(* --------------------------------------------------------------------
* Copyright (c) - 2012--2016 - IMDEA Software Institute
* Copyright (c) - 2012--2018 - Inria
* Copyright (c) - 2012--2018 - Ecole Polytechnique
*
* Distributed under the terms of the CeCILL-C-V1 license
* -------------------------------------------------------------------- *)
(* -------------------------------------------------------------------- *)
open EcUtils
open EcIdent
open EcPath
open EcTypes
open EcModules
open EcFol
open EcEnv
module BI = EcBigInt
(* -------------------------------------------------------------------- *)
exception IncompatibleType of env * (ty * ty)
exception IncompatibleForm of env * (form * form)
(* -------------------------------------------------------------------- *)
type 'a eqtest = env -> 'a -> 'a -> bool
type 'a eqntest = env -> ?norm:bool -> 'a -> 'a -> bool
module EqTest = struct
let rec for_type env t1 t2 =
ty_equal t1 t2 || for_type_r env t1 t2
and for_type_r env t1 t2 =
match t1.ty_node, t2.ty_node with
| Tunivar uid1, Tunivar uid2 -> EcUid.uid_equal uid1 uid2
| Tvar i1, Tvar i2 -> i1 = i2
| Ttuple lt1, Ttuple lt2 ->
List.length lt1 = List.length lt2
&& List.all2 (for_type env) lt1 lt2
| Tfun (t1, t2), Tfun (t1', t2') ->
for_type env t1 t1' && for_type env t2 t2'
| Tglob mp, _ when EcEnv.NormMp.tglob_reducible env mp ->
for_type env (EcEnv.NormMp.norm_tglob env mp) t2
| _, Tglob mp when EcEnv.NormMp.tglob_reducible env mp ->
for_type env t1 (EcEnv.NormMp.norm_tglob env mp)
| Tconstr (p1, lt1), Tconstr (p2, lt2) when EcPath.p_equal p1 p2 ->
if
List.length lt1 = List.length lt2
&& List.all2 (for_type env) lt1 lt2
then true
else
if Ty.defined p1 env
then for_type env (Ty.unfold p1 lt1 env) (Ty.unfold p2 lt2 env)
else false
| Tconstr(p1,lt1), _ when Ty.defined p1 env ->
for_type env (Ty.unfold p1 lt1 env) t2
| _, Tconstr(p2,lt2) when Ty.defined p2 env ->
for_type env t1 (Ty.unfold p2 lt2 env)
| _, _ -> false
(* ------------------------------------------------------------------ *)
let is_unit env ty = for_type env tunit ty
let is_bool env ty = for_type env tbool ty
let is_int env ty = for_type env tint ty
(* ------------------------------------------------------------------ *)
let for_type_exn env t1 t2 =
if not (for_type env t1 t2) then
raise (IncompatibleType (env, (t1, t2)))
(* ------------------------------------------------------------------ *)
let for_pv env ~norm p1 p2 =
pv_equal p1 p2 || (norm && (p1.pv_kind = p2.pv_kind) &&
let p1 = NormMp.norm_pvar env p1 in
let p2 = NormMp.norm_pvar env p2 in
EcPath.x_equal p1.pv_name p2.pv_name)
(* ------------------------------------------------------------------ *)
let for_xp env ~norm p1 p2 =
EcPath.x_equal p1 p2 || (norm &&
let p1 = NormMp.norm_xfun env p1 in
let p2 = NormMp.norm_xfun env p2 in
EcPath.x_equal p1 p2)
(* ------------------------------------------------------------------ *)
let for_mp env ~norm p1 p2 =
EcPath.m_equal p1 p2 || (norm &&
let p1 = NormMp.norm_mpath env p1 in
let p2 = NormMp.norm_mpath env p2 in
EcPath.m_equal p1 p2)
(* ------------------------------------------------------------------ *)
let for_expr env ~norm =
let module E = struct exception NotConv end in
let find alpha id = odfl id (Mid.find_opt id alpha) in
let noconv (f : expr -> expr -> bool) e1 e2 =
try f e1 e2 with E.NotConv -> false in
let check_lpattern alpha lp1 lp2 =
match lp1, lp2 with
| LSymbol (id1,_), LSymbol (id2,_) ->
Mid.add id1 id2 alpha
| LTuple lid1, LTuple lid2 when List.length lid1 = List.length lid2 ->
List.fold_left2
(fun alpha (id1,_) (id2,_) -> Mid.add id1 id2 alpha)
alpha lid1 lid2
