feat: make <num>#<term> bitvector literal notation global
chore: `toFin_ofNat`
This commit is contained in:
Leonardo de Moura
Kim Morrison
parent
faea7f98c1
commit
0d30517dca
2 changed files with 20 additions and 20 deletions
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@ -151,12 +151,12 @@ end Int
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section Syntax
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/-- Notation for bit vector literals. `i#n` is a shorthand for `BitVec.ofNat n i`. -/
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scoped syntax:max term:max noWs "#" noWs term:max : term
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macro_rules | `($i#$n) => `(BitVec.ofNat $n $i)
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syntax:max num noWs "#" noWs term:max : term
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macro_rules | `($i:num#$n) => `(BitVec.ofNat $n $i)
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/-- Unexpander for bit vector literals. -/
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@[app_unexpander BitVec.ofNat] def unexpandBitVecOfNat : Lean.PrettyPrinter.Unexpander
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| `($(_) $n $i) => `($i#$n)
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| `($(_) $n $i:num) => `($i:num#$n)
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| _ => throw ()
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/-- Notation for bit vector literals without truncation. `i#'lt` is a shorthand for `BitVec.ofNatLt i lt`. -/
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@ -504,7 +504,7 @@ equivalent to `a * 2^s`, modulo `2^n`.
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SMT-Lib name: `bvshl` except this operator uses a `Nat` shift value.
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-/
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protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := (a.toNat <<< s)#n
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protected def shiftLeft (a : BitVec n) (s : Nat) : BitVec n := BitVec.ofNat n (a.toNat <<< s)
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instance : HShiftLeft (BitVec w) Nat (BitVec w) := ⟨.shiftLeft⟩
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/--
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@ -139,15 +139,15 @@ theorem ofBool_eq_iff_eq : ∀(b b' : Bool), BitVec.ofBool b = BitVec.ofBool b'
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getLsb (x#'lt) i = x.testBit i := by
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simp [getLsb, BitVec.ofNatLt]
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@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (x#w).toNat = x % 2^w := by
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@[simp, bv_toNat] theorem toNat_ofNat (x w : Nat) : (BitVec.ofNat w x).toNat = x % 2^w := by
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simp [BitVec.toNat, BitVec.ofNat, Fin.ofNat']
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@[simp] theorem toFin_ofNat (x : Nat) : toFin x#w = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
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@[simp] theorem toFin_ofNat (x : Nat) : toFin (BitVec.ofNat w x) = Fin.ofNat' x (Nat.two_pow_pos w) := rfl
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-- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
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-- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
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theorem getLsb_ofNat (n : Nat) (x : Nat) (i : Nat) :
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getLsb (x#n) i = (i < n && x.testBit i) := by
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getLsb (BitVec.ofNat n x) i = (i < n && x.testBit i) := by
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simp [getLsb, BitVec.ofNat, Fin.val_ofNat']
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@[simp, deprecated toNat_ofNat (since := "2024-02-22")]
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@ -316,19 +316,19 @@ theorem zeroExtend'_eq {x : BitVec w} (h : w ≤ v) : x.zeroExtend' h = x.zeroEx
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let ⟨x, lt_n⟩ := x
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simp [truncate, zeroExtend]
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@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m (0#n) = 0#m := by
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@[simp] theorem zeroExtend_zero (m n : Nat) : zeroExtend m 0#n = 0#m := by
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apply eq_of_toNat_eq
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simp [toNat_zeroExtend]
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@[simp] theorem truncate_eq (x : BitVec n) : truncate n x = x := zeroExtend_eq x
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@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : x.toNat#m = truncate m x := by
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@[simp] theorem ofNat_toNat (m : Nat) (x : BitVec n) : BitVec.ofNat m x.toNat = truncate m x := by
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apply eq_of_toNat_eq
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simp
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/-- Moves one-sided left toNat equality to BitVec equality. -/
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theorem toNat_eq_nat (x : BitVec w) (y : Nat)
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: (x.toNat = y) ↔ (y < 2^w ∧ (x = y#w)) := by
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: (x.toNat = y) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
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apply Iff.intro
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· intro eq
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simp at eq
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@ -340,7 +340,7 @@ theorem toNat_eq_nat (x : BitVec w) (y : Nat)
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/-- Moves one-sided right toNat equality to BitVec equality. -/
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theorem nat_eq_toNat (x : BitVec w) (y : Nat)
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: (y = x.toNat) ↔ (y < 2^w ∧ (x = y#w)) := by
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: (y = x.toNat) ↔ (y < 2^w ∧ (x = BitVec.ofNat w y)) := by
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rw [@eq_comm _ _ x.toNat]
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apply toNat_eq_nat
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@ -416,7 +416,7 @@ protected theorem extractLsb_ofFin {n} (x : Fin (2^n)) (hi lo : Nat) :
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@[simp]
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protected theorem extractLsb_ofNat (x n : Nat) (hi lo : Nat) :
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extractLsb hi lo x#n = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
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extractLsb hi lo (BitVec.ofNat n x) = .ofNat (hi - lo + 1) ((x % 2^n) >>> lo) := by
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apply eq_of_getLsb_eq
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intro ⟨i, _lt⟩
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simp [BitVec.ofNat]
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@ -1008,10 +1008,10 @@ Definition of bitvector addition as a nat.
