Merge from LFSC (#26)

* Showing models as coq counter examples in tactic without constructing coq terms

* also read models when calling cvc4 with a file (deactivated because cvc4 crashes)

* Show counter examples with variables in the order they are quantified in the Coq goal

* Circumvent issue with ocamldep

* fix issue with dependencies

* fix issue with dependencies

* Translation and OCaml support for extract, zero_extend, sign_extend

* Show run times of components

* print time on stdout instead

* Tests now work with new version (master) of CVC4

* fix small printing issue

* look for date on mac os x

* proof of valid_check_bbShl: some cases to prove.

* full proof of "left shift checker".

*  full proof of "rigth shift checker".

* Support translation of terms bvlshr, bvshl but LFSC rules do not exists at the moment
Bug fix for bitvector extract (inverted arguments)

* Typo

* More modularity on the format of traces depending on the version of coq

* More straightforward definitions in Int63Native_standard

* Use the Int31 library with coq-8.5

* Use the most efficient operations of Int31

* Improved performance with coq-8.5

* Uniform treatment of sat and smt tactics

* Hopefully solved the problem with universes for the tactic

* Updated the installation instructions

* Holes for unsupported bit blasting rules

* Cherry-picking from smtcoq/smtcoq

* bug fix hole for bitblast

* Predefined arrays are not required anymore

* fix issue with coq bbT and bitof construction from ocaml

* bug fix in smtAtom for uninterpreted functions
fix verit test file

* fix issue with smtlib2 extract parsing

* It looks like we still need the PArray function instances for some examples (see vmcai_bytes.smt2)

* Solver specific reification:
Each solver has a list of supported theories which is passed to Atom.of_coq, this function creates uninterpreted functions / sorts for unsupported features.

* show counter-examples with const_farray instead of const for constant array definitions

* Vernacular commands to debug checkers.
Verit/Lfsc_Checker_Debug will always fail, reporting the first proof step of the certificate that failed be checked

* Update INSTALL.md

* show smtcoq proof when converting

* (Hopefully) repared the universes problems

* Corrected a bug with holes in proofs

* scripts for tests:
create a folder "work" under "lfsc/tests/", locate the benchmarks there.
create a folder "results" under "lfsc/tests/work/" in which you'll find the results of ./cvc4tocoq.

* make sure to give correct path for your benchs...

* Checker for array extensionality modulo symmetry of equality

* fix oversight with bitvectors larger than 63 bits

* some printing functions for smt2 ast

* handle smtlib2 files with more complicated equivalence with (= ... )

* revert: ./cvc4tocoq does not output lfsc proofs...

* bug fix one input was ignored

* Don't show verit translation of LFSC proof if environment variable DONTSHOWVERIT is set
(e.g. put export DONTSHOWVERIT="" in your .bashrc or .bashprofile)

* Also sort names of introduced variables when showing counter-example

* input files for which SMTCoq retuns false.

* input files for which SMTCoq retuns false.

* use debug checker for debug file

* More efficient debug checker

* better approximate number of failing step of certificate in debug checker

* fix mistake in ml4

* very first attempt to support goals in Prop

* bvs: comparison predicates in Prop and their <-> proofs with the ones in bool
farrays: equality predicate in Prop and its <-> proof with the one in bool.

* unit, Bool, Z, Pos: comparison and equality predicates in Prop.

* a typo fixed.

* an example of array equality in  Prop (converted into Bool by hand)...
TODO: enhance the search space of cvc4 tactic.

* first version of cvc4' tactic: "solves" the goals in Prop.
WARNING: supports only bv and array goals and might not be complete
TODO: add support for lia goals

* cvc4' support for lia
WARNING: might not be complete!

* small fix in cvc4' and some variations of examples

* small fix + support for goals in Bool and Bool = true + use of solve tactical
WARNING: does not support UF and INT63 goals in Prop

* cvc4': better arrangement

* cvc4': Prop2Bool by context search...

* cvc4': solve tactial added -> do not modify unsolved goals.

* developer documentation for the smtcoq repo

* cvc4': rudimentary support for uninterpreted function goals in Prop.

* cvc4': support for goals with Leibniz equality...
WARNING: necessary use of "Grab Existential Variables." to instantiate variable types for farrays!

* cvc4': Z.lt adapted + better support from verit...

* cvc4': support for Z.le, Z.ge, Z.gt.

* Try arrays with default value (with a constructor for constant arrays), but extensionality is not provable

* cvc4': support for equality over uninterpreted types

* lfsc demo: goals in Coq's Prop.

* lfsc demo: goals in Bool.

* Fix issue with existential variables generated by prop2bool.
- prop2bool tactic exported by SMTCoq
- remove useless stuff

* update usage and installation instructions

* Update INSTALL.md

* highlighting

* the tactic: bool2prop.

* clean up

* the tactic smt: very first version.

* smt: return unsolved goals in Prop.

