https://github.com/EasyCrypt/easycrypt
Tip revision: fd8edc177f3f33bf10ece3f61a39b7de4f687263 authored by Pierre-Yves Strub on 09 June 2020, 10:27:13 UTC
refactor & merge min/max
refactor & merge min/max
Tip revision: fd8edc1
ecCoreFol.ml
(* --------------------------------------------------------------------
* 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 EcTypes
open EcModules
type memory = EcMemory.memory
module BI = EcBigInt
module Mp = EcPath.Mp
module Sp = EcPath.Sp
module Sm = EcPath.Sm
module Sx = EcPath.Sx
open EcBigInt.Notations
(* -------------------------------------------------------------------- *)
type gty =
| GTty of EcTypes.ty
| GTmodty of module_type * mod_restr
| GTmem of EcMemory.memtype
type quantif =
| Lforall
| Lexists
| Llambda
type binding = (EcIdent.t * gty)
type bindings = binding list
let mhr = EcIdent.create "&hr"
let mleft = EcIdent.create "&1"
let mright = EcIdent.create "&2"
type hoarecmp = FHle | FHeq | FHge
type form = {
f_node : f_node;
f_ty : ty;
f_fv : int EcIdent.Mid.t; (* local, memory, module ident *)
f_tag : int;
}
and f_node =
| Fquant of quantif * bindings * form
| Fif of form * form * form
| Fmatch of form * form list * ty
| Flet of lpattern * form * form
| Fint of BI.zint
| Flocal of EcIdent.t
| Fpvar of EcTypes.prog_var * memory
| Fglob of EcPath.mpath * memory
| Fop of EcPath.path * ty list
| Fapp of form * form list
| Ftuple of form list
| Fproj of form * int
| FhoareF of hoareF (* $hr / $hr *)
| FhoareS of hoareS
| FbdHoareF of bdHoareF (* $hr / $hr *)
| FbdHoareS of bdHoareS
| FequivF of equivF (* $left,$right / $left,$right *)
| FequivS of equivS
| FeagerF of eagerF
| Fpr of pr (* hr *)
and eagerF = {
eg_pr : form;
eg_sl : stmt; (* No local program variables *)
eg_fl : EcPath.xpath;
eg_fr : EcPath.xpath;
eg_sr : stmt; (* No local program variables *)
eg_po : form
}
and equivF = {
ef_pr : form;
ef_fl : EcPath.xpath;
ef_fr : EcPath.xpath;
ef_po : form;
}
and equivS = {
es_ml : EcMemory.memenv;
es_mr : EcMemory.memenv;
es_pr : form;
es_sl : stmt;
es_sr : stmt;
es_po : form; }
and hoareF = {
hf_pr : form;
hf_f : EcPath.xpath;
hf_po : form;
}
and hoareS = {
hs_m : EcMemory.memenv;
hs_pr : form;
hs_s : stmt;
hs_po : form; }
and bdHoareF = {
bhf_pr : form;
bhf_f : EcPath.xpath;
bhf_po : form;
bhf_cmp : hoarecmp;
bhf_bd : form;
}
and bdHoareS = {
bhs_m : EcMemory.memenv;
bhs_pr : form;
bhs_s : stmt;
bhs_po : form;
bhs_cmp : hoarecmp;
bhs_bd : form;
}
and pr = {
pr_mem : memory;
pr_fun : EcPath.xpath;
pr_args : form;
pr_event : form;
}
(*-------------------------------------------------------------------- *)
let qt_equal : quantif -> quantif -> bool = (==)
let qt_hash : quantif -> int = Hashtbl.hash
(*-------------------------------------------------------------------- *)
let gty_equal ty1 ty2 =
match ty1, ty2 with
| GTty ty1, GTty ty2 ->
EcTypes.ty_equal ty1 ty2
| GTmodty (p1, r1), GTmodty (p2, r2) ->
EcModules.mty_equal p1 p2 && mr_equal r1 r2
| GTmem mt1, GTmem mt2 ->
EcMemory.mt_equal mt1 mt2
| _ , _ -> false
let gty_hash = function
| GTty ty -> EcTypes.ty_hash ty
| GTmodty (p, _) -> EcModules.mty_hash p
| GTmem _ -> 1
let gty_fv = function
| GTty ty -> ty.ty_fv
| GTmodty(_, (rx,r)) ->
let fv =
EcPath.Sm.fold (fun mp fv -> EcPath.m_fv fv mp) r EcIdent.Mid.empty in
EcPath.Sx.fold (fun xp fv -> EcPath.x_fv fv xp) rx fv
| GTmem mt -> EcMemory.mt_fv mt
let gtty (ty : EcTypes.ty) =
GTty ty
let gtmodty (mt : module_type) (mr : mod_restr) =
GTmodty (mt, mr)
let gtmem (mt : EcMemory.memtype) =
GTmem mt
(*-------------------------------------------------------------------- *)
let b_equal (b1 : bindings) (b2 : bindings) =
let b1_equal (x1, ty1) (x2, ty2) =
EcIdent.id_equal x1 x2 && gty_equal ty1 ty2
in
List.all2 b1_equal b1 b2
let b_hash (bs : bindings) =
let b1_hash (x, ty) =
Why3.Hashcons.combine (EcIdent.tag x) (gty_hash ty)
in
Why3.Hashcons.combine_list b1_hash 0 bs
(* -------------------------------------------------------------------- *)
let hcmp_hash : hoarecmp -> int = Hashtbl.hash
(*-------------------------------------------------------------------- *)
let f_equal : form -> form -> bool = (==)
let f_compare f1 f2 = f2.f_tag - f1.f_tag
let f_hash f = f.f_tag
let f_fv f = f.f_fv
let f_ty f = f.f_ty
module MSHf = EcMaps.MakeMSH(struct
type t = form
let tag f = f.f_tag
end)
module Mf = MSHf.M
module Sf = MSHf.S
module Hf = MSHf.H
let hf_equal hf1 hf2 =
f_equal hf1.hf_pr hf2.hf_pr
&& f_equal hf1.hf_po hf2.hf_po
&& EcPath.x_equal hf1.hf_f hf2.hf_f
let hs_equal hs1 hs2 =
f_equal hs1.hs_pr hs2.hs_pr
&& f_equal hs1.hs_po hs2.hs_po
&& s_equal hs1.hs_s hs2.hs_s
&& EcMemory.me_equal hs1.hs_m hs2.hs_m
let bhf_equal bhf1 bhf2 =
f_equal bhf1.bhf_pr bhf2.bhf_pr
&& f_equal bhf1.bhf_po bhf2.bhf_po
&& EcPath.x_equal bhf1.bhf_f bhf2.bhf_f
&& bhf1.bhf_cmp = bhf2.bhf_cmp
&& f_equal bhf1.bhf_bd bhf2.bhf_bd
let bhs_equal bhs1 bhs2 =
f_equal bhs1.bhs_pr bhs2.bhs_pr
&& f_equal bhs1.bhs_po bhs2.bhs_po
&& s_equal bhs1.bhs_s bhs2.bhs_s
&& EcMemory.me_equal bhs1.bhs_m bhs2.bhs_m
&& bhs1.bhs_cmp = bhs2.bhs_cmp
&& f_equal bhs1.bhs_bd bhs2.bhs_bd
let eqf_equal ef1 ef2 =
f_equal ef1.ef_pr ef2.ef_pr
&& f_equal ef1.ef_po ef2.ef_po
&& EcPath.x_equal ef1.ef_fl ef2.ef_fl
&& EcPath.x_equal ef1.ef_fr ef2.ef_fr
let eqs_equal es1 es2 =
f_equal es1.es_pr es2.es_pr
&& f_equal es1.es_po es2.es_po
&& s_equal es1.es_sl es2.es_sl
&& s_equal es1.es_sr es2.es_sr
&& EcMemory.me_equal es1.es_ml es2.es_ml
&& EcMemory.me_equal es1.es_mr es2.es_mr
let egf_equal eg1 eg2 =
f_equal eg1.eg_pr eg2.eg_pr
&& f_equal eg1.eg_po eg2.eg_po
&& EcModules.s_equal eg1.eg_sl eg2.eg_sl
&& EcPath.x_equal eg1.eg_fl eg2.eg_fl
&& EcPath.x_equal eg1.eg_fr eg2.eg_fr
&& EcModules.s_equal eg1.eg_sr eg2.eg_sr
let pr_equal pr1 pr2 =
EcIdent.id_equal pr1.pr_mem pr2.pr_mem
&& EcPath.x_equal pr1.pr_fun pr2.pr_fun
&& f_equal pr1.pr_event pr2.pr_event
&& f_equal pr1.pr_args pr2.pr_args
(* -------------------------------------------------------------------- *)
let hf_hash hf =
Why3.Hashcons.combine2
(f_hash hf.hf_pr) (f_hash hf.hf_po) (EcPath.x_hash hf.hf_f)
let hs_hash hs =
