<p>$x$ is a "bound variable" and $M$ is the "scope" in which it is bound.</p>

CC BY-SA 3.0
2012-02-21T18:58:44.040Z
I would say that the scope of $x$ is the whole expression $\lambda x.M$.
Emil Jeřábek
CC BY-SA 3.0
2012-02-21T19:17:36.543Z
@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
CC BY-SA 3.0
2012-02-21T20:05:40.320Z
Personally I couldn’t care less. However, the question is not how I like it, but what is the commonly accepted terminology, and I believe it is what I wrote above.
Emil Jeřábek
CC BY-SA 3.0
2012-02-21T21:02:30.420Z
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
CC BY-SA 3.0
2012-02-22T13:01:39.490Z
I apologize, I didn’t intend to be rude.
Emil Jeřábek
CC BY-SA 3.0
2012-02-21T18:19:31.827Z
2012-02-21T18:19:31.827Z
Marc Hamann
<p>In logic the $\phi$ in $\forall x . \phi$ is called <em>the matrix</em>, and $x$ the <em>bound variable</em> and $\forall x$ the <em>quantifier</em>. 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"?</p>

CC BY-SA 3.0
2012-02-22T13:00:49.863Z
2012-02-22T13:00:49.863Z
Andrej Bauer
<p>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"?</p>

<lo.logic><terminology><lambda-calculus>
Labels for terms in the lambda calculus
mshang
# Labels for terms in the lambda calculus

(Asked by: username_0 on 2012-02-21)

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"?

**Tags:** lo.logic, terminology, lambda-calculus


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## 2 answers

### Answer by username_1 on 2012-02-21. Score: 4 | Accepted answer

$x$ is a "bound variable" and $M$ is the "scope" in which it is bound.

> **Comments:**
> **username_2**: I would say that the scope of $x$ is the whole expression $\lambda x.M$.  
> **username_1**: @username_2 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... ;-)  
> **username_2**: Personally I couldn’t care less. However, the question is not how I like it, but what is the commonly accepted terminology, and I believe it is what I wrote above.  
> **username_3**: 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.  
> **username_2**: I apologize, I didn’t intend to be rude.  

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### Answer by username_4 on 2012-02-22. Score: 1

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"?


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