbl } let subst_mind sub mib = { mib with mind_params_ctxt = map_rel_context (subst_mps sub) mib.mind_params_ctxt; mind_packets = Array.smartmap (subst_mind_packet sub) mib.mind_packets } (* Modules *) let rec functor_map fty f0 = function | NoFunctor a -> NoFunctor (f0 a) | MoreFunctor (mbid,ty,e) -> MoreFunctor(mbid,fty ty,functor_map fty f0 e) let implem_map fs fa = function | Struct s -> Struct (fs s) | Algebraic a -> Algebraic (fa a) | impl -> impl let subst_with_body sub = function | WithMod(id,mp) -> WithMod(id,subst_mp sub mp) | WithDef(id,(c,ctx)) -> WithDef(id,(subst_mps sub c,ctx)) let rec subst_expr sub = function | MEident mp -> MEident (subst_mp sub mp) | MEapply (me1,mp2)-> MEapply (subst_expr sub me1, subst_mp sub mp2) | MEwith (me,wd)-> MEwith (subst_expr sub me, subst_with_body sub wd) let rec subst_expression sub me = functor_map (subst_module sub) (subst_expr sub) me and subst_signature sub sign = functor_map (subst_module sub) (subst_structure sub) sign and subst_structure sub struc = let subst_body = function | SFBconst cb -> SFBconst (subst_const_body sub cb) | SFBmind mib -> SFBmind (subst_mind sub mib) | SFBmodule mb -> SFBmodule (subst_module sub mb) | SFBmodtype mtb -> SFBmodtype (subst_module sub mtb) in List.map (fun (l,b) -> (l,subst_body b)) struc and subst_module sub mb = { mb with mod_mp = subst_mp sub mb.mod_mp; mod_expr = implem_map (subst_signature sub) (subst_expression sub) mb.mod_expr; mod_type = subst_signature sub mb.mod_type; mod_type_alg = Option.smartmap (subst_expression sub) mb.mod_type_alg }