[lojban] More on lojban programatic semantics: Strong typing and inferencing of types

[Brook Conner <nellardo@concentric.net>]

In keeping with the spirit of lojban of letting vagueness be vague and
letting specificity be specific, I've been thinking about the theory of
types and how it relates to a semantics of lojban.

A bit of background, first. In programming language theory, types
represent sets of values (possibly very large sets, like 32-bit
integers) with constraints upon the values, usually in the form of
various operations you can and cannot perform on them. Programming
languages like C and Pascal (the "Algol" family) have a few built in
types like integers, characters, and floating point numbers. They also
usually have ways of defining new types as aggregates of others, things
like lists and arrays (which are usually a sequence of values of the
same type) and things like structures or records (which are
heterogeonous, and often have names for the different parts).
Object-oriented languages extend this by allowing the programmer to
explicitly specify what operations can be performed on the type (i.e.,
the methods).  Many languages, like Lisp and Perl, have "run-time"
typing - you don't need to specify the type of things when writing the
program, but if you do something inappropriate (like using numerical add
on a string), the system will barf. Obviously, the former "static"
typing systems offer some nice rules that you can reason about your
program with (and can help the compiler generate better code). The
latter "dynamic" typing makes it much easier for programmers to develop
stuff quickly.

A third group of languages, including ML and Haskell, allows "type
inferencing". These systems are statically typed, but instead of
requiring the programmer to specify all types explicitly, the system
figures out the type of things based on how they are used. For instance,
it deduces that if you're using addition, you must be expecting some
kind of number.

This last approach is the one I think makes the most sense in the
context of lojban. Constraints on values (i.e, on sumti) can be
expressed if desired, but the semantics can determine that itself from
how the sumti are used. If you put a name in a mekso, you must mean that
the name should be a number of some kind. (this is in contrast to Perl,
which "does its best", and often does things which are reasonable if you
know about them but are otherwise opaque).

So, for example, you can use "poi" to annotate sumti with type
information, or simply an appropriate selbri for "declaring" variables:

ko jarco la stokuot. poi mekso -- show the "stock-quote", which is a
mathematical expression

la stokuot. mekso -- "stock-quote" is a mathematical expr.

la stokuot. namcu -- "stock-quote" is a number.

la stokuot. saclu -- "stock-quote" is a rational number


The diversity of "number" gismu that include units has a nice side
effect of reducing the kinds of goofs that crashed  the recent Mars
mission: if it's "minli", then it is miles. If it is "mitre", then it is
meters. And if you just used "namcu", then you'd run into problems
elsewhere - other gismu would be expecting a distance and would rightly
complain that a namcu is not (necessarily) a distance.

Now, of course, this implies a type hierarchy for lojban gismu. Which
might be a whole kettle of worms (unless it has already been done).
Determining that "grake" and "bunda" (grams and pounds) are in one
category, while "snidu" and "jeftu" (seconds and weeks) are in another
is straight-forward. But determining other class hierarchies might be
more complex. I don't *think* lojban gismu were defined with a specific
taxonomy in mind (lojbab? JWC?). And it may not be desirable to require
a specific taxonomy - it might have too much potential for cultural
bias. On the other hand, if the gismu are as culturally neutral as we
think they are, this shouldn't be a problem. However, how orthoganal are
various gismu? Will they all have unique places in the taxonomy or will
it be difficult to build a suitable graph?

As  always, I welcome thoughts and feedback.....

Brook

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