On Mon, Apr 16, 2012 at 08:16:42PM +0200, Waldek Hebisch wrote:
> Serge D. Mechveliani wrote:
> >
> > I am sorry, may I ask, again, a question about categories and standard
> > constructors?
> > This time it is more concrete.
> > Concerning my request on adding categories to standard constructors
> > Waldek wrote
> >
> > > Why do you need Integer (etc.) to have ParseCategory? You can have:
> > >
> > > ParseCategory(T : SetCategory) : Category == SetCategory with
> > > parseElem : String -> Product(T, String)
> > > [..]
> > >
> > > and then implement packages of that category.
> >
> > 2. Here is a concrete and small contrived example/question presented by
> > an Haskell program.
> >
>
> [..]
> Now, I admit that if you insist on your interface, that is
> all you have is just a type (which is build from limited
> set of constructors but allows arbitrary composition), then
> Spad does not offer solution to you problem (as opposed
> to workarounds).
Let it be all compositions of Integer, Product, List.
If `show' works for this, then I can program all the rest.
> OTOH, when we look at your real problem (that is of creating
> Haskell interface), than I feel that there is quite
> satisfactory solution. Namely, you start from a string
> describing type. Parsing this string you create type
> and a package containg appropriate function(s): a
> function to parse strings to the type and a function to
> unparse elements of the type to stings. Concretely, you have:
>
> UnparserCategory(T : Type) : Category == with (show : T -> Sting)
>
> SparseUnivariatePolynomialUnparser(R : Ring, UR : UnparserCategory(R)) : _
> UnparserCategory(SparseUnivariatePolynomial(R))
> == add
> show(x) ==
> x = 0 => "([], [])"
> dl := List(NonNegativeInteger) := reverse(map(degree, monomials(p)))
> cl := List(String) := reverse(map(show$UR, coefficients(p)))
> s1 : String := toString(first(dl))
> s2 := frist(cl)
> for i in rest(dl) for c in cl repeat
> s1 := concat(toString(i), concat(", "), s1)
> s2 := concat(c, concat(", "), s2)
> concat(["([", s1, "], [", s2, "])"])
>
> Note: I assumed that there is a function to convert integers to
> strings. ATM one has to do something like
>
> toString(i : Integer) : String == FORMAT(nil, "~d", i)$Lisp
>
> or
>
> toString(i : Integer) : String == unparse(i::InputForm)$InputForm
>
>
> Case of Product is easier:
>
> ProductUnparser(A : SetCategory, B : SetCategory,
> UA : UnparserCategory(A), UB : UnparserCategory(B)) _
> : UnparserCategory(Product(A, B))
> == add
>
> show(x) ==
> concat("[", concat(show(first(x))$UA, concat(", ", _
> concat(show(second(x)$UB, "]")))))
If you also similarly define `show' for List, will this work for
show ([ [construct(1,2), construct(3,4)],
[construct(5,6), construct(7,8)] ]
:: List List Product(Int, Int))
?
Thanks,
------
Sergei
[email protected]
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