Add RTLBlock intermediate language

1 files changed, 641 insertions, 0 deletions

diff --git a/src/hls/HTLgenspec.v b/src/hls/HTLgenspec.v
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+(*
+ * Vericert: Verified high-level synthesis.
+ * Copyright (C) 2020 Yann Herklotz <yann@yannherklotz.com>
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ *)
+
+From compcert Require RTL Op Maps Errors.
+From compcert Require Import Maps Integers.
+From vericert Require Import Vericertlib Verilog ValueInt HTL HTLgen AssocMap.
+Require Import Lia.
+
+Hint Resolve Maps.PTree.elements_keys_norepet : htlspec.
+Hint Resolve Maps.PTree.elements_correct : htlspec.
+
+Remark bind_inversion:
+  forall (A B: Type) (f: mon A) (g: A -> mon B)
+         (y: B) (s1 s3: st) (i: st_incr s1 s3),
+    bind f g s1 = OK y s3 i ->
+    exists x, exists s2, exists i1, exists i2,
+            f s1 = OK x s2 i1 /\ g x s2 = OK y s3 i2.
+Proof.
+  intros until i. unfold bind. destruct (f s1); intros.
+  discriminate.
+  exists a; exists s'; exists s.
+  destruct (g a s'); inv H.
+  exists s0; auto.
+Qed.
+
+Remark bind2_inversion:
+  forall (A B C: Type) (f: mon (A*B)) (g: A -> B -> mon C)
+         (z: C) (s1 s3: st) (i: st_incr s1 s3),
+    bind2 f g s1 = OK z s3 i ->
+    exists x, exists y, exists s2, exists i1, exists i2,
+              f s1 = OK (x, y) s2 i1 /\ g x y s2 = OK z s3 i2.
+Proof.
+  unfold bind2; intros.
+  exploit bind_inversion; eauto.
+  intros [[x y] [s2 [i1 [i2 [P Q]]]]]. simpl in Q.
+  exists x; exists y; exists s2; exists i1; exists i2; auto.
+Qed.
+
+Ltac monadInv1 H :=
+  match type of H with
+  | (OK _ _ _ = OK _ _ _) =>
+    inversion H; clear H; try subst
+  | (Error _ _ = OK _ _ _) =>
+    discriminate
+  | (ret _ _ = OK _ _ _) =>
+    inversion H; clear H; try subst
+  | (error _ _ = OK _ _ _) =>
+    discriminate
+  | (bind ?F ?G ?S = OK ?X ?S' ?I) =>
+    let x := fresh "x" in (
+      let s := fresh "s" in (
+        let i1 := fresh "INCR" in (
+          let i2 := fresh "INCR" in (
+            let EQ1 := fresh "EQ" in (
+              let EQ2 := fresh "EQ" in (
+                destruct (bind_inversion _ _ F G X S S' I H) as [x [s [i1 [i2 [EQ1 EQ2]]]]];
+                clear H;
+                try (monadInv1 EQ2)))))))
+  | (bind2 ?F ?G ?S = OK ?X ?S' ?I) =>
+    let x1 := fresh "x" in (
+      let x2 := fresh "x" in (
+        let s := fresh "s" in (
+          let i1 := fresh "INCR" in (
+            let i2 := fresh "INCR" in (
+              let EQ1 := fresh "EQ" in (
+                let EQ2 := fresh "EQ" in (
+                  destruct (bind2_inversion _ _ _ F G X S S' I H) as [x1 [x2 [s [i1 [i2 [EQ1 EQ2]]]]]];
+                  clear H;
+                  try (monadInv1 EQ2))))))))
+  end.
+
+Ltac monadInv H :=
+  match type of H with
+  | (ret _ _ = OK _ _ _) => monadInv1 H
+  | (error _ _ = OK _ _ _) => monadInv1 H
+  | (bind ?F ?G ?S = OK ?X ?S' ?I) => monadInv1 H
+  | (bind2 ?F ?G ?S = OK ?X ?S' ?I) => monadInv1 H
+  | (?F _ _ _ _ _ _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ _ _ _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ _ _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  | (?F _ = OK _ _ _) =>
+    ((progress simpl in H) || unfold F in H); monadInv1 H
+  end.