| _, _ -> raise E.NotConv in
let check_binding env alpha (id1, ty1) (id2, ty2) =
if not (for_type env ty1 ty2) then
raise E.NotConv;
Mid.add id1 id2 alpha in
let check_bindings env alpha b1 b2 =
if List.length b1 <> List.length b2 then
raise E.NotConv;
List.fold_left2 (check_binding env) alpha b1 b2 in
let rec aux alpha e1 e2 =
e_equal e1 e2 || aux_r alpha e1 e2
and aux_r alpha e1 e2 =
match e1.e_node, e2.e_node with
| Eint i1, Eint i2 ->
BI.equal i1 i2
| Elocal id1, Elocal id2 ->
EcIdent.id_equal (find alpha id1) id2
| Evar p1, Evar p2 ->
for_pv env ~norm p1 p2
| Eop(o1,ty1), Eop(o2,ty2) ->
p_equal o1 o2 && List.all2 (for_type env) ty1 ty2
| Equant(q1,b1,e1), Equant(q2,b2,e2) when qt_equal q1 q2 ->
let alpha = check_bindings env alpha b1 b2 in
noconv (aux alpha) e1 e2
| Eapp (f1, args1), Eapp (f2, args2) ->
aux alpha f1 f2 && List.all2 (aux alpha) args1 args2
| Elet (p1, f1', g1), Elet (p2, f2', g2) ->
aux alpha f1' f2'
&& noconv (aux (check_lpattern alpha p1 p2)) g1 g2
| Etuple args1, Etuple args2 -> List.all2 (aux alpha) args1 args2
| Eif (a1,b1,c1), Eif(a2,b2,c2) ->
aux alpha a1 a2 && aux alpha b1 b2 && aux alpha c1 c2
| Ematch (e1,es1,ty1), Ematch(e2,es2,ty2) ->
for_type env ty1 ty2
&& List.all2 (aux alpha) (e1::es1) (e2::es2)
| _, _ -> false
in fun e1 e2 -> aux Mid.empty e1 e2
(* ------------------------------------------------------------------ *)
let for_lv env ~norm lv1 lv2 =
match lv1, lv2 with
| LvVar(p1, _), LvVar(p2, _) ->
for_pv env ~norm p1 p2
| LvTuple p1, LvTuple p2 ->
List.all2
(fun (p1, _) (p2, _) -> for_pv env ~norm p1 p2)
p1 p2
| _, _ -> false
(* ------------------------------------------------------------------ *)
let rec for_stmt env ~norm s1 s2 =
s_equal s1 s2
|| List.all2 (for_instr env ~norm) s1.s_node s2.s_node
(* ------------------------------------------------------------------ *)
and for_instr env ~norm i1 i2 =
i_equal i1 i2 || for_instr_r env ~norm i1 i2
and for_instr_r env ~norm i1 i2 =
match i1.i_node, i2.i_node with
| Sasgn (lv1, e1), Sasgn (lv2, e2) ->
for_lv env ~norm lv1 lv2 && for_expr env ~norm e1 e2
| Srnd (lv1, e1), Srnd (lv2, e2) ->
for_lv env ~norm lv1 lv2 && for_expr env ~norm e1 e2
| Scall (lv1, f1, e1), Scall (lv2, f2, e2) ->
oall2 (for_lv env ~norm) lv1 lv2
&& for_xp env ~norm f1 f2
&& List.all2 (for_expr env ~norm) e1 e2
| Sif (a1, b1, c1), Sif(a2, b2, c2) ->
for_expr env ~norm a1 a2
&& for_stmt env ~norm b1 b2
&& for_stmt env ~norm c1 c2
| Swhile(a1,b1), Swhile(a2,b2) ->
for_expr env ~norm a1 a2 && for_stmt env ~norm b1 b2
| Sassert a1, Sassert a2 ->
for_expr env ~norm a1 a2
| Sabstract id1, Sabstract id2 ->
EcIdent.id_equal id1 id2
| _, _ -> false
(* ------------------------------------------------------------------ *)
let for_pv = fun env ?(norm = true) -> for_pv env ~norm
let for_xp = fun env ?(norm = true) -> for_xp env ~norm
let for_mp = fun env ?(norm = true) -> for_mp env ~norm
let for_instr = fun env ?(norm = true) -> for_instr env ~norm
let for_stmt = fun env ?(norm = true) -> for_stmt env ~norm
let for_expr = fun env ?(norm = true) -> for_expr env ~norm
end
(* -------------------------------------------------------------------- *)
type reduction_info = {
beta : bool;
delta_p : (path -> bool);
delta_h : (ident -> bool);
zeta : bool;
iota : bool;
eta : bool;
logic : rlogic_info;
modpath : bool;
user : bool;
}
and rlogic_info = [`Full | `ProductCompat] option
(* -------------------------------------------------------------------- *)
let full_red = {
beta = true;
delta_p = EcUtils.predT;
delta_h = EcUtils.predT;
zeta = true;
iota = true;
eta = true;
logic = Some `Full;
modpath = true;
