unknown
1970-01-01 00:00:00 UTC
I suspect that could help you alot to be aware of this stuff if
you're not already (sorry if I'm saying stuff that's obvious for you).
For instance, the issue came up in this thread: what should be the
definition of equivalent domains and how should that be computed? In
category theory, if A and B are domains of the same category, they are
isomorphic exactly when there exists morphisms f:A->B and g:B->A with
g o f = 1, f o g = 1. That's the right answer from the mathematical
point of view. If Aldor produces a different answer, it's going to
cause suffering down the road because it will be close to, but not
quite what one wants mathematically.
One of the things that encouraged me at the time was thinking
about the simplest Aldor category in the mathematical sense: objects
of the category are Aldor domains satisfying
Domain: Category == with # no signatures (my favorite base category
for a library)
and morphisms are Aldor functions. Even though Domain has no
signatures, the statement that it is a category in the mathematical
sense is true but not trivial - one has to *assume* that composition
of Aldor functions is associative. Also, this category already has
direct products and direct sums (essentially Record and Union). Given
the category Domain, you could introduce "Set" with "=" and produce
Set domains by applying a free construction domain constructor to
Domains just like in the group case.
Best regards,
- Saul
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you're not already (sorry if I'm saying stuff that's obvious for you).
For instance, the issue came up in this thread: what should be the
definition of equivalent domains and how should that be computed? In
category theory, if A and B are domains of the same category, they are
isomorphic exactly when there exists morphisms f:A->B and g:B->A with
g o f = 1, f o g = 1. That's the right answer from the mathematical
point of view. If Aldor produces a different answer, it's going to
cause suffering down the road because it will be close to, but not
quite what one wants mathematically.
One of the things that encouraged me at the time was thinking
about the simplest Aldor category in the mathematical sense: objects
of the category are Aldor domains satisfying
Domain: Category == with # no signatures (my favorite base category
for a library)
and morphisms are Aldor functions. Even though Domain has no
signatures, the statement that it is a category in the mathematical
sense is true but not trivial - one has to *assume* that composition
of Aldor functions is associative. Also, this category already has
direct products and direct sums (essentially Record and Union). Given
the category Domain, you could introduce "Set" with "=" and produce
Set domains by applying a free construction domain constructor to
Domains just like in the group case.
Best regards,
- Saul
Ralf
Mistakes...
Id(Obj:Category):Category == with
id: (A:Obj) -> (A->A)
default
id(A: Obj):(A->A) == (a:A):A +-> a --rhx: I changed this line.
homList(A:Categorify P,B:Categorify P):SingleInteger == add
should probably read
homList(A:Categorify P,B:Categorify P):List(A->B) ==
------=_Part_35554_8207286.1194378575395Mistakes...
Id(Obj:Category):Category == with
id: (A:Obj) -> (A->A)
default
id(A: Obj):(A->A) == (a:A):A +-> a --rhx: I changed this line.
homList(A:Categorify P,B:Categorify P):SingleInteger == add
should probably read
homList(A:Categorify P,B:Categorify P):List(A->B) ==
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