From ec319c9ec0acc975fcdfbfa2e378b82c9be9ab0a Mon Sep 17 00:00:00 2001
From: Yann Herklotz <git@yannherklotz.com>
Date: Sun, 30 Aug 2020 14:03:40 +0100
Subject: Add RTLBlock intermediate language

---
 src/verilog/Array.v | 337 ----------------------------------------------------
 1 file changed, 337 deletions(-)
 delete mode 100644 src/verilog/Array.v

(limited to 'src/verilog/Array.v')

diff --git a/src/verilog/Array.v b/src/verilog/Array.v
deleted file mode 100644
index fe0f6b2..0000000
--- a/src/verilog/Array.v
+++ /dev/null
@@ -1,337 +0,0 @@
-Set Implicit Arguments.
-
-Require Import Lia.
-Require Import Vericertlib.
-From Coq Require Import Lists.List Datatypes.
-
-Import ListNotations.
-
-Local Open Scope nat_scope.
-
-Record Array (A : Type) : Type :=
-  mk_array
-    { arr_contents : list A
-    ; arr_length : nat
-    ; arr_wf : length arr_contents = arr_length
-    }.
-
-Definition make_array {A : Type} (l : list A) : Array A :=
-  @mk_array A l (length l) eq_refl.
-
-Fixpoint list_set {A : Type} (i : nat) (x : A) (l : list A) {struct l} : list A :=
-  match i, l with
-  | _, nil => nil
-  | S n, h :: t => h :: list_set n x t
-  | O, h :: t => x :: t
-  end.
-
-Lemma list_set_spec1 {A : Type} :
-  forall l i (x : A),
-    i < length l -> nth_error (list_set i x l) i = Some x.
-Proof.
-  induction l; intros; destruct i; crush; firstorder.
-Qed.
-Hint Resolve list_set_spec1 : array.
-
-Lemma list_set_spec2 {A : Type} :
-  forall l i (x : A) d,
-    i < length l -> nth i (list_set i x l) d = x.
-Proof.
-  induction l; intros; destruct i; crush; firstorder.
-Qed.
-Hint Resolve list_set_spec2 : array.
-
-Lemma list_set_spec3 {A : Type} :
-  forall l i1 i2 (x : A),
-    i1 <> i2 ->
-    nth_error (list_set i1 x l) i2 = nth_error l i2.
-Proof.
-  induction l; intros; destruct i1; destruct i2; crush; firstorder.
-Qed.
-Hint Resolve list_set_spec3 : array.
-
-Lemma array_set_wf {A : Type} :
-  forall l ln i (x : A),
-    length l = ln -> length (list_set i x l) = ln.
-Proof.
-  induction l; intros; destruct i; auto.
-
-  invert H; crush; auto.
-Qed.
-
-Definition array_set {A : Type} (i : nat) (x : A) (a : Array A) :=
-  let l := a.(arr_contents) in
-  let ln := a.(arr_length) in
-  let WF := a.(arr_wf) in
-  @mk_array A (list_set i x l) ln (@array_set_wf A l ln i x WF).
-
-Lemma array_set_spec1 {A : Type} :
-  forall a i (x : A),
-    i < a.(arr_length) -> nth_error ((array_set i x a).(arr_contents)) i = Some x.
-Proof.
-  intros.
-
-  rewrite <- a.(arr_wf) in H.
-  unfold array_set. crush.
-  eauto with array.
-Qed.
-Hint Resolve array_set_spec1 : array.
-
-Lemma array_set_spec2 {A : Type} :
-  forall a i (x : A) d,
-    i < a.(arr_length) -> nth i ((array_set i x a).(arr_contents)) d = x.
-Proof.
-  intros.
-
-  rewrite <- a.(arr_wf) in H.
-  unfold array_set. crush.
-  eauto with array.
-Qed.
-Hint Resolve array_set_spec2 : array.
-
-Lemma array_set_len {A : Type} :
-  forall a i (x : A),
-    a.(arr_length) = (array_set i x a).(arr_length).
-Proof.
-  unfold array_set. crush.
-Qed.
-
-Definition array_get_error {A : Type} (i : nat) (a : Array A) : option A :=
-  nth_error a.(arr_contents) i.
