# sbv

SMT Based Verification: Symbolic Haskell theorem prover using SMT solving. http://leventerkok.github.com/sbv/

LTS Haskell 11.14: | 7.5 |

Stackage Nightly 2018-03-12: | 7.5 |

Latest on Hackage: | 7.9 |

**Levent Erkok**

**Levent Erkok (erkokl@gmail.com)**

#### Module documentation for 7.5

- Data
- Data.SBV
- Data.SBV.Control
- Data.SBV.Dynamic
- Data.SBV.Examples
- Data.SBV.Examples.BitPrecise
- Data.SBV.Examples.CodeGeneration
- Data.SBV.Examples.Crypto
- Data.SBV.Examples.Existentials
- Data.SBV.Examples.Misc
- Data.SBV.Examples.Optimization
- Data.SBV.Examples.Polynomials
- Data.SBV.Examples.Puzzles
- Data.SBV.Examples.Puzzles.Birthday
- Data.SBV.Examples.Puzzles.Coins
- Data.SBV.Examples.Puzzles.Counts
- Data.SBV.Examples.Puzzles.DogCatMouse
- Data.SBV.Examples.Puzzles.Euler185
- Data.SBV.Examples.Puzzles.Fish
- Data.SBV.Examples.Puzzles.MagicSquare
- Data.SBV.Examples.Puzzles.NQueens
- Data.SBV.Examples.Puzzles.SendMoreMoney
- Data.SBV.Examples.Puzzles.Sudoku
- Data.SBV.Examples.Puzzles.U2Bridge

- Data.SBV.Examples.Queries
- Data.SBV.Examples.Uninterpreted

- Data.SBV.Internals
- Data.SBV.Tools

- Data.SBV

## Changes

- Hackage: http://hackage.haskell.org/package/sbv
- GitHub: http://leventerkok.github.com/sbv/
- Latest Hackage released version: 7.9, 2018-06-15

### Version 7.9, 2018-06-15

Add support for bit-vector arithmetic underflow/overflow detection. The new 'ArithmeticOverflow' class captures conditions under which addition, subtraction, multiplication, division, and negation can underflow/overflow for both signed and unsigned bit-vector values. The implementation is based on http://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/z3prefix.pdf, and can be used to detect overflow caused bugs in machine arithmetic. See "Data.SBV.Tools.Overflow" for details.

Add 'sFromIntegralO', which is the overflow/underflow detecting variant of 'sFromIntegral'. This function returns (along with the converted result), a pair of booleans showing whether the conversion underflowed or overflowed.

Change the function 'getUnknownReason' to return a proper data-type ('SMTReasonUnknown') as opposed to a mere string. This is at the query level. Similarly, change

`Unknown`

result to return the same data-type at the sat/prove level.Interpolants: With Z3 4.8.0 release, Z3 folks have dropped support for producing interpolants. If you need interpolants, you will have to use the MathSAT backend now. Also, the MathSAT API is slightly different from how Z3 supported interpolants as well, which means your old code will need some modifications. See the example in Documentation.SBV.Examples.Queries.Interpolants for the new usage.

Add 'constrainWithAttribute' call, which can be used to attach arbitrary attribute to a constraint. Main use case is in interpolant generation with MathSAT.

C code generation: SBV now spits out linker flag -lm if needed. Thanks to Matt Peddie for reporting.

Code reorg: Simplify constant mapping table, by properly accounting for negative-zero floats.

Export 'sexprToVal' for the class SMTValue, which allows for custom definitions of value extractions. Thanks to Brian Schroeder for the patch.

Export 'Logic' directly from Data.SBV. (Previously was from Control.)

Fix a long standing issue (ever since we introduced queries) where 'sAssert' calls were run in the context of the final output boolean, which is simply the wrong thing to do.

### Version 7.8, Released 2018-05-18

Fix printing of min-bounds for signed 32/64 bit numbers: These are tricky since C does not allow -min_value as a valid literal! Instead we use the macros provided in stdint.h. Thanks to Matt Peddie for reporting this corner case.

Fix translation of the "abs" function, to make sure we use the correct variant. Thanks to Matt Peddie for reporting.

Fix handling of tables and arrays in pushed-contexts. Previously, we used initializers to get table/array values stored properly. However, this trick does not work if we are in a pushed-context; since a pop can forget the corresponding assignments. SBV now handles this corner case properly, by using tracker assertions to keep track of what array values must be restored at each pop. Thanks to Martin Brain on the SMTLib mailing list for the suggestion. (See https://github.com/LeventErkok/sbv/issues/374 for details.)