Why3.Hashcons.combine2
(f_hash hs.hs_pr) (f_hash hs.hs_po) (EcModules.s_hash hs.hs_s)
let bhf_hash bhf =
Why3.Hashcons.combine_list f_hash
(Why3.Hashcons.combine (hcmp_hash bhf.bhf_cmp) (EcPath.x_hash bhf.bhf_f))
[bhf.bhf_pr;bhf.bhf_po;bhf.bhf_bd]
let bhs_hash bhs =
Why3.Hashcons.combine_list f_hash
(Why3.Hashcons.combine (hcmp_hash bhs.bhs_cmp) (EcModules.s_hash bhs.bhs_s))
[bhs.bhs_pr;bhs.bhs_po;bhs.bhs_bd]
let ef_hash ef =
Why3.Hashcons.combine3
(f_hash ef.ef_pr) (f_hash ef.ef_po)
(EcPath.x_hash ef.ef_fl) (EcPath.x_hash ef.ef_fr)
let es_hash es =
Why3.Hashcons.combine3
(f_hash es.es_pr) (f_hash es.es_po)
(EcModules.s_hash es.es_sl) (EcModules.s_hash es.es_sr)
let eg_hash eg =
Why3.Hashcons.combine3
(f_hash eg.eg_pr) (f_hash eg.eg_po)
(Why3.Hashcons.combine (EcModules.s_hash eg.eg_sl) (EcPath.x_hash eg.eg_fl))
(Why3.Hashcons.combine (EcModules.s_hash eg.eg_sr) (EcPath.x_hash eg.eg_fr))
let pr_hash pr =
Why3.Hashcons.combine3
(EcIdent.id_hash pr.pr_mem)
(EcPath.x_hash pr.pr_fun)
(f_hash pr.pr_args)
(f_hash pr.pr_event)
(* -------------------------------------------------------------------- *)
module Hsform = Why3.Hashcons.Make (struct
type t = form
let equal_node f1 f2 =
match f1, f2 with
| Fquant(q1,b1,f1), Fquant(q2,b2,f2) ->
qt_equal q1 q2 && b_equal b1 b2 && f_equal f1 f2
| Fif(b1,t1,f1), Fif(b2,t2,f2) ->
f_equal b1 b2 && f_equal t1 t2 && f_equal f1 f2
| Fmatch(b1,es1,ty1), Fmatch(b2,es2,ty2) ->
List.all2 f_equal (b1::es1) (b2::es2)
&& ty_equal ty1 ty2
| Flet(lp1,e1,f1), Flet(lp2,e2,f2) ->
lp_equal lp1 lp2 && f_equal e1 e2 && f_equal f1 f2
| Fint i1, Fint i2 ->
BI.equal i1 i2
| Flocal id1, Flocal id2 ->
EcIdent.id_equal id1 id2
| Fpvar(pv1,s1), Fpvar(pv2,s2) ->
EcIdent.id_equal s1 s2 && EcTypes.pv_equal pv1 pv2
| Fglob(mp1,m1), Fglob(mp2,m2) ->
EcPath.m_equal mp1 mp2 && EcIdent.id_equal m1 m2
| Fop(p1,lty1), Fop(p2,lty2) ->
EcPath.p_equal p1 p2 && List.all2 ty_equal lty1 lty2
| Fapp(f1,args1), Fapp(f2,args2) ->
f_equal f1 f2 && List.all2 f_equal args1 args2
| Ftuple args1, Ftuple args2 ->
List.all2 f_equal args1 args2
| Fproj(f1,i1), Fproj(f2,i2) ->
i1 = i2 && f_equal f1 f2
| FhoareF hf1 , FhoareF hf2 -> hf_equal hf1 hf2
| FhoareS hs1 , FhoareS hs2 -> hs_equal hs1 hs2
| FbdHoareF bhf1, FbdHoareF bhf2 -> bhf_equal bhf1 bhf2
| FbdHoareS bhs1, FbdHoareS bhs2 -> bhs_equal bhs1 bhs2
| FequivF eqf1, FequivF eqf2 -> eqf_equal eqf1 eqf2
| FequivS eqs1, FequivS eqs2 -> eqs_equal eqs1 eqs2
| FeagerF eg1 , FeagerF eg2 -> egf_equal eg1 eg2
| Fpr pr1 , Fpr pr2 -> pr_equal pr1 pr2
| _, _ -> false
let equal f1 f2 =
ty_equal f1.f_ty f2.f_ty
&& equal_node f1.f_node f2.f_node
let hash f =
match f.f_node with
| Fquant(q, b, f) ->
Why3.Hashcons.combine2 (f_hash f) (b_hash b) (qt_hash q)
| Fif(b, t, f) ->
Why3.Hashcons.combine2 (f_hash b) (f_hash t) (f_hash f)
| Fmatch (f, fs, ty) ->
Why3.Hashcons.combine_list f_hash
(Why3.Hashcons.combine (f_hash f) (ty_hash ty))
fs
| Flet(lp, e, f) ->
Why3.Hashcons.combine2 (lp_hash lp) (f_hash e) (f_hash f)
| Fint i -> Hashtbl.hash i
| Flocal id -> EcIdent.tag id
| Fpvar(pv, m) ->
Why3.Hashcons.combine (EcTypes.pv_hash pv) (EcIdent.id_hash m)
| Fglob(mp, m) ->
Why3.Hashcons.combine (EcPath.m_hash mp) (EcIdent.id_hash m)
| Fop(p, lty) ->
Why3.Hashcons.combine_list ty_hash (EcPath.p_hash p) lty
| Fapp(f, args) ->
Why3.Hashcons.combine_list f_hash (f_hash f) args
| Ftuple args ->
Why3.Hashcons.combine_list f_hash 0 args
| Fproj(f,i) ->
Why3.Hashcons.combine (f_hash f) i
| FhoareF hf -> hf_hash hf
| FhoareS hs -> hs_hash hs
| FbdHoareF bhf -> bhf_hash bhf
| FbdHoareS bhs -> bhs_hash bhs
| FequivF ef -> ef_hash ef
| FequivS es -> es_hash es
| FeagerF eg -> eg_hash eg
| Fpr pr -> pr_hash pr
let fv_mlr = Sid.add mleft (Sid.singleton mright)
let fv_node f =
let union ex nodes =
List.fold_left (fun s a -> fv_union s (ex a)) Mid.empty nodes
in
match f with
| Fint _ -> Mid.empty
| Fop (_, tys) -> union (fun a -> a.ty_fv) tys
| Fpvar (pv,m) -> EcPath.x_fv (fv_add m Mid.empty) pv.pv_name
| Fglob (mp,m) -> EcPath.m_fv (fv_add m Mid.empty) mp
| Flocal id -> fv_singleton id
| Fapp (f, args) -> union f_fv (f :: args)
| Ftuple args -> union f_fv args
| Fproj(e, _) -> f_fv e
| Fif (f1, f2, f3) -> union f_fv [f1; f2; f3]
| Fmatch (b, fs, ty) -> fv_union ty.ty_fv (union f_fv (b :: fs))
| Fquant(_, b, f) ->
let do1 (id, ty) fv = fv_union (gty_fv ty) (Mid.remove id fv) in
List.fold_right do1 b (f_fv f)
| Flet(lp, f1, f2) ->
let fv2 = fv_diff (f_fv f2) (lp_fv lp) in
fv_union (f_fv f1) fv2
| FhoareF hf ->
let fv = fv_union (f_fv hf.hf_pr) (f_fv hf.hf_po) in
EcPath.x_fv (Mid.remove mhr fv) hf.hf_f
| FhoareS hs ->
let fv = fv_union (f_fv hs.hs_pr) (f_fv hs.hs_po) in
fv_union (EcModules.s_fv hs.hs_s) (Mid.remove (fst hs.hs_m) fv)
| FbdHoareF bhf ->
let fv =
fv_union (f_fv bhf.bhf_pr)
(fv_union (f_fv bhf.bhf_po) (f_fv bhf.bhf_bd)) in
EcPath.x_fv (Mid.remove mhr fv) bhf.bhf_f
| FbdHoareS bhs ->
let fv =
fv_union (f_fv bhs.bhs_pr)
(fv_union (f_fv bhs.bhs_po) (f_fv bhs.bhs_bd)) in
fv_union (EcModules.s_fv bhs.bhs_s) (Mid.remove (fst bhs.bhs_m) fv)
| FequivF ef ->
let fv = fv_union (f_fv ef.ef_pr) (f_fv ef.ef_po) in
let fv = fv_diff fv fv_mlr in
EcPath.x_fv (EcPath.x_fv fv ef.ef_fl) ef.ef_fr
| FequivS es ->
let fv = fv_union (f_fv es.es_pr) (f_fv es.es_po) in
let ml, mr = fst es.es_ml, fst es.es_mr in
let fv = fv_diff fv (Sid.add ml (Sid.singleton mr)) in
fv_union fv
(fv_union (EcModules.s_fv es.es_sl) (EcModules.s_fv es.es_sr))
| FeagerF eg ->
let fv = fv_union (f_fv eg.eg_pr) (f_fv eg.eg_po) in
let fv = fv_diff fv fv_mlr in
let fv = EcPath.x_fv (EcPath.x_fv fv eg.eg_fl) eg.eg_fr in
fv_union fv
(fv_union (EcModules.s_fv eg.eg_sl) (EcModules.s_fv eg.eg_sr))
| Fpr pr ->
let fve = Mid.remove mhr (f_fv pr.pr_event) in
let fv = EcPath.x_fv fve pr.pr_fun in
fv_union (f_fv pr.pr_args) (fv_add pr.pr_mem fv)
let tag n f =
let fv = fv_union (fv_node f.f_node) f.f_ty.ty_fv in
{ f with f_tag = n; f_fv = fv; }
end)
(* -------------------------------------------------------------------- *)
let gty_as_ty =
function GTty ty -> ty | _ -> assert false
let gty_as_mem =