user = true;
}
let no_red = {
beta = false;
delta_p = EcUtils.pred0;
delta_h = EcUtils.pred0;
zeta = false;
iota = false;
eta = false;
logic = None;
modpath = false;
user = false;
}
let beta_red = { no_red with beta = true; }
let betaiota_red = { no_red with beta = true; iota = true; }
let nodelta =
{ full_red with
delta_h = EcUtils.pred0;
delta_p = EcUtils.pred0; }
let delta = { no_red with delta_p = EcUtils.predT; }
let reduce_local ri hyps x =
if ri.delta_h x
then LDecl.unfold x hyps
else raise NotReducible
let reduce_op ri env p tys =
if ri.delta_p p
then Op.reduce env p tys
else raise NotReducible
let is_record env f =
match EcFol.destr_app f with
| { f_node = Fop (p, _) }, _ -> EcEnv.Op.is_record_ctor env p
| _ -> false
(* -------------------------------------------------------------------- *)
let rec h_red_x ri env hyps f =
match f.f_node with
(* β-reduction *)
| Fapp ({ f_node = Fquant (Llambda, _, _)}, _) when ri.beta ->
f_betared f
(* ζ-reduction *)
| Flocal x -> reduce_local ri hyps x
(* ζ-reduction *)
| Fapp ({ f_node = Flocal x }, args) ->
f_app_simpl (reduce_local ri hyps x) args f.f_ty
(* ζ-reduction *)
| Flet (LSymbol(x,_), e1, e2) when ri.zeta ->
let s = Fsubst.f_bind_local Fsubst.f_subst_id x e1 in
Fsubst.f_subst s e2
(* ι-reduction (let-tuple) *)
| Flet (LTuple ids, { f_node = Ftuple es }, e2) when ri.iota ->
let s =
List.fold_left2
(fun s (x,_) e1 -> Fsubst.f_bind_local s x e1)
Fsubst.f_subst_id ids es
in
Fsubst.f_subst s e2
(* ι-reduction (let-records) *)
| Flet (LRecord (_, ids), f1, f2) when ri.iota && is_record env f1 ->
let args = snd (EcFol.destr_app f1) in
let subst =
List.fold_left2 (fun subst (x, _) e ->
match x with
| None -> subst
| Some x -> Fsubst.f_bind_local subst x e)
Fsubst.f_subst_id ids args
in
Fsubst.f_subst subst f2
(* ι-reduction (records projection) *)
| Fapp ({ f_node = Fop (p, _); } as f1, args)
when ri.iota && EcEnv.Op.is_projection env p -> begin
try
match args with
| mk :: args -> begin
match (odfl mk (h_red_opt ri env hyps mk)).f_node with
| Fapp ({ f_node = Fop (mkp, _) }, mkargs) ->
if not (EcEnv.Op.is_record_ctor env mkp) then
raise NotReducible;
let v = oget (EcEnv.Op.by_path_opt p env) in
let v = proj3_2 (EcDecl.operator_as_proj v) in
let v = List.nth mkargs v in
f_app (odfl v (h_red_opt ri env hyps v)) args f.f_ty
| _ -> raise NotReducible
end
| _ -> raise NotReducible
with NotReducible ->
f_app (h_red_x ri env hyps f1) args f.f_ty
end
(* ι-reduction (tuples projection) *)
| Fproj(f1, i) when ri.iota ->
let f' = f_proj_simpl f1 i f.f_ty in
if f_equal f f' then f_proj (h_red_x ri env hyps f1) i f.f_ty else f'
(* ι-reduction (if-then-else) *)
| Fif (f1, f2, f3) when ri.iota ->
let f' = f_if_simpl f1 f2 f3 in
if f_equal f f' then f_if (h_red_x ri env hyps f1) f2 f3 else f'
(* ι-reduction (match-fix) *)
| Fapp ({ f_node = Fop (p, tys); } as f1, fargs)
when ri.iota && EcEnv.Op.is_fix_def env p -> begin
try
let op = oget (EcEnv.Op.by_path_opt p env) in
let fix = EcDecl.operator_as_fix op in
if List.length fargs < snd (fix.EcDecl.opf_struct) then
raise NotReducible;
let fargs, eargs = List.split_at (snd (fix.EcDecl.opf_struct)) fargs in
let args = Array.of_list fargs in
let pargs = List.fold_left (fun (opb, acc) v ->
let v = args.(v) in
let v = odfl v (h_red_opt ri env hyps v) in
match fst_map (fun x -> x.f_node) (EcFol.destr_app v) with
| (Fop (p, _), cargs) when EcEnv.Op.is_dtype_ctor env p -> begin
let idx = EcEnv.Op.by_path p env in
let idx = snd (EcDecl.operator_as_ctor idx) in
match opb with
| EcDecl.OPB_Leaf _ -> assert false
| EcDecl.OPB_Branch bs ->
((Parray.get bs idx).EcDecl.opb_sub, cargs :: acc)
