Let's abbreviate U := UnivariateTaylorSeries(Expression Integer,x,0) and
E := Expression(Integer).
That's what Axiom does. It tries to coerce to U, there is no such coerce
function.
But x::U works just fine.
Try the same thing in a .spad file and the compiler will complain.
(Better use a .as file and compile with Aldor. I cannot say much about
SPAD, since I don't know for sure.)
x::U on a command line is given to the interpreter. The interpreter
tries to be smart and tries hard to find a way to achieve what it
believes you meant.
Then maybe after checking some other coerce functions that
fail, it finds a coercion to Expression(Integer), furthermore there is
function *: (E, U) -> U. So Axiom does a minimal thing: it interprets
x*y as (x::E)*y
note that the coercion to U would go like
(x::E::U) * y
So x::U is equivalent to x::E::U?
I cannot say for sure. Some other Axiom gurus know how to ask axiom what
exact function call the interpreter actually finds. I don't. Keep
waiting or write to the axiom-developer mailing list. I am sure someone
is listening.
and would then be more costly. You surely also consider that
unreasonable to go the long way if there is a shorter path. No?
I'm just wondering why it doesn't try x::U right off.
Maybe it does. But as I said. There is no function coerce: Symbol->U.
So it fails and has to look for something else.
I'm getting the (probably wrong) impression that it looks at x::U,
decides that that's too long, then goes for x::E. I would think that
deciding x::U is too long would be too long.
Try to write an interpreter then you (maybe) appreciate what it
currently does and have some mercy with it. ;-)
Ralf
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