From 1432318faa4cb6a50eca2c7a371b43b3b9969666 Mon Sep 17 00:00:00 2001 From: Pierre Boutillier Date: Fri, 25 Apr 2014 16:17:15 +0200 Subject: Pos.iter arguments in a better order for cbn. --- theories/ZArith/BinInt.v | 6 +++--- theories/ZArith/BinIntDef.v | 8 ++++---- theories/ZArith/Zpow_alt.v | 6 +++--- theories/ZArith/Zpower.v | 14 +++++++------- 4 files changed, 17 insertions(+), 17 deletions(-) (limited to 'theories/ZArith') diff --git a/theories/ZArith/BinInt.v b/theories/ZArith/BinInt.v index 6948d420a..452e3d148 100644 --- a/theories/ZArith/BinInt.v +++ b/theories/ZArith/BinInt.v @@ -959,7 +959,7 @@ Proof. destruct m; easy || now destruct Hm. destruct a as [ |a|a]. (* a = 0 *) - replace (Pos.iter n div2 0) with 0 + replace (Pos.iter div2 0 n) with 0 by (apply Pos.iter_invariant; intros; subst; trivial). now rewrite 2 testbit_0_l. (* a > 0 *) @@ -982,7 +982,7 @@ Proof. rewrite ?Pos.iter_succ; apply testbit_even_0. destruct a as [ |a|a]. (* a = 0 *) - replace (Pos.iter n (mul 2) 0) with 0 + replace (Pos.iter (mul 2) 0 n) with 0 by (apply Pos.iter_invariant; intros; subst; trivial). apply testbit_0_l. (* a > 0 *) @@ -1013,7 +1013,7 @@ Proof. f_equal. now rewrite Pos.add_comm, Pos.add_sub. destruct a; unfold shiftl. (* ... a = 0 *) - replace (Pos.iter n (mul 2) 0) with 0 + replace (Pos.iter (mul 2) 0 n) with 0 by (apply Pos.iter_invariant; intros; subst; trivial). now rewrite 2 testbit_0_l. (* ... a > 0 *) diff --git a/theories/ZArith/BinIntDef.v b/theories/ZArith/BinIntDef.v index 958ce2ef7..4e7fdcdff 100644 --- a/theories/ZArith/BinIntDef.v +++ b/theories/ZArith/BinIntDef.v @@ -126,7 +126,7 @@ Infix "*" := mul : Z_scope. (** ** Power function *) -Definition pow_pos (z:Z) (n:positive) := Pos.iter n (mul z) 1. +Definition pow_pos (z:Z) := Pos.iter (mul z) 1. Definition pow x y := match y with @@ -306,7 +306,7 @@ Definition to_pos (z:Z) : positive := Definition iter (n:Z) {A} (f:A -> A) (x:A) := match n with - | pos p => Pos.iter p f x + | pos p => Pos.iter f x p | _ => x end. @@ -568,8 +568,8 @@ Definition testbit a n := Definition shiftl a n := match n with | 0 => a - | pos p => Pos.iter p (mul 2) a - | neg p => Pos.iter p div2 a + | pos p => Pos.iter (mul 2) a p + | neg p => Pos.iter div2 a p end. Definition shiftr a n := shiftl a (-n). diff --git a/theories/ZArith/Zpow_alt.v b/theories/ZArith/Zpow_alt.v index f3eb63a8a..73b1989e4 100644 --- a/theories/ZArith/Zpow_alt.v +++ b/theories/ZArith/Zpow_alt.v @@ -30,12 +30,12 @@ Infix "^^" := Zpower_alt (at level 30, right associativity) : Z_scope. Lemma Piter_mul_acc : forall f, (forall x y:Z, (f x)*y = f (x*y)) -> - forall p k, Pos.iter p f k = (Pos.iter p f 1)*k. + forall p k, Pos.iter f k p = (Pos.iter f 1 p)*k. Proof. intros f Hf. induction p; simpl; intros. - - set (g := Pos.iter p f 1) in *. now rewrite !IHp, Hf, Z.mul_assoc. - - set (g := Pos.iter p f 1) in *. now rewrite !IHp, Z.mul_assoc. + - set (g := Pos.iter f 1 p) in *. now rewrite !IHp, Hf, Z.mul_assoc. + - set (g := Pos.iter f 1 p) in *. now rewrite !IHp, Z.mul_assoc. - now rewrite Hf, Z.mul_1_l. Qed. diff --git a/theories/ZArith/Zpower.v b/theories/ZArith/Zpower.v index 7ccaa119c..1da3c7992 100644 --- a/theories/ZArith/Zpower.v +++ b/theories/ZArith/Zpower.v @@ -95,11 +95,11 @@ Section Powers_of_2. [m] shifted by [n] positions *) Definition shift_nat (n:nat) (z:positive) := nat_rect _ z (fun _ => xO) n. - Definition shift_pos (n z:positive) := Pos.iter n xO z. + Definition shift_pos (n z:positive) := Pos.iter xO z n. Definition shift (n:Z) (z:positive) := match n with | Z0 => z - | Zpos p => Pos.iter p xO z + | Zpos p => Pos.iter xO z p | Zneg p => z end. @@ -247,10 +247,10 @@ Section power_div_with_rest. end, 2 * d). Definition Zdiv_rest (x:Z) (p:positive) := - let (qr, d) := Pos.iter p Zdiv_rest_aux (x, 0, 1) in qr. + let (qr, d) := Pos.iter Zdiv_rest_aux (x, 0, 1) p in qr. Lemma Zdiv_rest_correct1 (x:Z) (p:positive) : - let (_, d) := Pos.iter p Zdiv_rest_aux (x, 0, 1) in + let (_, d) := Pos.iter Zdiv_rest_aux (x, 0, 1) p in d = two_power_pos p. Proof. rewrite Pos2Nat.inj_iter, two_power_pos_nat. @@ -260,7 +260,7 @@ Section power_div_with_rest. Qed. Lemma Zdiv_rest_correct2 (x:Z) (p:positive) : - let '(q,r,d) := Pos.iter p Zdiv_rest_aux (x, 0, 1) in + let '(q,r,d) := Pos.iter Zdiv_rest_aux (x, 0, 1) p in x = q * d + r /\ 0 <= r < d. Proof. apply Pos.iter_invariant; [|omega]. @@ -287,7 +287,7 @@ Section power_div_with_rest. Lemma Zdiv_rest_correct (x:Z) (p:positive) : Zdiv_rest_proofs x p. Proof. generalize (Zdiv_rest_correct1 x p); generalize (Zdiv_rest_correct2 x p). - destruct (Pos.iter p Zdiv_rest_aux (x, 0, 1)) as ((q,r),d). + destruct (Pos.iter Zdiv_rest_aux (x, 0, 1) p) as ((q,r),d). intros (H1,(H2,H3)) ->. now exists q r. Qed. @@ -299,7 +299,7 @@ Section power_div_with_rest. Proof. unfold Zdiv_rest. generalize (Zdiv_rest_correct1 x p); generalize (Zdiv_rest_correct2 x p). - destruct (Pos.iter p Zdiv_rest_aux (x, 0, 1)) as ((q,r),d). + destruct (Pos.iter Zdiv_rest_aux (x, 0, 1) p) as ((q,r),d). intros H ->. now rewrite two_power_pos_equiv in H. Qed. -- cgit v1.2.3