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@@ -5,11 +5,13 @@ SAT and SMT solvers. It relies on a certified checker for such witnesses. On top of it, vernacular commands and tactics to interface with the SAT solver zChaff -and the SMT solver veriT are provided. It is designed in a modular way +and the SMT solvers veriT and CVC4 are provided. It is designed in a modular way allowing to extend it easily to other solvers. +<!--- Extraction is probably broken SMTCoq also provides an extracted version of the checker, that can be run outside Coq. +---> The current stable version is version 1.3. @@ -33,34 +35,41 @@ easily re-usable for your own usage. #### Overview -The SMTCoq module can be used in Coq files via the `Require Import -SMTCoq.` command. For each supported solver, it provides: +After installation, the SMTCoq module can be used in Coq files via the +`Require Import SMTCoq.` command. For each supported solver, it +provides: -- a vernacular command to check answers: - `XXX_Checker "problem_file" "witness_file"` returns `true` only if - `witness_file` contains a zChaff proof of the unsatisfiability of the - problem stated in `problem_file`; +- a vernacular command to check answers: `XXX_Checker "problem_file" + "witness_file"` returns `true` only if `witness_file` contains a proof + of the unsatisfiability of the problem stated in `problem_file`; - a vernacular command to safely import theorems: `XXX_Theorem theo "problem_file" "witness_file"` produces a Coq term - `teo` whose type is the theorem stated in `problem_file` if + `theo` whose type is the theorem stated in `problem_file` if `witness_file` is a proof of the unsatisfiability of it, and fails otherwise. -- a safe tactic to try to solve a Coq goal using the chosen solver. +- safe tactics to try to solve a Coq goal using the chosen solver (or a + combination of solvers). +<!--- Extraction is probably broken The SMTCoq checker can also be extracted to OCaml and then used independently from Coq. +---> +We now give more details for each solver. + +<!--- Extraction is probably broken We now give more details for each solver, and explanations on extraction. +---> #### zChaff Compile and install zChaff as explained in the installation instructions. In the following, we consider that the command `zchaff` is -in your `PATH` variable environment. +in your `PATH` environment variable. ##### Checking zChaff answers of unsatisfiability and importing theorems @@ -72,7 +81,7 @@ To check the result given by zChaff on an unsatisfiable dimacs file produces a proof witness file named `resolve_trace`. - In a Coq file `file.v`, put: -``` +```coq Require Import SMTCoq. Zchaff_Checker "file.cnf" "resolve_trace". ``` @@ -82,7 +91,7 @@ Zchaff_Checker "file.cnf" "resolve_trace". - You can also produce Coq theorems from zChaff proof witnesses: the commands -``` +```coq Require Import SMTCoq. Zchaff_Theorem theo "file.cnf" "resolve_trace". ``` @@ -93,17 +102,18 @@ will produce a Coq term `theo` whose type is the theorem stated in ##### zChaff as a Coq decision procedure The `zchaff` tactic can be used to solve any goal of the form: -``` +```coq forall l, b1 = b2 ``` -where `l` is a list of Booleans (that can be concrete terms). +where `l` is a quantifier-free list of variables and `b1` and `b2` are +expressions of type `bool`. #### veriT Compile and install veriT as explained in the installation instructions. In the following, we consider that the command `veriT` is in your `PATH` -variable environment. +environment variable. ##### Checking veriT answers of unsatisfiability and importing theorems @@ -112,13 +122,13 @@ To check the result given by veriT on an unsatisfiable SMT-LIB2 file `file.smt2`: - Produce a veriT proof witness: -``` +```coq veriT --proof-prune --proof-merge --proof-with-sharing --cnf-definitional --disable-e --disable-ackermann --input=smtlib2 --proof=file.log file.smt2 ``` This command produces a proof witness file named `file.log`. - In a Coq file `file.v`, put: -``` +```coq Require Import SMTCoq. Section File. Verit_Checker "file.smt2" "file.log". @@ -128,9 +138,9 @@ End File. - Compile `file.v`: `coqc file.v`. If it returns `true` then veriT indeed proved that the problem was unsatisfiable. -- You can also produce Coq theorems from zChaff proof witnesses: the +- You can also produce Coq theorems from veriT proof witnesses: the commands -``` +```coq Require Import SMTCoq. Section File. Verit_Theorem theo "file.smt2" "file.log". @@ -139,16 +149,105 @@ End File. will produce a Coq term `theo` whose type is the theorem stated in `file.smt2`. -The theories that are currently supported are `QF_UF`, `QF_LIA`, -`QF_IDL` and their combinations. +The theories that are currently supported by these commands are `QF_UF` +(theory of equality), `QF_LIA` (linear integer arithmetic), `QF_IDL` +(integer difference logic), and their combinations. ##### veriT as a Coq decision procedure -The `verit` tactic can be used to solve any goal of the form: +The `verit_bool` tactic can be used to solve any goal of the form: +```coq +forall l, b1 = b2 +``` +where `l` is a quantifier-free list of variables and `b1` and `b2` are +expressions of type `bool`. + +In addition, the `verit` tactic applies to Coq goals of sort `Prop`: it +first converts the goal into a term of type `bool` (thanks to the +`reflect` predicate of `SSReflect`), and then calls the previous tactic +`verit_bool`. + +The theories that are currently supported by these tactics are `QF_UF` +(theory of equality), `QF_LIA` (linear integer arithmetic), `QF_IDL` +(integer difference logic), and their combinations. + + +#### CVC4 + +Compile and install `CVC4` as explained in the installation +instructions. In the following, we consider that the command `cvc4` is +in your `PATH` environment variable. + + +##### Checking CVC4 answers of unsatisfiability and importing theorems + +To check the result given by CVC4 on an unsatisfiable SMT-LIB2 file +`name.smt2`: + +- Produce a CVC4 proof witness: + +```bash +cvc4 --dump-proof --no-simplification --fewer-preprocessing-holes --no-bv-eq --no-bv-ineq --no-bv-algebraic name.smt2 > name.lfsc ``` + +This set of commands produces a proof witness file named `name.lfsc`. + +- In a Coq file `name.v`, put: +```coq +Require Import SMTCoq Bool List. +Import ListNotations BVList.BITVECTOR_LIST FArray. +Local Open Scope list_scope. +Local Open Scope farray_scope. +Local Open Scope bv_scope. + +Section File. + Lfsc_Checker "name.smt2" "name.lfsc". +End File. +``` + +- Compile `name.v`: `coqc name.v`. If it returns `true` then the problem + is indeed unsatisfiable. + +NB: Use `cvc4tocoq` script in `src/lfsc/tests` to automatize the above steps. + +- Ex: `./cvc4tocoq name.smt2` returns `true` only if the problem + `name.smt2` has been proved unsatisfiable by CVC4. + +The theories that are currently supported by these commands are `QF_UF` +(theory of equality), `QF_LIA` (linear integer arithmetic), `QF_IDL` +(integer difference logic), `QF_BV` (theory of fixed-size bit vectors), +`QF_A` (theory of arrays), and their combinations. + + +##### CVC4 as a Coq decision procedure + +The `cvc4_bool` tactic can be used to solve any goal of the form: +```coq forall l, b1 = b2 ``` -where `l` is a list of Booleans. Those Booleans can be any concrete -terms. The theories that are currently supported are `QF_UF`, `QF_LIA`, -`QF_IDL` and their combinations. + +where `l` is a quantifier-free list of variables and `b1` and `b2` are +expressions of type `bool`. + +In addition, the `cvc4` tactic applies to Coq goals of sort `Prop`: it + first converts the goal into a term of type `bool` (thanks to the + `reflect` predicate of `SSReflect`), it then calls the previous tactic + `cvc4_bool`, and it finally converts any unsolved subgoals returned by + CVC4 back to `Prop`, thus offering to the user the possibility to solve + these (usually simpler) subgoals. + +The theories that are currently supported by these tactics are `QF_UF` +(theory of equality), `QF_LIA` (linear integer arithmetic), `QF_IDL` +(integer difference logic), `QF_BV` (theory of fixed-size bit vectors), +`QF_A` (theory of arrays), and their combinations. + + +### The smt tactic + +The more powerful tactic `smt` combines all the previous tactics: it +first converts the goal to a term of type `bool` (thanks to the +`reflect` predicate of `SSReflect`), it then calls a combination of the +`cvc4_bool` and `verit_bool` tactics, and it finally converts any +unsolved subgoals back to `Prop`, thus offering to the user the +possibility to solve these (usually simpler) subgoals. |