end
| _ -> raise NotReducible)
(fix.EcDecl.opf_branches, []) (fst fix.EcDecl.opf_struct)
in
let pargs, (bds, body) =
match pargs with
| EcDecl.OPB_Leaf (bds, body), cargs -> (List.rev cargs, (bds, body))
| _ -> assert false
in
let subst =
List.fold_left2
(fun subst (x, _) fa -> Fsubst.f_bind_local subst x fa)
Fsubst.f_subst_id fix.EcDecl.opf_args fargs in
let subst =
List.fold_left2
(fun subst bds cargs ->
List.fold_left2
(fun subst (x, _) fa -> Fsubst.f_bind_local subst x fa)
subst bds cargs)
subst bds pargs in
let body = EcFol.form_of_expr EcFol.mhr body in
let body =
EcFol.Fsubst.subst_tvar
(EcTypes.Tvar.init (List.map fst op.EcDecl.op_tparams) tys) body in
f_app (Fsubst.f_subst subst body) eargs f.f_ty
with NotReducible ->
f_app (h_red_x ri env hyps f1) fargs f.f_ty
end
(* μ-reduction *)
| Fglob (mp, m) when ri.modpath ->
let f' = EcEnv.NormMp.norm_glob env m mp in
if f_equal f f' then raise NotReducible else f'
(* μ-reduction *)
| Fpvar (pv, m) when ri.modpath ->
let pv' = EcEnv.NormMp.norm_pvar env pv in
if pv_equal pv pv' then raise NotReducible else f_pvar pv' f.f_ty m
(* η-reduction *)
| Fquant (Llambda, [x, GTty _], { f_node = Fapp (fn, args) })
when ri.eta && can_eta x (fn, args)
-> f_app fn (List.take (List.length args - 1) args) f.f_ty
| _ ->
let strategies =
[ reduce_logic;
reduce_user;
reduce_delta;
reduce_context]
in
oget ~exn:NotReducible (List.Exceptionless.find_map
(fun strategy ->
try Some (strategy ri env hyps f) with NotReducible -> None)
strategies)
and reduce_logic ri env hyps f =
match f.f_node with
| Fapp ({f_node = Fop (p, tys); } as fo, args)
when is_some ri.logic && is_logical_op p
->
let pcompat =
match oget ri.logic with `Full -> true | `ProductCompat -> false
in
let f' =
match op_kind p, args with
| Some (`Not), [f1] when pcompat -> f_not_simpl f1
| Some (`Imp), [f1;f2] when pcompat -> f_imp_simpl f1 f2
| Some (`Iff), [f1;f2] when pcompat -> f_iff_simpl f1 f2
| Some (`And `Asym), [f1;f2] -> f_anda_simpl f1 f2
| Some (`Or `Asym), [f1;f2] -> f_ora_simpl f1 f2
| Some (`And `Sym ), [f1;f2] -> f_and_simpl f1 f2
| Some (`Or `Sym ), [f1;f2] -> f_or_simpl f1 f2
| Some (`Int_le ), [f1;f2] -> f_int_le_simpl f1 f2
| Some (`Int_lt ), [f1;f2] -> f_int_lt_simpl f1 f2
| Some (`Real_le ), [f1;f2] -> f_real_le_simpl f1 f2
| Some (`Real_lt ), [f1;f2] -> f_real_lt_simpl f1 f2
| Some (`Int_add ), [f1;f2] -> f_int_add_simpl f1 f2
| Some (`Int_opp ), [f] -> f_int_opp_simpl f
| Some (`Int_mul ), [f1;f2] -> f_int_mul_simpl f1 f2
| Some (`Int_edivz), [f1;f2] -> f_int_edivz_simpl f1 f2
| Some (`Real_add ), [f1;f2] -> f_real_add_simpl f1 f2
| Some (`Real_opp ), [f] -> f_real_opp_simpl f
| Some (`Real_mul ), [f1;f2] -> f_real_mul_simpl f1 f2
| Some (`Real_inv ), [f] -> f_real_inv_simpl f
| Some (`Eq ), [f1;f2] -> begin
match fst_map f_node (destr_app f1), fst_map f_node (destr_app f2) with
| (Fop (p1, _), args1), (Fop (p2, _), args2)
when EcEnv.Op.is_dtype_ctor env p1
&& EcEnv.Op.is_dtype_ctor env p2 ->
let idx p =
let idx = EcEnv.Op.by_path p env in
snd (EcDecl.operator_as_ctor idx)
in
if idx p1 <> idx p2
then f_false
else f_ands (List.map2 f_eq args1 args2)
| (_, []), (_, [])
when EqTest.for_type env f1.f_ty EcTypes.tunit
&& EqTest.for_type env f2.f_ty EcTypes.tunit ->
f_true
| _ ->
if f_equal f1 f2 || is_alpha_eq hyps f1 f2
then f_true
else f_eq_simpl f1 f2
end
| _ when ri.delta_p p ->
let op = reduce_op ri env p tys in
f_app_simpl op args f.f_ty
| _ -> f
in
if f_equal f f'
then f_app fo (h_red_args ri env hyps args) f.f_ty
else f'
| _ -> raise NotReducible
and reduce_delta ri env _hyps f =
match f.f_node with
