awk '/^)abbrev domain EXPR Expression/,/^@/ {print}' expr.spad.pamphlet
|grep '^[ \t]*Rep'
Rep := Fraction MP
Rep := MP
Rep := FreeAbelianGroup K
Rep := K
Expression(R) does not just have ONE representation, but the
representation depends on the parameter R.
As you can see from the nesting of this line
https://github.com/hemmecke/fricas-svn/blob/master/src/algebra/expr.spad.pamphlet#L112
,,, in case R is Integer, FriCAS will use Fraction(MP) where
MP ==> SparseMultivariatePolynomial(R, K)
K ==> Kernel %
Looks like the documentation is not lying. It's "Kernel over Expression"
(% here stands for Expression(R)).
Then look into
https://github.com/hemmecke/fricas-svn/blob/master/src/algebra/kl.spad.pamphlet#L226
to find out what Kernel(S) can do with the parameter S.
It's only
argument: % -> List S
kernel : (OP, List S, N) -> %
that are important.
So unless you construct an infinite kernel that refers from one of its
arguments back to itself (which is impossible without tricks, since the
arguments must be existing before you can give them to the "kernel"
function), there must be a base case (basically a symbol or nullary
operator) that does not involve any expression.
So yes, the Expression/Kernel data structures are recursive. But there
is no problem with the actual representation.
For a developer one can consider an Expression as a multivariate
polynomial where the variables might have a quite complicated structure.
But if you go down this complicated structure, you remove one complexity
level after the other.
Ralf
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