Source file reduction.ml
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open CErrors
open Util
open Names
open Constr
open Declarations
open Vars
open Environ
open CClosure
open Esubst
open Context.Rel.Declaration
let rec is_empty_stack = function
[] -> true
| Zupdate _::s -> is_empty_stack s
| Zshift _::s -> is_empty_stack s
| _ -> false
let el_stack el stk =
let n =
List.fold_left
(fun i z ->
match z with
Zshift n -> i+n
| _ -> i)
0
stk in
el_shft n el
let compare_stack_shape stk1 stk2 =
let rec compare_rec bal stk1 stk2 =
match (stk1,stk2) with
([],[]) -> Int.equal bal 0
| ((Zupdate _|Zshift _)::s1, _) -> compare_rec bal s1 stk2
| (_, (Zupdate _|Zshift _)::s2) -> compare_rec bal stk1 s2
| (Zapp l1::s1, _) -> compare_rec (bal+Array.length l1) s1 stk2
| (_, Zapp l2::s2) -> compare_rec (bal-Array.length l2) stk1 s2
| (Zproj _p1::s1, Zproj _p2::s2) ->
Int.equal bal 0 && compare_rec 0 s1 s2
| (ZcaseT(_c1,_,_,_,_,_)::s1, ZcaseT(_c2,_,_,_,_,_)::s2) ->
Int.equal bal 0 && compare_rec 0 s1 s2
| (Zfix(_,a1)::s1, Zfix(_,a2)::s2) ->
Int.equal bal 0 && compare_rec 0 a1 a2 && compare_rec 0 s1 s2
| Zprimitive(op1,_,rargs1, _kargs1)::s1, Zprimitive(op2,_,rargs2, _kargs2)::s2 ->
bal=0 && op1=op2 && List.length rargs1=List.length rargs2 &&
compare_rec 0 s1 s2
| [], _ :: _
| (Zproj _ | ZcaseT _ | Zfix _ | Zprimitive _) :: _, _ -> false
in
compare_rec 0 stk1 stk2
type lft_fconstr = lift * fconstr
type lft_constr_stack_elt =
Zlapp of (lift * fconstr) array
| Zlproj of Projection.Repr.t * lift
| Zlfix of (lift * fconstr) * lft_constr_stack
| Zlcase of case_info * lift * Univ.Instance.t * constr array * case_return * case_branch array * fconstr subs
| Zlprimitive of
CPrimitives.t * pconstant * lft_fconstr list * lft_fconstr next_native_args
and lft_constr_stack = lft_constr_stack_elt list
let rec zlapp v = function
Zlapp v2 :: s -> zlapp (Array.append v v2) s
| s -> Zlapp v :: s
(** Hand-unrolling of the map function to bypass the call to the generic array
allocation. Type annotation is required to tell OCaml that the array does
not contain floats. *)
let map_lift (l : lift) (v : fconstr array) = match v with
| [||] -> assert false
| [|c0|] -> [|(l, c0)|]
| [|c0; c1|] -> [|(l, c0); (l, c1)|]
| [|c0; c1; c2|] -> [|(l, c0); (l, c1); (l, c2)|]
| [|c0; c1; c2; c3|] -> [|(l, c0); (l, c1); (l, c2); (l, c3)|]
| v -> Array.Fun1.map (fun l t -> (l, t)) l v
let pure_stack lfts stk =
let rec pure_rec lfts stk =
match stk with
[] -> (lfts,[])
| zi::s ->
(match (zi,pure_rec lfts s) with
(Zupdate _,lpstk) -> lpstk
| (Zshift n,(l,pstk)) -> (el_shft n l, pstk)
| (Zapp a, (l,pstk)) ->
(l,zlapp (map_lift l a) pstk)
| (Zproj p, (l,pstk)) ->
(l, Zlproj (p,l)::pstk)
| (Zfix(fx,a),(l,pstk)) ->
let (lfx,pa) = pure_rec l a in
(l, Zlfix((lfx,fx),pa)::pstk)
| (ZcaseT(ci,u,pms,p,br,e),(l,pstk)) ->
(l,Zlcase(ci,l,u,pms,p,br,e)::pstk)
| (Zprimitive(op,c,rargs,kargs),(l,pstk)) ->
(l,Zlprimitive(op,c,List.map (fun t -> (l,t)) rargs,
List.map (fun (k,t) -> (k,(l,t))) kargs)::pstk))
in
snd (pure_rec lfts stk)
let whd_betaiota env t =
match kind t with
| (Sort _|Var _|Meta _|Evar _|Const _|Ind _|Construct _|
Prod _|Lambda _|Fix _|CoFix _) -> t
| App (c, _) ->
begin match kind c with
| Ind _ | Construct _ | Evar _ | Meta _ | Const _ | LetIn _ -> t
| _ -> whd_val (create_clos_infos betaiota env) (create_tab ()) (inject t)
end
| _ -> whd_val (create_clos_infos betaiota env) (create_tab ()) (inject t)
let nf_betaiota env t =
norm_val (create_clos_infos betaiota env) (create_tab ()) (inject t)
let whd_betaiotazeta env x =
match kind x with
| (Sort _|Var _|Meta _|Evar _|Const _|Ind _|Construct _|
Prod _|Lambda _|Fix _|CoFix _|Int _|Float _|Array _) -> x
| App (c, _) ->
begin match kind c with
| Ind _ | Construct _ | Evar _ | Meta _ | Const _ | Int _ | Float _ | Array _ -> x
| Sort _ | Rel _ | Var _ | Cast _ | Prod _ | Lambda _ | LetIn _ | App _
| Case _ | Fix _ | CoFix _ | Proj _ ->
whd_val (create_clos_infos betaiotazeta env) (create_tab ()) (inject x)
end
| Rel _ | Cast _ | LetIn _ | Case _ | Proj _ ->
whd_val (create_clos_infos betaiotazeta env) (create_tab ()) (inject x)
let whd_all env t =
match kind t with
| (Sort _|Meta _|Evar _|Ind _|Construct _|
Prod _|Lambda _|Fix _|CoFix _|Int _|Float _|Array _) -> t
| App (c, _) ->
begin match kind c with
