diff --git a/compiler/src/compiler/DeadCodeElim.v b/compiler/src/compiler/DeadCodeElim.v
index 10099f03..61608a25 100644
--- a/compiler/src/compiler/DeadCodeElim.v
+++ b/compiler/src/compiler/DeadCodeElim.v
@@ -15,7 +15,7 @@ Require Import bedrock2.MetricCosts.
 (*  below only for of_list_list_diff *)
 Require Import compiler.DeadCodeElimDef.
 
-Local Notation exec pick_sp := (exec (pick_sp := pick_sp) PreSpill isRegStr).
+Local Notation exec e pick_sp := (@exec _ _ _ _ _ _ _ _ PreSpill isRegStr pick_sp e).
 
 Section WithArguments1.
   Context {width: Z}.
diff --git a/compiler/src/compiler/FlatImp.v b/compiler/src/compiler/FlatImp.v
index eebc5990..d474edf6 100644
--- a/compiler/src/compiler/FlatImp.v
+++ b/compiler/src/compiler/FlatImp.v
@@ -21,6 +21,7 @@ Require Import coqutil.Datatypes.ListSet.
 Require Import coqutil.Map.OfListWord.
 Require Import coqutil.Word.Bitwidth.
 Require Import coqutil.Word.Interface.
+Require Import coqutil.Tactics.fwd.
 Local Hint Mode Word.Interface.word - : typeclass_instances.
 
 Inductive bbinop: Set :=
@@ -300,7 +301,7 @@ Module exec.
     Context {width: Z} {BW: Bitwidth width} {word: word.word width}.
     Context {mem: map.map word byte} {locals: map.map varname word}
             {env: map.map String.string (list varname * list varname * stmt varname)}.
-    Context {ext_spec: ExtSpec} {pick_sp: PickSp}.
+    Context {ext_spec: ExtSpec} .
     Context {varname_eq_spec: EqDecider varname_eqb}
             {word_ok: word.ok word}
             {mem_ok: map.ok mem}
@@ -349,7 +350,7 @@ Module exec.
       end mc.
 
     (* alternative semantics which allow non-determinism *)
-    Inductive exec:
+    Inductive exec {pick_sp: PickSp} :
       stmt varname ->
       leakage -> trace -> mem -> locals -> metrics ->
       (leakage -> trace -> mem -> locals -> metrics -> Prop)
@@ -457,7 +458,7 @@ Module exec.
         post k t m l mc ->
         exec SSkip k t m l mc post.
 
-    Lemma det_step: forall k0 t0 m0 l0 mc0 s1 s2 k1 t1 m1 l1 mc1 post,
+    Lemma det_step {pick_sp: PickSp} : forall k0 t0 m0 l0 mc0 s1 s2 k1 t1 m1 l1 mc1 post,
         exec s1 k0 t0 m0 l0 mc0 (fun k1' t1' m1' l1' mc1' => k1' = k1 /\ t1' = t1 /\ m1' = m1 /\ l1' = l1 /\ mc1 = mc1') ->
         exec s2 k1 t1 m1 l1 mc1 post ->
         exec (SSeq s1 s2) k0 t0 m0 l0 mc0 post.
@@ -468,14 +469,14 @@ Module exec.
       assumption.
     Qed.
 
-    Lemma seq_cps: forall s1 s2 k t m (l: locals) mc post,
+    Lemma seq_cps {pick_sp: PickSp} : forall s1 s2 k t m (l: locals) mc post,
         exec s1 k t m l mc (fun k' t' m' l' mc' => exec s2 k' t' m' l' mc' post) ->
         exec (SSeq s1 s2) k t m l mc post.
     Proof.
       intros. eapply seq. 1: eassumption. simpl. clear. auto.
     Qed.
 
-    Lemma call_cps: forall fname params rets binds args fbody argvs k t (l: locals) m mc st post,
+    Lemma call_cps {pick_sp: PickSp} : forall fname params rets binds args fbody argvs k t (l: locals) m mc st post,
         map.get e fname = Some (params, rets, fbody) ->
         map.getmany_of_list l args = Some argvs ->
         map.putmany_of_list_zip params argvs map.empty = Some st ->
@@ -491,7 +492,7 @@ Module exec.
       cbv beta. intros *. exact id.
     Qed.
 
