feat(phl): support backward ecall on bdHoare/phoare goals

Extend backward `ecall` to bdHoare statement goals, so a bdHoare/phoare
contract can be applied to the last call of a phoare goal — mirroring the
existing hoare backward `ecall`.

- ecPhlExists.ml: add `t_ecall_bdhoare_bwd` / `process_ecall_bdhoare`, and
  dispatch `FbdHoareS` in `process_ecall` (phoare added to the no-xhl error
  kinds). Program-variable contract arguments are handled via the existing
  ecall abstraction machinery; a trivial probability split routes the suffix
  call through `t_bdhoare_seq`, lifting the hoare prefix subgoal via
  `t_hoareS_conseq_bdhoare`.
- ecPhlConseq.mli: expose `t_hoareS_conseq_bdhoare` / `t_hoareF_conseq_bdhoare`.

Author: mbbarbosa

src/phl/ecPhlConseq.mli

@@ -23,6 +23,9 @@ val t_bdHoareF_conseq_bd  : hoarecmp -> ss_inv -> FApi.backward
 
 val t_hoareS_conseq_conj : ss_inv -> hs_inv -> ss_inv -> hs_inv -> FApi.backward
 
+val t_hoareS_conseq_bdhoare : FApi.backward
+val t_hoareF_conseq_bdhoare : FApi.backward
+
 (* -------------------------------------------------------------------- *)
 val t_equivF_conseq_nm    : ts_inv -> ts_inv -> FApi.backward
 val t_equivS_conseq_nm    : ts_inv -> ts_inv -> FApi.backward

src/phl/ecPhlExists.ml

@@ -447,6 +447,150 @@ let t_ecall_hoare_bwd ((cttpt, _) : proofterm * form) (tc : tcenv1) =
     EcPhlAuto.t_auto ?conv:None; (* Kill the conseq from the call rule *)
   ] tc
 