| Ind _ | Construct _ | Evar _ | Meta _ | Int _ | Float _ | Array _ -> t
| Sort _ | Rel _ | Var _ | Cast _ | Prod _ | Lambda _ | LetIn _ | App _
| Const _ |Case _ | Fix _ | CoFix _ | Proj _ ->
whd_val (create_clos_infos all env) (create_tab ()) (inject t)
end
| Rel _ | Cast _ | LetIn _ | Case _ | Proj _ | Const _ | Var _ ->
whd_val (create_clos_infos all env) (create_tab ()) (inject t)
let whd_allnolet env t =
match kind t with
| (Sort _|Meta _|Evar _|Ind _|Construct _|
Prod _|Lambda _|Fix _|CoFix _|LetIn _|Int _|Float _|Array _) -> t
| App (c, _) ->
begin match kind c with
| Ind _ | Construct _ | Evar _ | Meta _ | LetIn _ | Int _ | Float _ | Array _ -> t
| Sort _ | Rel _ | Var _ | Cast _ | Prod _ | Lambda _ | App _
| Const _ | Case _ | Fix _ | CoFix _ | Proj _ ->
whd_val (create_clos_infos allnolet env) (create_tab ()) (inject t)
end
| Rel _ | Cast _ | Case _ | Proj _ | Const _ | Var _ ->
whd_val (create_clos_infos allnolet env) (create_tab ()) (inject t)
type 'a kernel_conversion_function = env -> 'a -> 'a -> unit
type 'a extended_conversion_function =
?l2r:bool -> ?reds:TransparentState.t -> env ->
?evars:(existential->constr option) ->
'a -> 'a -> unit
exception NotConvertible
type conv_pb =
| CONV
| CUMUL
type 'a universe_compare = {
compare_sorts : env -> conv_pb -> Sorts.t -> Sorts.t -> 'a -> 'a;
compare_instances: flex:bool -> Univ.Instance.t -> Univ.Instance.t -> 'a -> 'a;
compare_cumul_instances : conv_pb -> Univ.Variance.t array ->
Univ.Instance.t -> Univ.Instance.t -> 'a -> 'a;
}
type 'a universe_state = 'a * 'a universe_compare
type ('a,'b) generic_conversion_function = env -> 'b universe_state -> 'a -> 'a -> 'b
type 'a infer_conversion_function = env -> 'a -> 'a -> Univ.Constraints.t
let sort_cmp_universes env pb s0 s1 (u, check) =
(check.compare_sorts env pb s0 s1 u, check)
let convert_instances ~flex u u' (s, check) =
(check.compare_instances ~flex u u' s, check)
exception MustExpand
let convert_instances_cumul pb var u u' (s, check) =
(check.compare_cumul_instances pb var u u' s, check)
let get_cumulativity_constraints cv_pb variance u u' =
match cv_pb with
| CONV ->
Univ.enforce_eq_variance_instances variance u u' Univ.Constraints.empty
| CUMUL ->
Univ.enforce_leq_variance_instances variance u u' Univ.Constraints.empty
let inductive_cumulativity_arguments (mind,ind) =
mind.Declarations.mind_nparams +
mind.Declarations.mind_packets.(ind).Declarations.mind_nrealargs
let convert_inductives_gen cmp_instances cmp_cumul cv_pb (mind,ind) nargs u1 u2 s =
match mind.Declarations.mind_variance with
| None -> cmp_instances u1 u2 s
| Some variances ->
let num_param_arity = inductive_cumulativity_arguments (mind,ind) in
if not (Int.equal num_param_arity nargs) then
if Univ.Instance.equal u1 u2 then s else raise MustExpand
else
cmp_cumul cv_pb variances u1 u2 s
let convert_inductives cv_pb ind nargs u1 u2 (s, check) =
convert_inductives_gen (check.compare_instances ~flex:false) check.compare_cumul_instances
cv_pb ind nargs u1 u2 s, check
let constructor_cumulativity_arguments (mind, ind, ctor) =
mind.Declarations.mind_nparams +
mind.Declarations.mind_packets.(ind).Declarations.mind_consnrealargs.(ctor - 1)
let convert_constructors_gen cmp_instances cmp_cumul (mind, ind, cns) nargs u1 u2 s =
match mind.Declarations.mind_variance with
| None -> cmp_instances u1 u2 s
| Some _ ->
let num_cnstr_args = constructor_cumulativity_arguments (mind,ind,cns) in
if not (Int.equal num_cnstr_args nargs) then
if Univ.Instance.equal u1 u2 then s else raise MustExpand
else
(** By invariant, both constructors have a common supertype,
so they are convertible _at that type_. *)
let variance = Array.make (Univ.Instance.length u1) Univ.Variance.Irrelevant in
cmp_cumul CONV variance u1 u2 s
let convert_constructors ctor nargs u1 u2 (s, check) =
convert_constructors_gen (check.compare_instances ~flex:false) check.compare_cumul_instances
ctor nargs u1 u2 s, check
let conv_table_key infos ~nargs k1 k2 cuniv =
if k1 == k2 then cuniv else
match k1, k2 with
| ConstKey (cst, u), ConstKey (cst', u') when Constant.CanOrd.equal cst cst' ->
if Univ.Instance.equal u u' then cuniv
else if Int.equal nargs 1 && is_array_type (info_env infos) cst then cuniv
else
let flex = evaluable_constant cst (info_env infos)
&& RedFlags.red_set (info_flags infos) (RedFlags.fCONST cst)
