On 21/07/2012, at 8:50 PM, Jacques Carette wrote:
> I think it would be better to treat things via functorial properties --
> so if a function knows how to map itself, then for all purposes T^1 will
> behave like T (i.e. in Haskell terms, fmap behaves like application).
BTW: this might be tricky in Felix because it has overloading.
> [You have discovered a number of these things yourself, as I see from
> your emails, I am just giving you what I know from experience]
We really need a theorist on board. There are a number of isomorphisms
relating to the "usual" laws of arithmetic applied to types that need
to be handled correctly:
T ^ A ^ B = T ^ (A * B)
T ^ A * T ^ B = T ^ (A + B)
N * T = T + T + T ... T (where N is a unitsum)
T ^ N = T * T * T .. T (where N is a unitsum)
etc etc. We could make all these explicit conversions,
but perhaps some of them can be implicit .. the question
is which ones? The choice isn't arbitrary or consistency
is lost, and it isn't arbitrary because it has to be reflected
in the representation.
--
john skaller
[email protected]
http://felix-lang.org
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