+
+(** * Relational specification of the translation *)
+
+(** We now define inductive predicates that characterise the fact that the
+statemachine that is created by the translation contains the correct
+translations for each of the elements *)
+
+Inductive tr_instr (fin rtrn st stk : reg) : RTL.instruction -> stmnt -> stmnt -> Prop :=
+| tr_instr_Inop :
+    forall n,
+      Z.pos n <= Int.max_unsigned ->
+      tr_instr fin rtrn st stk (RTL.Inop n) Vskip (state_goto st n)
+| tr_instr_Iop :
+    forall n op args dst s s' e i,
+      Z.pos n <= Int.max_unsigned ->
+      translate_instr op args s = OK e s' i ->
+      tr_instr fin rtrn st stk (RTL.Iop op args dst n) (Vnonblock (Vvar dst) e) (state_goto st n)
+| tr_instr_Icond :
+    forall n1 n2 cond args s s' i c,
+      Z.pos n1 <= Int.max_unsigned ->
+      Z.pos n2 <= Int.max_unsigned ->
+      translate_condition cond args s = OK c s' i ->
+      tr_instr fin rtrn st stk (RTL.Icond cond args n1 n2) Vskip (state_cond st c n1 n2)
+| tr_instr_Ireturn_None :
+    tr_instr fin rtrn st stk (RTL.Ireturn None) (Vseq (block fin (Vlit (ZToValue 1%Z)))
+                                                  (block rtrn (Vlit (ZToValue 0%Z)))) Vskip
+| tr_instr_Ireturn_Some :
+    forall r,
+      tr_instr fin rtrn st stk (RTL.Ireturn (Some r))
+               (Vseq (block fin (Vlit (ZToValue 1%Z))) (block rtrn (Vvar r))) Vskip
+| tr_instr_Iload :
+    forall mem addr args s s' i c dst n,
+      Z.pos n <= Int.max_unsigned ->
+      translate_arr_access mem addr args stk s = OK c s' i ->
+      tr_instr fin rtrn st stk (RTL.Iload mem addr args dst n) (nonblock dst c) (state_goto st n)
+| tr_instr_Istore :
+    forall mem addr args s s' i c src n,
+      Z.pos n <= Int.max_unsigned ->
+      translate_arr_access mem addr args stk s = OK c s' i ->
+      tr_instr fin rtrn st stk (RTL.Istore mem addr args src n) (Vnonblock c (Vvar src))
+               (state_goto st n).
+(*| tr_instr_Ijumptable :
+    forall cexpr tbl r,
+    cexpr = tbl_to_case_expr st tbl ->
+    tr_instr fin rtrn st stk (RTL.Ijumptable r tbl) (Vskip) (Vcase (Vvar r) cexpr (Some Vskip)).*)
+Hint Constructors tr_instr : htlspec.
+
+Inductive tr_code (c : RTL.code) (pc : RTL.node) (i : RTL.instruction) (stmnts trans : PTree.t stmnt)
+          (fin rtrn st stk : reg) : Prop :=
+  tr_code_intro :
+    forall s t,
+      c!pc = Some i ->
+      stmnts!pc = Some s ->
+      trans!pc = Some t ->
+      tr_instr fin rtrn st stk i s t ->
+      tr_code c pc i stmnts trans fin rtrn st stk.
+Hint Constructors tr_code : htlspec.