function GTmem m -> m | _ -> assert false
let gty_as_mod =
function GTmodty (mt, mr) -> (mt, mr) | _ -> assert false
let kind_of_gty = function
| GTty _ -> `Form
| GTmem _ -> `Mem
| GTmodty _ -> `Mod
(* -------------------------------------------------------------------- *)
let hoarecmp_opp cmp =
match cmp with
| FHle -> FHge
| FHeq -> FHeq
| FHge -> FHle
(* -------------------------------------------------------------------- *)
let mk_form node ty =
let aout =
Hsform.hashcons
{ f_node = node;
f_ty = ty;
f_fv = Mid.empty;
f_tag = -1; }
in assert (EcTypes.ty_equal ty aout.f_ty); aout
let f_node { f_node = form } = form
(* -------------------------------------------------------------------- *)
let f_op x tys ty = mk_form (Fop (x, tys)) ty
let f_app f args ty =
let f, args' =
match f.f_node with
| Fapp (f, args') -> (f, args')
| _ -> (f, [])
in let args' = args' @ args in
if List.is_empty args' then begin
(*if ty_equal ty f.f_ty then f else mk_form f.f_node ty *) f
end else mk_form (Fapp (f, args')) ty
(* -------------------------------------------------------------------- *)
let f_local x ty = mk_form (Flocal x) ty
let f_pvar x ty m = mk_form (Fpvar(x, m)) ty
let f_pvarg f ty m = f_pvar (pv_arg f) ty m
let f_pvloc f v m = f_pvar (EcTypes.pv_loc f v.v_name) v.v_type m
let f_pvlocs f vs m = List.map (fun v -> f_pvloc f v m) vs
let f_glob mp m = mk_form (Fglob (mp, m)) (tglob mp)
(* -------------------------------------------------------------------- *)
let f_tt = f_op EcCoreLib.CI_Unit.p_tt [] tunit
let f_true = f_op EcCoreLib.CI_Bool.p_true [] tbool
let f_false = f_op EcCoreLib.CI_Bool.p_false [] tbool
let f_bool = fun b -> if b then f_true else f_false
(* -------------------------------------------------------------------- *)
let f_tuple args =
match args with
| [] -> f_tt
| [x] -> x
| _ -> mk_form (Ftuple args) (ttuple (List.map f_ty args))
let f_quant q b f =
if List.is_empty b then f else
let (q, b, f) =
match f.f_node with
| Fquant(q',b',f') when q = q' -> (q, b@b', f')
| _ -> q, b , f in
let ty =
if q = Llambda
then toarrow (List.map (fun (_,gty) -> gty_as_ty gty) b) f.f_ty
else tbool in
mk_form (Fquant (q, b, f)) ty
let f_proj f i ty = mk_form (Fproj(f, i)) ty
let f_if f1 f2 f3 = mk_form (Fif (f1, f2, f3)) f2.f_ty
let f_match b fs ty = mk_form (Fmatch (b, fs, ty)) ty
let f_let q f1 f2 = mk_form (Flet (q, f1, f2)) f2.f_ty (* FIXME rename binding *)
let f_let1 x f1 f2 = f_let (LSymbol (x, f1.f_ty)) f1 f2
let f_exists b f = f_quant Lexists b f
let f_forall b f = f_quant Lforall b f
let f_lambda b f = f_quant Llambda b f
let f_forall_mems bds f =
f_forall (List.map (fun (m, mt) -> (m, GTmem mt)) bds) f
(* -------------------------------------------------------------------- *)
let ty_fbool1 = toarrow (List.make 1 tbool) tbool
let ty_fbool2 = toarrow (List.make 2 tbool) tbool
let fop_not = f_op EcCoreLib.CI_Bool.p_not [] ty_fbool1
let fop_and = f_op EcCoreLib.CI_Bool.p_and [] ty_fbool2
let fop_anda = f_op EcCoreLib.CI_Bool.p_anda [] ty_fbool2
let fop_or = f_op EcCoreLib.CI_Bool.p_or [] ty_fbool2
let fop_ora = f_op EcCoreLib.CI_Bool.p_ora [] ty_fbool2
let fop_imp = f_op EcCoreLib.CI_Bool.p_imp [] ty_fbool2
let fop_iff = f_op EcCoreLib.CI_Bool.p_iff [] ty_fbool2
let f_not f = f_app fop_not [f] tbool
let f_and f1 f2 = f_app fop_and [f1; f2] tbool
let f_anda f1 f2 = f_app fop_anda [f1; f2] tbool
let f_or f1 f2 = f_app fop_or [f1; f2] tbool
let f_ora f1 f2 = f_app fop_ora [f1; f2] tbool
let f_imp f1 f2 = f_app fop_imp [f1; f2] tbool
let f_iff f1 f2 = f_app fop_iff [f1; f2] tbool
let f_ands fs =
match List.rev fs with
| [] -> f_true
| f::fs -> List.fold_left ((^~) f_and) f fs
let f_andas fs =
match List.rev fs with
| [] -> f_true
| f::fs -> List.fold_left ((^~) f_anda) f fs
let f_ors fs =
match List.rev fs with
| [] -> f_false
| f::fs -> List.fold_left ((^~) f_or) f fs
let f_oras fs =
match List.rev fs with
| [] -> f_false
| f::fs -> List.fold_left ((^~) f_ora) f fs
let f_imps = List.fold_right f_imp
(* -------------------------------------------------------------------- *)
let fop_eq ty = f_op EcCoreLib.CI_Bool.p_eq [ty] (toarrow [ty; ty] tbool)
let f_eq f1 f2 = f_app (fop_eq f1.f_ty) [f1; f2] tbool
let f_eqs fs1 fs2 =
assert (List.length fs1 = List.length fs2);
f_ands (List.map2 f_eq fs1 fs2)
(* -------------------------------------------------------------------- *)
let f_hoareS_r hs = mk_form (FhoareS hs) tbool
let f_hoareF_r hf = mk_form (FhoareF hf) tbool
let f_hoareS hs_m hs_pr hs_s hs_po =
f_hoareS_r { hs_m; hs_pr; hs_s; hs_po; }
let f_hoareF hf_pr hf_f hf_po =
f_hoareF_r { hf_pr; hf_f; hf_po; }
(* -------------------------------------------------------------------- *)
let f_bdHoareS_r bhs = mk_form (FbdHoareS bhs) tbool
let f_bdHoareF_r bhf = mk_form (FbdHoareF bhf) tbool
let f_bdHoareS bhs_m bhs_pr bhs_s bhs_po bhs_cmp bhs_bd =
f_bdHoareS_r
{ bhs_m; bhs_pr; bhs_s; bhs_po; bhs_cmp; bhs_bd; }
let f_bdHoareF bhf_pr bhf_f bhf_po bhf_cmp bhf_bd =
f_bdHoareF_r { bhf_pr; bhf_f; bhf_po; bhf_cmp; bhf_bd; }
(* -------------------------------------------------------------------- *)
let f_equivS_r es = mk_form (FequivS es) tbool
let f_equivF_r ef = mk_form (FequivF ef) tbool
let f_equivS es_ml es_mr es_pr es_sl es_sr es_po =
f_equivS_r { es_ml; es_mr; es_pr; es_sl; es_sr; es_po; }
let f_equivF ef_pr ef_fl ef_fr ef_po =
f_equivF_r{ ef_pr; ef_fl; ef_fr; ef_po; }
(* -------------------------------------------------------------------- *)
let f_eagerF_r eg = mk_form (FeagerF eg) tbool
let f_eagerF eg_pr eg_sl eg_fl eg_fr eg_sr eg_po =
f_eagerF_r { eg_pr; eg_sl; eg_fl; eg_fr; eg_sr; eg_po; }
(* -------------------------------------------------------------------- *)
let f_pr_r pr = mk_form (Fpr pr) treal
let f_pr pr_mem pr_fun pr_args pr_event =
f_pr_r { pr_mem; pr_fun; pr_args; pr_event; }
(* -------------------------------------------------------------------- *)
let fop_int_opp = f_op EcCoreLib.CI_Int.p_int_opp [] (toarrow [tint] tint)
let fop_int_add = f_op EcCoreLib.CI_Int.p_int_add [] (toarrow [tint; tint] tint)