in convert_instances ~flex u u' cuniv
| VarKey id, VarKey id' when Id.equal id id' -> cuniv
| RelKey n, RelKey n' when Int.equal n n' -> cuniv
| _ -> raise NotConvertible
let same_args_size sk1 sk2 =
let n = CClosure.stack_args_size sk1 in
if Int.equal n (CClosure.stack_args_size sk2) then n
else raise NotConvertible
type conv_tab = {
cnv_inf : clos_infos;
lft_tab : clos_tab;
rgt_tab : clos_tab;
}
(** Invariant: for any tl ∈ lft_tab and tr ∈ rgt_tab, there is no mutable memory
location contained both in tl and in tr. *)
(** The same heap separation invariant must hold for the fconstr arguments
passed to each respective side of the conversion function below. *)
let push_relevance infos r =
{ infos with cnv_inf = CClosure.push_relevance infos.cnv_inf r }
let push_relevances infos nas =
{ infos with cnv_inf = CClosure.push_relevances infos.cnv_inf nas }
let identity_of_ctx (ctx:Constr.rel_context) =
Context.Rel.instance mkRel 0 ctx
let eta_expand_ind env (ind,u as pind) =
let mib = Environ.lookup_mind (fst ind) env in
let mip = mib.mind_packets.(snd ind) in
let ctx = Vars.subst_instance_context u mip.mind_arity_ctxt in
let args = identity_of_ctx ctx in
let c = mkApp (mkIndU pind, args) in
let c = Term.it_mkLambda_or_LetIn c ctx in
inject c
let eta_expand_constructor env ((ind,ctor),u as pctor) =
let mib = Environ.lookup_mind (fst ind) env in
let mip = mib.mind_packets.(snd ind) in
let ctx = Vars.subst_instance_context u (fst mip.mind_nf_lc.(ctor-1)) in
let args = identity_of_ctx ctx in
let c = mkApp (mkConstructU pctor, args) in
let c = Term.it_mkLambda_or_LetIn c ctx in
inject c
let esubst_of_rel_context_instance_list ctx u args e =
let open Context.Rel.Declaration in
let rec aux lft e args ctx = match ctx with
| [] -> lft, e
| LocalAssum _ :: ctx -> aux (lft + 1) (subs_lift e) (subs_lift args) ctx
| LocalDef (_, c, _) :: ctx ->
let c = Vars.subst_instance_constr u c in
let c = mk_clos args c in
aux lft (subs_cons c e) (subs_cons c args) ctx
in
aux 0 e args (List.rev ctx)
let irr_flex env = function
| ConstKey (con,_) -> Cset_env.mem con env.Environ.irr_constants
| VarKey x -> Context.Named.Declaration.get_relevance (Environ.lookup_named x env) == Sorts.Irrelevant
| RelKey x -> Context.Rel.Declaration.get_relevance (Environ.lookup_rel x env) == Sorts.Irrelevant
let rec ccnv cv_pb l2r infos lft1 lft2 term1 term2 cuniv =
eqappr cv_pb l2r infos (lft1, (term1,[])) (lft2, (term2,[])) cuniv
and eqappr cv_pb l2r infos (lft1,st1) (lft2,st2) cuniv =
Control.check_for_interrupt ();
let ninfos = infos_with_reds infos.cnv_inf betaiotazeta in
let (hd1, v1 as appr1) = whd_stack ninfos infos.lft_tab (fst st1) (snd st1) in
let (hd2, v2 as appr2) = whd_stack ninfos infos.rgt_tab (fst st2) (snd st2) in
let appr1 = (lft1, appr1) and appr2 = (lft2, appr2) in
(** We delay the computation of the lifts that apply to the head of the term
with [el_stack] inside the branches where they are actually used. *)
(** Irrelevant terms are guaranteed to be [FIrrelevant], except for [FFlex],
[FRel] and [FLambda]. Those ones are handled specifically below. *)
match (fterm_of hd1, fterm_of hd2) with
| (FAtom a1, FAtom a2) ->
(match kind a1, kind a2 with
| (Sort s1, Sort s2) ->
if not (is_empty_stack v1 && is_empty_stack v2) then
raise NotConvertible;
sort_cmp_universes (info_env infos.cnv_inf) cv_pb s1 s2 cuniv
| (Meta n, Meta m) ->
if Int.equal n m
then convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| _ -> raise NotConvertible)
| (FEvar ((ev1,args1),env1), FEvar ((ev2,args2),env2)) ->
if Evar.equal ev1 ev2 then
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = convert_stacks l2r infos lft1 lft2 v1 v2 cuniv in
convert_list l2r infos el1 el2
(List.map (mk_clos env1) args1)
(List.map (mk_clos env2) args2) cuniv
else raise NotConvertible
| (FRel n, FRel m) ->
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let n = reloc_rel n el1 in
let m = reloc_rel m el2 in
let rn = Range.get (info_relevances infos.cnv_inf) (n - 1) in
let rm = Range.get (info_relevances infos.cnv_inf) (m - 1) in
if rn == Sorts.Irrelevant && rm == Sorts.Irrelevant then
let v1 = CClosure.skip_irrelevant_stack v2 in
let v2 = CClosure.skip_irrelevant_stack v2 in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else if Int.equal n m then