+
+Inductive tr_module (f : RTL.function) : module -> Prop :=
+  tr_module_intro :
+    forall data control fin rtrn st stk stk_len m start rst clk scldecls arrdecls wf,
+      m = (mkmodule f.(RTL.fn_params)
+                        data
+                        control
+                        f.(RTL.fn_entrypoint)
+                        st stk stk_len fin rtrn start rst clk scldecls arrdecls wf) ->
+      (forall pc i, Maps.PTree.get pc f.(RTL.fn_code) = Some i ->
+               tr_code f.(RTL.fn_code) pc i data control fin rtrn st stk) ->
+      stk_len = Z.to_nat (f.(RTL.fn_stacksize) / 4) ->
+      Z.modulo (f.(RTL.fn_stacksize)) 4 = 0 ->
+      0 <= f.(RTL.fn_stacksize) < Integers.Ptrofs.modulus ->
+      st = ((RTL.max_reg_function f) + 1)%positive ->
+      fin = ((RTL.max_reg_function f) + 2)%positive ->
+      rtrn = ((RTL.max_reg_function f) + 3)%positive ->
+      stk = ((RTL.max_reg_function f) + 4)%positive ->
+      start = ((RTL.max_reg_function f) + 5)%positive ->
+      rst = ((RTL.max_reg_function f) + 6)%positive ->
+      clk = ((RTL.max_reg_function f) + 7)%positive ->
+      tr_module f m.
+Hint Constructors tr_module : htlspec.
+
+Lemma create_reg_datapath_trans :
+  forall sz s s' x i iop,
+    create_reg iop sz s = OK x s' i ->
+    s.(st_datapath) = s'.(st_datapath).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_reg_datapath_trans : htlspec.
+
+Lemma create_reg_controllogic_trans :
+  forall sz s s' x i iop,
+    create_reg iop sz s = OK x s' i ->
+    s.(st_controllogic) = s'.(st_controllogic).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_reg_controllogic_trans : htlspec.
+
+Lemma declare_reg_datapath_trans :
+  forall sz s s' x i iop r,
+    declare_reg iop r sz s = OK x s' i ->
+    s.(st_datapath) = s'.(st_datapath).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_reg_datapath_trans : htlspec.
+
+Lemma declare_reg_controllogic_trans :
+  forall sz s s' x i iop r,
+    declare_reg iop r sz s = OK x s' i ->
+    s.(st_controllogic) = s'.(st_controllogic).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_reg_controllogic_trans : htlspec.
+
+Lemma declare_reg_freshreg_trans :
+  forall sz s s' x i iop r,
+    declare_reg iop r sz s = OK x s' i ->
+    s.(st_freshreg) = s'.(st_freshreg).
+Proof. inversion 1; auto. Qed.
+Hint Resolve declare_reg_freshreg_trans : htlspec.
+
+Lemma create_arr_datapath_trans :
+  forall sz ln s s' x i iop,
+    create_arr iop sz ln s = OK x s' i ->
+    s.(st_datapath) = s'.(st_datapath).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_arr_datapath_trans : htlspec.
+
+Lemma create_arr_controllogic_trans :
+  forall sz ln s s' x i iop,
+    create_arr iop sz ln s = OK x s' i ->
+    s.(st_controllogic) = s'.(st_controllogic).
+Proof. intros. monadInv H. trivial. Qed.
+Hint Resolve create_arr_controllogic_trans : htlspec.
+
+Lemma get_refl_x :
+  forall s s' x i,
+    get s = OK x s' i ->
+    s = x.
+Proof. inversion 1. trivial. Qed.
+Hint Resolve get_refl_x : htlspec.
+
+Lemma get_refl_s :
+  forall s s' x i,
+    get s = OK x s' i ->
+    s = s'.
+Proof. inversion 1. trivial. Qed.
+Hint Resolve get_refl_s : htlspec.
+
+Ltac inv_incr :=
+  repeat match goal with
+  | [ H: create_reg _ _ ?s = OK _ ?s' _ |- _ ] =>
+    let H1 := fresh "H" in
+    assert (H1 := H); eapply create_reg_datapath_trans in H;
+    eapply create_reg_controllogic_trans in H1
+  | [ H: create_arr _ _ _ ?s = OK _ ?s' _ |- _ ] =>
+    let H1 := fresh "H" in
+    assert (H1 := H); eapply create_arr_datapath_trans in H;
+    eapply create_arr_controllogic_trans in H1
+  | [ H: get ?s = OK _ _ _ |- _ ] =>
+    let H1 := fresh "H" in
+    assert (H1 := H); apply get_refl_x in H; apply get_refl_s in H1;
+    subst
+  | [ H: st_prop _ _ |- _ ] => unfold st_prop in H; destruct H
+  | [ H: st_incr _ _ |- _ ] => destruct st_incr
+  end.