* Show when a certificate cannot be checked when running the tactic instead of at Qed

* Tactic improvements
- Handle negation/True/False in prop/bool conversions tactic.
- Remove alias for farray (this caused problem for matching on this type in tactics).
- Tactic `smt` that combines cvc4 and veriT.
- return subgoals in prop

* test change header

* smt: support for negated goals + some reorganization.

* conflicts resolved + some reorganization.

* a way to solve the issue with ambiguous coercions.

* reorganization.

* small change.

* another small change.

* developer documentation of the tactics.

* developer guide: some improvements.

* developer guide: some more improvements.

* developer guide: some more improvements.

* developer guide: some more improvements.

* pass correct environment for conversion + better error messages

* cleaning

* ReflectFacts added.

* re-organizing developers' guide.

* re-organizing developers' guide.

* re-organizing developers' guide.

* removing unused maps.

* headers.

* artifact readme getting started...

* first attempt

* second...

* third...

* 4th...

* 5th...

* 6th...

* 7th...

* 8th...

* 9th...

* 10th...

* 11th...

* 12th...

* 13th...

* 14th...

* 15th...

* 16th...

* 17th...

* Update artifact.md

Use links to lfsc repository like in the paper

* 18th...

* 19th...

* 20th...

* 21st...

* 22nd...

* 23rd...

* 24th...

* 25th...

* 26th...

* 27th...

* 28th...

* Update artifact.md

Small reorganization

* minor edits

* More minor edits

* revised description of tactics

* Final pass

* typo

* name changed: artifact-readme.md

* file added...

* passwd chaged...

* links...

* removal

* performance statement...

* typos...

* the link to the artifact image updated...

* suggestions by Guy...

* aux files removed...

* clean-up...

* clean-up...

* some small changes...

* small fix...

* additional information on newly created files after running cvc4tocoq script...

* some small fix...

* another small fix...

* typo...

* small fix...

* another small fix...

* fix...

* link to the artifact image...

* We do not want to force vm_cast for the Theorem commands

* no_check variants of the tactics

* TODO: a veriT test does not work anymore

* Compiles with both versions of Coq

* Test of the tactics in real conditions

* Comment on this case study

* an example for the FroCoS paper.

* Fix smt tactic that doesn't return cvc4's subgoals

* readme modifications

* readme modifications 2

* small typo in readme.

* small changes in readme.

* small changes in readme.

* typo in readme.

* Sync with https://github.com/LFSC/smtcoq

* Port to Coq 8.6

* README

* README

* INSTALL

* Missing file

* Yves' proposition for installation instructions

* Updated link to CVC4

* Compiles again with native-coq

* Compiles with both versions of Coq

* Command to bypass typechecking when generating a zchaff theorem

* Solved bug on cuts from Hole

* Counter-models for uninterpreted sorts (improves issue #13)

* OCaml version note (#15)

* update .gitignore

* needs OCaml 4.04.0

* Solving merge issues (under progress)

* Make SmtBtype compile

* Compilation of SmtForm under progress

* Make SmtForm compile

* Make SmtCertif compile

* Make SmtTrace compile

* Make SatAtom compile

* Make smtAtom compile

* Make CnfParser compile

* Make Zchaff compile

* Make VeritSyntax compile

* Make VeritParser compile

* Make lfsc/tosmtcoq compile

* Make smtlib2_genconstr compile

* smtCommand under progress

* smtCommands and verit compile again

* lfsc compiles

* ml4 compiles

* Everything compiles

* All ZChaff unit tests and most verit unit tests (but taut5 and un_menteur) go through

* Most LFSC tests ok; some fail due to the problem of verit; a few fail due to an error "Not_found" to investigate