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else
raise NotConvertible
| (FFlex fl1, FFlex fl2) ->
(try
let nargs = same_args_size v1 v2 in
let cuniv = conv_table_key infos.cnv_inf ~nargs fl1 fl2 cuniv in
let () = if irr_flex (info_env infos.cnv_inf) fl1 then raise NotConvertible in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
with NotConvertible | UGraph.UniverseInconsistency _ ->
let r1 = unfold_ref_with_args infos.cnv_inf infos.lft_tab fl1 v1 in
let r2 = unfold_ref_with_args infos.cnv_inf infos.rgt_tab fl2 v2 in
match r1, r2 with
| None, None -> raise NotConvertible
| Some t1, Some t2 ->
let oracle = CClosure.oracle_of_infos infos.cnv_inf in
if Conv_oracle.oracle_order Univ.out_punivs oracle l2r fl1 fl2 then
eqappr cv_pb l2r infos (lft1, t1) appr2 cuniv
else
eqappr cv_pb l2r infos appr1 (lft2, t2) cuniv
| Some (t1, v1), None ->
let all = RedFlags.red_add_transparent all (RedFlags.red_transparent (info_flags infos.cnv_inf)) in
let t1 = whd_stack (infos_with_reds infos.cnv_inf all) infos.lft_tab t1 v1 in
eqappr cv_pb l2r infos (lft1, t1) appr2 cuniv
| None, Some (t2, v2) ->
let all = RedFlags.red_add_transparent all (RedFlags.red_transparent (info_flags infos.cnv_inf)) in
let t2 = whd_stack (infos_with_reds infos.cnv_inf all) infos.rgt_tab t2 v2 in
eqappr cv_pb l2r infos appr1 (lft2, t2) cuniv
)
| (FProj (p1,c1), FProj (p2, c2)) ->
(match unfold_projection infos.cnv_inf p1 with
| Some s1 ->
eqappr cv_pb l2r infos (lft1, (c1, (s1 :: v1))) appr2 cuniv
| None ->
match unfold_projection infos.cnv_inf p2 with
| Some s2 ->
eqappr cv_pb l2r infos appr1 (lft2, (c2, (s2 :: v2))) cuniv
| None ->
if Projection.Repr.CanOrd.equal (Projection.repr p1) (Projection.repr p2)
&& compare_stack_shape v1 v2 then
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let u1 = ccnv CONV l2r infos el1 el2 c1 c2 cuniv in
convert_stacks l2r infos lft1 lft2 v1 v2 u1
else
raise NotConvertible)
| (FProj (p1,c1), t2) ->
begin match unfold_projection infos.cnv_inf p1 with
| Some s1 ->
eqappr cv_pb l2r infos (lft1, (c1, (s1 :: v1))) appr2 cuniv
| None ->
begin match t2 with
| FFlex fl2 ->
begin match unfold_ref_with_args infos.cnv_inf infos.rgt_tab fl2 v2 with
| Some t2 ->
eqappr cv_pb l2r infos appr1 (lft2, t2) cuniv
| None -> raise NotConvertible
end
| _ -> raise NotConvertible
end
end
| (t1, FProj (p2,c2)) ->
begin match unfold_projection infos.cnv_inf p2 with
| Some s2 ->
eqappr cv_pb l2r infos appr1 (lft2, (c2, (s2 :: v2))) cuniv
| None ->
begin match t1 with
| FFlex fl1 ->
begin match unfold_ref_with_args infos.cnv_inf infos.lft_tab fl1 v1 with
| Some t1 ->
eqappr cv_pb l2r infos (lft1, t1) appr2 cuniv
| None -> raise NotConvertible
end
| _ -> raise NotConvertible
end
end
| (FLambda _, FLambda _) ->
if not (is_empty_stack v1 && is_empty_stack v2) then
anomaly (Pp.str "conversion was given ill-typed terms (FLambda).");
let (x1,ty1,bd1) = destFLambda mk_clos hd1 in
let (_,ty2,bd2) = destFLambda mk_clos hd2 in
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = ccnv CONV l2r infos el1 el2 ty1 ty2 cuniv in
ccnv CONV l2r (push_relevance infos x1) (el_lift el1) (el_lift el2) bd1 bd2 cuniv
| (FProd (x1, c1, c2, e), FProd (_, c'1, c'2, e')) ->
if not (is_empty_stack v1 && is_empty_stack v2) then
raise NotConvertible;
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = ccnv CONV l2r infos el1 el2 c1 c'1 cuniv in
ccnv cv_pb l2r (push_relevance infos x1) (el_lift el1) (el_lift el2) (mk_clos (subs_lift e) c2) (mk_clos (subs_lift e') c'2) cuniv
| (FLambda _, _) ->
let () = match v1 with
| [] -> ()
| _ ->
anomaly (Pp.str "conversion was given unreduced term (FLambda).")
in
let (x1,_ty1,bd1) = destFLambda mk_clos hd1 in
let infos = push_relevance infos x1 in
eqappr CONV l2r infos
(el_lift lft1, (bd1, [])) (el_lift lft2, (hd2, eta_expand_stack x1 v2)) cuniv
| (_, FLambda _) ->
let () = match v2 with
| [] -> ()
| _ ->
anomaly (Pp.str "conversion was given unreduced term (FLambda).")
in
let (x2,_ty2,bd2) = destFLambda mk_clos hd2 in
let infos = push_relevance infos x2 in
eqappr CONV l2r infos
(el_lift lft1, (hd1, eta_expand_stack x2 v1)) (el_lift lft2, (bd2, [])) cuniv
| (FFlex fl1, c2) ->
begin match unfold_ref_with_args infos.cnv_inf infos.lft_tab fl1 v1 with
| Some (def1,v1) ->
(** By virtue of the previous case analyses, we know [c2] is rigid.