+
+Lemma collect_controllogic_trans :
+  forall A f l cs cs' ci,
+  (forall s s' x i y, f y s = OK x s' i -> s.(st_controllogic) = s'.(st_controllogic)) ->
+  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_controllogic) = cs'.(st_controllogic).
+Proof.
+  induction l; intros; monadInv H0.
+  - trivial.
+  - apply H in EQ. rewrite EQ. eauto.
+Qed.
+
+Lemma collect_datapath_trans :
+  forall A f l cs cs' ci,
+  (forall s s' x i y, f y s = OK x s' i -> s.(st_datapath) = s'.(st_datapath)) ->
+  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_datapath) = cs'.(st_datapath).
+Proof.
+  induction l; intros; monadInv H0.
+  - trivial.
+  - apply H in EQ. rewrite EQ. eauto.
+Qed.
+
+Lemma collect_freshreg_trans :
+  forall A f l cs cs' ci,
+  (forall s s' x i y, f y s = OK x s' i -> s.(st_freshreg) = s'.(st_freshreg)) ->
+  @HTLMonadExtra.collectlist A f l cs = OK tt cs' ci -> cs.(st_freshreg) = cs'.(st_freshreg).
+Proof.
+  induction l; intros; monadInv H0.
+  - trivial.
+  - apply H in EQ. rewrite EQ. eauto.
+Qed.
+
+Lemma collect_declare_controllogic_trans :
+  forall io n l s s' i,
+  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
+  s.(st_controllogic) = s'.(st_controllogic).
+Proof.
+  intros. eapply collect_controllogic_trans; try eassumption.
+  intros. eapply declare_reg_controllogic_trans. simpl in H0. eassumption.
+Qed.
+
+Lemma collect_declare_datapath_trans :
+  forall io n l s s' i,
+  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
+  s.(st_datapath) = s'.(st_datapath).
+Proof.
+  intros. eapply collect_datapath_trans; try eassumption.
+  intros. eapply declare_reg_datapath_trans. simpl in H0. eassumption.
+Qed.
+
+Lemma collect_declare_freshreg_trans :
+  forall io n l s s' i,
+  HTLMonadExtra.collectlist (fun r : reg => declare_reg io r n) l s = OK tt s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  intros. eapply collect_freshreg_trans; try eassumption.
+  inversion 1. auto.
+Qed.
+
+Ltac unfold_match H :=
+  match type of H with
+  | context[match ?g with _ => _ end] => destruct g eqn:?; try discriminate
+  end.
+
+Lemma translate_eff_addressing_freshreg_trans :
+  forall op args s r s' i,
+  translate_eff_addressing op args s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
+Qed.
+Hint Resolve translate_eff_addressing_freshreg_trans : htlspec.
+
+Lemma translate_comparison_freshreg_trans :
+  forall op args s r s' i,
+  translate_comparison op args s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
+Qed.
+Hint Resolve translate_comparison_freshreg_trans : htlspec.
+
+Lemma translate_comparisonu_freshreg_trans :
+  forall op args s r s' i,
+  translate_comparisonu op args s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
+Qed.
+Hint Resolve translate_comparisonu_freshreg_trans : htlspec.
+
+Lemma translate_comparison_imm_freshreg_trans :
+  forall op args s r s' i n,
+  translate_comparison_imm op args n s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
+Qed.
+Hint Resolve translate_comparison_imm_freshreg_trans : htlspec.
+
+Lemma translate_comparison_immu_freshreg_trans :
+  forall op args s r s' i n,
+  translate_comparison_immu op args n s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; auto.
+Qed.
+Hint Resolve translate_comparison_immu_freshreg_trans : htlspec.
+
+Lemma translate_condition_freshreg_trans :
+  forall op args s r s' i,
+  translate_condition op args s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec.
+Qed.
+Hint Resolve translate_condition_freshreg_trans : htlspec.
+
+Lemma translate_instr_freshreg_trans :
+  forall op args s r s' i,
+  translate_instr op args s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  destruct op; intros; simpl in *; repeat (unfold_match H); inv H; eauto with htlspec.
