Re: Type inference and related research...
If your interest is directed towards type systems of real-world programming
languages, focusing on type inference is not necessarily the most productive
direction to take. As I see it, the subject mostly dead-ends around the
point of sophistication of the Haskell type system, after which it becomes
undecidable or at least unwieldy. This does not seem like a feature that
will make it into future programming languages that are widely used.
Though, the underlying concept of unification is very powerful and seem more
promising -- if unification is your primary interest, then it could be very
useful to explore it in other, more practical, situations than
Here are two type-theoretic subjects that I feel hold the most promise
towards improving future type systems:
1. The representation of "very dependent types", as originated by Jason
Hickey. See http://www.cs.caltech.edu/~jyh/papers/fool3/default.html for
the original paper. In earlier type systems, terms could reference (by
symbolic binding or de Bruijn index) the 'parameter' part of outer lambda
expressions. Very dependent types also expose the 'function' part of outer
lambda expressions, but in a more general way than the recursive mu binder:
they preserve partially-known information.
Thus you can use very dependent types to form arbitrarily complex
dependent-typed records with recursive dependencies. This provides a
framework that seems an ideal framework for representing object-oriented
concepts such as self-type dependence (without resorting to a new binder as
in Cardelli's object calculi), as well as uniformly representing dependent
mathematic structures such as groups or rings. In my experience, very
dependent types have proven very easy to work with and well-known concepts
such as Cardelli's explicit substitutions approach, and Cardelli's
subtyping-of-recursive-types are easily extensible to very dependent types.
As far as I'm aware, there is only one paper on this topic and the value of
this research topic hasn't been widely recognized yet.
2. Type systems that combine non-determinism (at least at the type level)
with type-forming and type-specification operators. The breakthrough paper
on the topic is David McAllester's description of the Ontic language:
http://www.ai.mit.edu/people/dam/ontic-spec.ps. This also appears to be the
only paper on the topic and the value of the research hasn't been widely
The notion of non-determinism in Ontic isn't the scary or impractical kind
that is associated (by practical programmers) with languages like Prolog;
here it can be used purely as a type-system tool that enables you to express
such concepts as "the type containing the elements 1, 2, and 3"; "an element
whose value is either 1, 2, or 3", "a subtype of the type of natural
numbers", "the type of all subtypes of natural numbers", etc. The Ontic
type system provides a direct and intuitive representation of concepts which
are either difficult or indirect and circuitous to express in more
traditional dependent-type systems.
One of the neat things of Ontic is that the idea of a typechecker assigning
type judgements to each term context in the form "a:T" is replaced by the
more general idea of assigning a (hopefully finitary) set of possible values
to each term. This makes it easier to deal with complex subtyping
situations such as f-bounds and recursive types.
Please note that I am not a type theorist, but a practical programmer who
follows type theory research in search of ideas that may contribute towards
future practical programming languages, so my advice here is biased in a
direction that others are likely to disagree with.
----- Original Message -----
From: "Vahram" <email@example.com>
Sent: Monday, September 16, 2002 6:58 AM
Subject: Type inference and related research...
> [----- The Types Forum, http://www.cis.upenn.edu/~bcpierce/types -----]
> Hello everyone.
> I am a university student in Armenia, preparing for research in the
> field of type systems. Being new to research, I am seeking some help
> from the scientific community, whose member I will hopefully become
> one day. I have two problems. The first problem is figuring out a
> direction to do research in (I mean in this particular field), or at
> least obtaining a list of open problems and vaguely investigated
> areas. And the second problem is how to view "all" the work previously
> done in a topic that interests me, with Internet being the only source
> of information. I mean is there a way of having a list of works and
> some sort of guarantee that it is complete, is CiteSeer authoritative
> I am acquainted with the subject of type systems in general, and
> especially interested in polymorphic type inference and related
> topics. I would be very grateful if someone tells me about any poorly
> investigated problems in these fields. Maybe there's a particular
> problem arisen from some recent investigations that needs to be
> solved, or any newly evolving field to be examined. Since this is my
> first research in this area, the problem should not be a large or very
> sophisticated one, just something worth doing.
> I have been looking for a particular direction of research for a
> while, and have found a few so far. One such direction is so-called
> soft typing with its possible variations, another one is alternative
> or complementary (to Milner) methods of inferring types. I have found
> out that these topics are more or less developed. I do have some more
> problems in mind, such as investigating the class of typeable
> (type-inferrable) terms, or trying to apply typing or type inference
> methods in some more traditional fields, but I have little knowledge
> about any work done in these directions. I would like to know how
> realistic is doing research in the mentioned directions.
> All-in-all, I need a direction to do my research project.
> Please help me out. Any advice will be of great value for me.
> Thank you for your time and attention.
> With great respect,
> Vahram Avagyan.