let fop_int_mul = f_op EcCoreLib.CI_Int.p_int_mul [] (toarrow [tint; tint] tint)
let fop_int_pow = f_op EcCoreLib.CI_Int.p_int_pow [] (toarrow [tint; tint] tint)
let fop_int_edivz =
f_op EcCoreLib.CI_Int.p_int_edivz []
(toarrow [tint; tint] (ttuple [tint; tint]))
let f_int_opp f = f_app fop_int_opp [f] tint
let f_int_add f1 f2 = f_app fop_int_add [f1; f2] tint
let f_int_mul f1 f2 = f_app fop_int_mul [f1; f2] tint
let f_int_pow f1 f2 = f_app fop_int_pow [f1; f2] tint
let f_int_edivz f1 f2 = f_app fop_int_edivz [f1; f2] tint
let f_int_sub f1 f2 =
f_int_add f1 (f_int_opp f2)
let rec f_int (n : BI.zint) =
match BI.sign n with
| s when 0 <= s -> mk_form (Fint n) tint
| _ -> f_int_opp (f_int (~^ n))
(* -------------------------------------------------------------------- *)
let f_i0 = f_int BI.zero
let f_i1 = f_int BI.one
let f_im1 = f_int_opp f_i1
(* -------------------------------------------------------------------- *)
module FSmart = struct
type a_local = EcIdent.t * ty
type a_pvar = prog_var * ty * memory
type a_quant = quantif * bindings * form
type a_if = form tuple3
type a_match = form * form list * ty
type a_let = lpattern * form * form
type a_op = EcPath.path * ty list * ty
type a_tuple = form list
type a_app = form * form list * ty
type a_proj = form * ty
type a_glob = EcPath.mpath * memory
let f_local (fp, (x, ty)) (x', ty') =
if x == x' && ty == ty'
then fp
else f_local x' ty'
let f_pvar (fp, (pv, ty, m)) (pv', ty', m') =
if pv == pv' && ty == ty' && m == m'
then fp
else f_pvar pv' ty' m'
let f_quant (fp, (q, b, f)) (q', b', f') =
if q == q' && b == b' && f == f'
then fp
else f_quant q' b' f'
let f_glob (fp, (mp, m)) (mp', m') =
if mp == mp' && m == m'
then fp
else f_glob mp' m'
let f_if (fp, (c, f1, f2)) (c', f1', f2') =
if c == c' && f1 == f1' && f2 == f2'
then fp
else f_if c' f1' f2'
let f_match (fp, (b, fs, ty)) (b', fs', ty') =
if b == b' && fs == fs' && ty == ty'
then fp
else f_match b' fs' ty'
let f_let (fp, (lp, f1, f2)) (lp', f1', f2') =
if lp == lp' && f1 == f1' && f2 == f2'
then fp
else f_let lp' f1' f2'
let f_op (fp, (op, tys, ty)) (op', tys', ty') =
if op == op' && tys == tys' && ty == ty'
then fp
else f_op op' tys' ty'
let f_app (fp, (f, fs, ty)) (f', fs', ty') =
if f == f' && fs == fs' && ty == ty'
then fp
else f_app f' fs' ty'
let f_tuple (fp, fs) fs' =
if fs == fs' then fp else f_tuple fs'
let f_proj (fp, (f, ty)) (f', ty') i =
if f == f' && ty == ty'
then fp
else f_proj f' i ty'
let f_equivF (fp, ef) ef' =
if eqf_equal ef ef' then fp else mk_form (FequivF ef') fp.f_ty
let f_equivS (fp, es) es' =
if eqs_equal es es' then fp else f_equivS_r es'
let f_eagerF (fp, eg) eg' =
if egf_equal eg eg' then fp else mk_form (FeagerF eg') fp.f_ty
let f_hoareF (fp, hf) hf' =
if hf_equal hf hf' then fp else mk_form (FhoareF hf') fp.f_ty
let f_hoareS (fp, hs) hs' =
if hs_equal hs hs' then fp else f_hoareS_r hs'
let f_bdHoareF (fp, bhf) bhf' =
if bhf_equal bhf bhf' then fp else mk_form (FbdHoareF bhf') fp.f_ty
let f_bdHoareS (fp, bhs) bhs' =
if bhs_equal bhs bhs' then fp else f_bdHoareS_r bhs'
let f_pr (fp, pr) pr' =
if pr_equal pr pr' then fp else f_pr_r pr'
end
(* -------------------------------------------------------------------- *)
let f_map gt g fp =
match fp.f_node with
| Fquant(q, b, f) ->
let map_gty ((x, gty) as b1) =
let gty' =
match gty with
| GTty ty ->
let ty' = gt ty in if ty == ty' then gty else GTty ty'
| _ -> gty
in
if gty == gty' then b1 else (x, gty')
in
let b' = List.Smart.map map_gty b in
let f' = g f in
FSmart.f_quant (fp, (q, b, f)) (q, b', f')
| Fint _ -> fp
| Fglob _ -> fp
| Fif (f1, f2, f3) ->
FSmart.f_if (fp, (f1, f2, f3)) (g f1, g f2, g f3)
| Fmatch (b, fs, ty) ->
FSmart.f_match (fp, (b, fs, ty)) (g b, List.map g fs, gt ty)
| Flet (lp, f1, f2) ->
FSmart.f_let (fp, (lp, f1, f2)) (lp, g f1, g f2)
| Flocal id ->
let ty' = gt fp.f_ty in
FSmart.f_local (fp, (id, fp.f_ty)) (id, ty')
| Fpvar (id, s) ->
let ty' = gt fp.f_ty in
FSmart.f_pvar (fp, (id, fp.f_ty, s)) (id, ty', s)
| Fop (p, tys) ->
let tys' = List.Smart.map gt tys in
let ty' = gt fp.f_ty in
FSmart.f_op (fp, (p, tys, fp.f_ty)) (p, tys', ty')
| Fapp (f, fs) ->
let f' = g f in
let fs' = List.Smart.map g fs in
let ty' = gt fp.f_ty in
FSmart.f_app (fp, (f, fs, fp.f_ty)) (f', fs', ty')
| Ftuple fs ->
let fs' = List.Smart.map g fs in
FSmart.f_tuple (fp, fs) fs'
| Fproj (f, i) ->
let f' = g f in
let ty' = gt fp.f_ty in
FSmart.f_proj (fp, (f, fp.f_ty)) (f', ty') i
| FhoareF hf ->
let pr' = g hf.hf_pr in
let po' = g hf.hf_po in
FSmart.f_hoareF (fp, hf)
{ hf with hf_pr = pr'; hf_po = po'; }
| FhoareS hs ->
let pr' = g hs.hs_pr in
let po' = g hs.hs_po in
FSmart.f_hoareS (fp, hs)
{ hs with hs_pr = pr'; hs_po = po'; }
| FbdHoareF bhf ->
let pr' = g bhf.bhf_pr in
let po' = g bhf.bhf_po in
let bd' = g bhf.bhf_bd in
FSmart.f_bdHoareF (fp, bhf)
{ bhf with bhf_pr = pr'; bhf_po = po'; bhf_bd = bd'; }
| FbdHoareS bhs ->
let pr' = g bhs.bhs_pr in
let po' = g bhs.bhs_po in
let bd' = g bhs.bhs_bd in
FSmart.f_bdHoareS (fp, bhs)
{ bhs with bhs_pr = pr'; bhs_po = po'; bhs_bd = bd'; }
| FequivF ef ->
let pr' = g ef.ef_pr in
let po' = g ef.ef_po in
FSmart.f_equivF (fp, ef)
{ ef with ef_pr = pr'; ef_po = po'; }
| FequivS es ->
let pr' = g es.es_pr in
let po' = g es.es_po in
FSmart.f_equivS (fp, es)
{ es with es_pr = pr'; es_po = po'; }
| FeagerF eg ->
let pr' = g eg.eg_pr in
let po' = g eg.eg_po in
FSmart.f_eagerF (fp, eg)
{ eg with eg_pr = pr'; eg_po = po'; }
| Fpr pr ->
let args' = g pr.pr_args in
let ev' = g pr.pr_event in
FSmart.f_pr (fp, pr)
{ pr with pr_args = args'; pr_event = ev'; }
(* -------------------------------------------------------------------- *)
let f_iter g f =
match f.f_node with
| Fint _
| Flocal _
| Fpvar _
| Fglob _
| Fop _ -> ()
| Fquant (_ , _ , f1) -> g f1
| Fif (f1, f2, f3) -> g f1;g f2; g f3
| Fmatch (b, fs, _) -> List.iter g (b :: fs)
| Flet (_, f1, f2) -> g f1;g f2
| Fapp (e, es) -> List.iter g (e :: es)
| Ftuple es -> List.iter g es
| Fproj (e, _) -> g e
| FhoareF hf -> g hf.hf_pr; g hf.hf_po
| FhoareS hs -> g hs.hs_pr; g hs.hs_po
| FbdHoareF bhf -> g bhf.bhf_pr; g bhf.bhf_po