Fix corner case in ite branch equality with float/double arguments, where we were previously confusing +/-0 as equal to each other. Thanks to Matt Peddie for reporting.

Add a call 'cgOverwriteFiles', which suppresses code-generation prompts for overwriting files and quiets the prompts during code generation. Thanks to Matt Peddie for the suggestion.

Add support for uninterpreted function introductions in the query mode. Previously, this was only allowed before the query started, now we fully support uninterpreted functions in all modes.

New example: Documentation/SBV/Examples/Puzzles/HexPuzzle.hs, showing how to code cover properties using SBV, using a form of bounded model checking.

### Version 7.7, Released 2018-04-29

Add support for Symbolic characters ('SChar') and strings ('SString'.) Thanks to Joel Burget for the initial implementation.

The 'SChar' type currently corresponds to the Latin-1 character set, and is thus a subset of the Haskell 'Char' type. This is due to the current limitations in SMT-solvers. However, there is a pending SMTLib proposal to support unicode, and SBV will track these changes to have full unicode support: For further details see: http://smtlib.cs.uiowa.edu/theories-UnicodeStrings.shtml

The 'SString' type is the type of symbolic strings, consisting of characters from the Latin-1 character set currently, just like the planned 'SChar' improvements. Note that an 'SString' is

*not*simply a list of 'SChar' values: It is a symbolic type of its own and is processed as a single item. Conversions from list of characters is possible (via the 'implode' function). In the other direction, one cannot generally 'explode' a string, since it may be of arbitrary length and thus we would not know what concrete list to map it to. This is a bit unlike Haskell, but the differences dissipate quickly in general, and the power of being able to deal with a string as a symbolic entity on its own opens up many verification possibilities.Note that currently only Z3 and CVC4 has support for this logic, and they do differ in some details. Various character/string operations are supported, including length, concatenation, regular-expression matching, substrig operations, recognizers, etc. If you use this logic, you are likely to find bugs in solvers themselves as support is rather new: Please report.

If unsat-core extraction is enabled, SBV now returns the unsat-core directly with in a solver result. Thanks to Ara Adkins for the suggestion.

Add 'observe'. This function allows internal expressions to be given values, which will be part of the satisfyin model or the counter-example upon model construction. Useful for tracking expected/returned values. Also works with quickCheck.

Revamp Haddock documentation, hopefully easier to follow now.

Slightly modify the generated-C headers by removing whitespace. This allows for certain "lint" rules to pass when SBV generated code is used in conjunction with a larger code base. Thanks to Greg Horn for the pull request.

Improve implementation of 'svExp' to match that of '.^', making it more defined when the exponent is constant. Thanks to Brian Huffman for the patch.

Export the underlying polynomial representation for algorithmic reals from the Internals module for further user processing. Thanks to Jan Path for the patch.

### Version 7.6, Released 2018-03-18

GHC 8.4.1 compatibility: Work around compilation issues. SBV now compiles cleanly with GHC 8.4.1.

Define and export sWordN, sWordN

*, sIntN*, from the Dynamic interface, which simplifies creation of variables of arbitrary bit sizes. These are similar to sWord8, sInt8, etc.; except they create dynamic counterparts that can be of arbitrary bit size.

### Version 7.5, Released 2018-01-13

Remove obsolote references to tactics in a few haddock comments. Thanks to Matthew Pickering for reporting.

Added logic Logic_NONE, to be used in cases where SBV should not try to set the logic. This is useful when there is no viable value to set, and the back-end solver doesn't understand the SMT-Lib convention of using "ALL" as the logic name. (One example of this is the Yices solver.)

SBV now returns SMTException (instead of just calling error) in case the backend solver responds with error message. The type SMTException can be caught by the user programs, and it includes many fields as an indication of what went wrong. (The command sent, what was expected, what was seen, etc.) Note that if this exception is ever caught, the backend solver is no longer alive: You should either just throw it, or perform proper clean-up on your user code as required to set up a new context. The provided show instance formats the exception nicely for display purposes. See https://github.com/LeventErkok/sbv/issues/335 for details and thanks to Brian Huffman for reporting.

SIntegral class now has Integral as a super-class, which ensures the base-type it's used at is Integral. This was already true for all instances, so we are just making it more explicit.

Improve the implementation of .^ (exponentiation) to cover more cases, in particular signed exponents are now OK so long as they are concrete and positive, following Haskell convention.

