Monad

Don't expect a great answer from me as to what constitutes a monad; there's already a good question/answer on Stack Overflow.

Basically, it's a bit of glue that joins two functions together. I decided to write one for myself in C# to see what it would look like without any syntactic sugar that other languages might provide:

public static class Binding {
    public static Func<TInput, TOutput> Bind<TInput, TIntermediate, TOutput>(Func<TInput, TIntermediate> left, Func<TIntermediate, TOutput> right) {
        return arg => right(left(arg));
    }
}

It's designed so that the output of left "flows" into the input of right. The output of the rightmost function is returned to the caller as the result of the expression. Here are two functionally equivalent examples (one written normally, and the other with monads):

Func<string, IEnumerable<char>> js = s => s.Select(c => c - '0').Where(i => i % 2 == 0).Select(i => (char)(i + 'a')).Select(c => Char.ToUpper(c));

Func<string, IEnumerable<char>> ks = Binding.Bind<IEnumerable<char>, IEnumerable<int>, IEnumerable<char>>(
    k1 => k1.Select(c => c - '0'),
    Binding.Bind, IEnumerable<int>, IEnumerable<char>>(
        k2 => k2.Where(i => i % 2 == 0),
        Binding.Bind<IEnumerable<int>, IEnumerable<char>, IEnumerable<char>>(
            k3 => k3.Select(i => (char)(i + 'a')),
            k4 => k4.Select(c => Char.ToUpper(c)))));

Check that they work as expected:

Debug.Assert(ks("0123456789").SequenceEqual(new char[] {'A','C','E','G','I'}));