Fixes new Coq master warning deprecated-hint-without-locality.

Tej Chajed authored 4 years ago and Robbert Krebbers committed 4 years ago

Set Default Goal Selector "!" makes it illegal to ever apply a tactic
with more than one goal (instead, must focus with bullets or braces).

Fix both an error by my, and a provide compatibility with older Coq versions
whose `lia` is less powerful.

This follows iris/iris!387
This closes issue #54.

Thanks to @jules for the suggestion and an initial proof.

For example, change `(!! i)` into `(.!! x)` so that `!!` can also be used as
a prefix, as done in VST for example.

This closes issue #42.

I have used the `sed` script below. This script took care of nearly all uses
apart from a few occurrences where a space was missing, e.g. `(,foo)`. In
this case, `coqc` will just fail, allowing one to patch up things manually.

The script is slightly too eager on Iris developments, where it also replaces
`($ ...)` introduction patterns. When porting Iris developments you thus may
want to remove the line for `$`.

```
sed '
s/(= /(.= /g;
s/ =)/ =.)/g;
s/(≠ /(.≠ /g;
s/ ≠)/ ≠.)/g;
s/(≡ /(.≡ /g;
s/ ≡)/ ≡.)/g;
s/(≢ /(.≢ /g;
s/ ≢)/ ≢.)/g;
s/(∧ /(.∧ /g;
s/ ∧)/ ∧.)/g;
s/(∨ /(.∨ /g;
s/ ∨)/ ∨.)/g;
s/( /(. /g;
s/ )/ .)/g;
s/(→ /(.→ /g;
s/ →)/ →.)/g;
s/($ /(.$ /g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(, /(., /g;
s/ ,)/ ,.)/g;
s/(∘ /(.∘ /g;
s/ ∘)/ ∘.)/g;
s/(∪ /(.∪ /g;
s/ ∪)/ ∪.)/g;
s/(⊎ /(.⊎ /g;
s/ ⊎)/ ⊎.)/g;
s/(∩ /(.∩ /g;
s/ ∩)/ ∩.)/g;
s/(∖ /(.∖ /g;
s/ ∖)/ ∖.)/g;
s/(⊆ /(.⊆ /g;
s/ ⊆)/ ⊆.)/g;
s/(⊈ /(.⊈ /g;
s/ ⊈)/ ⊈.)/g;
s/(⊂ /(.⊂ /g;
s/ ⊂)/ ⊂.)/g;
s/(⊄ /(.⊄ /g;
s/ ⊄)/ ⊄.)/g;
s/(∈ /(.∈ /g;
s/ ∈)/ ∈.)/g;
s/(∉ /(.∉ /g;
s/ ∉)/ ∉.)/g;
s/(≫= /(.≫= /g;
s/ ≫=)/ ≫=.)/g;
s/(!! /(.!! /g;
s/ !!)/ !!.)/g;
s/(⊑ /(.⊑ /g;
s/ ⊑)/ ⊑.)/g;
s/(⊓ /(.⊓ /g;
s/ ⊓)/ ⊓.)/g;
s/(⊔ /(.⊔ /g;
s/ ⊔)/ ⊔.)/g;
s/(:: /(.:: /g;
s/ ::)/ ::.)/g;
s/(++ /(.++ /g;
s/ ++)/ ++.)/g;
s/(≡ₚ /(.≡ₚ /g;
s/ ≡ₚ)/ ≡ₚ.)/g;
s/(≢ₚ /(.≢ₚ /g;
s/ ≢ₚ)/ ≢ₚ.)/g;
s/(::: /(.::: /g;
s/ :::)/ :::.)/g;
s/(+++ /(.+++ /g;
s/ +++)/ +++.)/g;
' -i $(find -name "*.v")
```

This follows the associativity in Haskell. So, something like

  f <$> g <$> h

Is now parsed as:

  (f <$> g) <$> h

Since the functor is a generalized form of function application, this also now
also corresponds with the associativity of function application, which is also
left associative.

This allows for more control over `Hint Mode`.

This instance leads to exponential failing searches.

See also Coq bug #5712.

Rename:

- prefix_of -> prefix and suffix_of -> suffix because that saves keystrokes
  in lemma names. However, keep the infix notations with l1 `prefix_of` l2 and
  l1 `suffix_of` l2 because those are easier to read.
- change the notation l1 `sublist` l2 into l1 `sublist_of` l2 to be consistent.
- rename contains -> submseteq and use the notation ⊆+

This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.

Also, make our redefinition of done more robust under different
orders of Importing modules.

Also do some minor clean up.