Hello Waldek,
the code below is a cut down version of what I would like to have.
In fact, the code works if I replace the line
Y: (E: EuclideanDomain, A: QEtaAlgebra E) -> QEtaComputationCategory(E, A)
by
Y: QEtaComputationCategory(C, F)
and use Y instead of Y(C, F) in the body of algebraBasis.
However, I would like Y to be a functor, because, roughly speaking,
there would be another parameter F2: QEtaAlgebra(C) and I would like to
call a function from Y(C, F2).
I've seen a similar construction in Aldor.
https://github.com/pippijn/aldor/blob/master/aldor/lib/algebra/src/multpoly/multpolydom/sm_rmp.as#L28
=============================================================
RecursiveMultivariatePolynomial0(_
UP: (R: Join(ArithmeticType, ExpressionType), avar: Symbol == new()
) -> UnivariatePolynomialAlgebra(R), _
R :Ring, _
V : VariableType): RecursiveMultivariatePolynomialCategory0(R,V) with {
univariate: % -> UP %;
++ `univariate(p)' returns `p' as a univariate polynomial
++ w.r.t. its main variable. This assumes that `p'
++ is not a constant.
multivariate: (UP(%), V) -> %;
++ `multivariate(p,v)' returns `p' as a multivariate
++ polynomial whose main variable is `v'. An error
++ is raised if one coeffcient of `p' does not have
++ degree zero w.r.t. `v'.
} == add {
import from Boolean, R, V, Z, MI, NNI;
RVU ==> Record(var:V,terms:U);
U ==> UP(%);
Rep == Union(base:R,poly:RVU);
......
}
=============================================================
There, the R in the definition of the argument UP is local and not the
same as the R: Ring (second argument of RecursiveMultivariatePolynomial0).
When I compile the attached qq.spad, I get the following...
------------------------------------------------------------------------
initializing NRLIB QETAPKG1 for QEtaPackage1
compiling into NRLIB QETAPKG1
compiling exported algebraBasis : (F,List F) -> List F
****** comp fails at level 4 with expression: ******
error in function algebraBasis
(SEQ
(LET (|:| |y| (Y C F))
(|initialize| | << m >> |))
(|exit| 1 (|return| 1 (|basisElements| |y|))))
****** level 4 ******
$x:= m
$m:= (List A)
$f:=
((((|y| #) (|m| # . #1=#) (|t| # #) (|m| . #1#) ...)))
>> Apparent user error:
Cannot coerce m
of mode (List F)
to mode (List A)
Replacing A by F in the specification of Y, is not an option, since
eventually, I like to call Y(C, F2) and it doesn't work anyway. It gives
------------------------------------------------------------------------
initializing NRLIB QETAPKG1 for QEtaPackage1
compiling into NRLIB QETAPKG1
compiling exported algebraBasis : List F -> List F
Internal Error
Error while instantiating type YCF
Any idea how I can pass a functor in SPAD?
Ralf
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)abbrev category QETAALG QEtaAlgebra
QEtaAlgebra(C: CommutativeRing): Category == CoercibleTo OutputForm
)abbrev category QETACAT QEtaComputationCategory
QEtaComputationCategory(C: EuclideanDomain, F: QEtaAlgebra C): Category == with
initialize: List F -> %
basisElements: % -> List F
)abbrev package QETAPKG1 QEtaPackage1
QEtaPackage1(C, F, Y): Exports == Implementation where
C: EuclideanDomain
F: QEtaAlgebra C
Y: (E: EuclideanDomain, A: QEtaAlgebra E) -> QEtaComputationCategory(E, A)
Exports ==> with
algebraBasis: List F -> List F
Implementation ==> add
algebraBasis(m: List F): List F ==
y: Y(C, F) := initialize(m)
return basisElements y