| FbdHoareS bhs -> g bhs.bhs_pr; g bhs.bhs_po
| FequivF ef -> g ef.ef_pr; g ef.ef_po
| FequivS es -> g es.es_pr; g es.es_po
| FeagerF eg -> g eg.eg_pr; g eg.eg_po
| Fpr pr -> g pr.pr_args; g pr.pr_event
(* -------------------------------------------------------------------- *)
let form_exists g f =
match f.f_node with
| Fint _
| Flocal _
| Fpvar _
| Fglob _
| Fop _ -> false
| Fquant (_ , _ , f1) -> g f1
| Fif (f1, f2, f3) -> g f1 || g f2 || g f3
| Fmatch (b, fs, _) -> List.exists g (b :: fs)
| Flet (_, f1, f2) -> g f1 || g f2
| Fapp (e, es) -> List.exists g (e :: es)
| Ftuple es -> List.exists g es
| Fproj (e, _) -> g e
| FhoareF hf -> g hf.hf_pr || g hf.hf_po
| FhoareS hs -> g hs.hs_pr || g hs.hs_po
| FbdHoareF bhf -> g bhf.bhf_pr || g bhf.bhf_po
| FbdHoareS bhs -> g bhs.bhs_pr || g bhs.bhs_po
| FequivF ef -> g ef.ef_pr || g ef.ef_po
| FequivS es -> g es.es_pr || g es.es_po
| FeagerF eg -> g eg.eg_pr || g eg.eg_po
| Fpr pr -> g pr.pr_args || g pr.pr_event
(* -------------------------------------------------------------------- *)
let form_forall g f =
match f.f_node with
| Fint _
| Flocal _
| Fpvar _
| Fglob _
| Fop _ -> true
| Fquant (_ , _ , f1) -> g f1
| Fif (f1, f2, f3) -> g f1 && g f2 && g f3
| Fmatch (b, fs, _) -> List.for_all g (b :: fs)
| Flet (_, f1, f2) -> g f1 && g f2
| Fapp (e, es) -> List.for_all g (e :: es)
| Ftuple es -> List.for_all g es
| Fproj (e, _) -> g e
| FhoareF hf -> g hf.hf_pr && g hf.hf_po
| FhoareS hs -> g hs.hs_pr && g hs.hs_po
| FbdHoareF bhf -> g bhf.bhf_pr && g bhf.bhf_po
| FbdHoareS bhs -> g bhs.bhs_pr && g bhs.bhs_po
| FequivF ef -> g ef.ef_pr && g ef.ef_po
| FequivS es -> g es.es_pr && g es.es_po
| FeagerF eg -> g eg.eg_pr && g eg.eg_po
| Fpr pr -> g pr.pr_args && g pr.pr_event
(* -------------------------------------------------------------------- *)
let f_ops f =
let aout = ref EcPath.Sp.empty in
let rec doit f =
match f.f_node with
| Fop (p, _) -> aout := Sp.add p !aout
| _ -> f_iter doit f
in doit f; !aout
(* -------------------------------------------------------------------- *)
exception DestrError of string
let destr_error e = raise (DestrError e)
(* -------------------------------------------------------------------- *)
let destr_forall1 f =
match f.f_node with
| Fquant(Lforall,(x,t)::bd,p) -> x,t,f_forall bd p
| _ -> destr_error "forall"
let destr_forall f =
match f.f_node with
| Fquant(Lforall,bd,p) -> bd, p
| _ -> destr_error "forall"
let decompose_forall f =
match f.f_node with
| Fquant(Lforall,bd,p) -> bd, p
| _ -> [], f
let destr_lambda f =
match f.f_node with
| Fquant(Llambda,bd,p) -> bd, p
| _ -> destr_error "lambda"
let decompose_lambda f =
match f.f_node with
| Fquant(Llambda,bd,p) -> bd, p
| _ -> [], f
let destr_exists1 f =
match f.f_node with
| Fquant(Lexists,(x,t)::bd,p) -> x,t,f_exists bd p
| _ -> destr_error "exists"
let destr_exists f =
match f.f_node with
| Fquant(Lexists,bd,p) -> bd, p
| _ -> destr_error "exists"
let destr_let f =
match f.f_node with
| Flet(lp, e1,e2) -> lp,e1,e2
| _ -> destr_error "let"
let destr_let1 f =
match f.f_node with
| Flet(LSymbol(x,ty), e1,e2) -> x,ty,e1,e2
| _ -> destr_error "let1"
let destr_equivS f =
match f.f_node with
| FequivS es -> es
| _ -> destr_error "equivS"
let destr_equivF f =
match f.f_node with
| FequivF es -> es
| _ -> destr_error "equivF"
let destr_eagerF f =
match f.f_node with
| FeagerF eg -> eg
| _ -> destr_error "eagerF"
let destr_hoareS f =
match f.f_node with
| FhoareS es -> es
| _ -> destr_error "hoareS"
let destr_hoareF f =
match f.f_node with
| FhoareF es -> es
| _ -> destr_error "hoareF"
let destr_bdHoareS f =
match f.f_node with
| FbdHoareS es -> es
| _ -> destr_error "bdHoareS"
let destr_bdHoareF f =
match f.f_node with
| FbdHoareF es -> es
| _ -> destr_error "bdHoareF"
let destr_pr f =
match f.f_node with
| Fpr pr -> pr
| _ -> destr_error "pr"
let destr_programS side f =
match side, f.f_node with
| None , FhoareS hs -> (hs.hs_m, hs.hs_s)
| None , FbdHoareS bhs -> (bhs.bhs_m, bhs.bhs_s)
| Some b, FequivS es -> begin
match b with
| `Left -> (es.es_ml, es.es_sl)
| `Right -> (es.es_mr, es.es_sr)
end
| _, _ -> destr_error "programS"
let destr_int f =
match f.f_node with
| Fint n -> n
| Fapp (op, [{f_node = Fint n}]) when f_equal op fop_int_opp ->
BI.neg n
| _ -> destr_error "destr_int"
let destr_pvar f =
match f.f_node with
| Fpvar(x,m) -> (x,m)
| _ -> destr_error "destr_pvar"
let destr_glob f =
match f.f_node with
| Fglob(p,m) -> (p,m)
| _ -> destr_error "destr_glob"
(* -------------------------------------------------------------------- *)
let is_op_and_sym p = EcPath.p_equal EcCoreLib.CI_Bool.p_and p
let is_op_and_asym p = EcPath.p_equal EcCoreLib.CI_Bool.p_anda p
let is_op_and_any p = is_op_and_sym p || is_op_and_asym p
let is_op_or_sym p = EcPath.p_equal EcCoreLib.CI_Bool.p_or p
let is_op_or_asym p = EcPath.p_equal EcCoreLib.CI_Bool.p_ora p
let is_op_or_any p = is_op_or_sym p || is_op_or_asym p
let is_op_not p = EcPath.p_equal EcCoreLib.CI_Bool.p_not p
let is_op_imp p = EcPath.p_equal EcCoreLib.CI_Bool.p_imp p
let is_op_iff p = EcPath.p_equal EcCoreLib.CI_Bool.p_iff p
let is_op_eq p = EcPath.p_equal EcCoreLib.CI_Bool.p_eq p
(* -------------------------------------------------------------------- *)
let destr_op = function
{ f_node = Fop (op, tys) } -> op, tys | _ -> destr_error "op"
let destr_app = function
{ f_node = Fapp (f, fs) } -> (f, fs) | f -> (f, [])
let destr_op_app f =
let (fo, args) = destr_app f in destr_op fo, args
let destr_tuple = function
{ f_node = Ftuple fs } -> fs | _ -> destr_error "tuple"
let destr_local = function
{ f_node = Flocal id } -> id | _ -> destr_error "local"
let destr_pvar = function
{ f_node = Fpvar (pv, m) } -> (pv, m) | _ -> destr_error "pvar"
let destr_proj = function
{ f_node = Fproj (f, i) } -> (f, i) | _ -> destr_error "proj"
let destr_app1 ~name pred form =
match destr_app form with
| { f_node = Fop (p, _) }, [f] when pred p -> f
| _ -> destr_error name
let destr_app2 ~name pred form =
match destr_app form with
| { f_node = Fop (p, _) }, [f1; f2] when pred p -> (f1, f2)
| _ -> destr_error name