-    Lemma loop_cps: forall body1 cond body2 k t m l mc post,
+    Lemma loop_cps {pick_sp: PickSp} : forall body1 cond body2 k t m l mc post,
       exec body1 k t m l mc (fun k t m l mc => exists b,
         eval_bcond l cond = Some b /\
         (b = false -> post (leak_bool false :: k) t m l (cost_SLoop_false cond mc)) /\
@@ -507,7 +508,7 @@ Module exec.
       - assumption.
     Qed.
 
-    Lemma weaken: forall k t l m mc s post1,
+    Lemma weaken {pick_sp: PickSp} : forall k t l m mc s post1,
         exec s k t m l mc post1 ->
         forall post2,
           (forall k' t' m' l' mc', post1 k' t' m' l' mc' -> post2 k' t' m' l' mc') ->
@@ -530,7 +531,7 @@ Module exec.
         intros. simp. eauto 10.
     Qed.
 
-    Lemma seq_assoc: forall s1 s2 s3 k t m l mc post,
+    Lemma seq_assoc {pick_sp: PickSp} : forall s1 s2 s3 k t m l mc post,
         exec (SSeq s1 (SSeq s2 s3)) k t m l mc post ->
         exec (SSeq (SSeq s1 s2) s3) k t m l mc post.
     Proof.
@@ -543,7 +544,7 @@ Module exec.
       eauto.
     Qed.
 
-    Lemma seq_assoc_bw: forall s1 s2 s3 k t m l mc post,
+    Lemma seq_assoc_bw {pick_sp: PickSp} : forall s1 s2 s3 k t m l mc post,
         exec (SSeq (SSeq s1 s2) s3) k t m l mc post ->
         exec (SSeq s1 (SSeq s2 s3)) k t m l mc post.
     Proof. intros. simp. eauto 10 using seq. Qed.
@@ -556,7 +557,7 @@ Module exec.
              end;
       simp.
 
-    Lemma intersect: forall k t l m mc s post1,
+    Lemma intersect {pick_sp: PickSp} : forall k t l m mc s post1,
         exec s k t m l mc post1 ->
         forall post2,
           exec s k t m l mc post2 ->
@@ -634,6 +635,140 @@ Module exec.
         eauto.
     Qed.
 