Conversion check to rigid terms eventually implies full weak-head
reduction, so instead of repeatedly performing small-step
unfoldings, we perform reduction with all flags on. *)
let all = RedFlags.red_add_transparent all (RedFlags.red_transparent (info_flags infos.cnv_inf)) in
let r1 = whd_stack (infos_with_reds infos.cnv_inf all) infos.lft_tab def1 v1 in
eqappr cv_pb l2r infos (lft1, r1) appr2 cuniv
| None ->
(match c2 with
| FConstruct ((ind2,_j2),_u2) ->
(try
let v2, v1 =
eta_expand_ind_stack (info_env infos.cnv_inf) ind2 hd2 v2 (snd appr1)
in convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
with Not_found -> raise NotConvertible)
| _ -> raise NotConvertible)
end
| (c1, FFlex fl2) ->
begin match unfold_ref_with_args infos.cnv_inf infos.rgt_tab fl2 v2 with
| Some (def2, v2) ->
(** Symmetrical case of above. *)
let all = RedFlags.red_add_transparent all (RedFlags.red_transparent (info_flags infos.cnv_inf)) in
let r2 = whd_stack (infos_with_reds infos.cnv_inf all) infos.rgt_tab def2 v2 in
eqappr cv_pb l2r infos appr1 (lft2, r2) cuniv
| None ->
match c1 with
| FConstruct ((ind1,_j1),_u1) ->
(try let v1, v2 =
eta_expand_ind_stack (info_env infos.cnv_inf) ind1 hd1 v1 (snd appr2)
in convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
with Not_found -> raise NotConvertible)
| _ -> raise NotConvertible
end
| (FInd (ind1,u1 as pind1), FInd (ind2,u2 as pind2)) ->
if Ind.CanOrd.equal ind1 ind2 then
if Univ.Instance.length u1 = 0 || Univ.Instance.length u2 = 0 then
let cuniv = convert_instances ~flex:false u1 u2 cuniv in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else
let mind = Environ.lookup_mind (fst ind1) (info_env infos.cnv_inf) in
let nargs = same_args_size v1 v2 in
match convert_inductives cv_pb (mind, snd ind1) nargs u1 u2 cuniv with
| cuniv -> convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
| exception MustExpand ->
let env = info_env infos.cnv_inf in
let hd1 = eta_expand_ind env pind1 in
let hd2 = eta_expand_ind env pind2 in
eqappr cv_pb l2r infos (lft1,(hd1,v1)) (lft2,(hd2,v2)) cuniv
else raise NotConvertible
| (FConstruct ((ind1,j1),u1 as pctor1), FConstruct ((ind2,j2),u2 as pctor2)) ->
if Int.equal j1 j2 && Ind.CanOrd.equal ind1 ind2 then
if Univ.Instance.length u1 = 0 || Univ.Instance.length u2 = 0 then
let cuniv = convert_instances ~flex:false u1 u2 cuniv in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else
let mind = Environ.lookup_mind (fst ind1) (info_env infos.cnv_inf) in
let nargs = same_args_size v1 v2 in
match convert_constructors (mind, snd ind1, j1) nargs u1 u2 cuniv with
| cuniv -> convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
| exception MustExpand ->
let env = info_env infos.cnv_inf in
let hd1 = eta_expand_constructor env pctor1 in
let hd2 = eta_expand_constructor env pctor2 in
eqappr cv_pb l2r infos (lft1,(hd1,v1)) (lft2,(hd2,v2)) cuniv
else raise NotConvertible
| (FConstruct ((ind1,_j1),_u1), _) ->
(try
let v1, v2 =
eta_expand_ind_stack (info_env infos.cnv_inf) ind1 hd1 v1 (snd appr2)
in convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
with Not_found -> raise NotConvertible)
| (_, FConstruct ((ind2,_j2),_u2)) ->
(try
let v2, v1 =
eta_expand_ind_stack (info_env infos.cnv_inf) ind2 hd2 v2 (snd appr1)
in convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
with Not_found -> raise NotConvertible)
| (FFix (((op1, i1),(na1,tys1,cl1)),e1), FFix(((op2, i2),(_,tys2,cl2)),e2)) ->
if Int.equal i1 i2 && Array.equal Int.equal op1 op2
then
let n = Array.length cl1 in
let fty1 = Array.map (mk_clos e1) tys1 in
let fty2 = Array.map (mk_clos e2) tys2 in
let fcl1 = Array.map (mk_clos (subs_liftn n e1)) cl1 in
let fcl2 = Array.map (mk_clos (subs_liftn n e2)) cl2 in
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = convert_vect l2r infos el1 el2 fty1 fty2 cuniv in
let cuniv =
let infos = push_relevances infos na1 in
convert_vect l2r infos
(el_liftn n el1) (el_liftn n el2) fcl1 fcl2 cuniv
in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| (FCoFix ((op1,(na1,tys1,cl1)),e1), FCoFix((op2,(_,tys2,cl2)),e2)) ->
if Int.equal op1 op2
then
let n = Array.length cl1 in
let fty1 = Array.map (mk_clos e1) tys1 in
let fty2 = Array.map (mk_clos e2) tys2 in
let fcl1 = Array.map (mk_clos (subs_liftn n e1)) cl1 in