let destr_app1_eq ~name p f = destr_app1 ~name (EcPath.p_equal p) f
let destr_app2_eq ~name p f = destr_app2 ~name (EcPath.p_equal p) f
let destr_not = destr_app1 ~name:"not" is_op_not
let destr_and = destr_app2 ~name:"and" is_op_and_any
let destr_or = destr_app2 ~name:"or" is_op_or_any
let destr_imp = destr_app2 ~name:"imp" is_op_imp
let destr_iff = destr_app2 ~name:"iff" is_op_iff
let destr_eq = destr_app2 ~name:"eq" is_op_eq
let destr_and3 f =
try
let c1, (c2, c3) = snd_map destr_and (destr_and f)
in (c1, c2, c3)
with DestrError _ -> raise (DestrError "and3")
let destr_eq_or_iff =
destr_app2 ~name:"eq-or-iff" (fun p -> is_op_eq p || is_op_iff p)
let destr_or_r form =
match destr_app form with
| { f_node = Fop (p, _) }, [f1; f2] when is_op_or_sym p -> (`Sym , (f1, f2))
| { f_node = Fop (p, _) }, [f1; f2] when is_op_or_asym p -> (`Asym, (f1, f2))
| _ -> destr_error "or"
let destr_and_r form =
match destr_app form with
| { f_node = Fop (p, _) }, [f1; f2] when is_op_and_sym p -> (`Sym , (f1, f2))
| { f_node = Fop (p, _) }, [f1; f2] when is_op_and_asym p -> (`Asym, (f1, f2))
| _ -> destr_error "and"
let destr_nots form =
let rec aux b form =
match try Some (destr_not form) with DestrError _ -> None with
| None -> (b, form)
| Some form -> aux (not b) form
in aux true form
(* -------------------------------------------------------------------- *)
let is_from_destr dt f =
try ignore (dt f); true with DestrError _ -> false
let is_true f = f_equal f f_true
let is_false f = f_equal f f_false
let is_tuple f = is_from_destr destr_tuple f
let is_op f = is_from_destr destr_op f
let is_local f = is_from_destr destr_local f
let is_pvar f = is_from_destr destr_pvar f
let is_proj f = is_from_destr destr_proj f
let is_and f = is_from_destr destr_and f
let is_or f = is_from_destr destr_or f
let is_not f = is_from_destr destr_not f
let is_imp f = is_from_destr destr_imp f
let is_iff f = is_from_destr destr_iff f
let is_eq f = is_from_destr destr_eq f
let is_forall f = is_from_destr destr_forall1 f
let is_exists f = is_from_destr destr_exists1 f
let is_let f = is_from_destr destr_let1 f
let is_equivF f = is_from_destr destr_equivF f
let is_equivS f = is_from_destr destr_equivS f
let is_eagerF f = is_from_destr destr_eagerF f
let is_hoareS f = is_from_destr destr_hoareS f
let is_hoareF f = is_from_destr destr_hoareF f
let is_bdHoareS f = is_from_destr destr_bdHoareS f
let is_bdHoareF f = is_from_destr destr_bdHoareF f
let is_pr f = is_from_destr destr_pr f
let is_eq_or_iff f = (is_eq f) || (is_iff f)
(* -------------------------------------------------------------------- *)
let split_args f =
match f_node f with
| Fapp (f, args) -> (f, args)
| _ -> (f, [])
(* -------------------------------------------------------------------- *)
let split_fun f =
match f_node f with
| Fquant (Llambda, bds, body) -> (bds, body)
| _ -> ([], f)
(* -------------------------------------------------------------------- *)
let quantif_of_equantif (qt : equantif) =
match qt with
| `ELambda -> Llambda
| `EForall -> Lforall
| `EExists -> Lexists
(* -------------------------------------------------------------------- *)
let rec form_of_expr mem (e : expr) =
match e.e_node with
| Eint n ->
f_int n
| Elocal id ->
f_local id e.e_ty
| Evar pv ->
f_pvar pv e.e_ty mem
| Eop (op, tys) ->
f_op op tys e.e_ty
| Eapp (ef, es) ->
f_app (form_of_expr mem ef) (List.map (form_of_expr mem) es) e.e_ty
| Elet (lpt, e1, e2) ->
f_let lpt (form_of_expr mem e1) (form_of_expr mem e2)
| Etuple es ->
f_tuple (List.map (form_of_expr mem) es)
| Eproj (e1, i) ->
f_proj (form_of_expr mem e1) i e.e_ty
| Eif (e1, e2, e3) ->
let e1 = form_of_expr mem e1 in
let e2 = form_of_expr mem e2 in
let e3 = form_of_expr mem e3 in
f_if e1 e2 e3
| Ematch (b, fs, ty) ->
let b' = form_of_expr mem b in
let fs' = List.map (form_of_expr mem) fs in
f_match b' fs' ty
| Equant (qt, b, e) ->
let b = List.map (fun (x, ty) -> (x, GTty ty)) b in
let e = form_of_expr mem e in
f_quant (quantif_of_equantif qt) b e
(* -------------------------------------------------------------------- *)
type f_subst = {
fs_freshen : bool; (* true means freshen locals *)
fs_mp : EcPath.mpath Mid.t;
fs_loc : form Mid.t;
fs_mem : EcIdent.t Mid.t;
fs_sty : ty_subst;
fs_ty : ty -> ty;
fs_opdef : (EcIdent.t list * expr) Mp.t;
fs_pddef : (EcIdent.t list * form) Mp.t;
fs_esloc : expr Mid.t;
}
(* -------------------------------------------------------------------- *)
module Fsubst = struct
let f_subst_id = {
fs_freshen = false;
fs_mp = Mid.empty;
fs_loc = Mid.empty;
fs_mem = Mid.empty;
fs_sty = ty_subst_id;
fs_ty = ty_subst ty_subst_id;
fs_opdef = Mp.empty;
fs_pddef = Mp.empty;
fs_esloc = Mid.empty;
}
let is_subst_id s =
s.fs_freshen = false
&& is_ty_subst_id s.fs_sty
&& Mid.is_empty s.fs_loc
&& Mid.is_empty s.fs_mem
&& Mp.is_empty s.fs_opdef
&& Mp.is_empty s.fs_pddef
&& Mid.is_empty s.fs_esloc
let f_subst_init ?freshen ?mods ?sty ?opdef ?prdef () =
let sty = odfl ty_subst_id sty in
{ f_subst_id
with fs_freshen = odfl false freshen;
fs_mp = odfl Mid.empty mods;
fs_sty = sty;
fs_ty = ty_subst sty;
fs_opdef = odfl Mp.empty opdef;
fs_pddef = odfl Mp.empty prdef;
fs_esloc = Mid.empty; }
(* ------------------------------------------------------------------ *)
let f_bind_local s x t =
let merger o = assert (o = None); Some t in
{ s with fs_loc = Mid.change merger x s.fs_loc }
let f_bind_mem s m1 m2 =
let merger o = assert (o = None); Some m2 in
{ s with fs_mem = Mid.change merger m1 s.fs_mem }
let f_bind_mod s x mp =
let merger o = assert (o = None); Some mp in
let smp = Mid.change merger x s.fs_mp in
let sty = s.fs_sty in
let sty = { sty with ts_mp = EcPath.m_subst sty.ts_p smp } in
{ s with fs_mp = smp; fs_sty = sty; fs_ty = ty_subst sty }
let f_bind_rename s xfrom xto ty =
let xf = f_local xto ty in
let xe = e_local xto ty in
let s = f_bind_local s xfrom xf in
let merger o = assert (o = None); Some xe in
{ s with fs_esloc = Mid.change merger xfrom s.fs_esloc }
(* ------------------------------------------------------------------ *)
let f_rem_local s x =
