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author | ckeller <ckeller@users.noreply.github.com> | 2019-01-28 23:19:12 +0100 |
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committer | GitHub <noreply@github.com> | 2019-01-28 23:19:12 +0100 |
commit | 7021c53d4ecf97c82ccebb6bb45f5305d8b482ea (patch) | |
tree | ba7537e1e813cabf9ee0d910f845c71fa5f446e7 /examples/Example.v | |
parent | 36548d6634864a131cc83ce21491c797163de305 (diff) | |
download | smtcoq-7021c53d4ecf97c82ccebb6bb45f5305d8b482ea.tar.gz smtcoq-7021c53d4ecf97c82ccebb6bb45f5305d8b482ea.zip |
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
Diffstat (limited to 'examples/Example.v')
-rw-r--r-- | examples/Example.v | 146 |
1 files changed, 126 insertions, 20 deletions
diff --git a/examples/Example.v b/examples/Example.v index 0dba915..c07fb40 100644 --- a/examples/Example.v +++ b/examples/Example.v @@ -1,3 +1,15 @@ +(**************************************************************************) +(* *) +(* 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 SMTCoq.SMTCoq.] loads the SMTCoq library. If you are using native-coq instead of Coq 8.6, replace it with: Require Import SMTCoq. @@ -5,7 +17,15 @@ Require Import SMTCoq.SMTCoq. Require Import Bool. -Local Open Scope int63_scope. + +Local Open Scope Z_scope. + +Import BVList.BITVECTOR_LIST. +Local Open Scope bv_scope. + +Import FArray. +Local Open Scope farray_scope. + (* Examples that check ZChaff certificates *) @@ -15,12 +35,21 @@ Check sat. Zchaff_Checker "hole4.cnf" "hole4.log". -(* Example that checks a VeriT certificate, for logic QF_UF *) + +(* Example that checks a VeriT certificate, for logic QF_UFLIA *) Section Verit. - Verit_Checker "euf.smt2" "euf.log". + Verit_Checker "lia.smt2" "lia.vtlog". End Verit. + +(* Example that checks a LFSC certificate, for logic QF_UFLIA *) + +Section Lfsc. + Lfsc_Checker "lia.smt2" "lia.lfsc". +End Lfsc. + + (* Examples of the zchaff tactic (requires zchaff in your PATH environment variable): - with booleans @@ -33,41 +62,119 @@ Proof. Qed. Goal forall i j k, - let a := i == j in - let b := j == k in - let c := k == i in + let a := (i == j)%int in + let b := (j == k)%int in + let c := (k == i)%int in (a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a) = false. Proof. zchaff. Qed. -(* Examples of the verit tactic (requires verit in your PATH environment - variable): - - with booleans - - in logics QF_UF and QF_LIA *) + +(* Examples of the verit tactics (requires verit in your PATH environment + variable), which handle + - propositional logic + - theory of equality + - linear integer arithmetic *) Goal forall a b c, ((a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a)) = false. Proof. - verit. + verit_bool. Qed. - Goal forall (a b : Z) (P : Z -> bool) (f : Z -> Z), - negb (f a =? b) || negb (P (f a)) || (P b). + (negb (Z.eqb (f a) b)) || (negb (P (f a))) || (P b). Proof. - verit. + verit_bool. Qed. Goal forall b1 b2 x1 x2, - implb - (ifb b1 - (ifb b2 (2*x1+1 =? 2*x2+1) (2*x1+1 =? 2*x2)) - (ifb b2 (2*x1 =? 2*x2+1) (2*x1 =? 2*x2))) - ((implb b1 b2) && (implb b2 b1) && (x1 =? x2)). + implb + (ifb b1 + (ifb b2 (Z.eqb (2*x1+1) (2*x2+1)) (Z.eqb (2*x1+1) (2*x2))) + (ifb b2 (Z.eqb (2*x1) (2*x2+1)) (Z.eqb (2*x1) (2*x2)))) + ((implb b1 b2) && (implb b2 b1) && (Z.eqb x1 x2)). +Proof. + verit_bool. +Qed. + +Goal forall + (x y: Z) + (f: Z -> Z), + x = y + 1 -> f y = f (x - 1). Proof. verit. Qed. + +(* Examples of the smt tactic (requires verit and cvc4 in your PATH environment + variable): + - propositional logic + - theory of equality + - linear integer arithmetic + - theory of fixed-sized bit-vectors + - theory of arrays *) + +Goal forall a b c, ((a || b || c) && ((negb a) || (negb b) || (negb c)) && ((negb a) || b) && ((negb b) || c) && ((negb c) || a)) = false. +Proof. + smt. +Qed. + +Goal forall (a b : Z) (P : Z -> bool) (f : Z -> Z), + (negb (Z.eqb (f a) b)) || (negb (P (f a))) || (P b). +Proof. + smt. +Qed. +Goal forall b1 b2 x1 x2, + implb + (ifb b1 + (ifb b2 (Z.eqb (2*x1+1) (2*x2+1)) (Z.eqb (2*x1+1) (2*x2))) + (ifb b2 (Z.eqb (2*x1) (2*x2+1)) (Z.eqb (2*x1) (2*x2)))) + ((implb b1 b2) && (implb b2 b1) && (Z.eqb x1 x2)). +Proof. + smt. +Qed. + +Goal forall + (x y: Z) + (f: Z -> Z), + x = y + 1 -> f y = f (x - 1). +Proof. + smt. +Qed. + +Goal forall (bv1 bv2 bv3: bitvector 4), + bv1 = #b|0|0|0|0| /\ + bv2 = #b|1|0|0|0| /\ + bv3 = #b|1|1|0|0| -> + bv_ultP bv1 bv2 /\ bv_ultP bv2 bv3. +Proof. + smt. +Qed. + +Goal forall (a b c d: farray Z Z), + b[0 <- 4] = c -> + d = b[0 <- 4][1 <- 4] -> + a = d[1 <- b[1]] -> + a = c. +Proof. + smt. +Qed. + +Goal forall (a b: farray Z Z) (v w x y z t: Z) + (r s: bitvector 4) + (f: Z -> Z) + (g: farray Z Z -> Z) + (h: bitvector 4 -> Z), + a[x <- v] = b /\ a[y <- w] = b -> + a[z <- w] = b /\ a[t <- v] = b -> + r = s -> v < x + 10 /\ v > x - 5 -> + ~ (g a = g b) \/ f (h r) = f (h s). +Proof. + smt. +Qed. + + (* Examples of using the conversion tactics *) Local Open Scope positive_scope. @@ -231,7 +338,6 @@ Section group. Lemma unique_identity e': (forall z, op e' z =? z) -> e' =? e. Proof. intros pe'. verit_base pe'; vauto. Qed. - Lemma simplification_right x1 x2 y: op x1 y =? op x2 y -> x1 =? x2. Proof. intro H. verit_base H; vauto. Qed. |