User Manual

This manual includes lots of information about how to use CVC4.

It is a work in-progress.

What is CVC4?

CVC4 is the last of a long line of SMT solvers that started with SVC and includes CVC, CVC-Lite and CVC3. Technically, it is an automated validity checker for a many-sorted (i.e., typed) first-order logic with built-in theories. The current built-in theories are the theories of:

• equality over free (aka uninterpreted) function and predicate symbols,
• real and integer linear arithmetic (with some support for non-linear arithmetic),
• bit vectors,
• arrays,
• tuples,
• records,
• user-defined inductive data types.

CVC4 checks whether a given formula $\phi$ is valid in the built-in theories under a given set $\Gamma$ of assumptions, a context. More precisely, it checks whether

$\Gamma\models_T \phi$

that is, whether $\phi$ is a logical consequence in $T$ of the set of formulas $\Gamma$, where $T$ is the union of CVC4's built-in theories.

Roughly speaking, when $\phi$ is a universal formula and $\Gamma$ is a set of existential formulas (i.e., when $\phi$ and $\Gamma$ contain at most universal, respectively existential, quantifiers), CVC4 is a decision procedure: it is guaranteed (modulo bugs and memory limits) to return a correct "valid" or "invalid" answer eventually. In all other cases, CVC4 is deductively sound but incomplete: it will never say that an invalid formula is valid, but it may either never return or give up and return "unknown" for some formulas.

Currently, when CVC4 returns "valid" for a query formula $\phi$ under a context $\Gamma$ it provides no evidence to back its claim. Future versions will also return a proof certificate, a formal proof that $\Gamma'\models_T \phi$ for some subset $\Gamma'$ of $\Gamma$.

When CVC4 returns "invalid" it can return both a counter-example to $\phi$'s validity under the context $\Gamma$ and a counter-model. Both a counter-example and a counter-model are a set $\Delta$ of additional formulas consistent with $\Gamma$ in $T$, but entailing the negation of $\phi$. Formally:

$\Gamma \cup \Delta \not\models_T \mathit{false}$ and $\Gamma \cup \Delta \models_T \lnot \phi$.

The difference is that a counter-model is given as a set of equations providing a concrete assignment of values for the free symbols in $\Gamma$ and $\phi$ (see the section on CVC4's native input language for more details).

Obtaining and compiling CVC4

CVC4 is distributed in the following ways:

• Binary packages
• Source packages
• Source repository checkout

Obtaining binary packages

Binary packages are available for CVC4.

Obtaining source packages

Sources are available from the same site as the binaries.

Source repository

The CVC4 source repository is currently hosted by CIMS and requires a CIMS account. Please contact a member of the development team for access. Please see the additional instructions for #Building_CVC4 from_a_repository_checkout here.

Building from source

Quick-start instructions

To compile from a source package:

1. Install antlr
2. Configure cvc4
3. Compile cvc4
4. Install cvc4 [optional]

   cd contrib
   ./get-antlr-3.4
   cd ..
   ./configure --with-antlr-dir=`pwd`/antlr-3.4 ANTLR=`pwd`/antlr-3.4/bin/antlr3
   make
   make check   [recommended]
   make install [optional]

(To build from a repository checkout, see below.)

Common make Options

• "make install" will install into the "--prefix" option you gave to

the configure script (/usr/local by default).

   ./configure --prefix=~/install_targets/cvc4 ...
   make install

• You should run "make check" before installation to ensure that CVC4 has been

built correctly. In particular, GCC version 4.5.1 seems to have a bug in the optimizer that results in incorrect behavior (and wrong results) in many builds. This is a known problem for Minisat, and since Minisat is at the core of CVC4, a problem for CVC4. "make check" easily detects this problem (by showing a number of FAILed test cases). It is ok if the unit tests aren't run as part of "make check", but all system tests and regression tests should pass without incident.

• To build API documentation, use "make doc". Documentation is produced

under builds/doc/ but is not installed by "make install".

Examples and tutorials are not installed with "make install." See below.

For more information about the build system itself (probably not necessary for casual users), see the Appendix at the bottom of this file.

