# Labels for terms in the lambda calculus

In the lambda calculus, are there commonly accepted names for $x$ and $M$ when they appear in $\lambda x [M]$ ? Something along the lines of "binder" and "bindee"?

$x$ is a "bound variable" and $M$ is the "scope" in which it is bound.
• I would say that the scope of $x$ is the whole expression $\lambda x.M$. – Emil Jeřábek Feb 21 '12 at 18:58
• @Emil Jeřábek Since $x$ can only be evaluated in $M$, I'm not sure what adding the lambda adds to the notion of scope. But hey, if that is how you like it... ;-) – Marc Hamann Feb 21 '12 at 19:17
• I agree with Marc here. The scope is the body $M$. BTW, expressions like "I couldn't care less" come across as very rude, though I'm sure that's not your intention. – Dave Clarke Feb 21 '12 at 21:02
In logic the $\phi$ in $\forall x . \phi$ is called the matrix, and $x$ the bound variable and $\forall x$ the quantifier. By this analogy I would call $M$ in $\lambda x . M$ the matrix, $x$ is the bound variable, and $\lambda x$ is the abstraction, or maybe the "abstractor"?