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UniMath / SymmetryBook

This book will be an undergraduate textbook written in the univalent style, taking advantage of the presence of symmetry in the logic at an early stage.
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Notation for constructors #113

Open UlrikBuchholtz opened 3 years ago

UlrikBuchholtz commented 3 years ago

Currently, many constructors, inl, inr, refl, are written with the argument as a subscript, but we also type them as functions. Perhaps it would be better to just use function application notation?

DanGrayson commented 3 years ago

Perhaps we could do it this way: use the notation foo_x only for families of elements in a family of types, and use the notation foo(x) only for function application. Section 2.2, where families are introduced. We could easily edit that to adhere to such a standard, and that would remove some notation ambiguity that will be irksome for the student.

marcbezem commented 3 years ago

As we discussed, this could become problematic if the subscript is a complicated expression, or is itself a family of elements. Sometimes, computations will happen in the subscript. I'm in favour of allowing both in all cases, dependent and non-dependent. For example, a sequence in R could be denoted as a function s : N -> R and also as a family of elements s_n for any n:N. In any particular case one can then make the best choice. In some cases the choices can be equally good.

DanGrayson commented 3 years ago

Yes, it can be a matter of taste whether you use a family or a function. Similarly, it can be a matter of taste whether you want subscripts or function applications.

bidundas commented 3 years ago

Agree. We don't need to be totally consistent at just this point.

Bjorn

On 1 Jul 2021, at 19:22, Daniel R. Grayson @.***> wrote:

Yes, it can be a matter of taste whether you use a family or a function. Similarly, it can be a matter of taste whether you want subscripts or function applications.

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