+    Lemma exec_extends_trace {pick_sp: PickSp} s k t m l mc post :
+      exec s k t m l mc post ->
+      exec s k t m l mc (fun k' t' m' l' mc' => post k' t' m' l' mc' /\ exists k'', k' = k'' ++ k).
+    Proof.
+      intros H. induction H; try (econstructor; intuition eauto; eexists; align_trace; fail).
+      - econstructor; intuition eauto. specialize H2 with (1 := H3). fwd.
+        eexists. intuition eauto. eexists. align_trace.
+      - econstructor; intuition eauto. fwd. specialize H3 with (1 := H4p0). fwd.
+        eexists. intuition eauto. eexists. intuition eauto.
+        eexists. align_trace.
+      - econstructor; intuition eauto. intros. eapply weaken. 1: eapply H1; eauto.
+        simpl. intros. fwd. eexists. eexists. intuition eauto. eexists. align_trace.
+      - eapply if_true; intuition eauto. eapply weaken. 1: eapply IHexec.
+        simpl. intros. fwd. intuition eauto. eexists. align_trace.
+      - eapply if_false; intuition eauto. eapply weaken. 1: eapply IHexec.
+        simpl. intros. fwd. intuition eauto. eexists. align_trace.
+      - clear H2 H4. econstructor; intuition eauto; fwd; eauto.
+        { eexists. align_trace. }
+        { eapply weaken. 1: eapply H3; eauto. simpl. intros. fwd.
+          instantiate (1 := fun k'0 t'0 m'0 l'0 mc'0 =>
+                              mid2 k'0 t'0 m'0 l'0 mc'0 /\ exists k'', k'0 = k'' ++ k).
+          simpl. intuition. eexists. align_trace. }
+        simpl in *. fwd. eapply weaken. 1: eapply H5; eauto.
+        simpl. intros. fwd. intuition. eexists. align_trace.
+      - econstructor; intuition eauto. fwd. eapply weaken. 1: eapply H1; eauto.
+        simpl. intros. fwd. intuition eauto. eexists. align_trace.
+    Qed.
+
+    Lemma exec_ext (pick_sp1: PickSp) s k t m l mc post :
+      exec (pick_sp := pick_sp1) s k t m l mc post ->
+      forall pick_sp2,
+        (forall k', pick_sp1 (k' ++ k) = pick_sp2 (k' ++ k)) ->
+        exec (pick_sp := pick_sp2) s k t m l mc post.
+    Proof.
+      Set Printing Implicit.
+      intros H1 pick_sp2. induction H1; intros; try solve [econstructor; eauto].
+      - econstructor. 4: eapply exec_extends_trace. all: intuition eauto.
+        { eapply IHexec. intros. rewrite associate_one_left.
+          repeat rewrite app_assoc. auto. }
+        fwd. specialize H3 with (1 := H5p0). fwd. intuition eauto.
+      - econstructor; eauto. intros. replace (pick_sp1 k) with (pick_sp2 k) in *.
+        { subst a. eapply weaken.
+        { eapply H1; eauto.
+          intros. eassert (H2' := H2 (_ ++ _ :: nil)). rewrite <- app_assoc in H2'. eapply H2'. }
+        eauto. }
+        symmetry. apply H2 with (k' := nil).
+      - eapply if_true; eauto. eapply IHexec.
+        intros. rewrite associate_one_left. repeat rewrite app_assoc. auto.
+      - eapply if_false; intuition eauto. eapply IHexec.
+        intros. rewrite associate_one_left. repeat rewrite app_assoc. auto.
+      - clear H2 H4. eapply loop. 1: eapply exec_extends_trace. all: intuition eauto; fwd; eauto.
+        { eapply weaken. 1: eapply exec_extends_trace.
+          { eapply H3; eauto.
+            intros. rewrite associate_one_left. repeat rewrite app_assoc. auto. }
+          simpl. intros. fwd.
+          instantiate (1 := fun k'0 t'0 m'0 l'0 mc'0 =>
+                              mid2 k'0 t'0 m'0 l'0 mc'0 /\ exists k'', k'0 = k'' ++ k).
+          simpl. intuition eauto. eexists. align_trace. }
+        simpl in *. fwd. eapply H5; eauto. intros.
+        repeat (rewrite app_assoc || rewrite (app_one_l _ (_ ++ k))). auto.
+      - econstructor. 1: eapply exec_extends_trace; eauto. simpl. intros. fwd.
+        eapply H0; eauto. intros. repeat rewrite app_assoc. apply H2.      
+    Qed.
+
+    Local Ltac solve_picksps_equal :=
+      intros; cbv beta; f_equal;
+      repeat (rewrite rev_app_distr || cbn [rev app]); rewrite List.skipn_app_r;
+      [|repeat (rewrite app_length || rewrite rev_length || simpl); blia];
+      repeat rewrite <- app_assoc; rewrite List.skipn_app_r;
+      [|rewrite rev_length; reflexivity];
+      repeat (rewrite rev_app_distr || cbn [rev app] || rewrite rev_involutive);