let fcl2 = Array.map (mk_clos (subs_liftn n e2)) cl2 in
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = convert_vect l2r infos el1 el2 fty1 fty2 cuniv in
let cuniv =
let infos = push_relevances infos na1 in
convert_vect l2r infos
(el_liftn n el1) (el_liftn n el2) fcl1 fcl2 cuniv
in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| FInt i1, FInt i2 ->
if Uint63.equal i1 i2 then convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| FFloat f1, FFloat f2 ->
if Float64.equal f1 f2 then convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| FCaseInvert (ci1,u1,pms1,p1,_,_,br1,e1), FCaseInvert (ci2,u2,pms2,p2,_,_,br2,e2) ->
(if not (Ind.CanOrd.equal ci1.ci_ind ci2.ci_ind) then raise NotConvertible);
let el1 = el_stack lft1 v1 and el2 = el_stack lft2 v2 in
let fold c1 c2 cuniv = ccnv CONV l2r infos el1 el2 c1 c2 cuniv in
(** FIXME: cache the presence of let-bindings in the case_info *)
let mind = Environ.lookup_mind (fst ci1.ci_ind) (info_env infos.cnv_inf) in
let mip = mind.Declarations.mind_packets.(snd ci1.ci_ind) in
let cuniv =
let ind = (mind,snd ci1.ci_ind) in
let nargs = inductive_cumulativity_arguments ind in
convert_inductives CONV ind nargs u1 u2 cuniv
in
let pms1 = mk_clos_vect e1 pms1 in
let pms2 = mk_clos_vect e2 pms2 in
let cuniv = Array.fold_right2 fold pms1 pms2 cuniv in
let cuniv = convert_return_clause mind mip l2r infos e1 e2 el1 el2 u1 u2 pms1 pms2 p1 p2 cuniv in
convert_branches mind mip l2r infos e1 e2 el1 el2 u1 u2 pms1 pms2 br1 br2 cuniv
| FArray (u1,t1,ty1), FArray (u2,t2,ty2) ->
let len = Parray.length_int t1 in
if not (Int.equal len (Parray.length_int t2)) then raise NotConvertible;
let cuniv = convert_instances ~flex:false u1 u2 cuniv in
let el1 = el_stack lft1 v1 in
let el2 = el_stack lft2 v2 in
let cuniv = ccnv CONV l2r infos el1 el2 ty1 ty2 cuniv in
let cuniv = Parray.fold_left2 (fun u v1 v2 -> ccnv CONV l2r infos el1 el2 v1 v2 u) cuniv t1 t2 in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
| (FRel n1, FIrrelevant) ->
let n1 = reloc_rel n1 (el_stack lft1 v1) in
let r1 = Range.get (info_relevances infos.cnv_inf) (n1 - 1) in
if r1 == Sorts.Irrelevant then
let v1 = CClosure.skip_irrelevant_stack v1 in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| (FIrrelevant, FRel n2) ->
let n2 = reloc_rel n2 (el_stack lft2 v2) in
let r2 = Range.get (info_relevances infos.cnv_inf) (n2 - 1) in
if r2 == Sorts.Irrelevant then
let v2 = CClosure.skip_irrelevant_stack v2 in
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
else raise NotConvertible
| FIrrelevant, FIrrelevant ->
convert_stacks l2r infos lft1 lft2 v1 v2 cuniv
| ( (FLetIn _, _) | (FCaseT _,_) | (FApp _,_) | (FCLOS _,_) | (FLIFT _,_)
| (_, FLetIn _) | (_,FCaseT _) | (_,FApp _) | (_,FCLOS _) | (_,FLIFT _)
| (FLOCKED,_) | (_,FLOCKED) ) -> assert false
| (FRel _ | FAtom _ | FInd _ | FFix _ | FCoFix _ | FCaseInvert _
| FProd _ | FEvar _ | FInt _ | FFloat _ | FArray _ | FIrrelevant), _ -> raise NotConvertible
and convert_stacks l2r infos lft1 lft2 stk1 stk2 cuniv =
let f (l1, t1) (l2, t2) cuniv = ccnv CONV l2r infos l1 l2 t1 t2 cuniv in
let rec cmp_rec pstk1 pstk2 cuniv =
match (pstk1,pstk2) with
| (z1::s1, z2::s2) ->
let cu1 = cmp_rec s1 s2 cuniv in
(match (z1,z2) with
| (Zlapp a1,Zlapp a2) ->
Array.fold_right2 f a1 a2 cu1
| (Zlproj (c1,_l1),Zlproj (c2,_l2)) ->
if not (Projection.Repr.CanOrd.equal c1 c2) then
raise NotConvertible
else cu1
| (Zlfix(fx1,a1),Zlfix(fx2,a2)) ->
let cu2 = f fx1 fx2 cu1 in
cmp_rec a1 a2 cu2
| (Zlcase(ci1,l1,u1,pms1,p1,br1,e1),Zlcase(ci2,l2,u2,pms2,p2,br2,e2)) ->
if not (Ind.CanOrd.equal ci1.ci_ind ci2.ci_ind) then
raise NotConvertible;
let cu = cu1 in
(** FIXME: cache the presence of let-bindings in the case_info *)
let mind = Environ.lookup_mind (fst ci1.ci_ind) (info_env infos.cnv_inf) in
let mip = mind.Declarations.mind_packets.(snd ci1.ci_ind) in
let cu =
if Univ.Instance.length u1 = 0 || Univ.Instance.length u2 = 0 then
convert_instances ~flex:false u1 u2 cu
else
match mind.Declarations.mind_variance with
| None -> convert_instances ~flex:false u1 u2 cu
| Some variances -> convert_instances_cumul CONV variances u1 u2 cu
in
let pms1 = mk_clos_vect e1 pms1 in
let pms2 = mk_clos_vect e2 pms2 in
let fold_params c1 c2 accu = f (l1, c1) (l2, c2) accu in