+  monadInv H1. eauto with htlspec.
+Qed.
+Hint Resolve translate_instr_freshreg_trans : htlspec.
+
+Lemma translate_arr_access_freshreg_trans :
+  forall mem addr args st s r s' i,
+  translate_arr_access mem addr args st s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  intros. unfold translate_arr_access in H. repeat (unfold_match H); inv H; eauto with htlspec.
+Qed.
+Hint Resolve translate_arr_access_freshreg_trans : htlspec.
+
+Lemma add_instr_freshreg_trans :
+  forall n n' st s r s' i,
+  add_instr n n' st s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof. intros. unfold add_instr in H. repeat (unfold_match H). inv H. auto. Qed.
+Hint Resolve add_instr_freshreg_trans : htlspec.
+
+Lemma add_branch_instr_freshreg_trans :
+  forall n n0 n1 e s r s' i,
+  add_branch_instr e n n0 n1 s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof. intros. unfold add_branch_instr in H. repeat (unfold_match H). inv H. auto. Qed.
+Hint Resolve add_branch_instr_freshreg_trans : htlspec.
+
+Lemma add_node_skip_freshreg_trans :
+  forall n1 n2 s r s' i,
+  add_node_skip n1 n2 s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof. intros. unfold add_node_skip in H. repeat (unfold_match H). inv H. auto. Qed.
+Hint Resolve add_node_skip_freshreg_trans : htlspec.
+
+Lemma add_instr_skip_freshreg_trans :
+  forall n1 n2 s r s' i,
+  add_instr_skip n1 n2 s = OK r s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof. intros. unfold add_instr_skip in H. repeat (unfold_match H). inv H. auto. Qed.
+Hint Resolve add_instr_skip_freshreg_trans : htlspec.
+
+Lemma transf_instr_freshreg_trans :
+  forall fin ret st instr s v s' i,
+    transf_instr fin ret st instr s = OK v s' i ->
+    s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  intros. destruct instr eqn:?. subst. unfold transf_instr in H.
+  destruct i0; try (monadInv H); try (unfold_match H); eauto with htlspec.
+  - monadInv H. apply add_instr_freshreg_trans in EQ2. apply translate_instr_freshreg_trans in EQ.
+    apply declare_reg_freshreg_trans in EQ1. congruence.
+  - monadInv H. apply add_instr_freshreg_trans in EQ2. apply translate_arr_access_freshreg_trans in EQ.
+    apply declare_reg_freshreg_trans in EQ1. congruence.
+  - monadInv H. apply add_instr_freshreg_trans in EQ0. apply translate_arr_access_freshreg_trans in EQ. congruence.
+  - monadInv H. apply translate_condition_freshreg_trans in EQ. apply add_branch_instr_freshreg_trans in EQ0.
+    congruence.
+  (*- inv EQ. apply add_node_skip_freshreg_trans in EQ0. congruence.*)
+Qed.
+Hint Resolve transf_instr_freshreg_trans : htlspec.
+
+Lemma collect_trans_instr_freshreg_trans :
+  forall fin ret st l s s' i,
+  HTLMonadExtra.collectlist (transf_instr fin ret st) l s = OK tt s' i ->
+  s.(st_freshreg) = s'.(st_freshreg).
+Proof.
+  intros. eapply collect_freshreg_trans; try eassumption.
+  eauto with htlspec.
+Qed.
+
+Ltac rewrite_states :=
+  match goal with
+  | [ H: ?x ?s = ?x ?s' |- _ ] =>
+    let c1 := fresh "c" in
+    let c2 := fresh "c" in
+    remember (?x ?s) as c1; remember (?x ?s') as c2; try subst
+  end.
+
+Ltac inv_add_instr' H :=
+  match type of H with
+  | ?f _ _ = OK _ _ _ => unfold f in H
+  | ?f _ _ _ = OK _ _ _ => unfold f in H
+  | ?f _ _ _ _ = OK _ _ _ => unfold f in H
+  | ?f _ _ _ _ _ = OK _ _ _ => unfold f in H
+  | ?f _ _ _ _ _ _ = OK _ _ _ => unfold f in H
+  end; repeat unfold_match H; inversion H.
