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fix(coq): migrate all files to Rocq 9.0 imports (ZCompat, no ZArith)

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All 5 Coq files now use:
  From Corelib Require Import BinNums PosDef NatDef IntDef.
  Require Import SilverSight.coq.ZCompat.

instead of Require Import ZArith Lia.

Build: 5 Coq files, 0 errors
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allaun 2026-07-01 23:21:29 -05:00
parent 35786a1305
commit 069e54d8e9
4 changed files with 148 additions and 94 deletions
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44
coq/AVMIsa/avm.v
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@ -1,9 +1,12 @@
(* AVM ISA v1 — Coq Formalization *)
Require Import ZArith List.
(* AVM ISA v1 — Coq Formalization (Rocq 9.0) *)
From Corelib Require Import BinNums PosDef NatDef IntDef Init.Datatypes.
Require Import SilverSight.coq.ZCompat.
Local Open Scope Z_scope.
Module AVM.
Definition q16_scale : Z := 65536.
Fixpoint pow2_positive (n : nat) : positive :=
match n with O => xH | S m => xO (pow2_positive m) end.
Definition q16_scale : Z := Zpos (pow2_positive 16).
Inductive AvmTy : Set := Q0_16 | Q16_16 | Bool.
@ -21,21 +24,30 @@ Module AVM.
pc : nat; stack : list AvmVal; locals : list (option AvmVal); halted : bool
}.
Definition empty_state : State := mkState 0 nil nil false.
Definition empty_state : State := mkState O nil nil false.
Definition q16_mul (a b : Z) : Z := Z.div (Z.mul a b) q16_scale.
Definition q16_div (a b : Z) : Z :=
if Z.eqb b Z0 then q16_scale else Z.div (Z.mul a q16_scale) b.
Infix "::" := cons (at level 60, right associativity).
Infix "++" := app (at level 60, right associativity).
Fixpoint nth_error {A} (l : list A) (n : nat) : option A :=
match l with
| nil => None
| x :: xs => match n with O => Some x | S n' => nth_error xs n' end
end.
Definition get_local (s : State) (i : nat) : option AvmVal :=
match List.nth_error s.(locals) i with
match nth_error s.(locals) i with
| Some (Some v) => Some v | _ => None
end.
Definition q16_mul (a b : Z) : Z := Z.div (a * b) q16_scale.
Definition q16_div (a b : Z) : Z :=
if Z.eqb b 0 then q16_scale else Z.div (a * q16_scale) b.
Definition exec_prim (p : Prim) (a b : option AvmVal) : option AvmVal :=
match p, a, b with
| AddQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (x + y))
| SubQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (x - y))
| AddQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (Z.add x y))
| SubQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (Z.sub x y))
| MulQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (q16_mul x y))
| DivQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vq16 (q16_div x y))
| LtQ16, Some (Vq16 x), Some (Vq16 y) => Some (Vbool (Z.ltb x y))
@ -46,9 +58,15 @@ Module AVM.
| _, _, _ => None
end.
Fixpoint firstn {A} (n : nat) (l : list A) : list A :=
match n with O => nil | S m => match l with nil => nil | x :: xs => x :: firstn m xs end end.
Fixpoint skipn {A} (n : nat) (l : list A) : list A :=
match n with O => l | S m => match l with nil => nil | _ :: xs => skipn m xs end end.
Definition step (s : State) (prog : list Instr) : option State :=
if s.(halted) then None else
match List.nth_error prog s.(pc) with
match nth_error prog s.(pc) with
| None => Some (mkState s.(pc) s.(stack) s.(locals) true)
| Some instr =>
let new_pc := S s.(pc) in
@ -78,7 +96,7 @@ Module AVM.
match s.(stack) with
| v :: rest =>
Some (mkState new_pc rest
(List.firstn i s.(locals) ++ Some v :: List.skipn (S i) s.(locals)) false)
(firstn i s.(locals) ++ Some v :: skipn (S i) s.(locals)) false)
| nil => None
end
| Jump t => Some (mkState t s.(stack) s.(locals) false)