+      repeat rewrite <- app_assoc; reflexivity.
+
+    Lemma exec_to_other_trace (pick_sp: PickSp) s k1 k2 t m l mc post :
+      exec s k1 t m l mc post ->
+      exec (pick_sp := fun k => pick_sp (rev (skipn (length k2) (rev k)) ++ k1))
+        s k2 t m l mc (fun k2' t' m' l' mc' =>
+                         exists k'',
+                           k2' = k'' ++ k2 /\
+                             post (k'' ++ k1) t' m' l' mc').
+    Proof.
+      intros H. generalize dependent k2. induction H; intros.
+      - econstructor; intuition eauto. apply H2 in H3. fwd.
+        eexists. intuition eauto. eexists. intuition eauto. 1: align_trace.
+        auto.
+      - econstructor; intuition eauto.
+        { eapply exec_ext with (pick_sp1 := _). 1: eapply IHexec; eauto. solve_picksps_equal. }
+        cbv beta in *. fwd. apply H3 in H4p1.
+        fwd. eexists. intuition eauto. eexists. intuition eauto. eexists.
+        split; [align_trace|]. repeat rewrite <- app_assoc. auto.
+      - econstructor; intuition eauto. eexists. split; [align_trace|]. auto.
+      - econstructor; intuition eauto. eexists. split; [align_trace|]. auto.
+      - econstructor; intuition eauto. eexists. split; [align_trace|]. auto.
+      - econstructor; intuition eauto. intros.
+        replace (rev k2) with (rev k2 ++ nil) in * by apply app_nil_r.
+        rewrite List.skipn_app_r in * by (rewrite rev_length; reflexivity).
+        simpl in *. eapply weaken.
+        { eapply exec_ext with (pick_sp1 := _). 1: eapply H1; eauto. solve_picksps_equal. }
+      simpl. intros. fwd. eexists _, _. intuition eauto. eexists (_ ++ _ :: nil).
+      rewrite <- app_assoc. simpl. rewrite <- (app_assoc _ _ k). simpl. eauto.
+      - econstructor; intuition eauto. eexists. split; [align_trace|]. auto.
+      - econstructor; intuition eauto.
+      - econstructor; intuition eauto. eexists. split; [align_trace|]. auto.
+      - eapply if_true; intuition eauto. eapply weaken.
+        { eapply exec_ext with (pick_sp1 := _). 1: eapply IHexec. solve_picksps_equal. }
+        simpl. intros. fwd. eexists. split; [align_trace|].
+        repeat rewrite <- app_assoc. auto.
+      - eapply if_false; intuition eauto. eapply weaken.
+        { eapply exec_ext with (pick_sp1 := _). 1: eapply IHexec. solve_picksps_equal. }
+        simpl. intros. fwd. eexists. split; [align_trace|].
+        repeat rewrite <- app_assoc. auto.
+      - eapply loop. 1: eapply IHexec. all: intuition eauto; fwd; eauto.
+        { eexists. split; [align_trace|]. simpl. auto. }
+        { eapply exec_ext with (pick_sp1 := _).
+          { eapply weaken. 1: eapply H3; eauto. simpl. intros.
+            instantiate (1 := fun k'0 t'0 m'0 l'0 mc'0 =>
+                                exists k''0,
+                                  k'0 = k''0 ++ k2 /\
+                                    mid2 (k''0 ++ k) t'0 m'0 l'0 mc'0).
+            fwd. eexists. split; [align_trace|].
+            repeat rewrite <- app_assoc. simpl. auto. }
+          solve_picksps_equal. }
+        simpl in *. fwd. eapply exec_ext with (pick_sp1 := _).
+        { eapply weaken. 1: eapply H5; eauto. simpl. intros. fwd.
+          eexists. split; [align_trace|].
+          repeat rewrite <- app_assoc. auto. }
+        solve_picksps_equal.
+      - econstructor; intuition. fwd. eapply weaken.
+        { eapply exec_ext with (pick_sp1 := _). 1: eapply H1; eauto. solve_picksps_equal. }
+        simpl. intros. fwd. eexists. split; [align_trace|].
+        repeat rewrite <- app_assoc. auto.
+      - econstructor. eexists. split; [align_trace|]. assumption.
+    Qed.
+
   End FlatImpExec.
 End exec.
 Notation exec := exec.exec.
diff --git a/compiler/src/compiler/FlatToRiscvCommon.v b/compiler/src/compiler/FlatToRiscvCommon.v
index 579964be..fede6d63 100644
--- a/compiler/src/compiler/FlatToRiscvCommon.v
+++ b/compiler/src/compiler/FlatToRiscvCommon.v
@@ -291,8 +291,8 @@ Section WithParameters.
       let '(argnames, retnames, fbody) := fun_impl in
       exists pos, map.get finfo f = Some pos /\ pos mod 4 = 0.
 