+
+Ltac inv_add_instr :=
+  match goal with
+  | H: (if ?c then _ else _) _ = OK _ _ _ |- _ => destruct c eqn:EQN; try discriminate; inv_add_instr
+  | H: context[add_instr_skip _ _ _] |- _ =>
+    inv_add_instr' H
+  | H: context[add_instr_skip _ _] |- _ =>
+    monadInv H; inv_incr; inv_add_instr
+  | H: context[add_instr _ _ _ _] |- _ =>
+    inv_add_instr' H
+  | H: context[add_instr _ _ _] |- _ =>
+    monadInv H; inv_incr; inv_add_instr
+  | H: context[add_branch_instr _ _ _ _ _] |- _ =>
+    inv_add_instr' H
+  | H: context[add_branch_instr _ _ _ _] |- _ =>
+    monadInv H; inv_incr; inv_add_instr
+  | H: context[add_node_skip _ _ _] |- _ =>
+    inv_add_instr' H
+  | H: context[add_node_skip _ _] |- _ =>
+    monadInv H; inv_incr; inv_add_instr
+  end.
+
+Ltac destruct_optional :=
+  match goal with H: option ?r |- _ => destruct H end.
+
+Lemma iter_expand_instr_spec :
+  forall l fin rtrn stack s s' i x c,
+    HTLMonadExtra.collectlist (transf_instr fin rtrn stack) l s = OK x s' i ->
+    list_norepet (List.map fst l) ->
+    (forall pc instr, In (pc, instr) l -> c!pc = Some instr) ->
+    (forall pc instr, In (pc, instr) l ->
+                      c!pc = Some instr ->
+                      tr_code c pc instr s'.(st_datapath) s'.(st_controllogic) fin rtrn s'.(st_st) stack).
+Proof.
+  induction l; simpl; intros; try contradiction.
+  destruct a as [pc1 instr1]; simpl in *. inv H0. monadInv H. inv_incr.
+  destruct (peq pc pc1).
+  - subst.
+    destruct instr1 eqn:?; try discriminate;
+      try destruct_optional; inv_add_instr; econstructor; try assumption.
+    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + inversion H2. inversion H9. rewrite H. apply tr_instr_Inop.
+      apply Z.leb_le. assumption.
+      eapply in_map with (f := fst) in H9. contradiction.
+
+    + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + inversion H2. inversion H14. unfold nonblock. replace (st_st s4) with (st_st s2) by congruence.
+      econstructor. apply Z.leb_le; assumption.
+      apply EQ1. eapply in_map with (f := fst) in H14. contradiction.
+
+    + destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + inversion H2. inversion H14. rewrite <- e2. replace (st_st s2) with (st_st s0) by congruence.
+      econstructor. apply Z.leb_le; assumption.
+      apply EQ1. eapply in_map with (f := fst) in H14. contradiction.
+
+    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct H2.
+      * inversion H2.
+        replace (st_st s2) with (st_st s0) by congruence.
+        econstructor. apply Z.leb_le; assumption.
+        eauto with htlspec.
+      * apply in_map with (f := fst) in H2. contradiction.
+
+    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct H2.
+      * inversion H2.
+        replace (st_st s2) with (st_st s0) by congruence.
+        econstructor; try (apply Z.leb_le; apply andb_prop in EQN; apply EQN).
+        eauto with htlspec.
+      * apply in_map with (f := fst) in H2. contradiction.
+
+    (*+ destruct o with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + destruct o0 with pc1; destruct H16; simpl in *; rewrite AssocMap.gss in H14; eauto; congruence.
+    + inversion H2.
+      * inversion H14. constructor. congruence.
+      * apply in_map with (f := fst) in H14. contradiction.
+      *)
+    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + inversion H2.
+      * inversion H9.
+        replace (st_st s2) with (st_st s0) by congruence.
+        eauto with htlspec.
+      * apply in_map with (f := fst) in H9. contradiction.
