SBV: Symbolic Bit Vectors in Haskell
====================================
Express properties about bit-precise Haskell programs and automatically prove
them using SMT solvers.
```haskell
$ ghci -XScopedTypeVariables
Prelude> :m Data.SBV
Prelude Data.SBV> prove $ \(x::SWord8) -> x `shiftL` 2 .== 4*x
Q.E.D.
Prelude Data.SBV> prove $ forAll ["x"] $ \(x::SWord8) -> x `shiftL` 2 .== x
Falsifiable. Counter-example:
x = 128 :: SWord8
```
The function `prove` has the following type:
```haskell
prove :: Provable a => a -> IO ThmResult
```
The class `Provable` comes with instances for n-ary predicates, for arbitrary n.
The predicates are just regular Haskell functions over symbolic signed and unsigned
bit-vectors. Functions for checking satisfiability (`sat` and `allSat`) are also provided.
In addition, functions using the SBV library can be compiled to C automatically.
Resources
=========
The sbv library is hosted at [http://github.com/LeventErkok/sbv](http://github.com/LeventErkok/sbv).
The hackage site
[http://hackage.haskell.org/package/sbv](http://hackage.haskell.org/package/sbv) is the best place
for details on the API and the example use cases.
Comments, bug reports, and patches are always welcome.
Overview
========
The Haskell sbv library provides support for dealing with Symbolic Bit Vectors
in Haskell. It introduces the types:
- `SBool`: Symbolic Booleans (bits)
- `SWord8`, `SWord16`, `SWord32`, `SWord64`: Symbolic Words (unsigned)
- `SInt8`, `SInt16`, `SInt32`, `SInt64`: Symbolic Ints (signed)
- `SInteger`: Symbolic unbounded integers (signed)
- Arrays of symbolic values
- Symbolic polynomials over GF(2^n ), polynomial arithmetic, and CRCs
- Uninterpreted constants and functions over symbolic values, with user
defined SMT-Lib axioms
The user can construct ordinary Haskell programs using these types, which behave
very similar to their concrete counterparts. In particular these types belong to the
standard classes `Num`, `Bits`, (custom versions of) `Eq` and `Ord`, along with several
other custom classes for simplifying bit-precise programming with symbolic values. The
framework takes full advantage of Haskell's type inference to avoid many common mistakes.
Furthermore, functions built out of these types can also be:
- proven correct via an external SMT solver (the `prove` function)
- checked for satisfiability (the `sat`, and `allSat` functions)
- used in synthesis (the `sat` function with existentials)
- optimized with respect to cost functions (the 'optimize', 'maximize', and 'minimize' functions)
- quick-checked
- used in concrete test case generation (the 'genTest' function), rendered as values in various
languages, including Haskell and C.
If a predicate is not valid, `prove` will return a counterexample: An
assignment to inputs such that the predicate fails. The `sat` function will
return a satisfying assignment, if there is one. The `allSat` function returns
all satisfying assignments, lazily.
The SBV library can also compile Haskell functions that manipulate symbolic
values directly to C, rendering them as straight-line C programs.
Use of SMT solvers
==================
The sbv library uses third-party SMT solvers via the standard SMT-Lib interface:
[http://goedel.cs.uiowa.edu/smtlib/](http://goedel.cs.uiowa.edu/smtlib/)
The SBV library is designed to work with any SMT-Lib compliant SMT-solver, although integration with
individual solvers require some library work.
Currently, we fully support
the [Z3](http://research.microsoft.com/en-us/um/redmond/projects/z3/) SMT solver from Microsoft,
and
the [Yices](http://yices.csl.sri.com) SMT solver from SRI.
Both solvers are available for Windows, Linux, and Mac OSX.
Prerequisites
=============
You **should** have at least one of
Z3 [(download)](http://research.microsoft.com/en-us/um/redmond/projects/z3/download.html), or
Yices [(download)](http://yices.csl.sri.com/download-yices2.shtml) (version 2.X)
installed on your machine, preferably both. Note that z3 is the default solver used by 'sat',
'allSat', 'prove', etc. commands. To use "yices", use the 'satWith', 'proveWith', 'allSatWith' variants.
Make sure the executables for the solvers are in your path. Alternatively, you can specify the location
of the yices executable in the environment variable `SBV_YICES` and the options to yices in `SBV_YICES_OPTIONS`.
(The default for the latter is `"-m -f"`). Similarly the environment variables `SBV_Z3` and `SBV_Z3_OPTIONS` can
be used for choosing executable location and custom options for Z3. (The default for the latter is
`"/in /smt2"` on Windows and `"-in -smt2"` on Mac and Linux. You should use Z3 version 3.2 or later.)
Examples
=========
Please see the files under the
[Examples](http://github.com/LeventErkok/sbv/tree/master/Data/SBV/Examples)
directory for a number of interesting applications and use cases. Amongst others,
it contains solvers for Sudoku and N-Queens puzzles as mandatory SMT solver examples in
the Puzzles directory.
Installation
============
The sbv library is cabalized. Assuming you have cabal/ghc installed, it should merely
be a matter of running
cabal install sbv
Please see [INSTALL](http://github.com/LeventErkok/sbv/tree/master/INSTALL) for installation details.
Once the installation is done, you can run the executable `SBVUnitTests` which will
execute the regression test suite for sbv on your machine to ensure all is well.
Copyright, License
==================
The sbv library is distributed with the BSD3 license. See [COPYRIGHT](http://github.com/LeventErkok/sbv/tree/master/COPYRIGHT) for
details. The [LICENSE](http://github.com/LeventErkok/sbv/tree/master/LICENSE) file contains
the [BSD3](http://en.wikipedia.org/wiki/BSD_licenses) verbiage.
Thanks
======
The following people reported bugs, provided comments/feedback, or contributed to the development of SBV in various ways:
Ian Blumenfeld, Ian Calvert, Iavor Diatchki, Tom Hawkins, Lee Pike, Austin Seipp, Don Stewart, Josef Svenningsson,
and Nis Wegmann.