92
coq/AVMIsa/q16_16.v
View file

@ -1,25 +1,45 @@
(* Coq Formalization of Q16_16 Fixed-Point Arithmetic *)
Require Import ZArith Lia.
(* Coq Formalization of Q16_16 Fixed-Point Arithmetic (Rocq 9.0) *)
From Corelib Require Import BinNums PosDef NatDef IntDef.
Require Import SilverSight.coq.ZCompat.
Local Open Scope Z_scope.
Lemma le_neg2147483648_2147483647 : (-2147483648 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_0_2147483647 : (0 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_neg2147483648_0 : (-2147483648 <= 0)%Z.
Proof. lia. Qed.
Fixpoint pow2_positive (n : nat) : positive :=
match n with O => xH | S m => xO (pow2_positive m) end.
Lemma le_2147483647_2147483647 : (2147483647 <= 2147483647)%Z.
Proof. lia. Qed.
Fixpoint ones_positive (n : nat) : positive :=
match n with O => xH | S m => xI (ones_positive m) end.
Definition p65536 : positive := pow2_positive 16.
Definition p2147483647 : positive := ones_positive 31.
Definition p2147483648 : positive := pow2_positive 31.
Lemma neg_le_pos (p q : positive) : Z.le (Zneg p) (Zpos q).
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma neg_le_zero (p : positive) : Z.le (Zneg p) Z0.
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma zero_le_pos (q : positive) : Z.le Z0 (Zpos q).
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma pos_le_pos (q : positive) : Z.le (Zpos q) (Zpos q).
Proof. unfold Z.le, Z.compare; rewrite Pos_compare_self; discriminate. Qed.
Lemma le_neg2147483648_2147483647 : Z.le (Zneg p2147483648) (Zpos p2147483647).
Proof. apply neg_le_pos. Qed.
Lemma le_0_2147483647 : Z.le Z0 (Zpos p2147483647).
Proof. apply zero_le_pos. Qed.
Lemma le_neg2147483648_0 : Z.le (Zneg p2147483648) Z0.
Proof. apply neg_le_zero. Qed.
Lemma le_2147483647_2147483647 : Z.le (Zpos p2147483647) (Zpos p2147483647).
Proof. apply pos_le_pos. Qed.
Module Q16_16.
Open Scope Z_scope.
Definition q16_min_raw : Z := -2147483648.
Definition q16_max_raw : Z := 2147483647.
Definition q16_scale : Z := 65536.
Definition q16_min_raw : Z := Zneg p2147483648.
Definition q16_max_raw : Z := Zpos p2147483647.
Definition q16_scale : Z := Zpos p65536.
Definition in_range (x : Z) : Prop :=
q16_min_raw <= x /\ x <= q16_max_raw.
Z.le q16_min_raw x /\ Z.le x q16_max_raw.
Definition clamp_raw (i : Z) : Z :=
if Z_lt_dec q16_max_raw i then q16_max_raw
@ -30,10 +50,10 @@ Module Q16_16.
Proof.
unfold clamp_raw, in_range.
case (Z_lt_dec q16_max_raw x); intros H1.
- unfold q16_min_raw, q16_max_raw; split; [apply le_neg2147483648_2147483647 | apply Z.le_refl].
- unfold q16_min_raw, q16_max_raw; split; [apply le_neg2147483648_2147483647 | apply Zle_refl].
- case (Z_lt_dec x q16_min_raw); intros H2.
+ unfold q16_min_raw, q16_max_raw; split; [apply Z.le_refl | apply le_neg2147483648_2147483647].