Common configure Options

• --prefix=PREFIX install architecture-independent files in PREFIX (by default /usr/local)
• --with-build={production,debug,default,competition}
• --with-antlr-dir=PATH
• --with-cln/--with-gmp selects the numbers package to use by default (#Optional requirements)
• --enable-static-binary build a fully statically-linked binary. (This is recommended for Mac OS X users that want to be able to use gdb.)
• ANTLR=PATH location of the antlr3 script
• --with-boost=DIR installation location of the boost libraries (most users will not need this)

See ./configure --help for more.

Build dependencies

The following tools and libraries are required to run CVC4. Versions given are minimum versions; more recent versions should be compatible.

• GNU C and C++ (gcc and g++), reasonably recent versions
• GNU Make
• GNU Bash
• GMP v4.2 (GNU Multi-Precision arithmetic library)
• libantlr3c v3.2 or v3.4 (ANTLR parser generator C support library)
• The Boost C++ base libraries
• MacPorts [highly recommended if on a Mac; see #MacPorts]

The hardest to obtain and install is the libantlr3c requirement, and is explained next.

If "make" is non-GNU on your system, make sure to invoke "gmake" (or whatever GNU Make is installed as). If your usual shell is not Bash, the configure script should auto-correct this. If it does not, you'll see strange shell syntax errors, and you may need to explicitly set SHELL or CONFIG_SHELL to the location of bash on your system.

Installing libantlr3c: ANTLR parser generator C support library

For libantlr3c, you can use the convenience script in contrib/get-antlr-3.4 in the source distribution---this will download, patch, compile and install libantlr3c into your cvc4 directory as cvc4/antlr-3.4/.

 cd contrib
 ./get-antlr-3.4

CVC4 must be configured with the antlr library installation directory, --with-antlr-dir, and an antlr executable script file, ANTLR. If libantlr3c was installed via get-antlr-3.4, the following configure line should suffice for CVC44

 ./configure --with-antlr-dir=`pwd`/antlr-3.4 ANTLR=`pwd`/antlr-3.4/bin/antlr3

For 64 bit machines, libantlr3c needs to be configured with 64 bit explicitly

 ./configure --enable-64bit ...

The get-antlr-3.4 script makes a guess at whether the machine is 64 bit and adds the appropriate flag. To force the script to compile 32 bit:

 MACHINE_TYPE="x86" ./get-antlr3.4

To force the script to compile 64 bit:

 MACHINE_TYPE="x86_64" ./get-antlr3.4

For a longer discussion, instructions for manual installation, and more in depth troubleshooting, see Developer's Guide#ANTLR3.

MacPorts

On a Mac, it is highly recommended that you use MacPorts (see http://www.macports.org/). Doing so is easy. Then, simply run the script contrib/mac-build, which installs a few ports from the MacPorts repository, then compiles and installs antlr3c using the get-antlr-3.4 script. The mac-build script should set you up with all requirements, and will tell you how to configure CVC4 when it completes successfully.

Installing the Boost C++ base libraries

A Boost package is available on most Linux distributions; check yours for a package named something like libboost-dev or boost-devel. There are a number of additional Boost packages in some distributions, but this "basic" one should be sufficient for building CVC4.

Should you want to install Boost manually, or to learn more about the Boost project, please visit http://www.boost.org/.

Optional requirements

None of these is required, but can improve CVC4 as described below:

• Optional: SWIG 2.0.x (Simplified Wrapper and Interface Generator)
• Optional: CLN v1.3 or newer (Class Library for Numbers)
• Optional: CUDD v2.4.2 or newer (Colorado University Decision Diagram package)
• Optional: GNU Readline library (for an improved interactive experience)
• Optional: The Boost C++ threading library (libboost_thread)
• Optional: CxxTest unit testing framework

SWIG is necessary to build the Java API (and of course a JDK is necessary, too). SWIG 1.x won't work; you'll need 2.0, and the more recent the better. On Mac, we've seen SWIG segfault when generating CVC4 language bindings; version 2.0.8 or higher is recommended to avoid this. See Language bindings below for build instructions.

CLN is an alternative multiprecision arithmetic package that can offer better performance and memory footprint than GMP. CLN is covered by the GNU General Public License, version 3; so if you choose to use CVC4 with CLN support, you are licensing CVC4 under that same license. (Usually CVC4's license is more permissive than GPL is; see the file COPYING in the CVC4 source distribution for details.) Please visit http://www.ginac.de/CLN/ for more details about CLN.

