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Require Export Bedrock.Word Bedrock.Nomega.
Require Import NArith PArith Ndigits Compare_dec Arith.
Require Import ProofIrrelevance Ring List.
Require Export MultiBoundedWord QhasmCommon.
Import ListNotations.
(* Tuple Manipulations *)
Fixpoint Tuple (T: Type) (n: nat): Type :=
match n with
| O => T
| S m => (T * (Tuple T m))%type
end.
Definition just {T} (x: T): Tuple T O := x.
Definition cross {T n} (x: T) (tup: Tuple T n): Tuple T (S n) := (x, tup).
Definition getLen {T n} (tup: Tuple T n) := (S n).
Fixpoint tget' {T n} (tup: Tuple T n) (x: nat): T.
induction x, n; try exact tup.
exact (fst tup).
exact (tget' _ _ (snd tup) x).
Defined.
Definition tget {T n} (tup: Tuple T n) (x: nat): T :=
tget' tup (n - x).
Lemma tget_inc: forall {T k} (x: nat) (v: T) (tup: Tuple T k),
(x <= k)%nat -> tget tup x = tget (cross v tup) x.
Proof.
intros; unfold cross, tget.
replace (S k - x) with (S (k - x)) by intuition.
unfold tget'; simpl; intuition.
Qed.
Ltac tupleize n :=
repeat match goal with
| [T: Tuple _ ?k, w: word n |- _] => let H := fresh in
replace w with (tget (cross w T) (S k)) by (simpl; intuition);
assert (forall m, (m <= k)%nat -> tget T m = tget (cross w T) m) as H
by (intros; apply tget_inc; intuition);
repeat rewrite H by intuition;
generalize (cross w T); clear w T H; intro T
| [w: word n |- _] =>
replace w with (tget (just w) O) by (simpl; intuition);
generalize (just w); clear w; let T := fresh in intro T
end.
(* Conversion from nvec functions to wvec functions *)
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