The principle of compositionality is formulated as:
The meaning of a complex expression is a function of the meaning of its parts and of the syntactic rules by which they are combined. (Partee, ter Meulen and Wall, 1990: 318)
If I have understood proponents of this principle correctly (from mainly reading the Wikipedia article on the subject) idioms and metaphors and other notions demanding extralinguistic contexts are often excepted from this.
My wonder is, if we remove all of these entities, what is really left of language beyond simpler predicate logical expressions? Are there alternative to the principle of compositionality?