CUDD is a decision diagram package that changes the behavior of the CVC4 arithmetic solver in some cases; it may or may not improve the arithmetic solver's performance. See below for instructions on obtaining and building CUDD.

The GNU Readline library is optionally used to provide command editing, tab completion, and history functionality at the CVC prompt (when running in interactive mode). Check your distribution for a package named "libreadline-dev" or "readline-devel" or similar.

The Boost C++ threading library (often packaged independently of the Boost base library) is needed to run CVC4 in "portfolio" (multithreaded) mode. Check your distribution for a package named "libboost-thread-dev" or similar.

CxxTest is necessary to run CVC4's unit tests (included with the distribution). Running these is not really required for users of CVC4; "make check" will skip unit tests if CxxTest isn't available, and go on to run the extensive system- and regression-tests in the source tree. However, if you're interested, you can download CxxTest at http://cxxtest.com/ .

Building with CUDD (optional)

CUDD, if desired, must be installed delicately. The CVC4 configure script attempts to auto-detect the locations and names of CUDD headers and libraries the way that the Fedora RPMs install them, the way that our NYU-provided Debian packages install them, and the way they exist when you download and build the CUDD sources directly. If you install from Fedora RPMs or our Debian packages, the process should be completely automatic, since the libraries and headers are installed in a standard location. If you download the sources yourself, you need to build them in a special way. Fortunately, the "contrib/build-cudd-2.4.2-with-libtool.sh" script in the CVC4 source tree does exactly what you need: it patches the CUDD makefiles to use libtool, builds the libtool libraries, then reverses the patch to leave the makefiles as they were. Once you run this script on an unpacked CUDD 2.4.2 source distribution, then CVC4's configure script should pick up the libraries if you provide --with-cudd-dir=/PATH/TO/CUDD/SOURCES.

If you want to force linking to CUDD, provide --with-cudd to the configure script; this makes it a hard requirement rather than an optional add-on.

The NYU-provided Debian packaging of CUDD 2.4.2 and CUDD 2.5.0 are here (along with the CVC4 Debian packages):

 deb http://cvc4.cs.nyu.edu/debian/ unstable/

On Debian (and Debian-derived distributions like Ubuntu), you only need to drop that one line in your /etc/apt/sources.list file, then install with your favorite package manager.

The Debian source package "cudd", available from the same repository, includes a diff of all changes made to cudd makefiles.

Language bindings

There are several options available for using CVC4 from the API.

First, CVC4 offers a complete and flexible API for manipulating expressions, maintaining a stack of assertions, and checking satisfiability, and related things. The C++ libraries (libcvc4.so and libcvc4parser.so) and required headers are installed normally via a "make install". This API is also available from Java (via CVC4.jar and libcvc4jni.so) by configuring with --enable-language-bindings=java. You'll also need SWIG 2.0 installed (and you might need to help configure find it if you installed it in a nonstandard place with --with-swig-dir=/path/to/swig/installation). You may also need to give the configure script the path to your Java headers (in particular, jni.h). You might do so with (for example):

 ./configure --enable-language-bindings=java \
     JAVA_CPPFLAGS=-I/usr/lib/jvm/java-6-openjdk-amd64/include

There is also a "C++ compatibility API" (#include <cvc4/cvc3_compat.h> and link against libcvc4compat.so) that attempts to maintain source-level backwards-compatibility with the CVC3 C++ API. The compatibility library is built by default, and --enable-language-bindings=java enables the Java compatibility library (CVC4compat.jar and libcvc4compatjni.so). --enable-language-bindings=c enables the C compatibility library (#include <cvc4/bindings/compat/c/c_interface.h> and link against libcvc4bindings_c_compat.so), and if you want both C and Java bindings, use --enable-language-bindings=c,java. These compatibility language bindings do NOT require SWIG.

The examples/ directory in the source distribution includes some basic examples (the "simple vc" and "simple vc compat" family of examples) of all these interfaces.

In principle, since we use SWIG to generate the native Java API, we could support other languages as well. However, using CVC4 from other languages is not supported, nor expected to work, at this time. If you're interested in helping to develop, maintain, and test a language binding, please contact us via the users' mailing list at cvc-users@cs.nyu.edu.

