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feat: add missing UInt bitwise toNat theorems #6187

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feat: add missing UInt bitwise toNat theorems #6187

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7 changes: 5 additions & 2 deletions src/Init/Data/UInt/Basic.lean
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Expand Up @@ -246,6 +246,9 @@ instance (a b : UInt64) : Decidable (a ≤ b) := UInt64.decLe a b
instance : Max UInt64 := maxOfLe
instance : Min UInt64 := minOfLe

theorem System.Platform.numBits_lt_usize : numBits < USize.size := by
cases numBits_eq <;> simp_all [USize.size]

@[extern "lean_usize_mul"]
def USize.mul (a b : USize) : USize := ⟨a.toBitVec * b.toBitVec⟩
@[extern "lean_usize_div"]
Expand All @@ -261,9 +264,9 @@ def USize.lor (a b : USize) : USize := ⟨a.toBitVec ||| b.toBitVec⟩
@[extern "lean_usize_xor"]
def USize.xor (a b : USize) : USize := ⟨a.toBitVec ^^^ b.toBitVec⟩
@[extern "lean_usize_shift_left"]
def USize.shiftLeft (a b : USize) : USize := ⟨a.toBitVec <<< (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
def USize.shiftLeft (a b : USize) : USize := ⟨a.toBitVec <<< (mod b (USize.ofNatCore System.Platform.numBits System.Platform.numBits_lt_usize)).toBitVec⟩
@[extern "lean_usize_shift_right"]
def USize.shiftRight (a b : USize) : USize := ⟨a.toBitVec >>> (mod b (USize.ofNat System.Platform.numBits)).toBitVec⟩
def USize.shiftRight (a b : USize) : USize := ⟨a.toBitVec >>> (mod b (USize.ofNatCore System.Platform.numBits System.Platform.numBits_lt_usize)).toBitVec⟩
@[extern "lean_uint32_to_usize"]
def UInt32.toUSize (a : UInt32) : USize := USize.ofNat32 a.toBitVec.toNat a.toBitVec.isLt
@[extern "lean_usize_to_uint32"]
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21 changes: 14 additions & 7 deletions src/Init/Data/UInt/Bitwise.lean
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Expand Up @@ -9,17 +9,24 @@ import Init.Data.Fin.Bitwise
import Init.Data.BitVec.Lemmas

set_option hygiene false in
macro "declare_bitwise_uint_theorems" typeName:ident : command =>
macro "declare_bitwise_uint_theorems" typeName:ident bits:term:arg : command =>
let toNat_and := Lean.mkIdentFrom typeName (typeName.getId.modifyBase (·.str "toNat_and"))
`(
namespace $typeName

@[simp] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
@[simp] protected theorem toNat_and (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..
@[simp] protected theorem toNat_or (a b : $typeName) : (a ||| b).toNat = a.toNat ||| b.toNat := BitVec.toNat_or ..
@[simp] protected theorem toNat_xor (a b : $typeName) : (a ^^^ b).toNat = a.toNat ^^^ b.toNat := BitVec.toNat_xor ..
@[simp] protected theorem toNat_shiftLeft (a b : $typeName) : (a <<< b).toNat = a.toNat <<< (b.toNat % $bits) % 2 ^ $bits := BitVec.toNat_shiftLeft
@[simp] protected theorem toNat_shiftRight (a b : $typeName) : (a >>> b).toNat = a.toNat >>> (b.toNat % $bits) := BitVec.toNat_ushiftRight ..

@[deprecated $toNat_and (since := "2024-11-23")] protected theorem and_toNat (a b : $typeName) : (a &&& b).toNat = a.toNat &&& b.toNat := BitVec.toNat_and ..

end $typeName
)

declare_bitwise_uint_theorems UInt8
declare_bitwise_uint_theorems UInt16
declare_bitwise_uint_theorems UInt32
declare_bitwise_uint_theorems UInt64
declare_bitwise_uint_theorems USize
declare_bitwise_uint_theorems UInt8 8
declare_bitwise_uint_theorems UInt16 16
declare_bitwise_uint_theorems UInt32 32
declare_bitwise_uint_theorems UInt64 64
declare_bitwise_uint_theorems USize System.Platform.numBits
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