| Fop (p, tys) when ri.delta_p p ->
reduce_op ri env p tys
| Fapp ({ f_node = Fop (p, tys) }, args) when ri.delta_p p ->
let op = reduce_op ri env p tys in
f_app_simpl op args f.f_ty
| _ -> raise NotReducible
and reduce_context ri env hyps f =
match f.f_node with
(* contextual rule - let *)
| Flet (lp, f1, f2) -> f_let lp (h_red_x ri env hyps f1) f2
(* Contextual rule - application args. *)
| Fapp (f1, args) ->
f_app (h_red_x ri env hyps f1) args f.f_ty
(* Contextual rule - bindings *)
| Fquant (Lforall as t, b, f1)
| Fquant (Lexists as t, b, f1) -> begin
let ctor =
match t, ri.logic with
| Lforall, Some `Full -> f_forall_simpl
| Lforall, _ -> f_forall
| Lexists, Some `Full -> f_exists_simpl
| Lexists, _ -> f_exists
| Llambda, _ -> assert false in
try
let env = Mod.add_mod_binding b env in
ctor b (h_red_x ri env hyps f1)
with NotReducible ->
let f' = ctor b f1 in
if f_equal f f' then raise NotReducible else f'
end
| _ -> raise NotReducible
and reduce_user_gen simplify ri env hyps f
=
if not ri.user then raise NotReducible;
let p =
match f_node (fst (destr_app f)) with
| Fop (p, _) -> `Path p
| Ftuple _ -> `Tuple
| _ -> raise NotReducible in
let rules = EcEnv.Reduction.get p env in
let module R = EcTheory in
oget ~exn:NotReducible (List.Exceptionless.find_map (fun rule ->
let ue = EcUnify.UniEnv.create None in
let tvi = EcUnify.UniEnv.opentvi ue rule.R.rl_tyd None in
let pv = ref Mid.empty in
try
let rec doit f ptn =
match destr_app f, ptn with
| ({ f_node = Fop (p, tys) }, args), R.Rule (`Op (p', tys'), args')
when EcPath.p_equal p p' && List.length args = List.length args' ->
let tys' = List.map (EcTypes.Tvar.subst tvi) tys' in
begin
try List.iter2 (EcUnify.unify env ue) tys tys'
with EcUnify.UnificationFailure _ -> raise NotReducible end;
List.iter2 doit args args'
| ({ f_node = Ftuple args} , []), R.Rule (`Tuple, args')
when List.length args = List.length args' ->
List.iter2 doit args args'
| ({ f_node = Fint i }, []), R.Int j when EcBigInt.equal i j ->
()
| _, R.Var x -> begin
match Mid.find_opt x !pv with
| None -> pv := Mid.add x f !pv
| Some f' -> check_alpha_equal ri hyps f f'
end
| _ -> raise NotReducible in
doit f rule.R.rl_ptn;
if not (EcUnify.UniEnv.closed ue) then
raise NotReducible;
let subst f =
let tysubst = { ty_subst_id with ts_u = EcUnify.UniEnv.assubst ue } in
let subst = Fsubst.f_subst_init ~sty:tysubst () in
let subst = Mid.fold (fun x f s -> Fsubst.f_bind_local s x f) !pv subst in
Fsubst.f_subst subst (Fsubst.subst_tvar tvi f)
in
List.iter (fun cond ->
if not (f_equal (simplify (subst cond)) f_true) then
raise NotReducible)
rule.R.rl_cond;
Some (subst rule.R.rl_tg)
with NotReducible -> None)
rules)
and reduce_user ri env hyps f =
reduce_user_gen (simplify ri env hyps) ri env hyps f
and can_eta x (f, args) =
match List.rev args with
| { f_node = Flocal y } :: args ->
let check v = not (Mid.mem x v.f_fv) in
id_equal x y && List.for_all check (f :: args)
| _ -> false
and h_red_args ri env hyps args =
match args with
| [] -> raise NotReducible
| a :: args ->
try h_red_x ri env hyps a :: args
with NotReducible -> a :: h_red_args ri env hyps args
and h_red_opt ri env hyps f =
try Some (h_red_x ri env hyps f)
with NotReducible -> None
and check_alpha_equal ri hyps f1 f2 =
let env = LDecl.toenv hyps in
let exn = IncompatibleForm (env, (f1, f2)) in
let error () = raise exn in
let ensure t = if not t then error () in
let check_ty env subst ty1 ty2 =
ensure (EqTest.for_type env ty1 (subst.fs_ty ty2)) in
let add_local (env, subst) (x1,ty1) (x2,ty2) =
check_ty env subst ty1 ty2;
env,
if id_equal x1 x2 then subst
else Fsubst.f_bind_rename subst x2 x1 ty1 in