Removed the 'FromBits' class. Its functionality is now merged with the new 'SFiniteBits' class, see below.

Introduce 'SFiniteBits' class, which only incorporates finite-words in it, i.e., SWord/SInt for 8-16-32-64. In particular it leaves out SInteger, SFloat, SDouble, and SReal. Important in recognizing bit-vectors of finite size, essentially. Here are the methods:

`class (SymWord a, Num a, Bits a) => SFiniteBits a where sFiniteBitSize :: SBV a -> Int -- ^ Bit size lsb :: SBV a -> SBool -- ^ Least significant bit of a word, always stored at index 0. msb :: SBV a -> SBool -- ^ Most significant bit of a word, always stored at the last position. blastBE :: SBV a -> [SBool] -- ^ Big-endian blasting of a word into its bits. Also see the 'FromBits' class. blastLE :: SBV a -> [SBool] -- ^ Little-endian blasting of a word into its bits. Also see the 'FromBits' class. fromBitsBE :: [SBool] -> SBV a -- ^ Reconstruct from given bits, given in little-endian fromBitsLE :: [SBool] -> SBV a -- ^ Reconstruct from given bits, given in little-endian sTestBit :: SBV a -> Int -> SBool -- ^ Replacement for 'testBit', returning 'SBool' instead of 'Bool' sExtractBits :: SBV a -> [Int] -> [SBool] -- ^ Variant of 'sTestBit', where we want to extract multiple bit positions. sPopCount :: SBV a -> SWord8 -- ^ Variant of 'popCount', returning a symbolic value. setBitTo :: SBV a -> Int -> SBool -> SBV a -- ^ A combo of 'setBit' and 'clearBit', when the bit to be set is symbolic. fullAdder :: SBV a -> SBV a -> (SBool, SBV a) -- ^ Full adder, returns carry-out from the addition. Only for unsigned quantities. fullMultiplier :: SBV a -> SBV a -> (SBV a, SBV a) -- ^ Full multipler, returns both high and low-order bits. Only for unsigned quantities. sCountLeadingZeros :: SBV a -> SWord8 -- ^ Count leading zeros in a word, big-endian interpretation sCountTrailingZeros :: SBV a -> SWord8 -- ^ Count trailing zeros in a word, big-endian interpretation`

Note that the functions 'sFiniteBitSize', 'sCountLeadingZeros', and 'sCountTrailingZeros' are new. Others have existed in SBV before, we are just grouping them together now in this new class.

Tightened certain signatures where SBV was too liberal, using the SFiniteBits class. New signatures are:

`sSignedShiftArithRight :: (SFiniteBits a, SIntegral b) => SBV a -> SBV b -> SBV a crc :: (SFiniteBits a, SFiniteBits b) => Int -> SBV a -> SBV b -> SBV b readSTree :: (SFiniteBits i, SymWord e) => STree i e -> SBV i -> SBV e writeSTree :: (SFiniteBits i, SymWord e) => STree i e -> SBV i -> SBV e -> STree i e`

Thanks to Thomas DuBuisson for reporting.

### Version 7.4, 2017-11-03

Export queryDebug from the Control module, allowing custom queries to print debugging messages with the verbose flag is set.

Relax value-parsing to allow for non-standard output from solvers. For instance, MathSAT/Yices prints reals as integers when they do not have a fraction. We now support such cases, relaxing the standard slightly. Thanks to Geoffrey Ramseyer for reporting.

Fix optimization routines when applied to signed-bitvector goals. Thanks to Anders Kaseorg for reporting. Since SMT-Lib does not distinguish between signed and unsigned bit-vectors, we have to be careful when expressing goals that are over signed values. See https://github.com/LeventErkok/sbv/issues/333 for details.

### Version 7.3, 2017-09-06

Query mode: Add support for arrays in query mode. Thanks to Brad Hardy for providing the use-case and debugging help.

Query mode: Add support for tables. (As used by 'select' calls.)

### Version 7.2, 2017-08-29

Reworked implementation of shifts and rotates: When a signed quantity was being shifted right by more than its size, SBV used to return 0. Robert Dockins pointed out that the correct answer is actually -1 in such cases. The new implementation merges the dynamic and typed interfaces, and drops support for non-constant shifts of unbounded integers, which is not supported by SMTLib. Thanks to Robert for reporting the issue and identifying the root cause.

Rework how quantifiers are handled: We now generate separate asserts for prefix-existentials. This allows for better (smaller) quantified code, while preserving semantics.

