Rebase + remove WordizeUtil dependency from Z/Interpretations

1 files changed, 45 insertions, 8 deletions

diff --git a/src/Util/WordUtil.v b/src/Util/WordUtil.v
index 4c74fe9b4..f0e6ef335 100644
--- a/src/Util/WordUtil.v
+++ b/src/Util/WordUtil.v
@@ -1,5 +1,6 @@
 Require Import Coq.Numbers.Natural.Peano.NPeano.
 Require Import Coq.ZArith.ZArith.
+Require Import Coq.NArith.NArith.
 Require Import Crypto.Util.NatUtil.
 Require Import Crypto.Util.Tactics.
 Require Import Bedrock.Word.
@@ -51,6 +52,32 @@ Proof.
   auto.
 Qed.
 
+Lemma Npow2_gt0 : forall x, (0 < Npow2 x)%N.
+Proof.
+  intros; induction x.
+
+  - simpl; apply N.lt_1_r; intuition.
+
+  - replace (Npow2 (S x)) with (2 * (Npow2 x))%N by intuition.
+      apply (N.lt_0_mul 2 (Npow2 x)); left; split; apply N.neq_0_lt_0.
+
+    + intuition; inversion H.
+
+    + apply N.neq_0_lt_0 in IHx; intuition.
+Qed.
+
+Lemma Npow2_N: forall n, Npow2 n = (2 ^ N.of_nat n)%N.
+Proof.
+  induction n.
+
+  - simpl; intuition.
+
+  - rewrite Nat2N.inj_succ.
+    rewrite N.pow_succ_r; try apply N_ge_0.
+    rewrite <- IHn.
+    simpl; intuition.
+Qed.
+
 Lemma Npow2_Zlog2 : forall x n,
     (Z.log2 (Z.of_N x) < Z.of_nat n)%Z
  -> (x < Npow2 n)%N.
@@ -243,16 +270,26 @@ Ltac wordsize_eq_tac := cbv beta delta [wordsize_eq] in *; omega*.
 Ltac gt84_abstract t := t. (* TODO: when we drop Coq 8.4, use [abstract] here *)
 Hint Extern 100 (wordsize_eq _ _) => gt84_abstract wordsize_eq_tac : typeclass_instances.
 
-Program Fixpoint cast_word {n m} : forall {pf:wordsize_eq n m}, word n -> word m :=
-  match n, m return wordsize_eq n m -> word n -> word m with
-  | O, O => fun _ _ => WO
-  | S n', S m' => fun _ w => WS (whd w) (@cast_word _ _ _ (wtl w))
-  | _, _ => fun _ _ => !
+Fixpoint correct_wordsize_eq (x y : nat) : wordsize_eq x y -> x = y
+  := match x, y with
+     | O, O => fun _ => eq_refl
+     | S x', S y' => fun pf => f_equal S (correct_wordsize_eq x' y' (f_equal pred pf))
+     | _, _ => fun x => x
+     end.
+
+Lemma correct_wordsize_eq_refl n pf : correct_wordsize_eq n n pf = eq_refl.
+Proof.
+  induction n; [ reflexivity | simpl ].
+  rewrite IHn; reflexivity.
+Qed.
+
+Definition cast_word {n m} {pf:wordsize_eq n m} : word n -> word m :=
+  match correct_wordsize_eq n m pf in _ = y return word n -> word y with
+  | eq_refl => fun w => w
   end.
-Global Arguments cast_word {_ _ _} _. (* 8.4 does not pick up the forall braces *)
 
 Lemma cast_word_refl {n} pf (w:word n) : @cast_word n n pf w = w.
-Proof. induction w; simpl; auto using f_equal. Qed.
+Proof. unfold cast_word; rewrite correct_wordsize_eq_refl; reflexivity. Qed.
 
 Lemma wordToNat_cast_word {n} (w:word n) m pf :
   wordToNat (@cast_word n m pf w) = wordToNat w.
@@ -721,4 +758,4 @@ Axiom winit : forall sz, word (sz+1) -> word sz. Arguments winit {_} _.
 Axiom combine_winit_wlast : forall {sz} a b (c:word (sz+1)),
     @combine sz a 1 b = c <-> a = winit c /\ b = (WS (wlast c) WO).
 Axiom winit_combine : forall sz a b, @winit sz (combine a b) = a.
-Axiom wlast_combine : forall sz a b, @wlast sz (combine a (WS b WO)) = b.
\ No newline at end of file
+Axiom wlast_combine : forall sz a b, @wlast sz (combine a (WS b WO)) = b.