I'm Working on Implementing a Programming Language All My Own

    f(x) = x * 2

"let x = 1" has the same meaning in mathematics as well as JavaScript and Rust.

Instead of := you should use => for assignment.

This is touching on a pet peeve of mine: Mathematics and programming are similar in many aspects, but this is not one of them. In mathematics = is not a comparison, but a statement.

More generally, mathematics is about tautologies, that is statements that are always true. In programming, a comparison is evaluated to either true or false.

That doesn’t mean that there’s no room for conditionals in mathematics (one example is piecewise function definitions). But it’s not the same. Heck, even the definition of “function” is different between mathematics and programming.

For example, in most languages you have a notation like f(g(h(x))) which calls the functions in the exact opposite order of reading which is unnecessarily confusing.

Personally, I think this argument only holds water for languages that are rooted in mathematics (e.g. Haskell, Lean, Rocq, F*, ...). If your computational model comes from a place of physical hardware, instructions, registers, memory etc. you're going to end up with something very different than an abstract machine based on lambda calculus. Both valid ways to design a PL.

(I find it baffling in the extreme that in many mainstream languages the convention is to write type annotations as “x: T”, both prima facie and because in those languages the notation then collides with field assignment!)

Historically, distinguishing an equality operator from an assignment one has existed for many decades. Whether using colon for the latter is "absolutely correct" is the subject of valid debate.

An equally compelling case could be made for any of the following assignment operators as well:

  foo <- 42
  foo -> 42
  foo <= 42
  foo => 42
  foo <-> 42   if expressing substitutability is important
  foo := 42    Pascal lives!
  (foo 42)     so does LISP!
  foo is 42    for those who prefer English operators
  f(foo) = 42  for mathematically inclined languages

    c = a + b;

Nope, make it explicit. You're moving the value of an expression to a placeholder. The only sensible way to write that would be

    ADD a TO b GIVING c

Modern tech is too advanced to meaningfully learn about it by tinkering with small toy projects. These "foundational technologies" are gigantic specializations that require an extraordinary investment of time to master.

Looking back now over the years, I wish I tinkered less and narrowed my focus more.