-  Local Notation stmt := (stmt Z). Check exec.
-  Local Notation exec pick_sp := (exec (pick_sp := pick_sp) PostSpill isRegZ).
+  Local Notation stmt := (stmt Z). Check @exec.
+  Local Notation exec pick_sp e := (@exec _ _ _ _ _ _ _ _ PostSpill isRegZ e pick_sp).
   
   (* note: [e_impl_reduced] and [funnames] will shrink one function at a time each time
      we enter a new function body, to make sure functions cannot call themselves, while
diff --git a/compiler/src/compiler/FlatToRiscvFunctions.v b/compiler/src/compiler/FlatToRiscvFunctions.v
index e596539b..f3dd3455 100644
--- a/compiler/src/compiler/FlatToRiscvFunctions.v
+++ b/compiler/src/compiler/FlatToRiscvFunctions.v
@@ -476,9 +476,8 @@ Section Proofs.
       destruct cond; [destruct op | ];
         simpl in *; Simp.simp; repeat (simulate'; simpl_bools; simpl); rewrite option_map_option_map'; intuition.
   Qed.
-
-
-  Local Notation exec pick_sp := (exec (pick_sp := pick_sp) PostSpill isRegZ).
+  
+  Local Notation exec e pick_sp := (@exec _ _ _ _ _ _ _ _ PostSpill isRegZ pick_sp e).
 
   Definition cost_compile_spec mc :=
     Platform.MetricLogging.addMetricInstructions 95
diff --git a/compiler/src/compiler/Pipeline.v b/compiler/src/compiler/Pipeline.v
index 60865d3c..219244cc 100644
--- a/compiler/src/compiler/Pipeline.v
+++ b/compiler/src/compiler/Pipeline.v
@@ -279,7 +279,7 @@ Section WithWordAndMem.
       refine ({|
                  Program := string_keyed_map (list string * list string * FlatImp.stmt string);
                  Valid := map.forall_values ParamsNoDup;
-                 Call := locals_based_call_spec (fun pick_sp => FlatImp.exec (pick_sp := pick_sp) PreSpill isRegStr);
+                 Call := locals_based_call_spec (fun pick_sp e => @FlatImp.exec _ _ _ _ _ _ _  _ PreSpill isRegStr e pick_sp);
                |}).
       1: exact tt. intros.
       cbv [locals_based_call_spec] in *. fwd. do 4 eexists. intuition eauto.
@@ -304,7 +304,7 @@ Section WithWordAndMem.
       refine ({|
                  Program := string_keyed_map (list Z * list Z * FlatImp.stmt Z);
                  Valid := map.forall_values ParamsNoDup;
-                 Call := locals_based_call_spec (fun pick_sp => FlatImp.exec (pick_sp := pick_sp) PreSpill isRegZ);
+                 Call := locals_based_call_spec (fun pick_sp e => @FlatImp.exec _ _ _ _ _ _ _ _ PreSpill isRegZ e pick_sp);
                |}).
       1: exact tt. intros.
       cbv [locals_based_call_spec] in *. fwd. do 4 eexists. intuition eauto.
@@ -319,7 +319,7 @@ Section WithWordAndMem.
       refine ({|
                  Program := string_keyed_map (list Z * list Z * FlatImp.stmt Z);
                  Valid := map.forall_values FlatToRiscvDef.valid_FlatImp_fun;
-                 Call := locals_based_call_spec_spilled (fun pick_sp => FlatImp.exec (pick_sp := pick_sp) PostSpill isRegZ);
+                 Call := locals_based_call_spec_spilled (fun e pick_sp => @FlatImp.exec _ _ _ _ _ _ _ _ PostSpill isRegZ pick_sp e);
                |}).
       1: exact tt. intros.
       cbv [locals_based_call_spec_spilled] in *. fwd. do 4 eexists. intuition eauto.
@@ -461,7 +461,9 @@ Section WithWordAndMem.
         simpl in H0. assumption.
       }
 
