Revision 9d08a76fb50773e0b6b1afad31f37dfb821fee75 authored by Benjamin Gregoire on 24 November 2022, 16:10:02 UTC, committed by Benjamin Gregoire on 24 November 2022, 16:10:02 UTC
1 parent 69c9c2e
ecPhlTrans.ml
(* -------------------------------------------------------------------- *)
open EcUtils
open EcParsetree
open EcTypes
open EcFol
open EcEnv
open EcPV
open EcMatching
open EcTransMatching
open EcModules
open EcMaps
open EcCoreGoal
open EcLowPhlGoal
module TTC = EcProofTyping
(* -------------------------------------------------------------------- *)
module Low = struct
(* ------------------------------------------------------------------ *)
let transitivity_side_cond hyps prml prmr poml pomr p q p1 q1 pomt p2 q2 =
let env = LDecl.toenv hyps in
let cond1 =
let fv1 = PV.fv env mright p1 in
let fv2 = PV.fv env mleft p2 in
let fv = PV.union fv1 fv2 in
let elts, glob = PV.ntr_elements fv in
let bd, s = generalize_subst env mhr elts glob in
let s1 = PVM.of_mpv s mright in
let s2 = PVM.of_mpv s mleft in
let concl = f_and (PVM.subst env s1 p1) (PVM.subst env s2 p2) in
f_forall_mems [prml;prmr] (f_imp p (f_exists bd concl)) in
let cond2 =
let m2 = LDecl.fresh_id hyps "&m" in
let q1 = Fsubst.f_subst_mem mright m2 q1 in
let q2 = Fsubst.f_subst_mem mleft m2 q2 in
f_forall_mems [poml;(m2,pomt);pomr] (f_imps [q1;q2] q) in
(cond1, cond2)
(* ------------------------------------------------------------------ *)
let t_equivS_trans_r (mt, c2) (p1, q1) (p2, q2) tc =
let hyps = FApi.tc1_hyps tc in
let es = tc1_as_equivS tc in
let m1, m3 = es.es_ml, es.es_mr in
let cond1, cond2 =
transitivity_side_cond hyps
m1 m3 m1 m3 es.es_pr es.es_po p1 q1 mt p2 q2 in
let cond3 =
f_equivS_r { es with
es_mr = (mright,mt);
es_sr = c2;
es_pr = p1;
es_po = q1;
} in
let cond4 =
f_equivS_r { es with
es_ml = (mleft, mt);
es_sl = c2;
es_pr = p2;
es_po = q2;
} in
FApi.xmutate1 tc `Trans [cond1; cond2; cond3; cond4]
(* ------------------------------------------------------------------ *)
let t_equivF_trans_r f (p1, q1) (p2, q2) tc =
let env, hyps, _ = FApi.tc1_eflat tc in
let ef = tc1_as_equivF tc in
let (prml, prmr), (poml, pomr) = Fun.equivF_memenv ef.ef_fl ef.ef_fr env in
let (_, pomt) = snd (Fun.hoareF_memenv f env) in
let cond1, cond2 =
transitivity_side_cond
hyps prml prmr poml pomr
ef.ef_pr ef.ef_po p1 q1 pomt p2 q2 in
let cond3 = f_equivF p1 ef.ef_fl f q1 in
let cond4 = f_equivF p2 f ef.ef_fr q2 in
FApi.xmutate1 tc `Trans [cond1; cond2; cond3; cond4]
end
(* -------------------------------------------------------------------- *)
let t_equivS_trans = FApi.t_low3 "equiv-trans" Low.t_equivS_trans_r
let t_equivF_trans = FApi.t_low3 "equiv-trans" Low.t_equivF_trans_r
(* -------------------------------------------------------------------- *)
let process_replace_stmt s p c p1 q1 p2 q2 tc =
let es = tc1_as_equivS tc in
let ct = match s with `Left -> es.es_sl | `Right -> es.es_sr in
let mt = snd (match s with `Left -> es.es_ml | `Right -> es.es_mr) in
