Revision 4388214acf75d0162f5a29c2c42230f44f6c8187 authored by Pierre-Yves Strub on 12 December 2015, 19:59:46 UTC, committed by Pierre-Yves Strub on 12 December 2015, 20:03:33 UTC
Syntax is `[~*]`. The full syntax of this i-p is now: `move=> [int?~?/?*]`
1 parent c09a98a
ecReduction.ml
(* --------------------------------------------------------------------
* Copyright (c) - 2012--2015 - IMDEA Software Institute
* Copyright (c) - 2012--2015 - Inria
*
* 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
module EqTest = struct
(* ------------------------------------------------------------------ *)
let for_xp_norm env p1 p2 =
EcPath.x_equal p1 p2
|| EcPath.x_equal (NormMp.norm_xfun env p1) (NormMp.norm_xfun env p2)
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)
| Tmem None, Tmem None -> true
| Tmem (Some mt1), Tmem (Some mt2) ->
(for_xp_norm env mt1.mt_path mt2.mt_path &&
EcSymbols.Msym.equal (fun (p1,ty1) (p2,ty2) -> p1 = p2 && for_type env ty1 ty2)
mt1.mt_vars mt2.mt_vars)
| _, _ -> 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_norm env p1 p2 =
pv_equal p1 p2 ||
(p1.pv_kind = p2.pv_kind &&
EcPath.x_equal
(NormMp.norm_pvar env p1).pv_name (NormMp.norm_pvar env p2).pv_name)
(* ------------------------------------------------------------------ *)
let for_mp_norm env p1 p2 =
EcPath.m_equal p1 p2
|| EcPath.m_equal (NormMp.norm_mpath env p1) (NormMp.norm_mpath env p2)
(* ------------------------------------------------------------------ *)
let for_expr_norm env =
let module E = struct exception NotConv end in
let find alpha id = odfl id (Mid.find_opt id alpha) 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 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_norm env p1 p2
| Eop(o1,ty1), Eop(o2,ty2) ->
p_equal o1 o2 && List.all2 (for_type env) ty1 ty2
| 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'
&& (try aux (check_lpattern alpha p1 p2) g1 g2 with E.NotConv -> false)
| 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_norm env lv1 lv2 =
match lv1, lv2 with
| LvVar(p1,_), LvVar(p2,_) -> for_pv_norm env p1 p2
| LvTuple p1, LvTuple p2 ->
List.all2 (fun (p1,_) (p2,_) -> for_pv_norm env p1 p2) p1 p2
| LvMap((m1,ty1),p1,e1,_), LvMap((m2,ty2),p2,e2,_) ->
p_equal m1 m2 &&
List.all2 (for_type env) ty1 ty2 &&
for_pv_norm env p1 p2 && for_expr_norm env e1 e2
| _, _ -> false
(* ------------------------------------------------------------------ *)
let rec for_stmt_norm env s1 s2 =
s_equal s1 s2
|| List.all2 (for_instr_norm env) s1.s_node s2.s_node
(* ------------------------------------------------------------------ *)
and for_instr_norm env i1 i2 =
i_equal i1 i2 || for_instr_norm_r env i1 i2
and for_instr_norm_r env i1 i2 =
match i1.i_node, i2.i_node with
| Sasgn(lv1,e1), Sasgn(lv2,e2) ->
for_lv_norm env lv1 lv2 && for_expr_norm env e1 e2
| Srnd(lv1,e1), Srnd(lv2,e2) ->
for_lv_norm env lv1 lv2 && for_expr_norm env e1 e2
| Scall(lv1, f1, e1), Scall(lv2,f2,e2) ->
oall2 (for_lv_norm env) lv1 lv2 &&
for_xp_norm env f1 f2 &&
List.all2 (for_expr_norm env) e1 e2
| Sif (a1,b1,c1), Sif(a2,b2,c2) ->
for_expr_norm env a1 a2
&& for_stmt_norm env b1 b2
&& for_stmt_norm env c1 c2
| Swhile(a1,b1), Swhile(a2,b2) ->
for_expr_norm env a1 a2 && for_stmt_norm env b1 b2
| Sassert a1, Sassert a2 ->
for_expr_norm env a1 a2
| Sabstract id1, Sabstract id2 -> EcIdent.id_equal id1 id2
| _, _ -> false
end
(* -------------------------------------------------------------------- *)
type reduction_info = {
beta : bool;
delta_p : (path -> bool);
delta_h : (ident -> bool);
zeta : bool;
iota : bool;
eta : bool;
logic : bool;
modpath : bool;
}
let full_red = {
beta = true;
delta_p = EcUtils.predT;
delta_h = EcUtils.predT;
zeta = true;
iota = true;
eta = true;
logic = true;
modpath = true;
}
let no_red = {
beta = false;
delta_p = EcUtils.pred0;
delta_h = EcUtils.pred0;
zeta = false;
iota = false;
eta = false;
logic = false;
modpath = 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 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 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] -> 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
odfl v (h_red_opt ri env hyps v)
| _ -> raise NotReducible
end
| _ -> raise NotReducible
with NotReducible ->
f_app (h_red 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 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 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 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 None body in
let body =
EcFol.Fsubst.subst_tvar
(EcTypes.Tvar.init (List.map fst op.EcDecl.op_tparams) tys) body in
