Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
fbb3055f82
The key idea is to notice that `signExtend` behavior is controlled by
the `msb`. When `msb = false`, `sext` behaves the same as `trunc`. When
`msb = true`, `sext` behaves like `trunc` but adds high 1-bits. This is
expressed using the negate-truncate-negate pattern. Lemma statements
below:
```lean
theorem signExtend_eq_neg_truncate_neg_of_msb_false {x : BitVec w} {v : Nat} (hmsb : x.msb = false) :
(x.signExtend v) = x.truncate v := by
theorem signExtend_eq_neg_truncate_neg_of_msb_true {x : BitVec w} {v : Nat} (hmsb : x.msb = true) :
(x.signExtend v) = ~~~((~~~x).truncate v) := by
```
These give the final theorem statement:
```lean
theorem getLsb_signExtend {x : BitVec w} {v i : Nat} :
(x.signExtend v).getLsb i = (decide (i < v) && if i < w then x.getLsb i else x.msb) := by
```
---------
Co-authored-by: Tobias Grosser <github@grosser.es>
Co-authored-by: Alex Keizer <alex@keizer.dev>
Co-authored-by: Kim Morrison <scott@tqft.net>
|
||
|---|---|---|
| .github | ||
| doc | ||
| images | ||
| nix | ||
| releases_drafts | ||
| script | ||
| src | ||
| stage0 | ||
| tests | ||
| .gitattributes | ||
| .gitignore | ||
| .ignore | ||
| CMakeLists.txt | ||
| CMakePresets.json | ||
| CODEOWNERS | ||
| CONTRIBUTING.md | ||
| flake.lock | ||
| flake.nix | ||
| lean-toolchain | ||
| lean.code-workspace | ||
| LICENSE | ||
| LICENSES | ||
| README.md | ||
| RELEASES.md | ||
This is the repository for Lean 4.
About
- Quickstart
- Homepage
- Theorem Proving Tutorial
- Functional Programming in Lean
- Manual
- Release notes starting at v4.0.0-m3
- Examples
- External Contribution Guidelines
- FAQ
Installation
See Setting Up Lean.
Contributing
Please read our Contribution Guidelines first.
Building from Source
See Building Lean (documentation source: doc/make/index.md).