Thursday, December 11, 2008

Academic officers: top-down contextual ambiguity resolution

'The officers taught at the academy'. This sentence appears unambiguous to us until we are presented with an upgraded version: 'The officers taught at the academy were very demanding'. Functional structures for them will be:

(1) ((at (taught (the officers))) (the academy))
(2) ((were ((at (taught (the officers))) (the academy))) (very demanding))

These structures share common part, namely the whole first sentence. But this common part should be evaluated to different results: in (1) it would be complete clause - sentence, while in (2) it's only a noun phrase. So it appears that the first sentence should actually have two valid interpretations, but we've already understood it unambiguously!

This can be resolved by implying that the whole construction should always have clause type. So when we assume 'taught' having two alternatives and calculate the (1) expression value with both, we could safely remove the noun phrase since it can't be final result. This top-level clausal implication can be even explicated by introducing one more function here, whose name could be '.' (dot). The only thing for it to do could be just to filter clauses out of all its argument's alternatives. But there's another way.

Let's assume that every functional language expression has only one interpretation. It's simple and it looks like humans do the same. So when (1) is considered in its standalone version, it will be unambiguously a clause. But then it appears that the sentence is not finished, and we get 'were' applied to this complex expression, which can't take clauses as arguments. So we now have to evaluate (1) in a different way, knowing now that its context requires it to be noun phrase. It should be not hard to find another alternative of 'taught' that will suit these new requirements: a passive participle.

At the top, a clause type will be expected, on other levels it will depend on a particular function. Function 'were' will want a noun phrase (and so will 'at' and 'the' do), the resulting function '(were ...)' will need a gerund ('very demanding').

Technically, the evaluator has to get the context requirements from somewhere. We can't calculate the expression result part-by-part, starting with '(the officers)' and then applying other functions to it, we should have the whole expression in our hands. It also means that functions don't take arguments as eagerly computed values any more, they take arguments as data instead and evaluate that data by themselves in a right context. Hello, LISP's macros.


Anton Nazarov said...

Great Lisp article! You should include it to Planet Lisp :)

Peter said...

Hmmm. The only thing from LISP here is the syntax. And maybe also the evaluation order, something between full-blown macros and lazy evaluation. I don't consider this text to be about LISP at all.