Patterns and Compositionality

[btanksley@hifn.com]

Massimo, why are all your messages sent with high importance?  ("X-Priority:
1" in the header.)

> From: Massimo Dentico [mailto:m.dentico@teseo.it]
> Subject: Re: Patterns and Compositionality

> Jim Little wrote:

> The  context  is: "[..]  If  generalizing  a  pattern  is  lambda-
> abstraction and inlining a pattern is beta-expansion [..]".  So, I
> have  rendered  explicit  my premises  just  to make  feasible  an
> objection to my reasoning. But the intuitive definition of pattern
> doesn't invalidate /a priori/ a more rigorous one.

Lambda calculus is not even _close_ to powerful enough to handle design
patterns -- it's not even powerful enough to easily handle function calls
when the called function is permitted to modify variables (although it is
sufficiently powerful to model either one, given some more complexity).  So
you can't establish a one-to-one correspondance between operations in lambda
calculus and pattern design or use.

So far, patterns have no been successfully formalized.  One reason for this
is that a true design pattern has to be commonly useful; if it's not, it may
be a clever design, but it's not suitable for a pattern.

> I suspect that  Fare speaks about the "hype"  (I'm not sure  about
> the meaning  of this word),  around  the useful  idea  of pattern,
> exactly  because  the  lack  of a precise definition  prevent  any
> attempt  of  rigorous  reasoning   (for  example,  comparisons  of 
> expressiveness with other frameworks).

Fare senses most strongly other's crimes when he himself is guilty of the
same thing.  Hype is the entire basis of our devotion to Tunes, and Fare is
responsible for that.  So hype can be used for good as well as evil ;-).

Patterns are useful.  This is one of the main parts of their definition, so
they can't help it.

The patterns used in C++ are not similar to the patterns used in C, and
neither one looks like the design patterns used in Beta (although the C++
patterns are mostly useful in Beta, the other way is not true; some C++
patterns are useless in Beta because Beta can express the same concepts as
part of the language).

> Instead the problem is:  the rigorous definition cathces the whole
> intuitive  definition?  The  paper  of Wegner (as I understand it)
> tries  to  answer  this  question  relatively  to  the  notion  of
> computability,  the intuitive  compared  to the formal notion.  He
> suggests  that   Multi-Stream  Interection  Machines  (MIMs)   and
> co-inductive  reasoning  give  a  stronger  model  of  computation
> compared  to  Turing  Machines,   lambda  calculus  and  inductive
> reasoning.

A very interesting hypothesis.  I lost the link to it, I think; or I never
read it.  Where may I look?

> The intention of my original post was  to highlight  the fact that
> if Wegner  and my equation are right  then,  even in the 
> field  of functional/logic 
> programming,   the  formal  model  of  reference
> (lambda  calculs)  doesn't  catch  the  expressive  power  of this
> languages.

Which language?

Or were you trying to say that lambda calculus can't model everything a
computer can compute?

> Massimo Dentico

-Billy