{ s with fs_loc = Mid.remove x s.fs_loc;
fs_esloc = Mid.remove x s.fs_esloc; }
let f_rem_mem s m =
{ s with fs_mem = Mid.remove m s.fs_mem }
let f_rem_mod s m =
let smp = Mid.remove m s.fs_mp in
let sty = s.fs_sty in
let sty = { sty with ts_mp = EcPath.m_subst sty.ts_p smp } in
{ s with fs_mp = smp; fs_sty = sty; fs_ty = ty_subst sty }
(* ------------------------------------------------------------------ *)
let add_local s (x,t as xt) =
let x' = if s.fs_freshen then EcIdent.fresh x else x in
let t' = s.fs_ty t in
if x == x' && t == t'
then (s, xt)
else (f_bind_rename s x x' t'), (x',t')
let add_locals = List.Smart.map_fold add_local
let subst_lpattern (s: f_subst) (lp:lpattern) =
match lp with
| LSymbol x ->
let (s, x') = add_local s x in
if x == x' then (s, lp) else (s, LSymbol x')
| LTuple xs ->
let (s, xs') = add_locals s xs in
if xs == xs' then (s, lp) else (s, LTuple xs')
| LRecord (p, xs) ->
let (s, xs') =
List.Smart.map_fold
(fun s ((x, t) as xt) ->
match x with
| None ->
let t' = s.fs_ty t in
if t == t' then (s, xt) else (s, (x, t'))
| Some x ->
let (s, (x', t')) = add_local s (x, t) in
if x == x' && t == t'
then (s, xt)
else (s, (Some x', t')))
s xs
in
if xs == xs' then (s, lp) else (s, LRecord (p, xs'))
let gty_subst s gty =
if is_subst_id s then gty else
match gty with
| GTty ty ->
let ty' = s.fs_ty ty in
if ty == ty' then gty else GTty ty'
| GTmodty (p, (rx, r)) ->
let sub = s.fs_sty.ts_mp in
let xsub = EcPath.x_substm s.fs_sty.ts_p s.fs_mp in
let p' = mty_subst s.fs_sty.ts_p sub p in
let rx' = Sx.fold (fun m rx' -> Sx.add (xsub m) rx') rx Sx.empty in
let r' = Sm.fold (fun m r' -> Sm.add (sub m) r') r Sm.empty in
if p == p' && Sx.equal rx rx' && Sm.equal r r'
then gty
else GTmodty (p', (rx', r'))
| GTmem mt ->
let mt' = EcMemory.mt_substm s.fs_sty.ts_p s.fs_mp s.fs_ty mt in
if mt == mt' then gty else GTmem mt'
(* ------------------------------------------------------------------ *)
let add_binding s (x, gty as xt) =
let gty' = gty_subst s gty in
let x' = if s.fs_freshen then EcIdent.fresh x else x in
if x == x' && gty == gty'
then
let s = match gty with
| GTty _ -> f_rem_local s x
| GTmodty _ -> f_rem_mod s x
| GTmem _ -> f_rem_mem s x
in
(s, xt)
else
let s = match gty' with
| GTty ty -> f_bind_rename s x x' ty
| GTmodty _ -> f_bind_mod s x (EcPath.mident x')
| GTmem _ -> f_bind_mem s x x'
in
(s, (x', gty'))
let add_bindings = List.map_fold add_binding
(* ------------------------------------------------------------------ *)
let subst_xpath s f =
let m_subst = EcPath.x_substm s.fs_sty.ts_p s.fs_mp in
m_subst f
let subst_stmt s c =
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p
s.fs_ty s.fs_opdef s.fs_mp s.fs_esloc in
EcModules.s_subst es c
let subst_me s me =
EcMemory.me_substm s.fs_sty.ts_p s.fs_mp s.fs_mem s.fs_ty me
let subst_m s m = Mid.find_def m m s.fs_mem
let subst_ty s ty = s.fs_ty ty
(* ------------------------------------------------------------------ *)
let rec f_subst ~tx s fp =
tx fp (match fp.f_node with
| Fquant (q, b, f) ->
let s, b' = add_bindings s b in
let f' = f_subst ~tx s f in
FSmart.f_quant (fp, (q, b, f)) (q, b', f')
| Flet (lp, f1, f2) ->
let f1' = f_subst ~tx s f1 in
let s, lp' = subst_lpattern s lp in
let f2' = f_subst ~tx s f2 in
FSmart.f_let (fp, (lp, f1, f2)) (lp', f1', f2')
| Flocal id -> begin
match Mid.find_opt id s.fs_loc with
| Some f -> f
| None ->
let ty' = s.fs_ty fp.f_ty in
FSmart.f_local (fp, (id, fp.f_ty)) (id, ty')
end
| Fop (p, tys) when Mp.mem p s.fs_opdef ->
let ty = s.fs_ty fp.f_ty in
let tys = List.Smart.map s.fs_ty tys in
let body = oget (Mp.find_opt p s.fs_opdef) in
f_subst_op ~tx s.fs_freshen ty tys [] body
| Fop (p, tys) when Mp.mem p s.fs_pddef ->
let ty = s.fs_ty fp.f_ty in
let tys = List.Smart.map s.fs_ty tys in
let body = oget (Mp.find_opt p s.fs_pddef) in
f_subst_pd ~tx ty tys [] body
| Fapp ({ f_node = Fop (p, tys) }, args) when Mp.mem p s.fs_opdef ->
let ty = s.fs_ty fp.f_ty in
let tys = List.Smart.map s.fs_ty tys in
let body = oget (Mp.find_opt p s.fs_opdef) in
f_subst_op ~tx s.fs_freshen ty tys (List.map (f_subst ~tx s) args) body
| Fapp ({ f_node = Fop (p, tys) }, args) when Mp.mem p s.fs_pddef ->
let ty = s.fs_ty fp.f_ty in
let tys = List.Smart.map s.fs_ty tys in
let body = oget (Mp.find_opt p s.fs_pddef) in
f_subst_pd ~tx ty tys (List.map (f_subst ~tx s) args) body
| Fop (p, tys) ->
let ty' = s.fs_ty fp.f_ty in
let tys' = List.Smart.map s.fs_ty tys in
let p' = s.fs_sty.ts_p p in
FSmart.f_op (fp, (p, tys, fp.f_ty)) (p', tys', ty')
| Fpvar (pv, m) ->
let pv' = pv_subst (EcPath.x_substm s.fs_sty.ts_p s.fs_mp) pv in
let m' = Mid.find_def m m s.fs_mem in
let ty' = s.fs_ty fp.f_ty in
FSmart.f_pvar (fp, (pv, fp.f_ty, m)) (pv', ty', m')
| Fglob (mp, m) ->
let m' = Mid.find_def m m s.fs_mem in
let mp' = s.fs_sty.ts_mp mp in
FSmart.f_glob (fp, (mp, m)) (mp', m')
| FhoareF hf ->
assert (not (Mid.mem mhr s.fs_mem) && not (Mid.mem mhr s.fs_mem));
let pr' = f_subst ~tx s hf.hf_pr in
let po' = f_subst ~tx s hf.hf_po in
let mp' = EcPath.x_substm s.fs_sty.ts_p s.fs_mp hf.hf_f in
FSmart.f_hoareF (fp, hf) { hf_pr = pr'; hf_po = po'; hf_f = mp'; }
| FhoareS hs ->
assert (not (Mid.mem (fst hs.hs_m) s.fs_mem));
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p
s.fs_ty s.fs_opdef s.fs_mp s.fs_esloc in
let pr' = f_subst ~tx s hs.hs_pr in
let po' = f_subst ~tx s hs.hs_po in
let st' = EcModules.s_subst es hs.hs_s in
let me' = EcMemory.me_substm s.fs_sty.ts_p s.fs_mp s.fs_mem s.fs_ty hs.hs_m in
FSmart.f_hoareS (fp, hs)
{ hs_pr = pr'; hs_po = po'; hs_s = st'; hs_m = me'; }
| FbdHoareF bhf ->
assert (not (Mid.mem mhr s.fs_mem) && not (Mid.mem mhr s.fs_mem));
let pr' = f_subst ~tx s bhf.bhf_pr in
let po' = f_subst ~tx s bhf.bhf_po in
let mp' = EcPath.x_substm s.fs_sty.ts_p s.fs_mp bhf.bhf_f in
let bd' = f_subst ~tx s bhf.bhf_bd in
FSmart.f_bdHoareF (fp, bhf)
{ bhf with bhf_pr = pr'; bhf_po = po';
bhf_f = mp'; bhf_bd = bd'; }
| FbdHoareS bhs ->
assert (not (Mid.mem (fst bhs.bhs_m) s.fs_mem));
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p s.fs_ty
s.fs_opdef s.fs_mp s.fs_esloc in