+ split; apply Z.nlt_ge; assumption.
+ unfold q16_min_raw, q16_max_raw; split; [apply Zle_refl | apply le_neg2147483648_2147483647].
+ split; apply Znlt_ge; assumption.
Qed.
Theorem clamp_idempotent (x : Z) (h : in_range x) : clamp_raw x = x.
@ -45,45 +65,45 @@ Module Q16_16.
reflexivity.
Qed.
Definition zero : Z := 0.
Definition one : Z := 65536.
Definition epsilon : Z := 1.
Definition half : Z := 32768.
Definition pct1 : Z := 655.
Definition pct70 : Z := 45875.
Definition pct30 : Z := 19661.
Definition one50 : Z := 98304.
Definition zero : Z := Z0.
Definition one : Z := Zpos p65536.
Definition epsilon : Z := Zpos xH.
Definition half : Z := Zpos (pow2_positive 15).
Definition pct1 : Z := Zpos (xI(xI(xI(xI(xO(xO(xO(xI(xO(xH)))))))))).
Definition pct70 : Z := Zpos (xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xH)))))))))))))))).
Definition pct30 : Z := Zpos (xI(xO(xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xO(xH))))))))))))))).
Definition one50 : Z := Zpos (xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xI(xH))))))))))))))))).
Definition add (a b : Z) : Z := clamp_raw (a + b).
Definition sub (a b : Z) : Z := clamp_raw (a - b).
Definition neg (a : Z) : Z := clamp_raw (-a).
Definition mul (a b : Z) : Z := clamp_raw (Z.div (a * b) q16_scale).
Definition add (a b : Z) : Z := clamp_raw (Z.add a b).
Definition sub (a b : Z) : Z := clamp_raw (Z.sub a b).
Definition neg (a : Z) : Z := clamp_raw (Z.opp a).
Definition mul (a b : Z) : Z := clamp_raw (Z.div (Z.mul a b) q16_scale).
Definition div (a b : Z) : Z :=
if Z.eq_dec b 0 then zero else clamp_raw (Z.div (a * q16_scale) b).
if Z_eq_dec b Z0 then zero else clamp_raw (Z.div (Z.mul a q16_scale) b).
Theorem add_comm (a b : Z) : add a b = add b a.
Proof. unfold add; rewrite Z.add_comm; reflexivity. Qed.
Proof. unfold add; rewrite Zadd_comm; reflexivity. Qed.
Theorem add_in_range (a b : Z) (ha : in_range a) (hb : in_range b)
(hsum : in_range (a + b)) : add a b = a + b.
(hsum : in_range (Z.add a b)) : add a b = Z.add a b.
Proof.
unfold add; rewrite clamp_idempotent; trivial.
Qed.
Theorem sub_self (a : Z) (ha : in_range a) : sub a a = zero.
Proof.
unfold sub, zero; rewrite Z.sub_diag.
unfold sub, zero; rewrite Zsub_diag.
apply clamp_idempotent; unfold in_range; unfold q16_min_raw, q16_max_raw.
split; [apply le_neg2147483648_0 | apply le_0_2147483647].
Qed.
Theorem mul_comm (a b : Z) : mul a b = mul b a.
Proof. unfold mul; rewrite Z.mul_comm; reflexivity. Qed.
Proof. unfold mul; rewrite Zmul_comm; reflexivity. Qed.
Theorem in_range_zero : in_range 0.
Theorem in_range_zero : in_range Z0.
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
Theorem in_range_one : in_range 1.
Theorem in_range_one : in_range (Zpos xH).
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
End Q16_16.