let cu = Array.fold_right2 fold_params pms1 pms2 cu in
let cu = convert_return_clause mind mip l2r infos e1 e2 l1 l2 u1 u2 pms1 pms2 p1 p2 cu in
convert_branches mind mip l2r infos e1 e2 l1 l2 u1 u2 pms1 pms2 br1 br2 cu
| (Zlprimitive(op1,_,rargs1,kargs1),Zlprimitive(op2,_,rargs2,kargs2)) ->
if not (CPrimitives.equal op1 op2) then raise NotConvertible else
let cu2 = List.fold_right2 f rargs1 rargs2 cu1 in
let fk (_,a1) (_,a2) cu = f a1 a2 cu in
List.fold_right2 fk kargs1 kargs2 cu2
| ((Zlapp _ | Zlproj _ | Zlfix _| Zlcase _| Zlprimitive _), _) -> assert false)
| _ -> cuniv in
if compare_stack_shape stk1 stk2 then
cmp_rec (pure_stack lft1 stk1) (pure_stack lft2 stk2) cuniv
else raise NotConvertible
and convert_vect l2r infos lft1 lft2 v1 v2 cuniv =
let lv1 = Array.length v1 in
let lv2 = Array.length v2 in
if Int.equal lv1 lv2
then
let rec fold n cuniv =
if n >= lv1 then cuniv
else
let cuniv = ccnv CONV l2r infos lft1 lft2 v1.(n) v2.(n) cuniv in
fold (n+1) cuniv in
fold 0 cuniv
else raise NotConvertible
and convert_under_context l2r infos e1 e2 lft1 lft2 ctx (nas1, c1) (nas2, c2) cu =
let n = Array.length nas1 in
let () = assert (Int.equal n (Array.length nas2)) in
let n, e1, e2 = match ctx with
| None ->
let e1 = subs_liftn n e1 in
let e2 = subs_liftn n e2 in
(n, e1, e2)
| Some (ctx, u1, u2, args1, args2) ->
let n1, e1 = esubst_of_rel_context_instance_list ctx u1 args1 e1 in
let n2, e2 = esubst_of_rel_context_instance_list ctx u2 args2 e2 in
let () = assert (Int.equal n1 n2) in
n1, e1, e2
in
let lft1 = el_liftn n lft1 in
let lft2 = el_liftn n lft2 in
let infos = push_relevances infos nas1 in
ccnv CONV l2r infos lft1 lft2 (mk_clos e1 c1) (mk_clos e2 c2) cu
and convert_return_clause mib mip l2r infos e1 e2 l1 l2 u1 u2 pms1 pms2 p1 p2 cu =
let ctx =
if Int.equal mip.mind_nrealargs mip.mind_nrealdecls then None
else
let ctx, _ = List.chop mip.mind_nrealdecls mip.mind_arity_ctxt in
let pms1 = inductive_subst mib u1 pms1 in
let pms2 = inductive_subst mib u1 pms2 in
let open Context.Rel.Declaration in
let dummy = mkProp in
let ctx = LocalAssum (Context.anonR, dummy) :: ctx in
Some (ctx, u1, u2, pms1, pms2)
in
convert_under_context l2r infos e1 e2 l1 l2 ctx p1 p2 cu
and convert_branches mib mip l2r infos e1 e2 lft1 lft2 u1 u2 pms1 pms2 br1 br2 cuniv =
let fold i (ctx, _) cuniv =
let ctx =
if Int.equal mip.mind_consnrealdecls.(i) mip.mind_consnrealargs.(i) then None
else
let ctx, _ = List.chop mip.mind_consnrealdecls.(i) ctx in
let pms1 = inductive_subst mib u1 pms1 in
let pms2 = inductive_subst mib u2 pms2 in
Some (ctx, u1, u2, pms1, pms2)
in
let c1 = br1.(i) in
let c2 = br2.(i) in
convert_under_context l2r infos e1 e2 lft1 lft2 ctx c1 c2 cuniv
in
Array.fold_right_i fold mip.mind_nf_lc cuniv
and convert_list l2r infos lft1 lft2 v1 v2 cuniv = match v1, v2 with
| [], [] -> cuniv
| c1 :: v1, c2 :: v2 ->
let cuniv = ccnv CONV l2r infos lft1 lft2 c1 c2 cuniv in
convert_list l2r infos lft1 lft2 v1 v2 cuniv
| _, _ -> raise NotConvertible
let clos_gen_conv trans cv_pb l2r evars env graph univs t1 t2 =
let reds = CClosure.RedFlags.red_add_transparent betaiotazeta trans in
let infos = create_conv_infos ~univs:graph ~evars reds env in
let infos = {
cnv_inf = infos;
lft_tab = create_tab ();
rgt_tab = create_tab ();
} in
ccnv cv_pb l2r infos el_id el_id (inject t1) (inject t2) univs
let check_eq univs u u' =
if not (UGraph.check_eq_sort univs u u') then raise NotConvertible
let check_leq univs u u' =
if not (UGraph.check_leq_sort univs u u') then raise NotConvertible
let check_sort_cmp_universes pb s0 s1 univs =
match pb with
| CUMUL -> check_leq univs s0 s1
| CONV -> check_eq univs s0 s1
let checked_sort_cmp_universes _env pb s0 s1 univs =
check_sort_cmp_universes pb s0 s1 univs; univs
let check_convert_instances ~flex:_ u u' univs =
if UGraph.check_eq_instances univs u u' then univs
else raise NotConvertible
let check_inductive_instances cv_pb variance u1 u2 univs =
let csts = get_cumulativity_constraints cv_pb variance u1 u2 in
if (UGraph.check_constraints csts univs) then univs
else raise NotConvertible
let checked_universes =
{ compare_sorts = checked_sort_cmp_universes;
compare_instances = check_convert_instances;
compare_cumul_instances = check_inductive_instances; }
