# 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

```rust
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
```rust
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

```rust
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.