https://github.com/ufmg-smite/lean-smt

Tactics for discharging Lean goals into SMT solvers.
https://github.com/ufmg-smite/lean-smt

lean4 smt

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Tactics for discharging Lean goals into SMT solvers.

• Host: GitHub
• URL: https://github.com/ufmg-smite/lean-smt
• Owner: ufmg-smite
• License: apache-2.0
• Created: 2021-11-23T20:54:14.000Z (about 3 years ago)
• Default Branch: main
• Last Pushed: 2024-05-23T03:18:18.000Z (8 months ago)
• Last Synced: 2024-05-23T03:39:23.714Z (8 months ago)
• Topics: lean4, smt
• Language: Lean
• Homepage:
• Size: 535 KB
• Stars: 72
• Watchers: 6
• Forks: 16
• Open Issues: 8
• Metadata Files:
  • Readme: README.md
  • License: LICENSE
  • Authors: AUTHORS

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• best-of-lean4 - GitHub - 47% open · ⏱️ 17.12.2024): (Packages)

README

        
# SMT Lean

This project aims to provide Lean tactics that discharge goals into SMT solvers.

It is under active development and is currently in a beta phase. While it is

ready for use, it is important to note that there are still some rough edges and

ongoing improvements being made.

## Supported Theories

`lean-smt` currently supports the theories of Uninterpreted Functions and Linear

Integer/Real Arithmetic with quantifiers. Mathlib is currently required for

Arithmetic. Support for the theory of Bitvectors is at an experimental stage. We

are working on adding support for other theories as well.

## Requirements

`lean-smt` depends on [`lean-cvc5`](https://github.com/abdoo8080/lean-cvc5) FFI,

which currently only supports Linux (x86_64) and macOS (AArch64 and x86_64).

## Usage

To use `lean-smt` in your project, add the following line to your list of

dependencies in `lakefile.lean`:

```lean

require smt from git "https://github.com/ufmg-smite/lean-smt.git" @ "main"

def libcpp : String :=

  if System.Platform.isWindows then "libstdc++-6.dll"

  else if System.Platform.isOSX then "libc++.dylib"

  else "libstdc++.so.6"

package foo where

  moreLeanArgs := #[s!"--load-dynlib={libcpp}"]

  moreGlobalServerArgs := #[s!"--load-dynlib={libcpp}"]

```

`lean-smt` comes with one main tactic, `smt`, that translates the current goal

into an SMT query, sends the query to cvc5, and (if the solver returns `unsat`)

replays cvc5's proof in Lean. cvc5's proofs sometimes contain holes, which are

sent back to the user as Lean goals. The user can then fill in these holes

manually or by using other tactics.

### Example

To use the `smt` tactic, you just need to import the `Smt` library:

```lean

import Smt

example {U : Type} [Nonempty U] {f : U → U → U} {a b c d : U}

  (h0 : a = b) (h1 : c = d) (h2 : p1 ∧ True) (h3 : (¬ p1) ∨ (p2 ∧ p3))

  (h4 : (¬ p3) ∨ (¬ (f a c = f b d))) : False := by

  smt [h0, h1, h2, h3, h4]

```