Rework the interaction between quantifiers and optimization routines. Optimization routines now properly handle quantified formulas, so long as the quantified metric does not involve any universal quantification itself. Thanks to Matthew Danish for reporting the issue.

Development/Infrastructure: Lots of work around the continuous integration for SBV. We now build/test on Linux/Mac/Windows on every commit. Thanks to Travis/Appveyor for providing free remote infrastructure. There are still gotchas and some reductions in tests due to host capacity issues. If you would like to be involved and improve the test suite, please get in touch!

### Version 7.1, 2017-07-29

Add support for 'getInterpolant' in Query mode.

Support for SMT-results that can contain multi-line strings, which is rare but it does happen. Previously SBV incorrectly interpreted such responses to be erroneous.

Many improvements to build infrastructure and code clean-up.

Fix a bug in the implementation of

`svSetBit`

. Thanks to Robert Dockins for the report.

### Version 7.0, 2017-07-19

NB. SBV now requires GHC >= 8.0.1 to compile. If you are stuck with an older version of GHC, please get in contact.

This is a major rewrite of the internals of SBV, and is a backwards compatibility breaking release. While we kept the top-level and most commonly used APIs the same (both types and semantics), much of the internals and advanced features have been rewritten to move SBV to a new model of execution: SBV no longer runs your program symbolically and calls the SMT solver afterwards. Instead, the interaction with the solver happens interleaved with the actual program execution. The motivation is to allow the end-users to send/receive arbitrary SMTLib commands to the solver, instead of the cooked-up recipes. SBV still provides all the recipes for its existing functionality, but users can now interact with the solver directly. See the module "Data.SBV.Control" for the main API, together with the new functions 'runSMT' and 'runSMTWith'.

The 'Tactic' based solver control (introduced in v6.0) is completely removed, and is replaced by the above described mechanism which gives the user a lot of flexibility instead. Use queries for anything that required a tactic before.

The call 'allSat' has been reworked so it performs only one call to the underlying solver and repeatedly issues check-sat to get new assignments. This differs from the previous implementation where we spun off a new call to the executable for each successive model. While this is more efficient and much more preferable, it also means that the results are no longer lazily computed: If there is an infinite number of solutions (or a very large number), you can no longer merely do a 'take' on the result. While this is inconvenient, it fits better with our new methodology of query based interaction. Note that the old behavior can be modeled, if required, by the user; by explicitly interleaving the calls to 'sat.' Furthermore, we now provide a new configuration parameter named 'allSatMaxModelCount' which can be used to limit the number models we seek. The default is to get all models, however long that might take.

The Bridge modules (

`Data.SBV.Bridge.Yices`

,`Data.SBV.Bridge.Z3`

) etc. are all removed. The bridge functionality was hardly used, where different solvers were much easier to access using the`with`

functions. (Such as`proveWith`

,`satWith`

etc.) This should result in no loss of functionality, except for occasional explicit mention of solvers in your code, if you were using bridge modules to start with.Optimization routines have been changed to take a priority as an argument, (i.e., Lexicographic, Independent, etc.). The old method of supplying the priority via tactics is no longer supported.

Pareto-front extraction has been reworked, reflecting the changes in Z3 for this functionality. Since pareto-fronts can be infinite in number, the user is now allowed to specify a "limit" to stop the solver from querying ad infinitum. If the limit is not specified, then sbv will query till it exhausts all the pareto-fronts, or till it runs out of memory in case there is an infinite number of them.

Extraction of unsat-cores has changed. To use this feature, we now use custom queries. See "Data.SBV.Examples.Misc.UnsatCore" for an example. Old style of unsat-core extraction is no longer supported.

The 'timing' option of SMTConfig has been reworked. Since we now start the solver immediately, it is no longer sensible to distinguish between "SBV" time, "translation" time etc. Instead, we print one simple "Elapsed" time if requested. If you need a detailed timing analysis, use the new 'transcript' option to SMTConfig: It will produce a file with precise timing intervals for each command issued to help you figure out how long each step took.