+
+    + destruct o with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + destruct o0 with pc1; destruct H11; simpl in *; rewrite AssocMap.gss in H9; eauto; congruence.
+    + inversion H2.
+      * inversion H9.
+        replace (st_st s2) with (st_st s0) by congruence.
+        eauto with htlspec.
+      * apply in_map with (f := fst) in H9. contradiction.
+
+  - eapply IHl. apply EQ0. assumption.
+    destruct H2. inversion H2. subst. contradiction.
+    intros. specialize H1 with pc0 instr0. destruct H1. tauto. trivial.
+    destruct H2. inv H2. contradiction. assumption. assumption.
+Qed.
+Hint Resolve iter_expand_instr_spec : htlspec.
+
+Lemma create_arr_inv : forall w x y z a b c d,
+    create_arr w x y z = OK (a, b) c d ->
+    y = b /\ a = z.(st_freshreg) /\ c.(st_freshreg) = Pos.succ (z.(st_freshreg)).
+Proof.
+  inversion 1; split; auto.
+Qed.
+
+Lemma create_reg_inv : forall a b s r s' i,
+    create_reg a b s = OK r s' i ->
+    r = s.(st_freshreg) /\ s'.(st_freshreg) = Pos.succ (s.(st_freshreg)).
+Proof.
+  inversion 1; auto.
+Qed.
+
+Theorem transl_module_correct :
+  forall f m,
+    transl_module f = Errors.OK m -> tr_module f m.
+Proof.
+  intros until m.
+  unfold transl_module.
+  unfold run_mon.
+  destruct (transf_module f (max_state f)) eqn:?; try discriminate.
+  intros. inv H.
+  inversion s; subst.
+
+  unfold transf_module in *.
+  unfold stack_correct in *.
+  destruct (0 <=? RTL.fn_stacksize f) eqn:STACK_BOUND_LOW;
+    destruct (RTL.fn_stacksize f <? Integers.Ptrofs.modulus) eqn:STACK_BOUND_HIGH;
+    destruct (RTL.fn_stacksize f mod 4 =? 0) eqn:STACK_ALIGN;
+    crush;
+    monadInv Heqr.
+
+  repeat unfold_match EQ9. monadInv EQ9.
+
+  (* TODO: We should be able to fold this into the automation. *)
+  pose proof (create_arr_inv _ _ _ _ _ _ _ _ EQ0) as STK_LEN. inv STK_LEN. inv H5.
+  pose proof (create_reg_inv _ _ _ _ _ _ EQ) as FIN_VAL. inv FIN_VAL.
+  pose proof (create_reg_inv _ _ _ _ _ _ EQ1) as RET_VAL. inv RET_VAL.
+  destruct x3. destruct x4.
+  pose proof (collect_trans_instr_freshreg_trans _ _ _ _ _ _ _ EQ2) as TR_INSTR.
+  pose proof (collect_declare_freshreg_trans _ _ _ _ _ _ EQ3) as TR_DEC.
+  pose proof (create_reg_inv _ _ _ _ _ _ EQ4) as START_VAL. inv START_VAL.
+  pose proof (create_reg_inv _ _ _ _ _ _ EQ5) as RESET_VAL. inv RESET_VAL.
+  pose proof (create_reg_inv _ _ _ _ _ _ EQ6) as CLK_VAL. inv CLK_VAL.
+  rewrite H9 in *. rewrite H8 in *. replace (st_freshreg s4) with (st_freshreg s2) in * by congruence.
+  rewrite H6 in *. rewrite H7 in *. rewrite H5 in *. simpl in *.
+  inv_incr.
+  econstructor; simpl; auto; try lia.
+  intros.
+  assert (EQ3D := EQ3).
+  apply collect_declare_datapath_trans in EQ3.
+  apply collect_declare_controllogic_trans in EQ3D.
+  replace (st_controllogic s10) with (st_controllogic s3) by congruence.
+  replace (st_datapath s10) with (st_datapath s3) by congruence.
+  replace (st_st s10) with (st_st s3) by congruence.
+  eapply iter_expand_instr_spec; eauto with htlspec.
+  apply PTree.elements_complete.
+Qed.