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The fix consists in using declared_ids to guarantee that we never
define symbols that have not been declared at the current assertion
level in models. A proper fix requires a lot of work as we need to
rework the push/pop mechanism of CDCL.

This PR is rebased #1280 to ensure we won't mix identifiers from
different assertion levels as it could happen with string-based
identifiers.

This PR changes the way we construct identifiers for names (in Symbols) and
variables (in Var).

We plan to completely replace the AE identifiers with identifiers from Dolmen.
This PR serves as an intermediate step from string-based identifiers to Dolmen
identifiers.

- All the identifiers are now managed in the Id module.
- Constant terms are used for declared or defined identifiers in the input file.
- Internal identifiers are still pre-mangled strings. Replacing them with
  Dolmen identifiers requires careful investigation, particularly in the AC(X)
  implementation.
- I haven't removed Id.typed yet. After this PR, the user identifiers will be
  typed, so we do not need to store them separately. If we use the internal
  type of the identifier, we will need to implement a conversion function from
  Dolmen type to Alt-Ergo type, which is not trivial. I prefer keeping this
  type and remove it after transitioning from Alt-Ergo types to Dolmen types.
- The new API of Id prevents us from creating duplicate fresh/fresh_ac/abstract
  identifiers.
- I still check that user identifiers do not start with . or @. In Before this
  PR, we mangled the identifier if it happened. In this PR, we crash. I don't
  have a strong opinion on this behavior, it was just simpler to implement
  this way.
- I use identifiers for term variables too. I preserved the internal
  representation because:
  1. The notion of local variables is AE-specific, whereas the local name in
     Dolmen identifiers is a distinct concept.
  2. After this PR, variables are typed but what is the type of Underscore?
     May be forall a. a?

This PR have been tested on ae-format (+2-2).
The fix consists in using `declared_ids` to guarantee that we never
define symbols that have not been declared at the current assertion
level in models. A proper fix requires a lot of work as we need to
rework the push/pop mechanism of CDCL.

This PR is rebased OCamlPro#1280 to ensure we won't mix identifiers from
different assertion levels as it could happen with string-based
identifiers.
@Halbaroth Halbaroth linked an issue Jan 30, 2025 that may be closed by this pull request
@Halbaroth Halbaroth marked this pull request as draft February 19, 2025 15:43
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CDCL produces model values for popped symbols

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