How to make a *truly* better alternative to C++

Here, care to discuss.

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Is C++ relevant any more?

I truly doubt C++ is of any relevance in the programming world. Of course there is a percentage of software still done in C++, but with the release of even faster CPUs and memory systems, the importance of being close to the metal will fade away. Most business apps are coded in C#, VB and Java, most drivers in plain C, a good percentange of soft-real time software is quickly migrating to Java (defense apps, my domain), and hard real-time apps in Ada.

But, let's suppose, for the sake of discussion, that the world needs a compiled close-to-the-metal programming language with high-level constructs. But there are so many things that could be corrected in C++, I don't even know where to start:

1) no headers. Use import files.
2) standardize the ABI where it should be standard.
3) have garbage collection.
4) simplify syntax.
5) put type inference, first-class functions, closures.

The above is enough to turn C++ to another language, if we are to make a new language, why not forget about C++ altogether and make something fresh, something innovative, which incorporates the latest developments of the PL world?

I have mixed feelings about

I have mixed feelings about that. C++ gives you sheer power, including the one inherited from C that lets you map structs onto areas in memory.

But, let's suppose, for the sake of discussion, that the world needs a compiled close-to-the-metal programming language with high-level constructs

This is not a "let's suppose", this is a reality. A hell of a lot of software is written for microcontrollers where you need to address memory mapped GPIO and the like. C++ is far from dead in these application domains.
Granted, ADA would do nicely, but it shares the same problem as C++, that I would add as item #6 in your list:
It takes very long to become proficient in C++, and as a result, there is not much talent out there.

When programming in the large ("enterprise systems") in C++, you have to solve the problem at hand plus the problems inherent to C++ that you mentioned.

The solution probably lies in a language with the properties you described with no-fuss linkage to C or C++, a language that is not a showcase of concepts but designed for a broad application range.
I am no language designer. My current favorites are ADA and OCaml.

For some domains (low-level

For some domains (low-level programming like os-kernels, drivers or certain embedded apps) it's still neccessary to manage memory by hand and don't use a general memory manager with gc. Any replacement language must have the abilitiy to do manual memory management.

Same for typing: Too strict typing won't work for a low-level language, because sometimes you have to type data depending on the runtime context.

Maybe C/C++ are enough for all time to solve those (fewer and fewer) low-level problems, but I think too that it's a good idea to clean up those languages.

But maybe the Microsofts way to put unsecure features (like Pointers) into otherwise secure languages like C# is the way to go? What about for example a 'bare-metal' ocaml with optional 'by-hand' memory-management and unchecked type-casts? A programmer could use safe language-features for most of his program then and use unsecure features only where needed without getting impedance mismatch when interfacing the 'app' and the 'low-level' part of the program.

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