(* Translation of the stmt *)
let regexpstmt = trans_block p in
let map = match RegexpStmt.search regexpstmt ct.s_node with
| None -> Mstr.empty
| Some m -> m in
let c = TTC.tc1_process_prhl_stmt tc s ~map c in
t_equivS_trans (mt, c) (p1, q1) (p2, q2) tc
(* -------------------------------------------------------------------- *)
let process_trans_stmt s c p1 q1 p2 q2 tc =
let es = tc1_as_equivS tc in
let mt = snd (match s with `Left -> es.es_ml | `Right -> es.es_mr) in
(* Translation of the stmt *)
let c = TTC.tc1_process_prhl_stmt tc s c in
t_equivS_trans (mt,c) (p1, q1) (p2, q2) tc
(* -------------------------------------------------------------------- *)
let process_trans_fun f p1 q1 p2 q2 tc =
let env = FApi.tc1_env tc in
let f = EcTyping.trans_gamepath env f in
t_equivF_trans f (p1, q1) (p2, q2) tc
(* -------------------------------------------------------------------- *)
let process_equiv_trans (tk, tf) tc =
let env, hyps, _ = FApi.tc1_eflat tc in
let (p1, q1, p2, q2) =
match tf with
| TFform(p1, q1, p2, q2) ->
begin match tk with
| TKfun f ->
let ef = tc1_as_equivF tc in
let f = EcTyping.trans_gamepath env f in
let (_, prmt), (_, pomt) = Fun.hoareF_memenv f env in
let (prml, prmr), (poml, pomr) = Fun.equivF_memenv ef.ef_fl ef.ef_fr env in
let process ml mr fo =
TTC.pf_process_form !!tc (LDecl.push_all [ml; mr] hyps) tbool fo in
let p1 = process prml (mright, prmt) p1 in
let q1 = process poml (mright, pomt) q1 in
let p2 = process (mleft,prmt) prmr p2 in
let q2 = process (mleft,pomt) pomr q2 in
(p1,q1,p2,q2)
| TKstmt (s, _) | TKparsedStmt (s, _, _) ->
let es = tc1_as_equivS tc in
let mt = snd (match s with `Left -> es.es_ml | `Right -> es.es_mr) in
let p1, q1 =
let hyps = LDecl.push_all [es.es_ml; (mright, mt)] hyps in
TTC.pf_process_form !!tc hyps tbool p1,
TTC.pf_process_form !!tc hyps tbool q1 in
let p2, q2 =
let hyps = LDecl.push_all [(mleft, mt); es.es_mr] hyps in
TTC.pf_process_form !!tc hyps tbool p2,
TTC.pf_process_form !!tc hyps tbool q2 in
(p1,q1,p2,q2)
end
| TFeq ->
let side =
match tk with
| TKfun _ -> tc_error !!tc "transitivity * does not work on functions"
| TKstmt(s,_) -> s
| TKparsedStmt(s,_,_) -> s in
let es = tc1_as_equivS tc in
let c,m = match side with `Left -> es.es_sl, es.es_ml | `Right -> es.es_sr, es.es_mr in
let fv = EcPV.PV.fv env (fst m) es.es_po in
let fvr = EcPV.s_read env c in
let mk_eqs fv =
let vfv, gfv = EcPV.PV.elements fv in
let veq = List.map (fun (x,ty) -> f_eq (f_pvar x ty mleft) (f_pvar x ty mright)) vfv in
let geq = List.map (fun mp -> f_eqglob mp mleft mp mright) gfv in
f_ands (veq @ geq) in
let pre = mk_eqs (EcPV.PV.union fvr fv) in
let post = mk_eqs fv in
if side = `Left then (pre, post, es.es_pr, es.es_po)
else (es.es_pr, es.es_po, pre, post) in
match tk with
| TKfun f -> process_trans_fun f p1 q1 p2 q2 tc
| TKstmt (s, c) -> process_trans_stmt s c p1 q1 p2 q2 tc
| TKparsedStmt (s, p, c) -> process_replace_stmt s p c p1 q1 p2 q2 tc
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