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@[simp] theorem add_ofFin (x : BitVec n) (y : Fin (2^n)) :
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x + .ofFin y = .ofFin (x.toFin + y) := rfl
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theorem ofNat_add {n} (x y : Nat) : (x + y)#n = x#n + y#n := by
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theorem ofNat_add {n} (x y : Nat) : BitVec.ofNat n (x + y) = BitVec.ofNat n x + BitVec.ofNat n y := by
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apply eq_of_toNat_eq ; simp [BitVec.ofNat]
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theorem ofNat_add_ofNat {n} (x y : Nat) : x#n + y#n = (x + y)#n :=
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theorem ofNat_add_ofNat {n} (x y : Nat) : BitVec.ofNat n x + BitVec.ofNat n y = BitVec.ofNat n (x + y) :=
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(ofNat_add x y).symm
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protected theorem add_assoc (x y z : BitVec n) : x + y + z = x + (y + z) := by
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@ -1057,10 +1057,10 @@ theorem sub_def {n} (x y : BitVec n) : x - y = .ofNat n (x.toNat + (2^n - y.toNa
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rfl
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-- Remark: we don't use `[simp]` here because simproc` subsumes it for literals.
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-- If `x` and `n` are not literals, applying this theorem eagerly may not be a good idea.
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theorem ofNat_sub_ofNat {n} (x y : Nat) : x#n - y#n = .ofNat n (x + (2^n - y % 2^n)) := by
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theorem ofNat_sub_ofNat {n} (x y : Nat) : BitVec.ofNat n x - BitVec.ofNat n y = .ofNat n (x + (2^n - y % 2^n)) := by
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apply eq_of_toNat_eq ; simp [BitVec.ofNat]
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@[simp] protected theorem sub_zero (x : BitVec n) : x - (0#n) = x := by apply eq_of_toNat_eq ; simp
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@[simp] protected theorem sub_zero (x : BitVec n) : x - 0#n = x := by apply eq_of_toNat_eq ; simp
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@[simp] protected theorem sub_self (x : BitVec n) : x - x = 0#n := by
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apply eq_of_toNat_eq
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@ -1080,7 +1080,7 @@ theorem sub_toAdd {n} (x y : BitVec n) : x - y = x + - y := by
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apply eq_of_toNat_eq
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simp
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@[simp] theorem neg_zero (n:Nat) : -0#n = 0#n := by apply eq_of_toNat_eq ; simp
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@[simp] theorem neg_zero (n:Nat) : -BitVec.ofNat n 0 = BitVec.ofNat n 0 := by apply eq_of_toNat_eq ; simp
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theorem add_sub_cancel (x y : BitVec w) : x + y - y = x := by
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apply eq_of_toNat_eq
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@ -1157,7 +1157,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
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x ≤ BitVec.ofFin y ↔ x.toFin ≤ y := Iff.rfl
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@[simp] theorem ofFin_le (x : Fin (2^n)) (y : BitVec n) :
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BitVec.ofFin x ≤ y ↔ x ≤ y.toFin := Iff.rfl
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@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (x#n) ≤ (y#n) ↔ x % 2^n ≤ y % 2^n := by
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@[simp] theorem ofNat_le_ofNat {n} (x y : Nat) : (BitVec.ofNat n x) ≤ (BitVec.ofNat n y) ↔ x % 2^n ≤ y % 2^n := by
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simp [le_def]
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@[bv_toNat] theorem lt_def (x y : BitVec n) :
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@ -1167,7 +1167,7 @@ theorem ofInt_mul {n} (x y : Int) : BitVec.ofInt n (x * y) =
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x < BitVec.ofFin y ↔ x.toFin < y := Iff.rfl
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@[simp] theorem ofFin_lt (x : Fin (2^n)) (y : BitVec n) :
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BitVec.ofFin x < y ↔ x < y.toFin := Iff.rfl
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@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : (x#n) < (y#n) ↔ x % 2^n < y % 2^n := by
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@[simp] theorem ofNat_lt_ofNat {n} (x y : Nat) : BitVec.ofNat n x < BitVec.ofNat n y ↔ x % 2^n < y % 2^n := by
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simp [lt_def]
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protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x < y := by
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@ -1180,7 +1180,7 @@ protected theorem lt_of_le_ne (x y : BitVec n) (h1 : x <= y) (h2 : ¬ x = y) : x
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/-! ### intMax -/
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/-- The bitvector of width `w` that has the largest value when interpreted as an integer. -/
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def intMax (w : Nat) : BitVec w := (2^w - 1)#w
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def intMax (w : Nat) : BitVec w := BitVec.ofNat w (2^w - 1)
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theorem getLsb_intMax_eq (w : Nat) : (intMax w).getLsb i = decide (i < w) := by
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simp [intMax, getLsb]
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