Lambda the Ultimate

Functions in the language I'm building may have optional parameters, i.e. parameters that may or may not be supplied by the caller.

In Common Lisp, unsupplied optional parameters receive NIL as their value. I want to avoid NIL, because I'd like to add an optional type system to the language later, and I don't want to have NIL as a value that's "in every type".

So I've thought of making the type of optional parameters be like Haskell's Maybe: when the parameter is supplied with a value X, the function body receives it as Just X, and when the parameter is not supplied, it's Nothing (this means that for optional parameters, matching against Just or Nothing is always required in the function body).

Thoughts?

Matija Pretnar, Gordon Plotkin (2009) Handlers of Algebraic Effects:

We present an algebraic treatment of exception handlers and,
more generally, introduce handlers for other computational effects repre-
sentable by an algebraic theory. These include nondeterminism, interac-
tive input/output, concurrency, state, time, and their combinations; in
all cases the computation monad is the free-model monad of the theory.
Each such handler corresponds to a model of the theory for the effects
at hand. The handling construct, which applies a handler to a compu-
tation, is based on the one introduced by Benton and Kennedy, and is
interpreted using the homomorphism induced by the universal property
of the free model. This general construct can be used to describe previ-
ously unrelated concepts from both theory and practice.

Handling a computational effect, such as raising an exception, amounts to homomorphically mapping the handled computation onto another computation. So, for example, raise is interpreted as the exception handling code given to the handler.

While encompassing both returning and non-returning handlers, this idea becomes more interesting when you start to handle the other effects, such as lookup and update. Then you can get things like state rollback when an exception occurs, and others (CSS renaming and hiding, stream redirection, timeout). Thus the semantics of handlers gives rise to a new programming construct.

If you want a gentler introduction to the subject (along with Plotkin's algebraic theory of effects and Levy's Call-by-Push-Value), try Pretnar's 2010 thesis.