public Pair <X, List <B> > TraversePair <X, B>(Func <A, Pair <X, B> > f, Monoid <X> m)
{
return(FoldRight <Pair <X, List <B> > >(
(a, b) => f(a).Constrain(m).ZipWith <List <B>, List <B> >(b.Constrain(m), aa => bb => aa + bb).Pair
, m.Id.And(List <B> .Empty)
));
}
public Pair <X, Tree <B> > TraversePair <X, B>(Func <A, Pair <X, B> > f, Monoid <X> m)
{
return(f(root).Constrain(m).ZipWith <List <Tree <B> >, Tree <B> >(
children.TraversePair(w => w.TraversePair(f, m), m).Constrain(m)
, b => bs => b.TreeNode(bs)
).Pair);
}
public A SumLeft(Monoid <A> m) => FoldLeft(m.Op, m.Id);
public A SumRight(Monoid <A> m) => FoldRight(m.Op, m.Id);
public PairAndMonoid <A, B> Constrain(Monoid <A> m)
{
return(new PairAndMonoid <A, B>(this, m));
}
internal PairAndMonoid(Pair <A, B> pair, Monoid <A> m)
{
this.pair = pair;
this.m = m;
}
public Monoid <A> Monoid(A id) => Monoid <A> .monoid(op, id);
public A SumLeft(Monoid <A> m)
{
return(FoldLeft <A>(m.Op, m.Id));
}
public Pair <X, NonEmptyList <B> > TraversePair <X, B>(Func <A, Pair <X, B> > f, Monoid <X> m) => f(head).Constrain(m).ZipWith <List <B>, NonEmptyList <B> >(tail.TraversePair(f, m).Constrain(m), h => t => h & t).Pair;
public Monoid <Pair <A, B> > Pair <B>(Monoid <B> s) => Semigroup.Pair(s.Semigroup).Monoid(id.And(s.Id));
public PairAndMonoid <A, B> Constrain(Monoid <A> m) => new PairAndMonoid <A, B>(this, m);
public Pair <X, ListZipper <B> > TraversePair <X, B>(Func <A, Pair <X, B> > f, Monoid <X> m)
{
var t = this;
var r =
from ll in lefts.Reverse.TraversePair(f, m).Constrain(m)
from xx in f(t.focus).Constrain(m)
from rr in t.rights.TraversePair(f, m).Constrain(m)
select new ListZipper <B>(ll, xx, rr);
return(r.Pair);
}
public B SumMapRight <B>(Func <A, B> f, Monoid <B> m)
{
return(FoldRight <B>((a, b) => m.Op(f(a), b), m.Id));
}
public B SumMapRight <B>(Func <A, B> f, Monoid <B> m) => FoldRight((a, b) => m.Op(f(a), b), m.Id);
public Pair <W, Either <A, X> > TraversePair <W, X>(Func <B, Pair <W, X> > f, Monoid <W> m)
{
return(Fold(a => m.Id.And(a.Left <A, X>()), b => f(b).Select(x => x.Right <A, X>())));
}
public B SumMapLeft <B>(Func <A, B> f, Monoid <B> m)
{
return(FoldLeft <B>((a, b) => m.Op(a, f(b)), m.Id));
}
public Pair <X, Input <B> > TraversePair <X, B>(Func <E, Pair <X, B> > f, Monoid <X> m)
{
return(val.TraversePair(o => o.TraversePair(f, m), m).Select(o => new Input <B>(o)));
}
public Monoid <A> Monoid(A id)
{
return(Monoid <A> .monoid(op, id));
}
public A SumRight(Monoid <A> m)
{
return(FoldRight <A>(m.Op, m.Id));
}