let check_lpattern env subst lp1 lp2 =
match lp1, lp2 with
| LSymbol xt1, LSymbol xt2 -> add_local (env, subst) xt1 xt2
| LTuple lid1, LTuple lid2 when List.length lid1 = List.length lid2 ->
List.fold_left2 add_local (env,subst) lid1 lid2
| _, _ -> error() in
let check_memtype env mt1 mt2 =
match mt1, mt2 with
| None, None -> ()
| Some lmt1, Some lmt2 ->
let xp1, xp2 = EcMemory.lmt_xpath lmt1, EcMemory.lmt_xpath lmt2 in
ensure (EqTest.for_xp env xp1 xp2);
let m1, m2 = EcMemory.lmt_bindings lmt1, EcMemory.lmt_bindings lmt2 in
ensure (EcSymbols.Msym.equal
(fun (p1,ty1) (p2,ty2) ->
p1 = p2 && EqTest.for_type env ty1 ty2) m1 m2)
| _, _ -> error () in
(* TODO all declaration in env, do it also in add local *)
let check_binding (env, subst) (x1,gty1) (x2,gty2) =
let gty2 = Fsubst.gty_subst subst gty2 in
match gty1, gty2 with
| GTty ty1, GTty ty2 ->
ensure (EqTest.for_type env ty1 ty2);
env,
if id_equal x1 x2 then subst else
Fsubst.f_bind_rename subst x2 x1 ty1
| GTmodty (p1, r1) , GTmodty(p2, r2) ->
ensure (ModTy.mod_type_equiv env p1 p2 &&
NormMp.equal_restr env r1 r2);
Mod.bind_local x1 p1 r1 env,
if id_equal x1 x2 then subst
else Fsubst.f_bind_mod subst x2 (EcPath.mident x1)
| GTmem me1, GTmem me2 ->
check_memtype env me1 me2;
env,
if id_equal x1 x2 then subst
else Fsubst.f_bind_mem subst x2 x1
| _, _ -> error () in
let check_bindings env subst bd1 bd2 =
List.fold_left2 check_binding (env,subst) bd1 bd2 in
let check_local subst id1 f2 id2 =
match (Mid.find_def f2 id2 subst.fs_loc).f_node with
| Flocal id2 -> ensure (EcIdent.id_equal id1 id2)
| _ -> assert false in
let check_mem subst m1 m2 =
let m2 = Mid.find_def m2 m2 subst.fs_mem in
ensure (EcIdent.id_equal m1 m2) in
let check_pv env subst pv1 pv2 =
let pv2 = pv_subst (EcPath.x_substm subst.fs_sty.ts_p subst.fs_mp) pv2 in
ensure (EqTest.for_pv env pv1 pv2) in
let check_mp env subst mp1 mp2 =
let mp2 = EcPath.m_subst subst.fs_sty.ts_p subst.fs_mp mp2 in
ensure (EqTest.for_mp env mp1 mp2) in
let check_xp env subst xp1 xp2 =
let xp2 = EcPath.x_substm subst.fs_sty.ts_p subst.fs_mp xp2 in
ensure (EqTest.for_xp env xp1 xp2) in
let check_s env s s1 s2 =
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p
s.fs_ty Mp.empty s.fs_mp s.fs_esloc in
let s2 = EcModules.s_subst es s2 in
ensure (EqTest.for_stmt env s1 s2) in
let rec aux1 env subst f1 f2 =
if Fsubst.is_subst_id subst && f_equal f1 f2 then ()
else match f1.f_node, f2.f_node with
| Fquant(q1,bd1,f1'), Fquant(q2,bd2,f2') when
q1 = q2 && List.length bd1 = List.length bd2 ->
let env, subst = check_bindings env subst bd1 bd2 in
aux env subst f1' f2'
| Fif(a1,b1,c1), Fif(a2,b2,c2) ->
aux env subst a1 a2; aux env subst b1 b2; aux env subst c1 c2
| Flet(p1,f1',g1), Flet(p2,f2',g2) ->
aux env subst f1' f2';
let (env,subst) = check_lpattern env subst p1 p2 in
aux env subst g1 g2
| Fint i1, Fint i2 when EcBigInt.equal i1 i2 -> ()
| Flocal id1, Flocal id2 -> check_local subst id1 f2 id2
| Fpvar(p1,m1), Fpvar(p2,m2) ->
check_mem subst m1 m2;
check_pv env subst p1 p2
| Fglob(p1,m1), Fglob(p2,m2) ->
check_mem subst m1 m2;
check_mp env subst p1 p2
| Fop(p1, ty1), Fop(p2, ty2) when EcPath.p_equal p1 p2 ->
List.iter2 (check_ty env subst) ty1 ty2
| Fapp(f1',args1), Fapp(f2',args2) when
List.length args1 = List.length args2 ->
aux env subst f1' f2';
List.iter2 (aux env subst) args1 args2
| Ftuple args1, Ftuple args2 when List.length args1 = List.length args2 ->
List.iter2 (aux env subst) args1 args2
| Fproj(f1,i1), Fproj(f2,i2) when i1 = i2 ->
aux env subst f1 f2
| FhoareF hf1, FhoareF hf2 ->
check_xp env subst hf1.hf_f hf2.hf_f;
