From 7021c53d4ecf97c82ccebb6bb45f5305d8b482ea Mon Sep 17 00:00:00 2001 From: ckeller Date: Mon, 28 Jan 2019 23:19:12 +0100 Subject: 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 --- src/classes/SMT_classes.v | 173 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 173 insertions(+) create mode 100644 src/classes/SMT_classes.v (limited to 'src/classes/SMT_classes.v') 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. -- cgit