GitLab

Modify the logical relation judment to include an environment Δ that
contains a list of semantic types to interpret free type variables.

- Still does not compile

- Change the types in the examples slightly
- Use notations in the examples
- Modify some tactics to make the proofs more smooth

- This allows us to get rid of `rewrite !Closed_subst_id.`

- Twiggle with the burden of proof in log_related_arrow
- rel_rec_l/r returns a goal with an (unsimplified) lamsubst
  and can detect locked lambdas
- Fix some notational issues [hax.v]
- Rewrite the counter refinement proof to make greater use of lamsubst

We have to call tac_rel_rec_r in reshape_expr because reshape_expr
just decomposes the expression into a `(K',e')` without guaranteeing
that `e` is actually head-reducible. Because of that it might be the
case that `e` is `K[App (Rec f x e1) e2]`, but `e2` is not a value.

In the interpretation of recursive types

- rename `bin_log_related_bind_l` to `bin_log_related_wp_l`
- use `bin_log_related_wp_l` to simplify derived rules

Using the lambdasubst hack-- instead of formulating
lemmas for (App e1 v), formulate them for (e1[x:=v]).

..by introducing a hint database for typeability