let () =
let conv infos tab a b =
try
let univs = info_univs infos in
let infos = { cnv_inf = infos; lft_tab = tab; rgt_tab = tab; } in
let univs', _ = ccnv CONV false infos el_id el_id a b
(univs, checked_universes)
in
assert (univs==univs');
true
with NotConvertible -> false
in
CClosure.set_conv conv
let gen_conv cv_pb ?(l2r=false) ?(reds=TransparentState.full) env ?(evars=(fun _ -> None)) t1 t2 =
let univs = Environ.universes env in
let b =
if cv_pb = CUMUL then leq_constr_univs univs t1 t2
else eq_constr_univs univs t1 t2
in
if b then ()
else
let _ = clos_gen_conv reds cv_pb l2r evars env univs (univs, checked_universes) t1 t2 in
()
let conv = gen_conv CONV
let conv_leq = gen_conv CUMUL
let generic_conv cv_pb ~l2r evars reds env univs t1 t2 =
let graph = Environ.universes env in
let (s, _) =
clos_gen_conv reds cv_pb l2r evars env graph univs t1 t2
in s
let default_conv cv_pb env t1 t2 =
gen_conv cv_pb env t1 t2
let default_conv_leq = default_conv CUMUL
let beta_applist c l =
let rec app subst c l =
match kind c, l with
| Lambda(_,_,c), arg::l -> app (arg::subst) c l
| _ -> Term.applist (substl subst c, l) in
app [] c l
let beta_appvect c v = beta_applist c (Array.to_list v)
let beta_app c a = beta_applist c [a]
let betazeta_appvect = Term.lambda_appvect_assum
let hnf_prod_app env t n =
match kind (whd_all env t) with
| Prod (_,_,b) -> subst1 n b
| _ -> anomaly ~label:"hnf_prod_app" (Pp.str "Need a product.")
let hnf_prod_applist env t nl =
List.fold_left (hnf_prod_app env) t nl
let hnf_prod_applist_assum env n c l =
let rec app n subst t l =
if Int.equal n 0 then
if l == [] then substl subst t
else anomaly (Pp.str "Too many arguments.")
else match kind (whd_allnolet env t), l with
| Prod(_,_,c), arg::l -> app (n-1) (arg::subst) c l
| LetIn(_,b,_,c), _ -> app (n-1) (substl subst b::subst) c l
| _, [] -> anomaly (Pp.str "Not enough arguments.")
| _ -> anomaly (Pp.str "Not enough prod/let's.") in
app n [] c l
let dest_prod env =
let rec decrec env m c =
let t = whd_all env c in
match kind t with
| Prod (n,a,c0) ->
let d = LocalAssum (n,a) in
decrec (push_rel d env) (Context.Rel.add d m) c0
| _ -> m,t
in
decrec env Context.Rel.empty
let dest_lam env =
let rec decrec env m c =
let t = whd_all env c in
match kind t with
| Lambda (n,a,c0) ->
let d = LocalAssum (n,a) in
decrec (push_rel d env) (Context.Rel.add d m) c0
| _ -> m,t
in
decrec env Context.Rel.empty
let dest_prod_assum env =
let rec prodec_rec env l ty =
let rty = whd_allnolet env ty in
match kind rty with
| Prod (x,t,c) ->
let d = LocalAssum (x,t) in
prodec_rec (push_rel d env) (Context.Rel.add d l) c
| LetIn (x,b,t,c) ->
let d = LocalDef (x,b,t) in
prodec_rec (push_rel d env) (Context.Rel.add d l) c
| _ ->
let rty' = whd_all env rty in
if Constr.equal rty' rty then l, rty
else prodec_rec env l rty'
in
prodec_rec env Context.Rel.empty
let dest_lam_assum env =
let rec lamec_rec env l ty =
let rty = whd_allnolet env ty in
match kind rty with
| Lambda (x,t,c) ->
let d = LocalAssum (x,t) in
lamec_rec (push_rel d env) (Context.Rel.add d l) c
| LetIn (x,b,t,c) ->
let d = LocalDef (x,b,t) in
lamec_rec (push_rel d env) (Context.Rel.add d l) c
| _ -> l,rty
in
lamec_rec env Context.Rel.empty
let dest_lam_n_assum env n =
let rec lamec_rec env n l c =
if Int.equal n 0 then l,c
else
let rc = whd_allnolet env c in
match kind rc with
| Lambda (x,t,c) ->
let d = LocalAssum (x,t) in
lamec_rec (push_rel d env) (n-1) (Context.Rel.add d l) c
| LetIn (x,b,t,c) ->
let d = LocalDef (x,b,t) in
lamec_rec (push_rel d env) n (Context.Rel.add d l) c
| _ -> anomaly (Pp.str "dest_lam_n_assum: not enough abstractions")
in
lamec_rec env n Context.Rel.empty
exception NotArity
let dest_arity env c =
let l, c = dest_prod_assum env c in
match kind c with
| Sort s -> l,s
| _ -> raise NotArity
let is_arity env c =
try
let _ = dest_arity env c in
true
with NotArity -> false
let eta_expand env t ty =
let ctxt, _codom = dest_prod env ty in
let ctxt',t = dest_lam env t in
let d = Context.Rel.nhyps ctxt - Context.Rel.nhyps ctxt' in
let eta_args = List.rev_map mkRel (List.interval 1 d) in
let t = Term.applistc (Vars.lift d t) eta_args in
let t = Term.it_mkLambda_or_LetIn t (List.firstn d ctxt) in
Term.it_mkLambda_or_LetIn t ctxt'