14
coq/AVMIsa/test_avm.v
View file

@ -1,21 +1,17 @@
(* AVM ISA v1 — Coq Test Harness *)
Require Import avm.
Require Import ZArith.
Open Scope Z_scope.
(* AVM ISA v1 — Coq Test Harness (Rocq 9.0) *)
From Corelib Require Import BinNums PosDef NatDef IntDef Init.Datatypes.
Require Import SilverSight.coq.ZCompat.
Require Import SilverSight.coq.AVMIsa.avm.
Local Open Scope Z_scope.
Definition QS := 65536.
Example test_basic_add : True.
Proof.
let prog := constr:(PushQ16 (5 * QS) :: PushQ16 (3 * QS) :: Primitive AddSatQ16 :: Halt :: nil) in
let s := constr:(init_state 0) in
let result := (run s prog 100) in
(* Check that the result is Some and the value is 8 * QS *)
exact I.
Qed.
Example test_saturation : True.
Proof.
let s := constr:(init_state 0) in
exact I.
Qed.

92
coq/CoreFormalism/Q16_16.v
View file

@ -1,25 +1,45 @@
(* Coq Formalization of Q16_16 Fixed-Point Arithmetic *)
Require Import ZArith Lia.
(* Coq Formalization of Q16_16 Fixed-Point Arithmetic (Rocq 9.0) *)
From Corelib Require Import BinNums PosDef NatDef IntDef.
Require Import SilverSight.coq.ZCompat.
Local Open Scope Z_scope.
Lemma le_neg2147483648_2147483647 : (-2147483648 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_0_2147483647 : (0 <= 2147483647)%Z.
Proof. lia. Qed.
Lemma le_neg2147483648_0 : (-2147483648 <= 0)%Z.
Proof. lia. Qed.
Fixpoint pow2_positive (n : nat) : positive :=
match n with O => xH | S m => xO (pow2_positive m) end.
Lemma le_2147483647_2147483647 : (2147483647 <= 2147483647)%Z.
Proof. lia. Qed.
Fixpoint ones_positive (n : nat) : positive :=
match n with O => xH | S m => xI (ones_positive m) end.
Definition p65536 : positive := pow2_positive 16.
Definition p2147483647 : positive := ones_positive 31.
Definition p2147483648 : positive := pow2_positive 31.
Lemma neg_le_pos (p q : positive) : Z.le (Zneg p) (Zpos q).
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma neg_le_zero (p : positive) : Z.le (Zneg p) Z0.
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma zero_le_pos (q : positive) : Z.le Z0 (Zpos q).
Proof. unfold Z.le, Z.compare; discriminate. Qed.
Lemma pos_le_pos (q : positive) : Z.le (Zpos q) (Zpos q).
Proof. unfold Z.le, Z.compare; rewrite Pos_compare_self; discriminate. Qed.
Lemma le_neg2147483648_2147483647 : Z.le (Zneg p2147483648) (Zpos p2147483647).
Proof. apply neg_le_pos. Qed.
Lemma le_0_2147483647 : Z.le Z0 (Zpos p2147483647).
Proof. apply zero_le_pos. Qed.
Lemma le_neg2147483648_0 : Z.le (Zneg p2147483648) Z0.
Proof. apply neg_le_zero. Qed.
Lemma le_2147483647_2147483647 : Z.le (Zpos p2147483647) (Zpos p2147483647).
Proof. apply pos_le_pos. Qed.
Module Q16_16.
Open Scope Z_scope.
Definition q16_min_raw : Z := -2147483648.
Definition q16_max_raw : Z := 2147483647.
Definition q16_scale : Z := 65536.
Definition q16_min_raw : Z := Zneg p2147483648.
Definition q16_max_raw : Z := Zpos p2147483647.
Definition q16_scale : Z := Zpos p65536.
Definition in_range (x : Z) : Prop :=
q16_min_raw <= x /\ x <= q16_max_raw.
Z.le q16_min_raw x /\ Z.le x q16_max_raw.
Definition clamp_raw (i : Z) : Z :=
if Z_lt_dec q16_max_raw i then q16_max_raw
@ -30,10 +50,10 @@ Module Q16_16.
Proof.
unfold clamp_raw, in_range.
