On 5 October 2017 at 01:09, Ralf Hemmecke <[email protected]> wrote:
> On 10/05/2017 02:32 AM, Bill Page wrote:
>>> I think current situation is a good compromise. We can
>>> say in documentation that all instances of Maybe share
>>> a common value of failed(), and nested usage of Maybe
>>> is not recommended, Maybe should not be used as Rep
>>> itself but can be part of Rep. Do you agree?
>
>> I value correctness much more than performance except in
>> the most extreme and special cases.
>
> There is no general "correctness". Code only behaves correctly
> with respect to a certain specification.
>
OK perhaps some word other than "correctness" would be better. Anyone
can write some arbitrary specification after the fact in order to
claim that a given piece of code is "correct". What I am concerned
about is consistency of FriCAS as a whole.
> As Qian said, the specification would claim Maybe to a very
> special case. There is a fixed value "failed()" and that is global
> over all domains and not element of any other domain than
> Maybe(X).
I do not want 'Maybe' to be a special case, like not other domain in
FriCAS. It would be completely against the design philosophy of the
original Axiom system to introduce a "fixed value that is global over
all domains".
> Then Maybe(X) represensts
>
> X \cup \{failed()\}
>
> With that, of course, Maybe(Maybe(X)) must behave like Maybe(X).
You did not define what you mean by \cup . Types are not sets. \cup
could be take to be disjoint union in which case
X \cup \{failed()\}
is not equal to
\cup \{failed()\} \cup \{failed()\}
> I don't see any (big) problem with that, just that Maybe(X) is not the
> same as extending the domain by some new element, but it stands
> for "adding failed() to the domain". I don't see any problem with
> "correctness".
failed() is not a value, it is the absence of a value.
> However, then I would really opt for another name. Otherwise one might
> think that Maybe behaves according to the type equation
>
> FX = 1 + X
>
> (see https://wiki.haskell.org/Maybe). Actually, I don't know whether
> "Nothing" in Haskell is a global value, but I guess, it it not.
>
In Haskell Maybe is a functor.
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