Topic-Focus articulation

As it is known, every sentence can be divided into two logical parts. One (Topic) is what the sentence is about, another (Focus) is what the sentence actually says about its Topic. Topic is usually something given or presupposed to be given, Focus is something new or emphasized. To me the Topic seems like data from the knowledge base whilst the Focus seems like an operation on this data, a function on the Topic. Since Topic-Focus opposition is one of the most important distinctions for me in the text structure, I can't omit it from the functional representation.

We know one thing that can separate anything from anything in functional composition: a Lambda abstraction. So we'll use it also to separate Topic from Focus.

Let's introduce a special auxiliary function (actually it's more like a macro) SENT, which will take both Topic and Focus as its arguments and then apply function-Focus to argument-Topic, probably marking them in some special problem-dependent way. Thus every sentence would look like a call of SENT function with Focus and Topic arguments.

Example sentence:

Father loves son.

Its core functional structure:

(loves father son)

By default Topic is 'father', Focus is 'loves son'.

(SENT (λx loves x son) father)

We can stress FATHER, promoting it to the Focus and 'loves son' - to the Topic:

(SENT (λx x father) (λy loves y son))

Here we have two abstractions. If we suppose that SENT does nothing besides applying its first argument (Focus) to its second argument (Topic), we'll get

((λx x father) (λy loves y son))
<= replace x =>
((λy loves y son) father)
<= replace y =>
(loves father son)

We can stress SON:

(SENT (λx x son) (λy loves father y))
which can be replaced by shorter
(SENT (λx x son) (loves father))

We can stress LOVES:

(SENT loves father son)

Here the Topic consists of two entities rather than one. This is perfectly normal, we'll just apply 'loves' to 'father', and then the result - to 'son'. We'll get ((loves father) son) which is by definition of currying equal to the core structure.

I don't know yet how to represent multiple parallel contrastive sequences, like 'Father loves son, while mother hates him'. But such an approach feels promising to me.