-
-Lemma array_get_error_equal {A : Type} :
-  forall (a b : Array A) i,
-    a.(arr_contents) = b.(arr_contents) ->
-    array_get_error i a = array_get_error i b.
-Proof.
-  unfold array_get_error. crush.
-Qed.
-
-Lemma array_get_error_bound {A : Type} :
-  forall (a : Array A) i,
-    i < a.(arr_length) -> exists x, array_get_error i a = Some x.
-Proof.
-  intros.
-
-  rewrite <- a.(arr_wf) in H.
-  assert (~ length (arr_contents a) <= i) by lia.
-
-  pose proof (nth_error_None a.(arr_contents) i).
-  apply not_iff_compat in H1.
-  apply <- H1 in H0.
-
-  destruct (nth_error (arr_contents a) i) eqn:EQ; try contradiction; eauto.
-Qed.
-
-Lemma array_get_error_set_bound {A : Type} :
-  forall (a : Array A) i x,
-    i < a.(arr_length) -> array_get_error i (array_set i x a) = Some x.
-Proof.
-  intros.
-
-  unfold array_get_error.
-  eauto with array.
-Qed.
-
-Lemma array_gso {A : Type} :
-  forall (a : Array A) i1 i2 x,
-    i1 <> i2 ->
-    array_get_error i2 (array_set i1 x a) = array_get_error i2 a.
-Proof.
-  intros.
-
-  unfold array_get_error.
-  unfold array_set.
-  crush.
-  eauto with array.
-Qed.
-
-Definition array_get {A : Type} (i : nat) (x : A) (a : Array A) : A :=
-  nth i a.(arr_contents) x.
-
-Lemma array_get_set_bound {A : Type} :
-  forall (a : Array A) i x d,
-    i < a.(arr_length) -> array_get i d (array_set i x a) = x.
-Proof.
-  intros.
-
-  unfold array_get.
-  eauto with array.
-Qed.
-
-Lemma array_get_get_error {A : Type} :
-  forall (a : Array A) i x d,
-    array_get_error i a = Some x ->
-    array_get i d a = x.
-Proof.
-  intros.
-  unfold array_get.
-  unfold array_get_error in H.
-  auto using nth_error_nth.
-Qed.
-
-(** Tail recursive version of standard library function. *)
-Fixpoint list_repeat' {A : Type} (acc : list A) (a : A) (n : nat) : list A :=
-  match n with
-  | O => acc
-  | S n => list_repeat' (a::acc) a n
-  end.
-
-Lemma list_repeat'_len {A : Type} : forall (a : A) n l,
-    length (list_repeat' l a n) = (n + Datatypes.length l)%nat.
-Proof.
-  induction n; intros; crush; try reflexivity.
-
-  specialize (IHn (a :: l)).
-  rewrite IHn.
-  crush.
-Qed.
-
-Lemma list_repeat'_app {A : Type} : forall (a : A) n l,
-    list_repeat' l a n = list_repeat' [] a n ++ l.
-Proof.
-  induction n; intros; crush; try reflexivity.
-
-  pose proof IHn.
-  specialize (H (a :: l)).
-  rewrite H. clear H.
-  specialize (IHn (a :: nil)).
-  rewrite IHn. clear IHn.
-  remember (list_repeat' [] a n) as l0.
-
-  rewrite <- app_assoc.
-  f_equal.
-Qed.
-
-Lemma list_repeat'_head_tail {A : Type} : forall n (a : A),
-  a :: list_repeat' [] a n = list_repeat' [] a n ++ [a].
-Proof.
-  induction n; intros; crush; try reflexivity.
-  rewrite list_repeat'_app.
-
-  replace (a :: list_repeat' [] a n ++ [a]) with (list_repeat' [] a n ++ [a] ++ [a]).
-  2: { rewrite app_comm_cons. rewrite IHn; auto.
-       rewrite app_assoc. reflexivity. }
-  rewrite app_assoc. reflexivity.
-Qed.
-
-Lemma list_repeat'_cons {A : Type} : forall (a : A) n,
-    list_repeat' [a] a n = a :: list_repeat' [] a n.
-Proof.
-  intros.