aux env subst hf1.hf_pr hf2.hf_pr;
aux env subst hf1.hf_po hf2.hf_po
| FhoareS hs1, FhoareS hs2 ->
check_s env subst hs1.hs_s hs2.hs_s;
(* FIXME should check the memenv *)
aux env subst hs1.hs_pr hs2.hs_pr;
aux env subst hs1.hs_po hs2.hs_po
| FbdHoareF hf1, FbdHoareF hf2 ->
ensure (hf1.bhf_cmp = hf2.bhf_cmp);
check_xp env subst hf1.bhf_f hf2.bhf_f;
aux env subst hf1.bhf_pr hf2.bhf_pr;
aux env subst hf1.bhf_po hf2.bhf_po;
aux env subst hf1.bhf_bd hf2.bhf_bd
| FbdHoareS hs1, FbdHoareS hs2 ->
ensure (hs1.bhs_cmp = hs2.bhs_cmp);
check_s env subst hs1.bhs_s hs2.bhs_s;
(* FIXME should check the memenv *)
aux env subst hs1.bhs_pr hs2.bhs_pr;
aux env subst hs1.bhs_po hs2.bhs_po;
aux env subst hs1.bhs_bd hs2.bhs_bd
| FequivF ef1, FequivF ef2 ->
check_xp env subst ef1.ef_fl ef2.ef_fl;
check_xp env subst ef1.ef_fr ef2.ef_fr;
aux env subst ef1.ef_pr ef2.ef_pr;
aux env subst ef1.ef_po ef2.ef_po
| FequivS es1, FequivS es2 ->
check_s env subst es1.es_sl es2.es_sl;
check_s env subst es1.es_sr es2.es_sr;
(* FIXME should check the memenv *)
aux env subst es1.es_pr es2.es_pr;
aux env subst es1.es_po es2.es_po
| FeagerF eg1, FeagerF eg2 ->
check_xp env subst eg1.eg_fl eg2.eg_fl;
check_xp env subst eg1.eg_fr eg2.eg_fr;
aux env subst eg1.eg_pr eg2.eg_pr;
aux env subst eg1.eg_po eg2.eg_po;
check_s env subst eg1.eg_sl eg2.eg_sl;
check_s env subst eg1.eg_sr eg2.eg_sr
| Fpr pr1, Fpr pr2 ->
check_mem subst pr1.pr_mem pr2.pr_mem;
check_xp env subst pr1.pr_fun pr2.pr_fun;
aux env subst pr1.pr_args pr2.pr_args;
aux env subst pr1.pr_event pr2.pr_event
| _, _ -> error ()
and aux env subst f1 f2 =
try aux1 env subst f1 f2
with e when e == exn ->
match h_red_opt ri env hyps f1 with
| Some f1 -> aux env subst f1 f2
| None ->
match h_red_opt ri env hyps f2 with
| Some f2 -> aux env subst f1 f2
| None when EqTest.for_type env f1.f_ty f2.f_ty -> begin
let ty, codom =
match f1.f_node, f2.f_node with
| Fquant (Llambda, (_, GTty ty) :: bd, f1'), _ ->
ty, toarrow (List.map (gty_as_ty |- snd) bd) f1'.f_ty
| _, Fquant(Llambda, (_, GTty ty) :: bd, f2') ->
ty, toarrow (List.map (gty_as_ty |- snd) bd) f2'.f_ty
| _, _ -> raise e
in
let x = f_local (EcIdent.create "_") ty in
let f1 = f_app_simpl f1 [x] codom in
let f2 = f_app_simpl f2 [x] codom in
aux env subst f1 f2
end
| _ -> raise e
in aux env Fsubst.f_subst_id f1 f2
and check_alpha_eq f1 f2 = check_alpha_equal no_red f1 f2
and check_conv f1 f2 = check_alpha_equal full_red f1 f2
and is_alpha_eq hyps f1 f2 =
try check_alpha_eq hyps f1 f2; true
with _ -> false
and simplify ri env hyps f =
let f' = try h_red_x ri env hyps f with NotReducible -> f in
if f == f'
then simplify_rec ri env hyps f
else simplify ri env hyps f'
and simplify_rec ri env hyps f =
match f.f_node with
| Fapp ({ f_node = Fop _ } as fo, args) ->
let args' = List.map (simplify ri env hyps) args in
let app1 = (fo, args , f.f_ty) in
let app2 = (fo, args', f.f_ty) in
let f' = EcFol.FSmart.f_app (f, app1) app2 in
(try h_red_x ri env hyps f' with NotReducible -> f')
| FhoareF hf when ri.modpath ->
let hf_f = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) hf.hf_f in
f_map (fun ty -> ty) (simplify ri env hyps) (f_hoareF_r { hf with hf_f })
| FbdHoareF hf when ri.modpath ->
let bhf_f = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) hf.bhf_f in
f_map (fun ty -> ty) (simplify ri env hyps) (f_bdHoareF_r { hf with bhf_f })
| FequivF ef when ri.modpath ->
let ef_fl = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) ef.ef_fl in
let ef_fr = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) ef.ef_fr in
f_map (fun ty -> ty) (simplify ri env hyps) (f_equivF_r { ef with ef_fl; ef_fr; })
