https://github.com/advancedresearch/pocket_prover-set

A base logical system for PocketProver to reason about set properties
https://github.com/advancedresearch/pocket_prover-set

Last synced: about 1 month ago
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A base logical system for PocketProver to reason about set properties

• Host: GitHub
• URL: https://github.com/advancedresearch/pocket_prover-set
• Owner: advancedresearch
• License: mit
• Created: 2018-02-23T09:43:34.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2022-10-07T21:46:59.000Z (over 1 year ago)
• Last Synced: 2024-05-21T02:16:28.596Z (about 1 month ago)
• Language: Rust
• Size: 13.7 KB
• Stars: 1
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Funding: .github/FUNDING.yml
  • License: LICENSE

Lists

• awesome-rust-formalized-reasoning - pocket_prover-set - set) - base logical system for PocketProver to reason about set properties. (Projects / Verification)

README

        
# pocket_prover-set

A base logical system for PocketProver to reason about set properties

```rust

extern crate pocket_prover;

extern crate pocket_prover_set;

use pocket_prover::*;

use pocket_prover_set::*;

fn main() {

    println!("Result {}", Set::imply(

        |s| s.fin_many,

        |s| not(s.inf_many)

    ));

}

```

There are 4 bits of information, used to derive all other properties:

- `any` - All types, including those not defined

- `uniq` - A unique value

- `fin_many` - Many but finite number of values

- `inf_many` - Many but infinite number of values

A set is empty (`.none()`) when all bits are set to 0.

A set is non-empty (`.some()`) when at least bit is set to 1.

A set is undefined when it is `any` but neither unique, finite or infinite.

Here is an example of a proof of 8 sets:

```rust

extern crate pocket_prover;

extern crate pocket_prover_set;

use pocket_prover::*;

use pocket_prover_set::*;

fn main() {

    println!("Result {}", <(Set, Set, Set, Set, Set, Set, Set, Set)>::imply(

        |sets| and(sets.uniqs(|xs| xorn(xs)), sets.0.uniq),

        |sets| not(sets.7.uniq)

    ));

}

```