Building CVC4 from a repository checkout

The following tools and libraries are additionally required to build CVC4 from from a repository checkout rather than from a prepared source tarball.

• Automake v1.11
• Autoconf v2.61
• Libtool v2.2
• ANTLR3 v3.2 or v3.4
• Java Development Kit (required for ANTLR3)

First, use "./autogen.sh" to create the configure script. Then proceed as normal for any distribution tarball. The parsers are pre-generated for the tarballs, but don't exist in the repository; hence the extra ANTLR3 and JDK requirements to generate the source code for the parsers, when building from the repository.

Examples and tutorials are not built or installed

Examples are not built by "make" or "make install". See examples/README in the source distribution for information on what to find in the examples/ directory, as well as information about building and installing them.

Appendix: Build architecture

The build system is generated by automake, libtool, and autoconf. It is somewhat nonstandard, though, which (for one thing) requires that GNU Make be used. If you ./configure in the top-level source directory, the objects will actually all appear in builds/${arch}/${build_id}. This is to allow multiple, separate builds in the same place (e.g., an assertions-enabled debugging build alongside a production build), without changing directories at the shell. The "current" build is maintained, and you can still use (e.g.) "make -C src/main" to rebuild objects in just one subdirectory.

You can also create your own build directory inside or outside of the source tree and configure from there. All objects will then be built in that directory, and you'll ultimately find the "cvc4" binary in src/main/, and the libraries under src/ and src/parser/.

Using the CVC4 binary

The CVC4 driver binary ("cvc4"), once installed, can be executed directly to enter into interactive mode:

$ cvc4
cvc4 1.0 assertions:off
CVC4>

You can then enter commands into CVC4 interactively:

CVC4> OPTION "incremental";
CVC4> OPTION "produce-models";
CVC4> TRANSFORM 25*25;
625
CVC4> x, y : INT;
CVC4> QUERY x = y;
invalid
CVC4> COUNTERMODEL;
x : INT = -1;
y : INT = 0;
CVC4> ASSERT x >= 0;
CVC4> QUERY x = y;
invalid
CVC4> COUNTERMODEL;
x : INT = 0;
y : INT = 1;
CVC4>

The above example shows two useful options, incremental and produce-models.

• The incremental option allows you to issue multiple QUERY (or CHECKSAT) commands, and allows the use of the PUSH and POP commands. Without this option, CVC4 optimizes itself for a single QUERY or CHECKSAT command (though you may issue any number of ASSERT commands). The incremental option may also be given by passing the -i command line option to CVC4.
• The produce-models option allows you to query the model (here, with the COUNTERMODEL command) after an "invalid" QUERY (or "satisfiable" CHECK-SAT). Without it, CVC4 doesn't do the bookkeeping necessary to support model generation. The produce-models option may also be given by passing the -m command line option to CVC4.

So, if you invoke CVC4 with -im, you don't need to pass those options at all:

$ cvc4 -im
cvc4 1.0 assertions:off
CVC4> x, y : INT;
CVC4> QUERY x = y;
invalid
CVC4> COUNTERMODEL;
x : INT = -1;
y : INT = 0;
CVC4> ASSERT x >= 0;
CVC4> QUERY x = y;
invalid
CVC4> COUNTERMODEL;
x : INT = 0;
y : INT = 1;
CVC4>

By default, CVC4 operates in CVC-language mode. If you enter something that looks like SMT-LIB, it will suggest that you use the "--lang smt" command-line option for SMT-LIB mode:

CVC4> (declare-fun x () Int)
Parse Error: <shell>:1.7: In CVC4 presentation language mode, but SMT-LIB format detected.  Use --lang smt for SMT-LIB support.
CVC4>

Verbosity

CVC4 has various levels of verbosity. By default, CVC4 is pretty quiet, only reporting serious warnings and notices. If you're curious about what it's doing, you can pass CVC4 the -v option:

$ cvc4 -v file.smt2
Invoking: (set-logic AUFLIRA)
Invoking: (set-info :smt-lib-version 2.000000)
Invoking: (set-info :category "crafted")
Invoking: (set-info :status unsat)
Invoking: (declare-fun x () Real)
etc...

