On 09/08/12, Jay Sulzberger <j...@panix.com> wrote:
This seems to be addressing my my question, but I am not sure that I can relate the above ideas to Haskell.
Here we are close to the distinction between a class of "objects
which satisfy a condition" vs "objects with added structure", for
which see:
http://math.ucr.edu/home/baez/qg-spring2004/discussion.html
http://ncatlab.org/nlab/show/stuff,+structure,+property
oo--JS.
Below is my current (naive) understanding and some further question:
"objects which satisfy a condition"
Could these objects be models that have the same signature (instances in Haskell).
Haskell type classes seem to be signature only (no equations, ignoring default methods) so in general they provide an empty theory with no logical consequences.
"objects with added structure"
I am struggling with this concept both in general and in relation to the hierarchy from my earlier posting.
Could this be "model expansion" where a theory describing an existing model is enriched with additional axioms.
The enriched theory is then satisfied by models with more structure (operations).
I am unsure about the size of this expanded model and the number of potential expanded models.
Would a expanded model have less elements?
Would there be fewer models for the enriched theory?
In relation to Haskell data types also have structure (constructors).
The data types can be used to build other data types (is this model expansion?)
I am not sure if the model (instance) of a sub-class could be considered as expanded model of its super-class.
Your reply was very helpful
Thanks,
Pat
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