GitLab

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

(These instances are not defined for any FinMap to avoid overlapping
instances for EqDecision, which may have awkward consequences for
type class search).

This reverts commit 20b4ae55bdf00edb751ccdab3eb876cb9b13c99f, which does
not seem to work with Coq 8.5pl2 (I accidentally tested with 8.5pl1).

This makes type checking more directed, and somewhat more predictable.

On the downside, it makes it impossible to declare the singleton on
lists as an instance of SingletonM and the insert and alter operations
on functions as instances of Alter and Insert. However, these were not
used often anyway.

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.

The port makes the following notable changes:

* The carrier types of separation algebras and integer environments are no
  longer in Set. Now they have a type at a fixed type level above Set. This
  both works better in 8.5 and makes the formalization more general.
  I have tried putting them at polymorphic type levels, but that increased the
  compilation time by an order of magnitude.
* I am using a custom f_equal tactic written in Ltac to circumvent bug #4069.
  That bug has been fixed, so this custom tactic can be removed when the next
  beta of 8.5 is out.

It would still be far more efficient to have a counter for the next memory
index in the executable semantics/frontend.

Major changes:
* Make void a base type, and include a proper void base value. This is necessary
  because expressions (free, functions without return value) can yield a void.
  We now also allow void casts conforming to the C standard.
* Various missing lemmas about typing, weakening, decidability, ...
* The operations "free" and "alloc" now operate on l-values instead of r-values.
  This removes some duplication.
* Improve notations of expressions and statements. Change the presence of the
  operators conforming to the C standard.

Small changes:
* Use the classes "Typed" and "TypeCheck" for validity of indexes in memory.
  This gives more uniform notations.
* New tactic "typed_inversion" performs inversion on an inductive predicate
  of type "Typed" and folds the premises.
* Remove a horrible hack in the definitions of the classes "FMap", "MBind",
  "OMap", "Alter" that was used to let "simpl" behave better. Instead, we have
  defined a tactic "csimpl" that folds the results after performing an
  ordinary "simpl".
* Fast operation to remove duplicates from lists using hashsets.
* Make various type constructors (mainly finite map implementations) universe
  polymorphic by packing them into an inductive. This way, the whole C syntax
  can live in type, avoiding the need for (slow) universe checks.

This commit includes the following changes:
* More theorems about pre-, partial and total orders.
* Define the lexicographic order on various commonly used data types.
* Mergesort and its correctness proof.
* Implement finite maps and sets using ordered association lists.

The refactoring includes:
* Use infix notations for the various list relations
* More consistent naming
* Put lemmas on one line whenever possible
* Change proofs into one-liners when possible
* Make better use of the "Implicit Types" command
* Improve the order of the list module by placing all definitions at the start,
  then the proofs, and finally the tactics.

Besides, there is some new machinery for proofs by reflection on lists. It is
used for a decision procedure for permutations and list containment.

Both the operational and axiomatic semantics are extended with sequence points
and a permission system based on fractional permissions. In order to achieve
this, the memory model has been completely revised, and is now built on top
of an abstract interface for permissions.

Apart from these changed, the library on lists and sets has been heavily
extended, and minor changed have been made to other parts of the prelude.

The development now corresponds exactly to the FoSSaCS 2013 paper.
Also, the prelude is updated to the one of the master branch.

* Define the standard strict order on pre orders.
* Prove that this strict order is well founded for finite sets and finite maps.
  We also provide some utilities to compute with well founded recursion.
* Improve the "simplify_option_equality" tactic to handle more cases.
* Axiomatize finiteness of finite maps by translation to lists, instead of by
  them having a finite domain.
* Prove many additional properties of finite maps.
* Add many functions and theorems on lists, including: permutations, resize,
  filter, ...

Most interestingly:
* Use [lia] instead of [omega] everywhere
* More many generic lemmas on the memory to the theory on finite maps.
* Many additional list lemmas.
* A new interface for a monad for collections, which is now also used by the
  collection tactics.
* Provide an additional finite collection implementation using unordered lists
  without duplicates removed. This implementation forms a monad (just the list
  monad in disguise).

The following things have been changed in this revision:

* We now give a small step semantics for expressions. The denotational semantics
  only works for side-effect free expressions.
* Dynamically allocated memory through alloc and free is now supported.
* The following expressions are added: assignment, function call, unary
  operators, conditional, alloc, and free.
* Some customary induction schemes for expressions are proven.
* The axiomatic semantics (and its interpretation) have been changed in order
  to deal with non-deterministic expressions.
* We have added inversion schemes based on small inversions for the operational
  semantics. Inversions using these schemes are much faster.
* We improved the statement preservation proof of the operational semantics.
* We now use a variant of SsReflect's [by] and [done], instead of Coq's [now]
  and [easy]. The [done] tactic is much faster as it does not perform
  inversions.
* Add theory, definitions and notations on vectors.
* Separate theory on contexts.
* Change [Arguments] declarations to ensure better unfolding.

improve some definitions, simplify some proofs.

The main changes are:

* Function calls in the operational semantics
* Mutually recursive function calls in the axiomatic semantics
* A general definition of the interpretation of the axiomatic semantics  so as
  to improve reusability (useful for function calls, and also for expressions
  in future versions)
* Type classes for stack independent, memory independent, and memory extensible
  assertions, and a lot of instances to automatically derive these properties.
* Many additional lemmas on the memory and more robust tactics to simplify
  goals involving is_free and mem_disjoint
* Proof of preservation of statements in the smallstep semantics

* Some new tactics: feed, feed destruct, feed inversion, etc...
* More robust tactic scripts using bullets and structured scripts
* Truncate most lines at 80 characters