For even more verbosity, you can pass CVC4 an additional -v:

$ cvc4 -vv file.smt2
Invoking: (set-logic AUFLIRA)
Invoking: (set-info :smt-lib-version 2.000000)
Invoking: (set-info :category "crafted")
Invoking: (set-info :status unsat)
Invoking: (declare-fun x () Real)
etc...
expanding definitions...
constraining subtypes...
applying substitutions...
simplifying assertions...
doing static learning...
etc...

Internally, verbosity is just an integer value. It starts at 0, and with every -v on the command line it is incremented; with every -q, decremented. It can also be set directly. From CVC language:

CVC4> OPTION "verbosity" 2;

Or from SMT-LIB language:

CVC4> (set-option :verbosity 2)

Getting statistics

Statistics can be dumped on exit (both normal and abnormal exits) with the --statistics command line option.

$ cvc4 --statistics foo.smt2
sat
sat::decisions, 0
sat::propagations, 3
sat::starts, 1
theory::uf::TheoryUF::functionTermsCount, 2
theory::uf::TheoryUF::mergesCount, 2
theory::uf::TheoryUF::termsCount, 6
theory<THEORY_UF>::propagations, 1 
driver::filename, foo.smt2
driver::sat/unsat, sat
driver::totalTime, 0.02015373
[many others]

Many statistics name-value pairs follow, one comma-separated pair per line.

Exit status

The exit status of CVC4 depends on the last QUERY or CHECK-SAT. If you wish to call CVC4 from a program (e.g., a shell script) and care only about the satisfiability or validity of a single formula, you can pass the -q option (as described above, under verbosity) and check the exit code. With -q, CVC4 should not produce any output unless it encounters a fatal error.

QUERY asks a validity question, and CHECK-SAT a satisfiability question, and these are dual problems; hence the terminology is different, but really "sat" and "invalid" are the same internally, as are "unsat" and "valid":

Solver's last result	Exit code	Notes
sat or invalid	10
unsat or valid	20
unknown	0	could be for any reason: time limit exceeded, no memory, incompleteness..
no result	0	no query or check-sat command issued
parse errors	0 (in interactive mode) 1 (otherwise)	see below
other errors	1 (usually)	see below

Most "normal errors" return a 1 as the exit code, but out of memory conditions, and others, can produce different exit codes. In interactive mode, parse errors are ignored and the next line read; so in interactive mode, you may see an exit code of 0 even in the presence of such an error.

In SMT-LIB mode, an SMT-LIB command script that sets its status via "set-info :status" also affects the exit code. So, for instance, the following SMT-LIB script returns an exit code of 10 even though it contains no "check-sat" command:

(set-logic QF_UF)
(set-info :status sat)
(exit)

Without the "set-info," it would have returned an exit code of 0.

CVC4's native input language

The native input language consists of a sequence of symbol declarations and commands, each followed by a semicolon (;).

Any text after the first occurrence of a percent character and to the end of the current line is a comment:

%%% This is a native language comment

Type System

CVC4's type system includes a set of built-in types which can be expanded with additional user-defined types.

The type system consists of first-order types, subtypes of first-order types, and higher-order types, all of which are interpreted as sets. For convenience, we will sometimes identify below the interpretation of a type with the type itself.

First-order types consist of basic types and structured types. The basic types are $\mathrm{BOOLEAN}$, $\mathrm{REAL}$, $\mathrm{BITVECTOR}(n)$ for all $n > 0$, as well as user-defined basic types (also called uninterpreted types). The structured types are array, tuple, record types, and ML-style user-defined (inductive) datatypes.

Subtypes include the built-in subtype $\mathrm{INT}$ of $\mathrm{REAL}$ and are covered in the Subtypes section.

Function types are the only higher-order types. More precisely, they are just second-order types since function symbols in CVC4, both built-in and user-defined, can take as argument or return only values of a first-order type.

Basic Types

The BOOLEAN Type

The $\mathrm{BOOLEAN}$ type is interpreted as the two-element set of Boolean values $\{\mathrm{TRUE},\; \mathrm{FALSE}\}$.

Note that CVC4's use of this type differs from CVC3's where $\mathrm{BOOLEAN}$ is used only as the type of formulas, but not as value type. CVC3 follows the two-tiered structure of classical first-order logic which distinguishes between formulas and terms, and allows terms to occur in formulas but not vice versa (with the exception of the IF-THEN-ELSE construct). CVC4 drops the distinction between terms and formulas and defines the latter just as terms of type $\mathrm{BOOLEAN}$. As such, formulas can occur as subterms of possibly non-Boolean terms.

