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## Presentation
This folder contains the F* proof of the correctness of the translation from the default calculus
This folder contains the F\* proof of the correctness of the translation from the default calculus
to the target lambda calculus. The proof is organized as follows:
* `Catala.DefaultCalculus.fst` contains the semantics of the default calculus as well as the
- `Catala.DefaultCalculus.fst` contains the semantics of the default calculus as well as the
type safety theorems and proofs;
* `Catala.LambdaCalculus.fst` contains the semantics of the lambda calculus as well as the
- `Catala.LambdaCalculus.fst` contains the semantics of the lambda calculus as well as the
type safety theorems and proofs;
* `Catala.Translation.Helpers.fst` contains various helpers related to the lambda calculus,
- `Catala.Translation.Helpers.fst` contains various helpers related to the lambda calculus,
used in the translation correctness proof;
* `Catala.Translation.fst` contains the definition of the translation as well as its proof
- `Catala.Translation.fst` contains the definition of the translation as well as its proof
of correctness, culminating in the last wrap-up theorem of the file.
The `*.hints` files are merely F\* technical helper files that speed up the proof replay by recording
a list of lemmas to feed in priority to the SMT solver.
## Proof replay
To replay the proofs, you will need to have [F*](https://github.com/FStarLang/FStar) installed
on your machine, and the `FSTAR_HOME` environement variable pointed to the location of the F*
To replay the proofs, you will need to have [F\*](https://github.com/FStarLang/FStar) installed
on your machine, and the `FSTAR_HOME` environement variable pointed to the location of the F\*
directory. You can then replay the proofs using:
make verify
@ -28,19 +31,10 @@ sure to strenghen the flaky proofs for the camera-ready version of the artefact.
## Disclaimer
This mechanization contains two distinct admitted lemmas, all related to administrative aspects of
the target lambda calculus. Both are in `Catala.TranslationHelpers.fst`.
This mechanization contains one admitted lemma, related to administrative aspects of
the target lambda calculus. It is in `Catala.TranslationHelpers.fst`.
* The first admit concerns `well_typed_terms_invariant_by_subst`, which is a classic result stating
that correclty typed terms with no free variables are invariant by substitution. The proof in F*
needs a version of context invariance different from the one we used to prove type safety, hence
this temporary admit.
* The second assumed hypothesis in inside `lift_multiple_l_steps_exceptions_head`, and is related
two lambda calculus terms, `init0` and `init2`. `init2` is the result of the double application
of the beta-reduction to `init0`. Both terms are reduced versions of the big, deeply embedded
term `process_exceptions`, which causes F* automation a lot of troubles. The difficulty with
the proof seems to stem from the instantiations of `well_typed_terms_invariant_by_subst`, which
is missing some key step.
We plan of course to prove those two hypothesis in due time for an upcoming artefact, and hope these
explanations did convince you that the rest of the proof remains solidly grounded.
The admit concerns `well_typed_terms_invariant_by_subst`, which is a classic result stating
that correclty typed terms with no free variables are invariant by substitution. The proof in F\*
needs a version of context invariance different from the one we used to prove type safety, hence
this temporary admit.