relmath

relmath is the G1 library crate inside the relmath-rs repository.

It provides exact finite unary and binary relations with deterministic BTreeSet-backed iteration order.

Current G1 Surface

The current public API covers:

• UnaryRelation<T> for finite unary relations (sets)
• BinaryRelation<A, B> for finite binary relations
• union, intersection, and difference
• domain, range, converse, and composition
• domain/range restriction plus image/preimage with unary relations
• identity on a carrier
• transitive and reflexive-transitive closure on homogeneous relations
• relation property checks for reflexivity, irreflexivity, symmetry, antisymmetry, transitivity, equivalence, and partial order

Composition uses relational order:

• r.compose(&s) means r ; s
• the result contains (a, c) when some b satisfies (a, b) in r and (b, c) in s

Current Limits

This crate currently implements the exact G1 core only:

• no n-ary relations
• no weighted or temporal relations
• no solver-backed or symbolic evaluation

The repository ships three focused examples under examples/:

• family for ancestry and reachability
• access_control for role-permission propagation
• workflow for state reachability

Example

use relmath::{BinaryRelation, UnaryRelation};

let parent = BinaryRelation::from_pairs([
    ("Ada", "Bob"),
    ("Bob", "Cara"),
]);

let people = UnaryRelation::from_values(["Ada", "Bob", "Cara", "Finn"]);
let grandparent = parent.compose(&parent);
let ancestor_or_self = parent.reflexive_transitive_closure(&people);

assert_eq!(grandparent.to_vec(), vec![("Ada", "Cara")]);
assert!(ancestor_or_self.contains(&"Ada", &"Cara"));
assert!(ancestor_or_self.contains(&"Finn", &"Finn"));

Status

This crate is the exact unary/binary relation core for the first public G1 release candidate.