| FeagerF eg when ri.modpath ->
let eg_fl = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) eg.eg_fl in
let eg_fr = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) eg.eg_fr in
f_map (fun ty -> ty) (simplify ri env hyps) (f_eagerF_r { eg with eg_fl ; eg_fr; })
| Fpr pr when ri.modpath ->
let pr_fun = EcEnv.NormMp.norm_xfun (LDecl.toenv hyps) pr.pr_fun in
f_map (fun ty -> ty) (simplify ri env hyps) (f_pr_r { pr with pr_fun })
| _ -> f_map (fun ty -> ty) (simplify ri env hyps) f
(* -------------------------------------------------------------------- *)
let is_conv hyps f1 f2 =
try check_conv hyps f1 f2; true with _ -> false
let h_red ri hyps f =
h_red_x ri (LDecl.toenv hyps) hyps f
let h_red_opt ri hyps f =
h_red_opt ri (LDecl.toenv hyps) hyps f
let simplify ri hyps f =
simplify ri (LDecl.toenv hyps) hyps f
(* -------------------------------------------------------------------- *)
type xconv = [`Eq | `AlphaEq | `Conv]
let xconv (mode : xconv) hyps =
match mode with
| `Eq -> f_equal
| `AlphaEq -> is_alpha_eq hyps
| `Conv -> is_conv hyps
(* -------------------------------------------------------------------- *)
module User = struct
type options = EcTheory.rule_option
type error =
| MissingVarInLhs of EcIdent.t
| MissingTyVarInLhs of EcIdent.t
| NotAnEq
| NotFirstOrder
| RuleDependsOnMemOrModule
| HeadedByVar
exception InvalidUserRule of error
module R = EcTheory
type rule = EcEnv.Reduction.rule
let compile ~opts ~prio (env : EcEnv.env) (p : EcPath.path) =
let simp =
if opts.EcTheory.ur_delta then
let hyps = EcEnv.LDecl.init env [] in
fun f -> odfl f (h_red_opt delta hyps f)
else fun f -> f in
let ax = EcEnv.Ax.by_path p env in
let bds, rl = EcFol.decompose_forall (simp ax.EcDecl.ax_spec) in
let bds =
let filter = function
| (x, GTty ty) -> (x, ty)
| _ -> raise (InvalidUserRule RuleDependsOnMemOrModule)
in List.map filter bds in
let lhs, rhs, conds =
try
let rec doit conds f =
match sform_of_form (simp f) with
| SFimp (f1, f2) -> doit (f1 :: conds) f2
| SFeq (f1, f2) -> (f1, f2, List.rev conds)
| _ -> raise (InvalidUserRule NotAnEq)
in doit [] rl
with InvalidUserRule NotAnEq
when opts.EcTheory.ur_eqtrue &&
ty_equal tbool (EcEnv.ty_hnorm rl.f_ty env)
-> (rl, f_true, List.rev [])
in
let rule =
let rec rule (f : form) : EcTheory.rule_pattern =
match EcFol.destr_app f with
| { f_node = Fop (p, tys) }, args ->
R.Rule (`Op (p, tys), List.map rule args)
| { f_node = Ftuple args }, [] ->
R.Rule (`Tuple, List.map rule args)
| { f_node = Fint i }, [] ->
R.Int i
| { f_node = Flocal x }, [] ->
R.Var x
| _ -> raise (InvalidUserRule NotFirstOrder)
in rule lhs in
let lvars, ltyvars =
let rec doit (lvars, ltyvars) = function
| R.Var x ->
(Sid.add x lvars, ltyvars)
| R.Int _ ->
(lvars, ltyvars)
| R.Rule (op, args) ->
let ltyvars =
match op with
| `Op (_, tys) ->
List.fold_left (
let rec doit ltyvars = function
| { ty_node = Tvar a } -> Sid.add a ltyvars
| _ as ty -> ty_fold doit ltyvars ty in doit)
ltyvars tys
| `Tuple -> ltyvars in
List.fold_left doit (lvars, ltyvars) args
in doit (Sid.empty, Sid.empty) rule in
let mvars =
Sid.diff (Sid.of_list (List.map fst bds)) lvars in
let mtyvars =
Sid.diff (Sid.of_list (List.map fst ax.EcDecl.ax_tparams)) ltyvars in
if not (Sid.is_empty mvars) then
raise (InvalidUserRule (MissingVarInLhs (Sid.choose mvars)));
if not (Sid.is_empty mtyvars) then
raise (InvalidUserRule (MissingTyVarInLhs (Sid.choose mtyvars)));
begin match rule with
| R.Var _ -> raise (InvalidUserRule (HeadedByVar));
| _ -> () end;
R.{ rl_tyd = ax.EcDecl.ax_tparams;
rl_vars = bds;
rl_cond = conds;
rl_ptn = rule;
rl_tg = rhs;
rl_prio = prio; }
end