Fsubst.f_subst subst body
with NotReducible ->
f_app (h_red 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
(* logical reduction *)
| Fapp ({f_node = Fop (p, tys); } as fo, args) when ri.logic && is_logical_op p ->
let f' =
match op_kind p, args with
| Some (`Not ), [f1] -> f_not_simpl f1
| 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 (`Imp ), [f1;f2] -> f_imp_simpl f1 f2
| Some (`Iff ), [f1;f2] -> f_iff_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 (`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_div ), [f1;f2] -> f_real_div_simpl f1 f2
| 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
| _ -> 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'
(* δ-reduction *)
| Fop (p, tys) ->
reduce_op ri env p tys
(* δ-reduction *)
| 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
(* η-reduction *)
| Fquant (Llambda, [x, GTty _], { f_node = Fapp (f, [{ f_node = Flocal y }]) })
when id_equal x y && not (Mid.mem x f.f_fv)
-> f
(* contextual rule - let *)
| Flet (lp, f1, f2) -> f_let lp (h_red ri env hyps f1) f2
(* Contextual rule - application args. *)
| Fapp (f1, args) ->
f_app (h_red 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 with
| Lforall -> f_forall_simpl
| Lexists -> f_exists_simpl
| _ -> assert false in
try
let env = Mod.add_mod_binding b env in
ctor b (h_red 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 h_red_args ri env hyps args =
match args with
| [] -> raise NotReducible
| a :: args ->
try h_red 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 ri env hyps f)
with NotReducible -> None
let 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_local subst x2 (f_local 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
(* 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_local subst x2 (f_local 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)
| _, _ -> 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_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_norm 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_norm 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_norm 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 in
let s2 = EcModules.s_subst es s2 in
ensure (EqTest.for_stmt_norm 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 i1 = i2 -> ()
| Flocal id1, Flocal id2 -> check_local subst id1 f2 id2
| Fpvar(p1,m1), Fpvar(p2,m2) ->
aux env subst m1 m2;
check_pv env subst p1 p2
| Fglob(p1,m1), Fglob(p2,m2) ->
aux env 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 hs1.hs_pr;
aux env subst hs1.hs_po hs2.hs_po
| FmuhoareF hf1, FmuhoareF hf2 ->
check_xp env subst hf1.muhf_f hf2.muhf_f;
aux env subst hf1.muhf_pr hf2.muhf_pr;
aux env subst hf1.muhf_po hf2.muhf_po
| FmuhoareS hs1, FmuhoareS hs2 ->
check_s env subst hs1.muh_s hs2.muh_s;
aux env subst hs1.muh_pr hs2.muh_pr;
aux env subst hs1.muh_po hs2.muh_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_local subst pr1.pr_mem (f_local pr2.pr_mem (tmem None)) 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 ->
let ty,codom =
match f1.f_node, f2.f_node with
| Fquant(Llambda,(_,GTty ty)::bd, f1'), _ ->
ty, toarrow (List.map (fun (_,gty)-> gty_as_ty gty) bd) f1'.f_ty
| _, Fquant(Llambda,(_,GTty ty)::bd,f2') ->
ty, toarrow (List.map (fun (_,gty)-> gty_as_ty gty) 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
in
aux env Fsubst.f_subst_id f1 f2
let check_alpha_eq = check_alpha_equal no_red
let check_conv = check_alpha_equal full_red
let is_alpha_eq hyps f1 f2 =
try check_alpha_eq hyps f1 f2; true
with _ -> false
let is_conv hyps f1 f2 =
try check_conv hyps f1 f2; true
with _ -> false
let h_red ri hyps f =
h_red ri (LDecl.toenv hyps) hyps f
let h_red_opt ri hyps f = h_red_opt ri (LDecl.toenv hyps) hyps f
let rec simplify ri hyps f =
let f' = try h_red ri hyps f with NotReducible -> f in
if f == f'
then simplify_rec ri hyps f
else simplify ri hyps f'
and simplify_rec ri hyps f =
match f.f_node with
| Fapp ({ f_node = Fop _ } as fo, args) ->
let args' = List.map (simplify ri 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 ri 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 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 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 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 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 hyps) (f_pr_r { pr with pr_fun })
| _ -> f_map (fun ty -> ty) (simplify ri 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
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