Pergola

This is a small crate that provides a generic unital-join-semilattice type (hereafter: "lattice") along with a few common instances.

Lattices are defined in two separate pieces: a definition trait LatticeDef that provides the type-and-functions for a given lattice and a user interface struct LatticeElt that's parameterized by a LatticeDef and provides convenient methods to work with (including impls of standard Rust operator traits).

This unusual split exists because many types have multiple equally viable lattices you can build on them (eg. u32-with-min or u32-with-max) and we want to avoid both coupling any given lattice definition to the type or accidentally inheriting an impl for any of the type's "standard semantics" as the lattice semantics, eg. we don't want to inherit u32's standard partial order as any lattice's partial order, unless explicitly building such a lattice.

Examples

Simple u32-with-max lattice

use pergola::{MaxDef,LatticeElt};

type Def = MaxDef<u32>;      // lattice def for "u32 with max for join"
type Elt = LatticeElt<Def>;  // element struct, implementing std traits
let v = Elt::new_from(1);
let u = Elt::new_from(2);
let w = v + u;               // calls join(), which calls max()
assert!(v < u);
assert!(v < w);

Composite tuple lattice

use pergola::{MaxDef,Tuple3,LatticeElt};

type NumDef = MaxDef<u32>;
type NumElt = LatticeElt<NumDef>;
type TupDef = Tuple3<NumDef,NumDef,NumDef>;
type TupElt = LatticeElt<TupDef>;
let n1: NumElt = (1).into();
let n2: NumElt = (2).into();
let n3: NumElt = (3).into();
let tup: TupElt = (n1, n2, n3).into();
assert!(tup.value.0 < tup.value.1);
assert!((tup.value.0 + tup.value.1) == tup.value.1);
let n1ref: &NumElt = &tup.value.0;
let n2ref: &NumElt = &tup.value.1;
assert!(n1ref < n2ref);

Trickier union-map-of-union-bitsets lattice

use pergola::{BTreeMapWithUnion,BitSetWithUnion,LatticeElt};
use bit_set::BitSet;
use std::collections::BTreeMap;

type Def = BTreeMapWithUnion<String,BitSetWithUnion>;
type Elt = LatticeElt<Def>;
let bs_a1 = BitSet::from_bytes(&[0b11110000]);
let bs_a2 = BitSet::from_bytes(&[0b00001111]);
let bs_b = BitSet::from_bytes(&[0b10101010]);
let v = Elt::new_from([(String::from("a"),bs_a1.into()),
                       (String::from("b"),bs_b.into())].iter().cloned().collect());
let u = Elt::new_from([(String::from("a"),bs_a2.into())].iter().cloned().collect());
let w = &v + &u;
assert!(!(v < u));  // bs_a1 is not a subset of bs_a2,
                    // so v["a"] is unordered wrt. u["a"].
assert!(v < w);     // However, w is a join and join unions
                    // the values at common keys, so v["a"] < w["a"].
assert!(u < w);     // And likewise the other input to the join.
assert_eq!(w.value["a"].value.0, BitSet::from_bytes(&[0b11111111]));
assert_eq!(w.value["b"].value.0, BitSet::from_bytes(&[0b10101010]));

Name

Wikipedia:

A pergola is an outdoor garden feature forming a shaded walkway, passageway, or sitting area of vertical posts or pillars that usually support cross-beams and a sturdy open lattice, often upon which woody vines are trained.