> int - the generic signed integer type; its size is platform dependent

"generic" means something like "vanilla" here, not "generic type". The choice 
of words is a newbie trap.

As to your results:

> the int refers to specific type rather than a type class

Yes, see above.

> the type int is distinct from int64, even on a 64bit platform
> 
> int64 is not implicitely convertible to int

Yes, for a reason: `int` is designed to be platform-dependent, `int64` is not. 
The compiler treating them as equivalent would be a bad idea. Even types which 
are identical on every platform can be distinct, we even have a keyword for it: 
`type myInt = distinct int`. Nim generally doesn't do many automatic type 
conversions out of the box, that's intentional.

> the type class int does not include the type int64 , i.e.

It's not a type class, see above

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