Example:

[To do]

The REAL Type

The $\mathrm{REAL}$ type is interpreted as the set of real numbers.

Note that these are the (infinite precision) mathematical reals, not the floating point numbers. Support for floating point types is planned for future versions.

x, y : REAL;
QUERY (( x <= y ) AND ( y <= x )) => ( x = y );

The INT Type

The $\mathrm{INT}$ type is interpreted as the set of integer numbers. $\mathrm{INT}$ is a subtype of $\mathrm{REAL}$.

Note that these are the (infinite precision) mathematical integers, not the finite precision machine integers used in most programming languages. The latter are models by bit vector types.

x, y : INT;

QUERY ((2 * x + 4 * y <= 1) AND ( y >= x)) => (x <= 0);

Bit Vector Types

For every positive integer $n$, the type $\mathrm{BITVECTOR}(n)$ is interpreted as the set of all bit vectors of size $n$. A rich set of bit vector operators is supported.

User-defined Basic Types

Users can define new basic types. Each of such types is interpreted as a set of unspecified cardinality but disjoint from any other type. User-defined basic types are created by declarations like the following:

% User declarations of basic types:

MyBrandNewType: TYPE;

Apples, Oranges: TYPE;

Structured Types

CVC4's structured types are divided in the following families.

Array Types

Array types are created by the mixfix type constructors $\mathrm{ARRAY}\ \_\ \mathrm{OF}\ \_$ whose arguments can be instantiated by any value type.

T1 : TYPE;

% Array types:

ArrayType1: TYPE = ARRAY T1 OF REAL;

ArrayType2: TYPE = ARRAY INT OF (ARRAY INT OF REAL);

ArrayType3: TYPE = ARRAY [INT, INT] OF INT;

An array type of the form $\mathrm{ARRAY}\ T_1\ \mathrm{OF}\ T_2$ is interpreted as the set of all total maps from $T_1$ to $T_2$. The main conceptual difference with the type $T_1 \to T_2$ is that arrays, contrary to functions, are first-class objects of the language: they can be arguments or results of functions. Moreover, array types come equipped with an update operation.

Tuple Types

Tuple types are created by the mixfix type constructors

$\begin{array}{l} [\ \_\ ] \\[1ex] [\ \_\ ,\ \_\ ] \\[1ex] [\ \_\ ,\ \_\ \ ,\ \_\ ] \\[1ex] \ldots \end{array}$

whose arguments can be instantiated by any value type.

IntArray: TYPE = ARRAY INT OF INT;

% Tuple type declarations

RealPair: TYPE = [REAL, REAL]

MyTuple: TYPE = [ REAL, IntArray, [INT, INT] ];

A tuple type of the form $[T_1, \ldots, T_n]$ is interpreted as the Cartesian product $T_1 \times \cdots \times T_n$.

Note that while the types $(T_1, \ldots, T_n) \to T$ and $[T_1 \times \cdots \times T_n] \to T$ are semantically equivalent, they are operationally different in CVC4. The first is the type of functions that take $n$ arguments of respective type $T_1$, $\ldots$, $T_n$, while the second is the type of functions that take one argument of an $n$-tuple type.

Inductive Data Types

Inductive data types are created by declarations of the form

$\begin{array}{l} \mathrm{DATATYPE} \\ \ \ \mathit{type\_name}_1 = C_{1,1} \mid C_{1,2} \mid \cdots \mid C_{1,m_1}, \\ \ \ \mathit{type\_name}_2 = C_{2,1} \mid C_{2,2} \mid \cdots \mid C_{2,m_2}, \\ \ \ \vdots \\ \ \ \mathit{type\_name}_n = C_{n,1} \mid C_{n,2} \mid \cdots \mid C_{n,m_n} \\ \mathrm{END}; \end{array}$

Each of the $C_{ij}$ is either a constant symbol or an expression of the form

$\mathit{cons}(\ \mathit{sel}_1: T_1,\ \ldots,\ \mathit{sel}_k: T_k\ )$

where $T_1, \ldots, T_k$ are any first-order types or type names for first-order types, including any $\mathit{type\_name}_i$. Such declarations introduce for the data type:

• constructor symbols $cons$ of type $(T_1, \ldots, T_k) \to \mathit{type\_name}_i$,
• selector symbols $\mathit{sel}_j$ of type $\mathit{type\_name}_i \to T_j$, and
• tester symbols $\mathit{is\_cons}$ of type $\mathit{type\_name}_i \to \mathrm{BOOLEAN}$.

