Bill Page wrote:
>
> Do you think we should be allowed to write something like the
> following in the OpenAxiom compiler (SPAD)?
>
> (X:Domain):Domain+->List X
>
> i.e. define a function that takes a domain as an argument and returns
> a domain? Could we use such a thing in a statically typed language? I
> suppose not.
>
In FriCAS there is no Domain, but code like this should work in
the compiler. In experimantal version of factoring code I have
(or had):
extField : FiniteAlgebraicExtensionField(F) := get_extension(n)
do_factor(p, n, extField)
and in do_factor there was loop coercing coefficients of p to
extField and calling factor(p)$extField (actually, and internal
factoring function).
The point is that get_extension tried to choose most efficient
extension and returend it. The rest of code just uses extField
only caring about its category, and not how it was choosen and
which particular extension it is.
Or look at simplifyCoeffs in pfo.spad.pamphlet. Here nR is
given by literal constructor, but parameter to this constructor
is only known at runtime. Equally well nR could have been
computed via a separate function. There is several places
in algebra where we compute new domains or packages at
runtime and than call functions from them. Due to limitation
of old Axiom compiler new domains are computed by inline
code. But in FriCAS they can by computed by functions.
Note that all that is statically known about such computed
domain is its category. If that category is Type than
there is litte which you can do with such domain. But
once you have more specific category, then such computed
domains have many uses.
Note: that is reason why categories are not first class.
With first class categories code using first class domains
would be impossible to check statically.
--
Waldek Hebisch
hebi...@math.uni.wroc.pl
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