# Function composition

**Function composition** is an algebraic notion which DiSciullo & Williams (1987) adopt from Categorial Grammar to account for an important difference between compounding and affixation. In compounding the non-head satisfies a theta-role of the head. The non-head of a complex word headed by an affix, however, does not satisfy a theta-role of the affix; rather the affix and the stem form a composed argument structure. In order to be able to relate the argument structure of an affixal head to its non-head, they propose that suffixes are functors with respect to their complements.

### Example

The English adjective *complete* has a Theme as its the external argument, and the nominal suffix -*ness* the "degree" argument R, as in (i). Since -*ness* is assumed to be a functor, function composition yields the composed argument structure in (ii):

(i) complete -ness => (ii) completeness (Th) (R) ((Th) R) functor

### Link

Utrecht Lexicon of Linguistics

### References

- Di Sciullo, A. M. and E. Williams 1987.
*On the Definition of Word,*MIT-press, Cambridge, Mass. - Spencer, A. 1991.
*Morphological Theory,*Blackwell, Oxford.