Four of the main kinds of compound noun in English (tatpurusa,
bahuvrihi, dvandva, synthetic) will suffice to
demonstrate the ILEX approach.
Tatpurusa (endocentric) compounds:
In endocentric or tatpurusa compounds, the MEAN of the whole
is subsumed by the MEAN of the HEAD of the PARTS.
A milk-bottle is a bottle, a mouse-trap is a trap:
MEAN(bottle) 
MEAN(milk-bottle),
MEAN(trap) MEAN(mouse-trap).
There are metaphorical variants: a pineapple is not an apple,
but functionally similar or jocularly relatable to an apple
(maybe when seen from a considerable distance or eaten blindfolded after
a hot curry). The MEAN of apple still subsumes the MEAN of
pineapple; the MEAN of both is subsumed by the MEAN of fruit.
The inheritance structure of `pineapple'
is very similar to that of `pussy-willow', illustrated above, but
but with a metapor relation RESEMBLE which applies both to the head
and the modifier
(`something like an apple which grows on something like a pine').
Bahuvrihi (exocentric) compounds: In bahuvrihi compounds, the MEAN of the whole is not subsumed by the MEAN of the HEAD of the PARTS, but by an elliptical `understood' semantic category.
The simplest kinds of exocentric compound are items such as `redskin' or `longlegs', paraphasable informally as `SOMEONE who will typically HAVE skin which is kinda red' and `SOMEONE who will typically HAVE legs which are kinda long', with a `has property' relation. Capitalisation indicates elliptical terms, parentheses indicate elliptical relations which are characteristic of the kind of compound concerned, italics indicate overt components. Capitalised and bracketed items are the largest factors in the partial compositionality of exocentric compounds.
A more complex type is pickpocket, i.e.
`SOMEONE who will typically professionally surreptiously pick[=extract] VALUABLES from someone else's pocket'.
Exocentric compounds are modelled with more deeply nested
inheritance structures than endocentric compounds.
Dvandva (coordinate) compounds:
The parts of coordinate compounds occur in a fixed order, and are
morphologically headed, but semantically have no head-modifier structure.
The functor is, basically, conjunction.
Examples of this relatively simple type are
`fighter-bomber', which is both a fighter and a bomber.
Synthetic compounds: The second element of a synthetic compound a derived noun whose ending enters into the same semantic construction as its stem and the preceding noun. Examples of this type are busdriver, screwdriver. The ORTH derivational structure of busdriver is bracketed as
ORTH(busdriver) =
CONCAT(ORTH(bus),ORTH(driver)) =
CONCAT
However, the MEAN structure is bracketed differently (omitting some details):
MEAN(busdriver) =Some apparent synthetic compounds involve so-called bracketing paradoxes, which can be explained as different compositional structures defined for SURF and MEAN attributes. One classical case has the semantic bracketing ((transformation al grammar) ian), i.e.
(SEMANTICALLY_LINK(MEAN(drive),(MEAN(x),MEAN(bus))))
versus the morphological bracketing ((transformation al) (grammar ian)).
(SEMANTICALLY_LINK (PROFESSIONALLY_PRODUCE, MEAN(`x'), SEMANTICALLY_LINK (MEAN(`al'), MEAN(`transformation')), MEAN(`grammar'))))