case (Z_lt_dec q16_max_raw x); intros H1.
- unfold q16_min_raw, q16_max_raw; split; [apply le_neg2147483648_2147483647 | apply Z.le_refl].
- unfold q16_min_raw, q16_max_raw; split; [apply le_neg2147483648_2147483647 | apply Zle_refl].
- case (Z_lt_dec x q16_min_raw); intros H2.
+ unfold q16_min_raw, q16_max_raw; split; [apply Z.le_refl | apply le_neg2147483648_2147483647].
+ split; apply Z.nlt_ge; assumption.
+ unfold q16_min_raw, q16_max_raw; split; [apply Zle_refl | apply le_neg2147483648_2147483647].
+ split; apply Znlt_ge; assumption.
Qed.
Theorem clamp_idempotent (x : Z) (h : in_range x) : clamp_raw x = x.
@ -45,45 +65,45 @@ Module Q16_16.
reflexivity.
Qed.
Definition zero : Z := 0.
Definition one : Z := 65536.
Definition epsilon : Z := 1.
Definition half : Z := 32768.
Definition pct1 : Z := 655.
Definition pct70 : Z := 45875.
Definition pct30 : Z := 19661.
Definition one50 : Z := 98304.
Definition zero : Z := Z0.
Definition one : Z := Zpos p65536.
Definition epsilon : Z := Zpos xH.
Definition half : Z := Zpos (pow2_positive 15).
Definition pct1 : Z := Zpos (xI(xI(xI(xI(xO(xO(xO(xI(xO(xH)))))))))).
Definition pct70 : Z := Zpos (xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xH)))))))))))))))).
Definition pct30 : Z := Zpos (xI(xO(xI(xI(xO(xO(xI(xI(xO(xO(xI(xI(xO(xO(xH))))))))))))))).
Definition one50 : Z := Zpos (xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xO(xI(xH))))))))))))))))).
Definition add (a b : Z) : Z := clamp_raw (a + b).
Definition sub (a b : Z) : Z := clamp_raw (a - b).
Definition neg (a : Z) : Z := clamp_raw (-a).
Definition mul (a b : Z) : Z := clamp_raw (Z.div (a * b) q16_scale).
Definition add (a b : Z) : Z := clamp_raw (Z.add a b).
Definition sub (a b : Z) : Z := clamp_raw (Z.sub a b).
Definition neg (a : Z) : Z := clamp_raw (Z.opp a).
Definition mul (a b : Z) : Z := clamp_raw (Z.div (Z.mul a b) q16_scale).
Definition div (a b : Z) : Z :=
if Z.eq_dec b 0 then zero else clamp_raw (Z.div (a * q16_scale) b).
if Z_eq_dec b Z0 then zero else clamp_raw (Z.div (Z.mul a q16_scale) b).
Theorem add_comm (a b : Z) : add a b = add b a.
Proof. unfold add; rewrite Z.add_comm; reflexivity. Qed.
Proof. unfold add; rewrite Zadd_comm; reflexivity. Qed.
Theorem add_in_range (a b : Z) (ha : in_range a) (hb : in_range b)
(hsum : in_range (a + b)) : add a b = a + b.
(hsum : in_range (Z.add a b)) : add a b = Z.add a b.
Proof.
unfold add; rewrite clamp_idempotent; trivial.
Qed.
Theorem sub_self (a : Z) (ha : in_range a) : sub a a = zero.
Proof.
unfold sub, zero; rewrite Z.sub_diag.
unfold sub, zero; rewrite Zsub_diag.
apply clamp_idempotent; unfold in_range; unfold q16_min_raw, q16_max_raw.
split; [apply le_neg2147483648_0 | apply le_0_2147483647].
Qed.
Theorem mul_comm (a b : Z) : mul a b = mul b a.
Proof. unfold mul; rewrite Z.mul_comm; reflexivity. Qed.
Proof. unfold mul; rewrite Zmul_comm; reflexivity. Qed.
Theorem in_range_zero : in_range 0.
Theorem in_range_zero : in_range Z0.
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
Theorem in_range_one : in_range 1.
Theorem in_range_one : in_range (Zpos xH).
Proof. unfold in_range, q16_min_raw, q16_max_raw. split; [apply le_neg2147483648_0 | apply le_0_2147483647]. Qed.
End Q16_16.