-      unfold locals_based_call_spec. intros. fwd.
+      unfold locals_based_call_spec. intros.
+      exists (fun pick_spL kH kL k => pick_spL ((rev (skipn (length kH) (rev k)) ++ kL))).
+      exists (fun k => k). intros. fwd.
       pose proof H0 as GI.
       unfold  useimmediate_functions in GI.
       eapply map.try_map_values_fw in GI. 2: eassumption.
@@ -470,8 +472,16 @@ Section WithWordAndMem.
       intros.
       eapply exec.weaken.
       - eapply useImmediate_correct_aux; eauto.
-      - simpl. destruct 1 as (?&?&?&?&?).
-        repeat (eexists; split; try eassumption).
+        eapply FlatImp.exec.exec_ext. 
+          1: eapply FlatImp.exec.exec_to_other_trace.
+          1: eassumption.
+          intros. simpl. simpl_rev. rewrite List.skipn_app_r.
+          2: rewrite length_rev; reflexivity.
+          simpl_rev. rewrite List.skipn_app_r.
+          2: rewrite length_rev; reflexivity.
+          rewrite rev_involutive. reflexivity.
+      - simpl. intros. fwd. eexists. intuition eauto.
+        do 3 eexists. intuition eauto.
         unfold cost_spill_spec in *; solve_MetricLog.
     Qed.
 
@@ -500,7 +510,13 @@ Section WithWordAndMem.
         simpl in H0. assumption.
       }
 
-      unfold locals_based_call_spec. intros. fwd.
+      unfold locals_based_call_spec. intros.
+      exists (fun pick_spL kH kL k => let '(argnames, retnames, fbody) :=
+                                match (map.get p1 fname) with Some finfo => finfo | None => (nil, nil, SSkip) end in
+                              fun kk => let k := rev (skipn (length kH) (rev kk)) in
+                                     pick_spL (rev kL ++ stmt_leakage eH (rev k, sH, used_
+                                  
+      eexists. eexists. intros. fwd.
       pose proof H0 as GI.
       unfold dce_functions in GI.
       eapply map.try_map_values_fw in GI. 2: eassumption.
@@ -508,8 +524,23 @@ Section WithWordAndMem.
       eexists _, _, _, _. split. 1: eassumption. split. 1: eassumption.
       intros.
       eapply @exec.weaken.
-      - eapply dce_correct_aux; eauto.
-        eapply MapEauto.agree_on_refl. 
+      - eapply exec.exec_ext. 1: eapply dce_correct_aux; eauto.
+        { eapply MapEauto.agree_on_refl. }
+        2: { intros. simpl. instantiate (1 := fun x => pick_spL (rev x)).
+             simpl. rewrite rev_involutive. reflexivity. }
+        intros. remember (k ++ kH) as kk eqn:Hkk.
+        replace k with (rev (skipn (length kH) (rev (k ++ kH)))).
+        { forget (k ++ kH) as kk0. subst.
+          set (finfo :=
+                 match (map.get p1 fname) with | Some finfo => finfo | None => (nil, nil, SSkip) end).
+          replace fbody with (snd finfo). 1: replace argnames with (fst (fst finfo)).
+          1: replace retnames with (snd (fst finfo)).
+          { 
+          instantiate (2 := fun _ _ _ _ => _). simpl. reflexivity.
+        1: reflexivity.
+        1: forget (k ++ kH) as kk. 1: instantiate (2 := fun _ _ _ _ => _). 1: reflexivity.
+        insta
+        intros. simpl. instantiate (2 := fun _ _ _ _ => _). simpl. reflexivity.
       - unfold compile_post. intros. fwd.
         exists retvals.
         split.
diff --git a/compiler/src/compiler/Spilling.v b/compiler/src/compiler/Spilling.v
index 834872e7..9558e0ba 100644
--- a/compiler/src/compiler/Spilling.v
+++ b/compiler/src/compiler/Spilling.v
@@ -24,8 +24,8 @@ Open Scope Z_scope.
 Section Spilling.
 
   Notation stmt := (stmt Z).
-  Notation execpre pick_sp := (exec (pick_sp := pick_sp) PreSpill isRegZ).
-  Notation execpost pick_sp := (exec (pick_sp := pick_sp) PostSpill isRegZ).
+  Notation execpre pick_sp e := (@exec _ _ _ _ _ _ _ _ PreSpill isRegZ e pick_sp).
+  Notation execpost pick_sp e := (@exec _ _ _ _ _ _ _ _ PostSpill isRegZ e pick_sp).
 
   Definition zero := 0.
   Definition ra := 1.