-
-  rewrite list_repeat'_head_tail; auto.
-  apply list_repeat'_app.
-Qed.
-
-Definition list_repeat {A : Type} : A -> nat -> list A := list_repeat' nil.
-
-Lemma list_repeat_len {A : Type} : forall n (a : A), length (list_repeat a n) = n.
-Proof.
-  intros.
-  unfold list_repeat.
-  rewrite list_repeat'_len.
-  crush.
-Qed.
-
-Lemma dec_list_repeat_spec {A : Type} : forall n (a : A) a',
-    (forall x x' : A, {x' = x} + {~ x' = x}) ->
-    In a' (list_repeat a n) -> a' = a.
-Proof.
-  induction n; intros; crush.
-
-  unfold list_repeat in *.
-  crush.
-
-  rewrite list_repeat'_app in H.
-  pose proof (X a a').
-  destruct H0; auto.
-
-  (* This is actually a degenerate case, not an unprovable goal. *)
-  pose proof (in_app_or (list_repeat' [] a n) ([a])).
-  apply H0 in H. invert H.
-
-  - eapply IHn in X; eassumption.
-  - invert H1; contradiction.
-Qed.
-
-Lemma list_repeat_head_tail {A : Type} : forall n (a : A),
-    a :: list_repeat a n = list_repeat a n ++ [a].
-Proof.
-  unfold list_repeat. apply list_repeat'_head_tail.
-Qed.
-
-Lemma list_repeat_cons {A : Type} : forall n (a : A),
-    list_repeat a (S n) = a :: list_repeat a n.
-Proof.
-  intros.
-
-  unfold list_repeat.
-  apply list_repeat'_cons.
-Qed.
-
-Lemma list_repeat_lookup {A : Type} :
-  forall n i (a : A),
-    i < n ->
-    nth_error (list_repeat a n) i = Some a.
-Proof.
-  induction n; intros.
-
-  destruct i; crush.
-
-  rewrite list_repeat_cons.
-  destruct i; crush; firstorder.
-Qed.
-
-Definition arr_repeat {A : Type} (a : A) (n : nat) : Array A := make_array (list_repeat a n).
-
-Lemma arr_repeat_length {A : Type} : forall n (a : A), arr_length (arr_repeat a n) = n.
-Proof.
-  unfold list_repeat. crush. apply list_repeat_len.
-Qed.
-
-Fixpoint list_combine {A B C : Type} (f : A -> B -> C) (x : list A) (y : list B) : list C :=
-  match x, y with
-  | a :: t, b :: t' => f a b :: list_combine f t t'
-  | _, _ => nil
-  end.
-
-Lemma list_combine_length {A B C : Type} (f : A -> B -> C) : forall (x : list A) (y : list B),
-    length (list_combine f x y) = min (length x) (length y).
-Proof.
-  induction x; intros; crush.
-
-  destruct y; crush; auto.
-Qed.
-
-Definition combine {A B C : Type} (f : A -> B -> C) (x : Array A) (y : Array B) : Array C :=
-  make_array (list_combine f x.(arr_contents) y.(arr_contents)).
-
-Lemma combine_length {A B C: Type} : forall x y (f : A -> B -> C),
-    x.(arr_length) = y.(arr_length) -> arr_length (combine f x y) = x.(arr_length).
-Proof.
-  intros.
-
-  unfold combine.
-  unfold make_array.
-  crush.
-
-  rewrite <- (arr_wf x) in *.
-  rewrite <- (arr_wf y) in *.
-
-  destruct (arr_contents x); destruct (arr_contents y); crush.
-  rewrite list_combine_length.
-  destruct (Min.min_dec (length l) (length l0)); congruence.
-Qed.
-
-Ltac array :=
-  try match goal with
-      | [ |- context[arr_length (combine _ _ _)] ] =>
-        rewrite combine_length
-      | [ |- context[length (list_repeat _ _)] ] =>
-        rewrite list_repeat_len
-      | |- context[array_get_error _ (arr_repeat ?x _) = Some ?x] =>
-        unfold array_get_error, arr_repeat
-      | |- context[nth_error (list_repeat ?x _) _ = Some ?x] =>
-        apply list_repeat_lookup
-      end.
-- 
cgit