let pr' = f_subst ~tx s bhs.bhs_pr in
let po' = f_subst ~tx s bhs.bhs_po in
let st' = EcModules.s_subst es bhs.bhs_s in
let me' = EcMemory.me_substm s.fs_sty.ts_p s.fs_mp s.fs_mem s.fs_ty bhs.bhs_m in
let bd' = f_subst ~tx s bhs.bhs_bd in
FSmart.f_bdHoareS (fp, bhs)
{ bhs with bhs_pr = pr'; bhs_po = po'; bhs_s = st';
bhs_bd = bd'; bhs_m = me'; }
| FequivF ef ->
assert (not (Mid.mem mleft s.fs_mem) && not (Mid.mem mright s.fs_mem));
let m_subst = EcPath.x_substm s.fs_sty.ts_p s.fs_mp in
let pr' = f_subst ~tx s ef.ef_pr in
let po' = f_subst ~tx s ef.ef_po in
let fl' = m_subst ef.ef_fl in
let fr' = m_subst ef.ef_fr in
FSmart.f_equivF (fp, ef)
{ ef_pr = pr'; ef_po = po'; ef_fl = fl'; ef_fr = fr'; }
| FequivS eqs ->
assert (not (Mid.mem (fst eqs.es_ml) s.fs_mem) &&
not (Mid.mem (fst eqs.es_mr) s.fs_mem));
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p s.fs_ty
s.fs_opdef s.fs_mp s.fs_esloc in
let s_subst = EcModules.s_subst es in
let pr' = f_subst ~tx s eqs.es_pr in
let po' = f_subst ~tx s eqs.es_po in
let sl' = s_subst eqs.es_sl in
let sr' = s_subst eqs.es_sr in
let ml' = EcMemory.me_substm s.fs_sty.ts_p s.fs_mp s.fs_mem s.fs_ty eqs.es_ml in
let mr' = EcMemory.me_substm s.fs_sty.ts_p s.fs_mp s.fs_mem s.fs_ty eqs.es_mr in
FSmart.f_equivS (fp, eqs)
{ es_ml = ml'; es_mr = mr';
es_pr = pr'; es_po = po';
es_sl = sl'; es_sr = sr'; }
| FeagerF eg ->
assert (not (Mid.mem mleft s.fs_mem) && not (Mid.mem mright s.fs_mem));
let m_subst = EcPath.x_substm s.fs_sty.ts_p s.fs_mp in
let pr' = f_subst ~tx s eg.eg_pr in
let po' = f_subst ~tx s eg.eg_po in
let fl' = m_subst eg.eg_fl in
let fr' = m_subst eg.eg_fr in
let es = e_subst_init s.fs_freshen s.fs_sty.ts_p s.fs_ty
s.fs_opdef s.fs_mp s.fs_esloc in
let s_subst = EcModules.s_subst es in
let sl' = s_subst eg.eg_sl in
let sr' = s_subst eg.eg_sr in
FSmart.f_eagerF (fp, eg)
{ eg_pr = pr'; eg_sl = sl';eg_fl = fl';
eg_fr = fr'; eg_sr = sr'; eg_po = po'; }
| Fpr pr ->
assert (not (Mid.mem mhr s.fs_mem));
let pr_mem = Mid.find_def pr.pr_mem pr.pr_mem s.fs_mem in
let pr_fun = EcPath.x_substm s.fs_sty.ts_p s.fs_mp pr.pr_fun in
let pr_args = f_subst ~tx s pr.pr_args in
let pr_event = f_subst ~tx s pr.pr_event in
FSmart.f_pr (fp, pr) { pr_mem; pr_fun; pr_args; pr_event; }
| _ -> f_map s.fs_ty (f_subst ~tx s) fp)
and f_subst_op ~tx freshen fty tys args (tyids, e) =
(* FIXME: factor this out *)
(* FIXME: is [mhr] good as a default? *)
let e =
let sty = Tvar.init tyids tys in
let sty = ty_subst { ty_subst_id with ts_v = Mid.find_opt^~ sty; } in
let sty = { e_subst_id with es_freshen = freshen; es_ty = sty ; } in
e_subst sty e
in
let (sag, args, e) =
match e.e_node with
| Equant (`ELambda, largs, lbody) when args <> [] ->
let largs1, largs2 = List.takedrop (List.length args ) largs in
let args1, args2 = List.takedrop (List.length largs1) args in
(Mid.of_list (List.combine (List.map fst largs1) args1),
args2, e_lam largs2 lbody)
| _ -> (Mid.of_list [], args, e)
in
let sag = { f_subst_id with fs_loc = sag } in
f_app (f_subst ~tx sag (form_of_expr mhr e)) args fty
and f_subst_pd ~tx fty tys args (tyids, f) =
(* FIXME: factor this out *)
(* FIXME: is fd_freshen value correct? *)
let f =
let sty = Tvar.init tyids tys in
let sty = ty_subst { ty_subst_id with ts_v = Mid.find_opt^~ sty; } in
let sty = { f_subst_id with fs_freshen = true; fs_ty = sty; } in
f_subst ~tx sty f
in
let (sag, args, f) =
match f.f_node with
| Fquant (Llambda, largs, lbody) when args <> [] ->
let largs1, largs2 = List.takedrop (List.length args ) largs in
let args1, args2 = List.takedrop (List.length largs1) args in
(Mid.of_list (List.combine (List.map fst largs1) args1),
args2, f_lambda largs2 lbody)
| _ -> (Mid.of_list [], args, f)
in
let sag = { f_subst_id with fs_loc = sag } in
f_app (f_subst ~tx sag f) args fty
(* ------------------------------------------------------------------ *)
let f_subst ?(tx = fun _ f -> f) s =
if is_subst_id s then identity else f_subst ~tx s
let f_subst_local x t =
let s = f_bind_local f_subst_id x t in
fun f -> if Mid.mem x f.f_fv then f_subst s f else f
let f_subst_mem m1 m2 =
let s = f_bind_mem f_subst_id m1 m2 in
fun f -> if Mid.mem m1 f.f_fv then f_subst s f else f
let f_subst_mod x mp =
let s = f_bind_mod f_subst_id x mp in
fun f -> if Mid.mem x f.f_fv then f_subst s f else f
(* ------------------------------------------------------------------ *)
let fty_subst sty =
{ f_subst_id with fs_sty = sty; fs_ty = ty_subst sty }
let uni_subst uidmap =
fty_subst { ty_subst_id with ts_u = uidmap }
let mapty sty =
f_subst (fty_subst sty)
let uni uidmap =
f_subst (uni_subst uidmap)
(* ------------------------------------------------------------------ *)
let subst_locals s =
Hf.memo_rec 107 (fun aux f ->
match f.f_node with
| Flocal id ->
(try Mid.find id s with Not_found -> f)
| _ -> f_map (fun ty -> ty) aux f)
let subst_local id f1 f2 =
subst_locals (Mid.singleton id f1) f2
(* ------------------------------------------------------------------ *)
let init_subst_tvar s =
let sty = { ty_subst_id with ts_v = Mid.find_opt^~ s } in
{ f_subst_id with
fs_freshen = true; fs_sty = sty; fs_ty = ty_subst sty }
let subst_tvar s =
f_subst (init_subst_tvar s)
end
(* -------------------------------------------------------------------- *)
let can_subst f =
match f.f_node with
| Fint _ | Flocal _ | Fpvar _ | Fop _ -> true
| _ -> false
(* -------------------------------------------------------------------- *)
type core_op = [
| `True
| `False
| `Not
| `And of [`Asym | `Sym]
| `Or of [`Asym | `Sym]
| `Imp
| `Iff
| `Eq
]
let core_ops =
let core_ops =
[EcCoreLib.CI_Bool.p_true , `True ;
EcCoreLib.CI_Bool.p_false , `False ;
EcCoreLib.CI_Bool.p_not , `Not ;
EcCoreLib.CI_Bool.p_anda , `And `Asym;
EcCoreLib.CI_Bool.p_and , `And `Sym ;
EcCoreLib.CI_Bool.p_ora , `Or `Asym;
EcCoreLib.CI_Bool.p_or , `Or `Sym ;
EcCoreLib.CI_Bool.p_imp , `Imp ;
EcCoreLib.CI_Bool.p_iff , `Iff ;
EcCoreLib.CI_Bool.p_eq , `Eq ; ]
in
let tbl = EcPath.Hp.create 11 in
List.iter (fun (p, k) -> EcPath.Hp.add tbl p k) core_ops;
tbl
let core_op_kind (p : EcPath.path) =
EcPath.Hp.find_opt core_ops p
