Manuel Eberl

2016-06-16 09:57:07 UTC

Hallo,

it appears that the infix operator $ is used both for the n-th component

of a vector and the n-th coefficient of a Formal Power Series.

Since I now use both Multivariate_Analysis and Formal_Power_Series, I

get lots of syntax ambiguity warnings all the time. We should probably

do something about this.

I see the following three options:

1. Rename one of the operators. Since Formal_Power_Series is used less

than vectors, this is probably the one to change in this case. I am not

sure, however, what it could be renamed to. The standard mathematical

notation is something like "[X^n] f", so I suppose we could go for

"⟨X^n⟩ f", but I'm not sure if that's a good idea.

2. Disable the "$" notation completely outside the FPS theory, or put it

in a locale that has to be interpreted every time one wants to use the

notation. On the down side, one still runs into problems when one wants

to use the $ notation for FPSs but has Multivariate_Analysis loaded as

well. I guess one could put both of them in locales, but I don't know if

we want that.

3. Use ad-hoc Overloading, similar to what is done for monads. One could

then also use $ e.g. for the n-th coefficient of a polynomial, or

perhaps even unify the notation with the n-th element of lists and

arrays etc. at some point. The down side of this is that when there are

ambiguities/type errors, the error messages get a bit confusing.

Note that "normal" overloading does not work, since the constant would

have to have the type "'a => nat => 'b", and that means one has to write

type annotations everywhere.

Any opinions? Whatever the outcome is, I will take care of implementing it.

Cheers,

Manuel

it appears that the infix operator $ is used both for the n-th component

of a vector and the n-th coefficient of a Formal Power Series.

Since I now use both Multivariate_Analysis and Formal_Power_Series, I

get lots of syntax ambiguity warnings all the time. We should probably

do something about this.

I see the following three options:

1. Rename one of the operators. Since Formal_Power_Series is used less

than vectors, this is probably the one to change in this case. I am not

sure, however, what it could be renamed to. The standard mathematical

notation is something like "[X^n] f", so I suppose we could go for

"⟨X^n⟩ f", but I'm not sure if that's a good idea.

2. Disable the "$" notation completely outside the FPS theory, or put it

in a locale that has to be interpreted every time one wants to use the

notation. On the down side, one still runs into problems when one wants

to use the $ notation for FPSs but has Multivariate_Analysis loaded as

well. I guess one could put both of them in locales, but I don't know if

we want that.

3. Use ad-hoc Overloading, similar to what is done for monads. One could

then also use $ e.g. for the n-th coefficient of a polynomial, or

perhaps even unify the notation with the n-th element of lists and

arrays etc. at some point. The down side of this is that when there are

ambiguities/type errors, the error messages get a bit confusing.

Note that "normal" overloading does not work, since the constant would

have to have the type "'a => nat => 'b", and that means one has to write

type annotations everywhere.

Any opinions? Whatever the outcome is, I will take care of implementing it.

Cheers,

Manuel