Setup

Consider some function

val f : 'a1 -> 'a2 -> 'r

It is somewhere (partially) applied as in

f a1

Wrapping

Consider a function wrapper type

val w : ('a -> 'b) -> ('a -> 'b)

There are two typechecking ways to wrap the above application of f:

• (w f) a1
• w (f a1)

Both typecheck to 'a2 -> 'r.

In a pure language the only possible implementation would be the identity. With w := id, both wraps would give the same result.

In an impure strict language with exceptions (like SML), the application order matters. A standard wrapper would be to catch and transform some exception.

• In (w f) a1 any exception thrown by f goes through ws logic.
• In w (f a1) exceptions in the first partial application (f a1) bypass ws logic.

Fazit

Function signatures in impure languages are sometimes misleading. Hidden side-effects can cause nasty surprises.