Racket:

  > (define (fact n)
      (if (= n 1)
          1
          (* n (fact (- n 1)))))
  > (fact 6)
  720

  # let rec fact = function
      | 1 -> 1
      | n when n > 1 -> n * (fact (n - 1))
    in fact 6;;
  - : int = 720

If you can provide (valid!) methods `T -> U` and `U -> T` for two types, why wouldn't `T = U` hold? (Atleast for types where `=` makes sense)

This is the definition I am using:

> S is a subtype of T, written S <: T, if a value of type S can safely be used in any context where a value of type T is expected.

from Pierce's "Software Foundations"

Of course, you may not want to make `String <: Number` and `Number <: String` (and thus `String = Number`), because there is no sensible way to do so; but this is an issue with the way PHP/JS handles subtyping, not with the notion of subtyping itself and certainly does not apply to the example of nullable types.

Unfortunately, I am not familiar enough with C++ to comment on the other question, sorry!

But surely, you can still use subtyping in other cases -- when it is already unboxed -- right?

Like so: `T <: T?` for all boxed `T`.

the presence of an implicit conversion rule `T -> T?` amounts to the observation that `T <: T?`, where <: is the subtyping relation

> make an unboxed integer nullable ...

I don't think any language allows this, in any case disallowing nullability for unboxed types amounts to the observation that `P !<: P?`, where !<: is "does not subtype"

I believe (unless I have misunderstood you) that both your examples are subsumed (heh) by subtyping

It seems aerospace engineers are just like priests and counselors in the courts of ancient kings.....

Comments URL: https://news.ycombinator.com/item?id=37055742

Points: 1

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Peak HN.

Comments URL: https://news.ycombinator.com/item?id=33050829

Points: 62

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Comments URL: https://news.ycombinator.com/item?id=30332436

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[0] - https://fonts.adobe.com/fonts/eb-garamond

Comments URL: https://news.ycombinator.com/item?id=30154885

Points: 7

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The main issue I have with these is that they are more geared towards beginners and focus on things like what ints/floats/strings are and what functions are etc,etc,, Is there a place where I can get a quick-and-dirty overview of the language that are geared towards people who are familiar with at least the basics preferable something that's short-ish (not book-length).

Come to think of it, is there any good way to find such tutorials for other languages/frameworks, preferably some central repo/collection (like Github "Awesome" lists) where I can find tutorials specific to my experience level in that language/framework?

Comments URL: https://news.ycombinator.com/item?id=27668109

Points: 2

# Comments: 3

Did anybody think this through more than once?

I would just like to point out that the GP did mention,

>...not culturally specific to Chinese...