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>
39 lines
1.3 KiB
Text
39 lines
1.3 KiB
Text
import Std.Tactic.BVDecide
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open BitVec
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theorem cast_unit_1 (x : BitVec 64) : Nat.cast 0 &&& x = 0 := by
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bv_decide
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theorem cast_unit_2 (x : BitVec 64) : x.zeroExtend 32 = (x.zeroExtend 64).zeroExtend 32 := by
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bv_decide
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theorem cast_unit_3 (x : BitVec 64) : x.zeroExtend 128 = (x.zeroExtend 64).zeroExtend 128 := by
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bv_decide
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theorem cast_unit_3' (x : BitVec 64) : x.truncate 128 = (x.truncate 64).zeroExtend 128 := by
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bv_decide
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theorem cast_unit_4 (x y : BitVec 32) : (x.zeroExtend 64).extractLsb 32 0 = (y.zeroExtend 64).extractLsb 32 0 → x = y := by
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bv_decide
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theorem cast_unit_5 (x y : BitVec 64) : (x ++ y).extractLsb 63 0 = (y ++ x).extractLsb 127 64 := by
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bv_decide
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theorem cast_unit_5' (x y : BitVec 64) : (BitVec.append x y).extractLsb 63 0 = (y ++ x).extractLsb 127 64 := by
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bv_decide
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theorem cast_unit_6 (x : BitVec 64) : x.signExtend 32 = (x.signExtend 64).signExtend 32 := by
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bv_decide
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theorem cast_unit_7 (x : BitVec 64) : x.signExtend 128 = (x.signExtend 64).signExtend 128 := by
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bv_decide
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theorem cast_unit_8 (x : BitVec 64) : (x.signExtend 128 = x.zeroExtend 128) ↔ (x.msb = false) := by
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bv_decide
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theorem cast_unit_9 (x : BitVec 32) : (x.replicate 20).zeroExtend 32 = x := by
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bv_decide
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theorem cast_unit_10 (x : BitVec 32) : (x.replicate 20).getLsbD 40 = x.getLsbD 8 := by
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bv_decide
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