6b62fed82e
This renames `BitVec.getLsb` to `getLsbD` (`D` for "default" value, i.e.
false), and introduces `getLsb?` and `getLsb'` (which we can rename to
`getLsb` after a deprecation cycle).
(Similarly for `getMsb`.)
Also adds a `GetElem` class so we can use `x[i]` and `x[i]?` notation.
Later, we will turn
```
theorem getLsbD_eq_getElem?_getD (x : BitVec w) (i : Nat) (h : i < w) :
x.getLsbD i = x[i]?.getD false
```
on as a `@[simp]` lemma.
This PR doesn't attempt to demonstrate the benefits, but I think both
arguments are going to get easier, and this will bring the BitVec API
closer in line to List/Array, etc.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
30 lines
872 B
Text
30 lines
872 B
Text
import Std.Tactic.BVDecide
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open BitVec
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theorem bitwise_unit_1 {x y : BitVec 64} : ~~~(x &&& y) = (~~~x ||| ~~~y) := by
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bv_decide
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theorem bitwise_unit_1' {x y : BitVec 64} : ~~~(BitVec.and x y) = ((BitVec.not x) ||| ~~~y) := by
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bv_decide
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theorem bitwise_unit_2 {x : BitVec 64} : x ^^^ x = 0 := by
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bv_decide
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theorem bitwise_unit_2' {x : BitVec 64} : (BitVec.xor x x) = 0 := by
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bv_decide
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theorem bitwise_unit_3 {x : BitVec 64} : (x ^^^ x).getLsbD 32 = false := by
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bv_decide
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theorem bitwise_unit_4 {x : BitVec 64} : (x ^^^ ~~~x).getLsbD 32 = true := by
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bv_decide
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theorem bitwise_unit_5 {x : BitVec 64} : (x ^^^ ~~~x).getLsbD 128 = false := by
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bv_decide
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theorem bitwise_unit_6 {x : BitVec 64} : (x ^^^ ~~~x).getLsbD 63 = (x ^^^ ~~~x).msb := by
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bv_decide
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theorem bitwise_unit_7 (x : BitVec 32) : x ^^^ 123#32 = 123#'(by decide) ^^^ x := by
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bv_decide
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