7
$\begingroup$

I'm trying to work through "Elements of Functional Languages" by Martin Henson. On p. 17 he says:

$v$ occurs free in $v$, $(\lambda v.v)v$, $vw$ and $(\lambda w.v)$ but not in $\lambda v.v$ or in $\lambda v.w$. And $v$ occurs bound in $\lambda v.v$ and in $(\lambda v.v)v$ but not in $v$, $vw$ or $(\lambda w.v)$. Note that free and bound variables are not opposites. A variable may occur free and bound in the same expression.

Can someone explain what this means?

  • 0
    Well, it means what it says; it gives examples for free and non-free variables, and for bound and non-bound variables. You should be more specific in saying what you don't understand.2012-03-09
  • 0
    Okay, what does _v occurs free in v_ mean? I do understand that λv.anything typically means _v_ is bound. But then what is _(λv.v)v_ trying to say?2012-03-09
  • 0
    $v$ occurs free in $v$ means that the *variable* $v$ occurs free in the *expression* $v$ (which only consists of one variable). Maybe this is what caused the confusion.2012-03-09

2 Answers 2