Re: [Axiom-developer] aldor stream oddities

[Franz Lehner]

> Now, in Axiom we should have a problem with saying that S is an additive 
> group.
That's true. All axioms are satisfied, except uniqueness of inverses 
and the neutral element. What should it be? A FuzzyAbelianGroup?
> (4) -> zero?(t-t)
>    (4)  false
>            Type: Boolean
>
> I don't.
Although zero? doesn't report it, t-t will always behave like the 0 
element. So in fact -t is the inverse of t for all practical purposes.
But I don't expect Axiom to prove equality where it is impossible to have 
a proof, just spit out a message like "true up to order n" and then prove 
equality myself.
> The category Ring is reserved for structures with complete equality testing.
Is this the plan for Axiom too?
What will happen to ExpressionField? I recall there are undecidable 
problems in the latter as well.

Here is a proposal (in SPAD) for a recursive stream generator which looks 
at all previous elements, not just the last one. It could probably be done with 
the existing generate(S->S,S), but this one looks more natural.

====================================================================
    Exports == with

      generate: (List S->S,S) -> Stream S
      ++ \spad{generate(f:List S->S,x)} generates an infinite stream
      ++ whose first element is x and whose nth element (\spad{n > 1})
      ++ is f applied to the list of all previous elements.
      ++ Note: \spad{generate(f,x) = [x,f([x]),f([x,f([x])]),..]

    Implementation == add

      lstgen:(List S->S,List S) -> Stream S

      lstgen(f:(List S) -> S,ls:List S):Stream S ==
            delay(ss:=f(ls); concat(ss, lstgen(f,concat(ls, ss))))

      generate(f:(List S)->S,s:S):Stream S == concat(s,lstgen(f,[s]))
====================================================================

again I only could test it as a package due to the bootstrap problem in 
the spoon.

regards
Franz