Haskell - is this a closure?

Question

There is a piece of source-code that originated in an answer to another one of my questions,

infFromPrefix :: Eq a => ([a] -> [a]) -> [a] -> [a] 
infFromPrefix rules prefix = inf where
    inf = prefix ++ case stripPrefix prefix (rules inf) of
        Just suffix -> suffix
        Nothing     -> error "Substitution does not preserve prefix"

where I am pretty sure that inf must be a closure as it has access to variables from its enclosing scope in the sense that it uses the parameters passed to infFromPrefix, but am unsure since essentially infFromPrefix and inf is the same function, the inf only allows a more succinct definition. An equivalent definition would be

infFromPrefix rules prefix = prefix ++ case stripPrefix prefix (rules $ infFromPrefix rules prefix) of
        Just suffix -> suffix
        Nothing     -> error "Substitution does not preserve prefix"

Am I correct, is inf a closure?

Answer 1

I would agree with Lennart and Daniel that closure is an implementation-specific term and is not something well-defined in general. Moreover, I don't hear Haskellers talk about closures a lot outside of the implementation issues; when programmers in other languages casually talk about "closures", they usually mean what we call "lambdas". (As in "does that language have closures?".)

Anyway, let's talk about GHC.

GHC (or, more precisely, STG) calls a closure any heap object that is not a constructor application.

(In case you think this is a broad definition, compare this with the original STG paper where even constructors were called closures.)

Your inf is certainly an STG closure; it is a thunk that will be allocated on the heap and returned to the caller.