Here are some examples of inductive data type declarations:

% simple enumeration type
% implicitly defined are the testers: is_red, is_yellow and is_blue
% (similarly for the other data types)

DATATYPE
  PrimaryColor = red | yellow | blue
END;


% infinite set of pairwise distinct values ..., v(-1), v(0), v(1), ...

DATATYPE
  Id = v (id: INT)
END;


% ML-style integer lists

DATATYPE
  IntList = nil | cons (head: INT, tail: IntList)
END;


% ASTs

DATATYPE
  Term = var (index: INT)
       | apply (arg_1: Term, arg_2: Term)
       | lambda (arg: INT, body: Term)
END;

% Trees

DATATYPE
  Tree = tree (value: REAL, children: TreeList),
  TreeList = nil_tl
           | cons_tl (first_t1: Tree, rest_t1: TreeList)
END;

Constructor, selector and tester symbols defined for a data type have global scope. So, for instance, it is not possible for two different data types to use the same name for a constructor.

An inductive data type is interpreted as a term algebra constructed by the constructor symbols over some sets of generators. For example, the type IntList in the example above is interpreted as the set of all terms constructed with nil and cons over the integers.

Because of this semantics, CVC4 allows only inductive data types, that is, data types whose values are essentially (labeled, ordered) finite trees. Infinite structures such as streams or even finite but cyclic ones such as circular lists are then excluded. For instance, none of the following declarations define inductive databtypes, and are rejected by CVC4:

DATATYPE
 IntStream = s (first:INT, rest: IntStream)
END;

DATATYPE
 RationalTree = node1 (child: RationalTree)
              | node2 (left_child: RationalTree, right_child:RationalTree)
END;

DATATYPE
  T1 =  c1 (s1: T2),
  T2 =  c2 (s2: T1)
END;

In concrete, a declaration of $n \geq 1$ datatypes $T_1, \ldots, T_n$ will be rejected if for any one of the types $T_1, \ldots, T_n$, it is impossible to build a finite term of that type using only the constructors of $T_1, \ldots, T_n$ and free constants of type other than $T_1, \ldots, T_n$.

Inductive data types are the only types where the user also chooses names for the built-in operations to:

• construct a value of the type (with the constructors),
• extract components from a value (with the selectors), or
• check if a value was constructed with a certain constructor or not (with the testers).

For all the other types, CVC4 provides predefined names for the built-in operations on the type.

Function Types

Function ($\to$) types are created by the mixfix type constructors

$\begin{array}{l} \_ \to \_ \\[1ex] (\ \_\ ,\ \_\ ) \to \_ \\[1ex] (\ \_\ ,\ \_\ ,\ \_\ ) \to \_ \\[1ex] \ldots \end{array}$

whose arguments can be instantiated by any first-order type.

% Function type declarations

UnaryFunType: TYPE = INT -> REAL;

BinaryFunType: TYPE = (REAL, REAL) -> ARRAY REAL OF REAL;

TernaryFunType: TYPE = (REAL, BITVECTOR(4), INT) -> BOOLEAN;

A function type of the form $(T_1, \ldots, T_n) \to T$ with $n > 0$ is interpreted as the set of all total functions from the Cartesian product $T_1 \times \cdots \times T_n$ to $T$.

The example above also shows how to introduce type names. A name like UnaryFunType above is just an abbreviation for the type $\mathrm{INT} \to \mathrm{REAL}$ and can be used interchangeably with it.

In general, any type defined by a type expression E can be given a name with the declaration:

name : TYPE = E;

CVC4's support for the SMT-LIB language

SMT-LIB compliance

Every effort has been made to make CVC4 compliant with the SMT-LIB 2.0 standard (http://smtlib.org/). However, when parsing SMT-LIB input, certain default settings don't match what is stated in the official standard. To make CVC4 adhere more strictly to the standard, use the "--smtlib" command-line option. Even with this setting, CVC4 is somewhat lenient; some non-conforming input may still be parsed and processed.

