# Is there a formal language of Combinatory Logic's expressions?

The Combinatory Logic uses expressions of the form (x y) called "applications" (here, we have an "application of x to y"). Thus, the language of CL is a set of "parenthetic expressions", each looking like a string of variables to which pairs of balanced parentheses are multiply applied in an exhaustive manner (that is, you cannot insert yet another pair of parentheses).

Is there a grammar which defines this language? (I am a novice in formal languages and I am not sure my question is correctly formulated)

• Isn't it a very simple one, just symbols and binary application? Jan 27, 2021 at 11:46

Even more generally, by definition, a formal language over an alphabet $$\Sigma$$ is just a collection of words over $$\Sigma$$. This means that any encoding of combinatory logic expressions which uses some fixed alphabet is automatically a formal language.