Re: [Axiom-developer] "has" and "with" (was curious algebra failure)

[Bill Page]

On 8/13/07, Gabriel Dos Reis wrote:
> ...
> When compiling the default definition of ** for Monad, the compiler
> notices that expt comes from RepeatedSquare(S), where S is the
> parameter of type Monad to Monad&.

This use of S is confusing to me. The spad code says:

   import RepeatedSquaring(%)

The S that I see is the *formal* parameter of RepeatedSquaring. It's type is

    SetCategory with "*": (%, %) -> %

as defined in repsqr.spad. But in Monad the parameter % in

   import RepeatedSquaring(%)

refers to some domain (currently unknown) that has type Monad.

How can I reconcile that with your statements about S above? Is the
"S" to which you refer some kind of dummy?

> If compiles all arguments x and n fine.
> Then it has to compile the package RepeatedSquare(S) -- as if it were
> a function call, since all instantiations are function calls.  To achieve
> that it asks the question whether S (of type Monad) is coercible to
>
>    SetCategory with "*": (%, %) -> %
>
> And the definition of coercible does not permit to return "yes".
>

But certainly it must return "yes" in an unmodified version of the
Spad compiler or (perhaps)  what needs to be coercible is not S of
type Monad but rather the dummy %. It's type is the category-value of
Monad:

  SetCategory with
       "*": (%,%) -> %
       rightPower: (%,PositiveInteger) -> %
       leftPower: (%,PositiveInteger) -> %
       "**": (%,PositiveInteger) -> %

which certainly is coercible to

   SetCategory with "*": (%, %) -> %

----------

Is it possible to trace how coerce is called in an unmodified Spad
compiler that compiles Monad without an error message?

Regards,
Bill Page.