commonads, monoids and trees

comonadsmonoidsandtrees.js

// Leaf : val -> ann -> Tree val ann
function Leaf(val, ann) {
  return {
    ann: ann,
    val: val,
    toString: () => `Leaf(${val}, ${ann})`,
    map: f => Leaf(val, f(ann)),
    extend: f => Leaf(val, f(Leaf(val, ann))),
    reduce: (f, acc) => f(acc, ann),
  };
}
// Branch : Tree val ann -> Tree val ann -> ann -> Tree val ann
function Branch(left, right, ann) {
  return {
    ann: ann,
    left: left,
    right: right,
    toString: () => `Branch(${left}, ${right}, ${ann})`,
    map: f => Branch(left.map(f), right.map(f), f(ann)),
    extend: f =>
      Branch(left.extend(f), right.extend(f), f(Branch(left, right, ann))),
    reduce: (f, acc) => right.reduce(f, left.reduce(f, f(acc, ann))),
  };
}
// Any : Bool -> Any
function Any(bool) {
  return {
    bool: bool,
    concat: a => Any(bool || a.bool),
  };
}
Any.empty = () => Any(false);
// foldMap : (Monoid m, Foldable f) => m -> (a -> m) -> f a -> m
const foldMap = (Monoid, f, Foldable) =>
  Foldable.reduce((acc, x) => acc.concat(f(x)), Monoid.empty())
// fold : (Monoid m, Foldable f) => m -> f m -> m
const fold = (Monoid, Foldable) => foldMap(Monoid, x => x, Foldable));
// changed : Tree val Bool -> Bool
const changed = tree => foldMap(Any, Any, tree).bool;