SBV: Symbolic Bit Vectors in Haskell

Express properties about bit-precise Haskell programs and automatically prove them using SMT solvers.

    $ 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:

    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.

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)
• Arrays of symbolic values
• Symbolic polynomials over GF(2^n ), and polynomial arithmetic
• 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, predicates (i.e., functions that return SBool) 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)
• quick-checked

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.

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/)

While the library is designed to work with any SMT-Lib compliant SMT-solver, solver specific support is required for parsing counter-example/model data since there is currently no agreed upon format for getting models from arbitrary SMT solvers. (The SMT-Lib2 initiative will potentially address this issue in the future, at which point the sbv library can be generalized as well.) Currently, we only support the Yices SMT solver from SRI as far as the counter-example and model generation support is concerned: [http://yices.csl.sri.com/](http://yices.csl.sri.com/) However, other solvers can be hooked up with relative ease.

Prerequisites

You should download and install Yices (version 2.X) on your machine, and make sure the "yices" executable is in your path before using the sbv library, as it is the current default solver. Alternatively, you can specify the location of 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".)

Examples

Please see the files under the 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 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 for details. The LICENSE file contains the BSD3 verbiage.