19bd0254c3
This PR moves `String.utf8EncodeChar` to the prelude to prepare for the imminent redefinition of `String`. The definition in the prelude uses modulo and division operations on natural numbers. In `String.Extra`, a `csimp` lemma is provided, showing that the new definition is equal to the previous one (which is now called `utf8EncodeCharFast`) which uses bitwise operations on `UInt8`.
56 lines
1.3 KiB
Text
56 lines
1.3 KiB
Text
/-
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Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
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-/
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module
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prelude
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public import Init.Data.Fin.Basic
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public section
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set_option linter.missingDocs true
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/-!
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This module exists to provide the very basic `BitVec` definitions required for
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`Init.Data.UInt.BasicAux`.
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-/
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namespace BitVec
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section Nat
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instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
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/-- Return the bound in terms of toNat. -/
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theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
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grind_pattern isLt => x.toNat, 2^w
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end Nat
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section arithmetic
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/--
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Adds two bitvectors. This can be interpreted as either signed or unsigned addition modulo `2^n`.
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Usually accessed via the `+` operator.
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SMT-LIB name: `bvadd`.
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-/
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@[expose]
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protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
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instance : Add (BitVec n) := ⟨BitVec.add⟩
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/--
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Subtracts one bitvector from another. This can be interpreted as either signed or unsigned subtraction
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modulo `2^n`. Usually accessed via the `-` operator.
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-/
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@[expose]
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protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
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instance : Sub (BitVec n) := ⟨BitVec.sub⟩
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end arithmetic
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end BitVec
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