Simulacrum VS refined

The Cats ecosystem offers mature named abstractions providing algebraic laws virtually identical to those offered by Haskell and PureScript and that have stood the test of time, at the cost of relying on a "design pattern" approach to implementation you have to squint a bit to see ("typeclasses" based on higher-kinded types and implicit arguments) and that sometimes doesn't play nicely with Scala's colored local type inference. The selling point of this, coupled with parametricity ("tagless-final style"), is the ability to reason algebraically about your code.

Scala has quite good support for refined types across multiple libraries. A solution using the refined library might look something like

Does the Refined library for Scala (at https://github.com/fthomas/refined; "eu.timepit" %% "refined") work in Scala 3? Does it work differently?

I'm trying to create a poor man version of refined types implementation with a simple validation of string content and check the return type via Implicit evidence on another function. It seems that the type got erased after it got returned from the check

Scala likes to do design-by-contract on the type level. You encode your pre- and post- conditions into types. Libraries like iron (scala 3) https://github.com/Iltotore/iron and refined (scala 2) https://github.com/fthomas/refined allow you to do all that without throwing any exceptions and they can even enforce some simple predicates at compile time.

Annotation is not the only way (and probably not the best IMHO) to do refined types. You might be interested in Iron in Scala 3 or Refined in Scala 2/3.

I think the way you model problems in Ada is superficially similar to refined types you find in some functional languages (e.g. Scala).

In one respect, nothing. You’re right. Even given refinement types as in Haskell or Scala, there is indeed a necessarily-partial function (refineV in Scala) to refine a value to its refinement type.

Perhaps refined would help you? It lets you set constraints (i.e. "rules") for values / types. You get compile-time enforcement for constants and fallible methods for runtime values (i.e. Either[Error, RefinedValue]).

This is more or less how derivation works when you want to use something like Refined types (it exposes Validate[Type, Refinement] typeclass if I remember correctly). Enumeratum exposes Enum[A], and newtypes expose Coercible[From, To].

You will probably be interested into Iron or Refined.