* Authors and headings

* Compiles with native-coq

* Typo

1 files changed, 173 insertions, 0 deletions

diff --git a/src/classes/SMT_classes.v b/src/classes/SMT_classes.v
new file mode 100644
index 0000000..5f79faf
--- /dev/null
+++ b/src/classes/SMT_classes.v
@@ -0,0 +1,173 @@
+(**************************************************************************)
+(*                                                                        *)
+(*     SMTCoq                                                             *)
+(*     Copyright (C) 2011 - 2019                                          *)
+(*                                                                        *)
+(*     See file "AUTHORS" for the list of authors                         *)
+(*                                                                        *)
+(*   This file is distributed under the terms of the CeCILL-C licence     *)
+(*                                                                        *)
+(**************************************************************************)
+
+
+Require Import Bool OrderedType.
+
+(** This file defines a number of typeclasses which are useful to build the
+    terms of SMT (in particular arrays indexed by instances of these
+    classes). *)
+
+
+(** Boolean equality to decidable equality *)
+Definition eqb_to_eq_dec :
+  forall T (eqb : T -> T -> bool) (eqb_spec : forall x y, eqb x y = true <-> x = y) (x y : T),
+    { x = y } + { x <> y }.
+  intros.
+  case_eq (eqb x y); intro.
+  left. apply eqb_spec; auto.
+  right. red. intro. apply eqb_spec in H0. rewrite H in H0. now contradict H0.
+  Defined.
+
+
+(** Types with a Boolean equality that reflects in Leibniz equality *)
+Class EqbType T := {
+ eqb : T -> T -> bool;
+ eqb_spec : forall x y, eqb x y = true <-> x = y
+}.
+
+
+(** Types with a decidable equality *)
+Class DecType T := {
+ eq_refl : forall x : T, x = x;
+ eq_sym : forall x y : T, x = y -> y = x;
+ eq_trans : forall x y z : T, x = y -> y = z -> x = z;
+ eq_dec : forall x y : T, { x = y } + { x <> y }
+}.
+
+
+Hint Immediate eq_sym.
+Hint Resolve eq_refl eq_trans.
+
+(** Types equipped with Boolean equality are decidable *)
+Instance EqbToDecType T `(EqbType T) : DecType T.
+Proof.
+  destruct H.
+  split; auto.
+  intros; subst; auto.
+  apply (eqb_to_eq_dec _ eqb0); auto.
+Defined.
+
+
+(** Class of types with a partial order *)
+Class OrdType T := {
+  lt: T -> T -> Prop;
+  lt_trans : forall x y z : T, lt x y -> lt y z -> lt x z;
+  lt_not_eq : forall x y : T, lt x y -> ~ eq x y
+  (* compare : forall x y : T, Compare lt eq x y *)
+}.
+
+Hint Resolve lt_not_eq lt_trans.
+
+
+Global Instance StrictOrder_OrdType T `(OrdType T) :
+  StrictOrder (lt : T -> T -> Prop).
+Proof.
+  split.
+  unfold Irreflexive, Reflexive, complement.
+  intros. apply lt_not_eq in H0; auto.
+  unfold Transitive. intros x y z. apply lt_trans.
+Qed.
+
+(** Augment class of partial order with a compare function to obtain a total
+    order *)
+Class Comparable T {ot:OrdType T} := {
+  compare : forall x y : T, Compare lt eq x y
+}.
+
+
+(** Class of inhabited types *)
+Class Inhabited T := {
+  default_value : T
+}.
+
+(** * CompDec: Merging all previous classes *)
+
+Class CompDec T := {
+  ty := T;
+  Eqb :> EqbType ty;
+  Decidable := EqbToDecType ty Eqb;
+  Ordered :> OrdType ty;       
+  Comp :> @Comparable ty Ordered;
+  Inh :> Inhabited ty
+}.
+
+
+Instance ord_of_compdec t `{c: CompDec t} : (OrdType t) := 
+  let (_, _, _, ord, _, _) := c in ord.
+
+Instance inh_of_compdec t `{c: CompDec t} : (Inhabited t) := 
+  let (_, _, _, _, _, inh) := c in inh.
+
+Instance comp_of_compdec t `{c: CompDec t} : @Comparable t (ord_of_compdec t).
+destruct c; trivial.
+Defined.
+
+Instance eqbtype_of_compdec t `{c: CompDec t} : EqbType t :=
+  let (_, eqbtype, _, _, _, inh) := c in eqbtype.
+
+Instance dec_of_compdec t `{c: CompDec t} : DecType t :=
+  let (_, _, dec, _, _, inh) := c in dec.
+
+
+Definition type_compdec {ty:Type} (cd : CompDec ty) := ty.
+
+Definition eqb_of_compdec {t} (c : CompDec t) : t -> t -> bool :=
+  match c with
+  | {| ty := ty; Eqb := {| eqb := eqb |} |} => eqb
+  end.
+
+
+Lemma compdec_eq_eqb {T:Type} {c : CompDec T} : forall x y : T,
+    x = y <-> eqb_of_compdec c x y = true.
+Proof.
+  destruct c. destruct Eqb0.
+  simpl. intros. rewrite eqb_spec0. reflexivity.
+Qed.
+
+Hint Resolve
+     ord_of_compdec
+     inh_of_compdec
+     comp_of_compdec
+     eqbtype_of_compdec
+     dec_of_compdec : typeclass_instances.
+
+
+Record typ_compdec : Type := Typ_compdec {
+  te_carrier : Type;
+  te_compdec : CompDec te_carrier
+}.
+
+Section CompDec_from.
+
+  Variable T : Type.
+  Variable eqb' : T -> T -> bool.
+  Variable lt' : T -> T -> Prop.
+  Variable d : T.
+
+  Hypothesis eqb_spec' : forall x y : T, eqb' x y = true <-> x = y.
+  Hypothesis lt_trans': forall x y z : T, lt' x y -> lt' y z -> lt' x z.
+  Hypothesis lt_neq': forall x y : T, lt' x y -> x <> y.
+  
+  Variable compare': forall x y : T, Compare lt' eq x y.
+  
+  Program Instance CompDec_from : (CompDec T) := {|
+    Eqb := {| eqb := eqb' |};
+    Ordered := {| lt := lt'; lt_trans := lt_trans' |};
+    Comp := {| compare := compare' |};
+    Inh := {| default_value := d |}
+  |}.
+
+  
+  Definition typ_compdec_from : typ_compdec :=
+    Typ_compdec T CompDec_from.
+  
+End CompDec_from.