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From "The effects of higher-order state and control on local relational reasoning"

- The typeclass `PureExec e1 e2` controls pure deterministic
  reductions
- General tactics rel_pure_l and rel_pure_r that depend on that typeclass
- The same typeclass can be used for WP tactics and tp tactics, potentially

- Add more binary ops to the language
- An example refinement for module types

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

- Remove commented out code
- Pull std++ related lemmas into a separate file

Dan Frumin authored May 11, 2017 and Dan Frumin committed Jul 03, 2017

We are switich away from De Bruijn indices because
1) it's hard to read terms with De Bruijn indices
2) they are making lots of things slower

A new formulation allows for doing more work inside HOSL.

Γ ⊨ e ≤log≤ e' : τ <=>
∀ Δ vvs ρ,
  spec_ctx ρ -∗
  □ ⟦ Γ ⟧* Δ vvs -∗
  ⟦ τ ⟧ₑ Δ (e.[env_subst (vvs.*1)], e'.[env_subst (vvs.*2)])

The case of lam and case expressions that before required the terms to be
well-typed now require terms to be closed.

Separated definition context and context refinement from soundness_binary file.

Squashed commit of the following:

commit a8d2dd620df2fe8531b590811b7f08d2bc1289b4
Author: Amin Timany <amintimany@gmail.com>
Date:   Sun May 29 13:54:07 2016 +0200

    Prove refinement of fine/coarse-grained stack

commit 6347ef920581b4f21b5dfa74d288afcf482c9b50
Author: Amin Timany <amintimany@gmail.com>
Date:   Sun May 29 01:37:23 2016 +0200

    Backup

commit 39552d8055f55458c9515e629707d496e26e92b7
Author: Amin Timany <amintimany@gmail.com>
Date:   Sat May 28 22:40:02 2016 +0200

    Backup

This is to avoid confusion when Coq loads the module.

There is one admit that needs to be taken care of. The admitted case is validity
of a monoid element of iprod. At the moment iris doesn't seem to have necessary
lemmas to prove this easily.

We still need to prove the many admitted lemmas in rules_binary module.