Upgrading from CVC3 to CVC4

Features not supported by CVC4 (yet)

Type Correctness Conditions (TCCs)

Type Correctness Conditions (TCCs), and the checking of such, are not supported by CVC4 1.0. Thus, a function defined only on integers can be applied to REAL (as INT is a subtype of REAL), and CVC4 will not complain, but may produce strange results. For example:

 f : INT -> INT;
 ASSERT f(1/3) = 0;
 ASSERT f(2/3) = 1;
 CHECKSAT;
 % sat
 COUNTEREXAMPLE;
 % f : (INT) -> INT = LAMBDA(x1:INT) : 0;

CVC3 can be used to produce TCCs for this input (with the +dump-tcc option). The TCC can be checked by CVC3 or another solver. (CVC3 can also check TCCs while solving with +tcc.)

If you were using the text interfaces of CVC3

The native language of all solvers in the CVC family, referred to as the "presentation language," has undergone some revisions for CVC4. The most notable is that CVC4 does _not_ add counterexample assertions to the current assertion set after a SAT/INVALID result. For example:

 x, y : INT;
 ASSERT x = 1 OR x = 2;
 ASSERT y = 1 OR y = 2;
 ASSERT x /= y;
 CHECKSAT;
 % sat
 QUERY x = 1;
 % invalid
 QUERY x = 2;
 % invalid

Here, CVC4 responds "invalid" to the second and third queries, because each has a counterexample (x=2 is a counterexample to the first, and x=1 is a counterexample to the second). However, CVC3 will respond with "valid" to one of these two, as the first query (the CHECKSAT) had the side-effect of locking CVC3 into one of the two cases; the later queries are effectively querying the counterexample that was found by the first. CVC4 removes this side-effect of the CHECKSAT and QUERY commands.

CVC4 supports rational literals (of type REAL) in decimal; CVC3 did not support decimals.

CVC4 does not have support for the IS_INTEGER predicate.

Useful command-line options

Statistics

Statistics can be dumped on exit (both normal and abnormal exits) with the --statistics command line option.

Time and resource limits

CVC4 can be made to self-timeout after a given number of milliseconds. Use the --tlimit command line option to limit the entire run of CVC4, or use --tlimit-per to limit each individual query separately. Preprocessing time is not counted by the time limit, so for some large inputs which require aggressive preprocessing, you may notice that --tlimit does not work very well. If you suspect this might be the case, you can use "-vv" (double verbosity) to see what CVC4 is doing.

Time-limited runs are not deterministic; two consecutive runs with the same time limit might produce different results (i.e., one may time out and responds with "unknown", while the other completes and provides an answer). To ensure that results are reproducible, use --rlimit or --rlimit-per. These options take a "resource count" (presently, based on the number of SAT conflicts) that limits the search time. A word of caution, though: there is no guarantee that runs of different versions of CVC4 or of different builds of CVC4 (e.g., two CVC4 binaries with different features enabled, or for different architectures) will interpret the resource count in the same manner.

CVC4 does not presently have a way to limit its memory use; you may opt to run it from a shell after using "ulimit" to limit the size of the heap.

Proof support

CVC4 1.0 has limited support for proofs, and they are disabled by default. (Run the configure script with --enable-proof to enable proofs). Proofs are exported in LFSC format and are limited to the propositional backbone of the discovered proof (theory lemmas are stated without proof in this release).

Portfolio solving

If enabled at configure-time (./configure --with-portfolio), a second CVC4 binary will be produced ("pcvc4"). This binary has support for running multiple instances of CVC4 in different threads. Use --threads=N to specify the number of threads, and use --thread0="options for thread 0" --thread1="options for thread 1", etc., to specify a configuration for the threads. Lemmas are *not* shared between the threads by default; to adjust this, use the --filter-lemma-length=N option to share lemmas of N literals (or smaller). (Some lemmas are ineligible for sharing because they include literals that are "local" to one thread.)

Currently, the portfolio **does not work** with quantifiers or with the theory of inductive datatypes. These limitations will be addressed in a future release.

Emacs support

For a suggestion of editing CVC4 source code with emacs, see the file contrib/editing-with-emacs. For a CVC language mode (the native input language for CVC4), see contrib/cvc-mode.el.