Syntactic functions define a subset of syntagmatic relations, in this fcase relations between complex objects and their parts. Syntactic functions are those syntagmatic relations which define the unique role of a parts of a complex object, such as a sentence, within the whole object. Examples of syntactic functions include SUBJECT, OBJECT, INDIRECT OBJECT.
A variety of grammar theory based entirely on syntactic functions is Categorial Grammar, with dependency relations at the core: a verb, for instance, is a functor which maps a noun on to a sentence, expressed: 
; in a noun-verb combination such as 
, the initial N is said to `cancel' the N as the denominator of the fraction, like a straightforward arithmetic operation.
Task: How is each of these functions defined, and which other functions can you identify and define?