[Haskell-cafe] Proving correctness

Alexander Solla alex.solla at gmail.com
Fri Feb 11 21:02:09 CET 2011

On Fri, Feb 11, 2011 at 3:06 AM, C K Kashyap <ckkashyap at gmail.com> wrote:

> Hi Folks,
> I've come across this a few times - "In Haskell, once can prove the
> correctness of the code" - Is this true?
> I know that static typing and strong typing of Haskell eliminate a whole
> class of problems - is that related to the proving correctness?
> Is it about Quickcheck - if so, how is it different from having test
> sutites in projects using mainstream languages?

Let's interpret a type as a "partial specification" of a value.  If we can
express this "partial specification" completely enough so that one (and only
one, at least ignoring values like bottom) value is a member of the type,
then any expression of that value must be formally correct.

There are a couple of issues:  the type system is strong, but it still has
limitations.  There are types we might like to express, but can't.  We might
be able to express "supersets" of the type we really want, and the type
inference engine will ensure that a value in the type meets at least this
partial specification, but it cannot check to see if it is the "right" value
in the type.  That is up to us.  Some of Haskell's properties, like
referential transparency, equational reasoning, etc. make this easier than
in other languages.

A related difficulty is that encoding specifications is a programming task
in itself.  Even if you correctly compile requirements, and are able to
completely encode them in the type system, you might still introduce a logic
mistake in this encoding.  A similar issue is that logic mistakes can creep
into the requirements compiling phase of a project.  In either of these
cases, your values would dutifully and correctly compute the wrong things.
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