# [Haskell-cafe] Composition, delegation and interfaces -- a 20K ft critique of Noop

Greg Meredith lgreg.meredith at biosimilarity.com
Thu Sep 17 15:30:01 EDT 2009

```Dear Programmers,
Someone just asked me to give my opinion on Noop's composition
It reminds me a little bit of
Self<http://en.wikipedia.org/wiki/Self_%28programming_language%29>which
found its way into JavaScript. It also reminds me a little of
type classes <http://en.wikipedia.org/wiki/Type_class>. In general, movement
away from inheritance is good. The proposal, however, feels a bit like
looking for the lost quarter where the light is good, rather than where you
lost it. Before considering delegation machinery, let's consider the
*value*of an interface. How many interfaces are there? One way to see
that is just
to consider all the sub interfaces of a single interface with n methods on
it. Hmmm... that's 2^n interfaces. That's a lot. Does that give us any
confidence that any one way of carving up functionality via interfaces is
going to be sane? Further, in practice, do we see random distribution
through this very large space?

What we see over and over again in practice is that the answer to these
questions is 'no!'. That means that there is *something* that binds a
collection of methods together. What might that something be? One place to
look is mathematics. Which maths should we look at? The maths of category
has been very fruitful both in explaining existing functional programming
techniques and -- perhaps more importantly -- suggesting ways to improve
them as well as wholly new techniques. What we find in category theory is
that it is natural to collect maps (read functions) together. A good example
of such a beast is a monad. A monad -- viewed categorically -- is

- a map, T, taking types to new types and functions on those types to new
functions. Let's call the universe of types and functions expressible in our
model of computation (as proscribed by our programming language), C. Then T
: C -> C.
- a higher order map, unit. Just like T takes C to C, we can understand a
"noop" like map that takes C to C, call it Id. Then unit : Id -> T. We
intuitively think about it as putting basic types inside the container T,
but it's really a higher order map.
- another higher order map, mult : T^2 -> T. We talk about it as a kind
of flattening (and in Scala it's called flatMap), but it's a higher order
map.

Now, one is not finished spelling out a monad when giving this collection of
maps. One must also show that they satisfy certain constraints.

- T is functorial, meaning T g f = T(g) T(f)
- unit and mult are natural transformations, look up the meaning because
unpacking it here would take to long
- mult( mult T ) = mult( T mult )
- mult( unit T ) = mult( T unit  )

This set of constraints must go with the monad. This example provides a
little more detail in terms of what binds a group of maps together, and
hence of what *might* replace the notion of interface and *explain* what we
see in practice. Good programmers invariably pick out just a few
factorizations of possible interfaces -- from the giant sea of
factorizations (read different ways to carve up the functionality). The
reason -- i submit -- is because in their minds there are some constraints
they know or at least intuit must hold -- but they have no good way at the
language level to express those constraints. A really practical language
should help the programmer by providing a way express and check the
constraints that hold amongst the maps in an interface.

i submit that this idea is not the same as "design by contract". i am not
proposing an Eiffel-like mechanism. Again, taking a functional approach to
computation via category theory leads one towards modeling interfaces as
means that a large number of the constraints come down to

- functoriality
- naturality
- coherence

Language support for this approach might include *keywords for these kinds
of assertions*. It is a gnarly beast to offer automatic and/or compiler
support for checking general constraints. Even this limited family of
constraints that i'm proposing can generate some very difficult
computations, with very bad complexity. However, for those situations where
a general purpose solution to check assertions of functoriality, naturality
and coherence are infeasible, one can use these hints to generate tests to
probe for possible failures. This idea follows the in the same spirit of
replacing proof with proof-checking.

Of course, this is not the only way to go. i've yet to be convinced that
category theory offers a good account of concurrency. Specifically,
categorical composition does not line up well with concurrent composition.
So, interfaces organized around types for concurrency is also something to
consider. In this case, one might find a natural beginning in interfaces in
which -- roughly speaking -- the methods constitute the tokens of a formal
language the constructors of which are given by the types for concurrency

Best wishes,

--greg

On Thu, Sep 17, 2009 at 11:14 AM, Charles F. Munat <charles at munat.com>wrote:

>

--
L.G. Meredith
Managing Partner
Biosimilarity LLC
1219 NW 83rd St
Seattle, WA 98117

+1 206.650.3740

http://biosimilarity.blogspot.com
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