[Haskell-cafe] Closures in Haskell and closures in set theory

[Peter Verswyvelen]

If I'm not mistaken, in set theory, a closure of R with respect to some 
property P is the smallest superset R* that has the property P.

To me, intuitively, a closure C in programming languages is a function 
that has bindings to variables declared in "parent" functions; so the 
inner function can not exist on its own, it needs a "parent 
environment". This seems to be related to set theory if we define R as 
the set of  parameters of C, and R* as this set extended with the 
"parent variables" to which C binds, and P as the property "C can be 
evaluated".

Does this make any sense at all?