+(* -------------------------------------------------------------------- *)
+(* Backward ecall on bdHoare/phoare goals (ecall without ->>).
+ *
+ * Mirrors t_ecall_hoare_bwd but for a bdHoare goal and a bdHoare/phoare
+ * contract.  We abstract program-variable arguments of the contract pterm
+ * into fresh local idents, dispatch to [t_call None ctt] (which routes
+ * via [t_call]'s (FbdHoareF, FbdHoareS) arm to [t_bdhoare_call]), then
+ * re-generalize over the abstracted idents in the residual goals.
+ *
+ * Unlike the hoare bwd variant, we do not elaborate a [t_hoare_seq]
+ * splitting the prefix from the call: the bdhoare seq variant requires
+ * an additional probability split which we cannot infer here.  As a
+ * result the user gets the same shape of subgoals that plain
+ * [call (lemma)] would produce, but with program-variable arguments
+ * handled by ecall's abstraction machinery.
+ *)
+let t_ecall_bdhoare_bwd ((cttpt, _) : proofterm * form) (tc : tcenv1) =
+  let hyps = FApi.tc1_hyps tc in
+  let env = EcEnv.LDecl.toenv hyps in
+  let concl = destr_bdHoareS (FApi.tc1_goal tc) in
+  let m = fst (concl.bhs_m) in
+  let call, _ = pf_last_call !!tc concl.bhs_s in
+
+  let pvs = PT.collect_pvars_from_pt cttpt in
+  let ids, _, pvs_as_inv, subst = abstract_pvs hyps [m] pvs in
+
+  let cttpt =
+    let pt_head, pt_args =
+      match cttpt with
+      | PTApply { pt_head; pt_args } -> (pt_head, pt_args)
+      | _ -> assert false in
+    let pt_args = List.map (PT.subst_pv_pt_arg env subst) pt_args in
+    PTApply { pt_head; pt_args } in
+
+  let cttpt, ctt = EcLowGoal.LowApply.check `Elim cttpt (`Hyps (hyps, !!tc)) in
+
+  let ctt =
+    EcReduction.h_red_opt EcReduction.full_red hyps ctt
+    |> odfl ctt in
+
+  let ids_subst =
+    List.fold_left2
+      (fun s (id, _) pv -> EcSubst.add_flocal s id (inv_of_inv pv))
+      EcSubst.empty ids pvs_as_inv in
+
+  let fpre, fpost =
+    let hf = destr_bdHoareF ctt in
+    (ss_inv_rebind (bhf_pr hf) m).inv, (ss_inv_rebind (bhf_po hf) m).inv
+  in
+
+  let post =
+    EcPhlCall.compute_hoare_call_post
+      hyps m (fpre, POE.empty fpost) call
+      (POE.empty (bhs_po concl).inv) in
+  let post = EcSubst.subst_form ids_subst post in
+
+  (* Trivial probability split for FHeq with bound 1%r (lossless body):
+       pR = true, f1=f2=1%r, g1=g2=0%r.  Yields:
+        - cond_phi : f_hoareS pre s1 post  (user-level prefix, as hoare)
+        - condf1   : pre  s1 true 1%r      (lossless prefix, trivial for det. code)
+        - condf2   : phi  s2 bhs_po 1%r    (suffix bdhoare, target of t_call)
+        - condg1   : pre  s1 false 0%r     (trivial)
+        - condbd   : 1*1+0*0 = bd          (trivial when bd=1%r)
+        - condnm   : forall r1 r2 ...      (trivial) *)
+  let seq_info =
+    let phi = { m; inv = post } in
+    let pR  = { m; inv = f_true } in
+    let f1  = { m; inv = f_r1 } in
+    let f2  = { m; inv = f_r1 } in
+    let g1  = { m; inv = f_r0 } in
+    let g2  = { m; inv = f_r0 } in
+    (phi, pR, f1, f2, g1, g2)
+  in
+
+  let tc = EcPhlSeq.t_bdhoare_seq (GapBefore cpos1_last) seq_info tc in
+  (* Subgoal order from t_bdhoare_seq (with f1≠0, f2≠0, g1=0):
+       [cond_phi; condf1; condf2; condg1; condbd; condnm]
+     We apply the exists+intros+t_call pipeline to condf2 (the suffix).
+     The intros chain leaves a single bdhoare goal on which t_call produces
+     two subgoals (contract obligation + conseq); we then dispatch via
+     t_seqsub.  *)
+  let condf2_tactic =
+    FApi.t_seqs [
+      t_hr_exists_intro_r pvs_as_inv;
+      t_hr_exists_elim_r ~bound:(List.length ids);
+      t_intros_i (List.fst ids);
+      FApi.t_seqsub
+        (EcPhlCall.t_call None ctt)
+        [ EcLowGoal.Apply.t_apply_bwd_hi ~dpe:true cttpt;
+          EcPhlAuto.t_auto ?conv:None; ];
+    ]
+  in
+
+  (* t_bdhoare_seq_r auto-closes condnm via t_try, so the count is 5 (or 6 if
+     that auto fails).  Use t_onalli with an index-based dispatcher to be
+     robust to either count.  Order (0-indexed):
+       0 -> cond_phi (HOARE prefix): lift to BDHOARE [pre ==> phi] FHeq 1%r
+            via t_hoareS_conseq_bdhoare.  This is sound under losslessness of
+            the prefix — which the user proves as part of the residual goal.
+            Subsequent ecalls then dispatch through our bdhoare arm and accept
+            phoare contracts.
+       2 -> condf2 (suffix call dance)
+       others -> auto (trivial bound conditions). *)
+  let tc =
+    FApi.t_onalli
+      (fun i ->
+        if i = 0 then EcPhlConseq.t_hoareS_conseq_bdhoare
+        else if i = 2 then condf2_tactic
+        else EcPhlAuto.t_auto ?conv:None)
+      tc
+  in
+
+  tc
+
+(* -------------------------------------------------------------------- *)
+let process_ecall_bdhoare
+  (dir   : APT.pdirection)
+  (pterm : APT.pecall)
+  (tc    : tcenv1)
+=
+  if dir <> `Backward then
+    tc_error !!tc "forward ecall on bdHoare/phoare goals is not supported";
+
+  let (ctt_path, ctt_tvi, ctt_args) = pterm in
+  let hyps = FApi.tc1_hyps tc in
+  let concl = destr_bdHoareS (FApi.tc1_goal tc) in
+
+  (* Type-check contract (lemma) - apply it fully to find the bdHoare contract *)
+  let ptenv = PT.ptenv_of_penv (LDecl.push_active_ss concl.bhs_m hyps) !!tc in
+  let contract = PT.process_pterm ptenv (APT.FPNamed (ctt_path, ctt_tvi)) in
+  let contract, _ = PT.process_pterm_args_app contract ctt_args in
+  let contract = PT.apply_pterm_to_max_holes hyps contract in
+
+  assert (PT.can_concretize contract.PT.ptev_env);
+  let contract = PT.concretize contract in
+
+  let call, _ = pf_last_call !!tc concl.bhs_s in
+
+  check_contract_type
+    ~phoare:true ~noexn:false ~loc:(L.loc ctt_path) ~name:(L.unloc ctt_path)
+    !!tc hyps (`Single call) (snd contract);
+
+  t_ecall_bdhoare_bwd contract tc
+
 (* -------------------------------------------------------------------- *)
 let process_ecall_hoare
   (dir   : APT.pdirection)
@@ -624,7 +768,12 @@ let process_ecall
         tc_error !!tc "cannot provide a side for Hoare goals";
       process_ecall_hoare dir pterm tc
 
+  | FbdHoareS _ ->
+      if Option.is_some oside then
+        tc_error !!tc "cannot provide a side for bdHoare/phoare goals";
+      process_ecall_bdhoare dir pterm tc
+
   | FequivS _ ->
       process_ecall_equiv dir oside pterm tc
 
-  | _ -> tc_error_noXhl ~kinds:[`Hoare `Stmt; `Equiv `Stmt] !!tc
+  | _ -> tc_error_noXhl ~kinds:[`Hoare `Stmt; `PHoare `Stmt; `Equiv `Stmt] !!tc