The following functions have been reworked, so they now also return the time-elapsed for each solver:

`satWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, SatResult)] satWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, SatResult) proveWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, ThmResult)] proveWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, ThmResult)`

Changed the way

`satWithAny`

and`proveWithAny`

works. Previously, these two functions ran multiple solvers, and took the result of the first one to finish, killing all the others. In addition, they*waited*for the still-running solvers to finish cleaning-up, as sending a 'ThreadKilled' is usually not instantaneous. Furthermore, a solver might simply take its time! We now send the interrupt but do not wait for the process to actually terminate. In rare occasions this could create zombie processes if you use a solver that is not cooperating, but we have seen not insignificant speed-ups for regular usage due to ThreadKilled wait times being rather long.Configuration option

`useLogic`

is removed. If required, this should be done by a call to the new 'setLogic' function:`setLogic QF_NRA`

Configuration option

`timeOut`

is removed. This was rarely used, and the solver support was rather sketchy. We now have a better mechanism in the query mode for timeouts, where it really matters. Please get in touch if you relied on this old mechanism. Correspondingly, the functions`isTheorem`

,`isSatisfiable`

,`isTheoremWith`

and`isSatisfiableWith`

had their time-out arguments removed and return types simplified.The function 'isSatisfiableInCurrentPath' is removed. Proper queries should be used for what this function tentatively attempted to provide. Please get in touch if you relied on this function and want to restructure your code to use proper queries.

Configuration option 'smtFile' is removed. Instead use 'transcript' now, which provides a much more detailed output that is directly loadable to a solver and has an accurate account of precisely what SBV sent.

Enumerations are now much easier to use symbolically, with the addition of the template-haskell splice mkSymbolicEnumeration. See "Data/SBV/Examples/Misc/Enumerate.hs" for an example.

Thanks to Kanishka Azimi, our external test suite is now run by Tasty! Kanishka modernized the test suite, and reworked the infrastructure that was showing its age. Thanks!

The function pConstrain and the Data.SBV.Tools.ExpectedValue are removed. Probabilistic constraints were rarely used, and if necessary can be implemented outside of SBV. If you were using this feature, please get in contact.

SArray and SFunArray has been reworked, and they no longer take and initial value. Similarly resetArray has been removed, as it did not really do what it advertised. If an initial value is needed, it is best to code this explicitly in your model.

### Version 6.1, 2017-05-26

Add support for unsat-core extraction. To use this feature, use the

`namedConstraint`

function:`namedConstraint :: String -> SBool -> Symbolic ()`

to associate a label to a constrain or a boolean term that can later be labeled by the backend solver as belonging to the unsat-core.

Unsat-cores are not enabled by default since they can be expensive; to use:

`satWith z3{getUnsatCore=True} $ do ...`

In the programmatic API, the function:

`extractUnsatCore :: Modelable a => a -> Maybe [String]`

can be used to programmatically extract the unsat-core. Note that backend solvers will only include the named expressions in the unsat-core, i.e., any unnamed yet part-of-the-core-unsat expressions will be missing; as speculated in the SMT-Lib document itself.

Currently, Z3, MathSAT, and CVC4 backends support unsat-cores.

(Thanks to Rohit Ramesh for the suggestion leading to this feature.)

Added function

`distinct`

, which returns true if all the elements of the given list are different. This function replaces the old`allDifferent`

function, which is now removed. The difference is that`distinct`

will produce much better code for SMT-Lib. If you used`allDifferent`

before, simply replacing it with`distinct`

should work.Add support for pseudo-boolean operations:

`pbAtMost :: [SBool] -> Int -> SBool pbAtLeast :: [SBool] -> Int -> SBool pbExactly :: [SBool] -> Int -> SBool pbLe :: [(Int, SBool)] -> Int -> SBool pbGe :: [(Int, SBool)] -> Int -> SBool pbEq :: [(Int, SBool)] -> Int -> SBool pbMutexed :: [SBool] -> SBool pbStronglyMutexed :: [SBool] -> SBool`

These functions, while can be directly coded in SBV, produce better translations to SMTLib for more efficient solving of cardinality constraints. Currently, only Z3 supports pseudo-booleans directly. For all other solvers, SBV will translate these to equivalent terms that do not require special functions.

The function getModel has been renamed to getAssignment. (The former name is now available as a query command.)

Export

`SolverCapabilities`

from`Data.SBV.Internals`

, in case users want access.Move code-generation facilities to

`Data.SBV.Tools.CodeGen`

, no longer exporting the relevant functions directly from`Data.SBV`

. This could break existing code, but the fix should be as simple as`import Data.SBV.Tools.CodeGen`

.Move the following two functions to

`Data.SBV.Internals`

:`compileToSMTLib generateSMTBenchmarks`

If you use them, please

`import Data.SBV.Internals`

.Reorganized

`EqSymbolic`

and`EqOrd`

classes to collect some of the similarly named function together. Users should see no impact due to this change.

### Version 6.0, 2017-05-07

This is a backwards compatibility breaking release, hence the major version bump from 5.15 to 6.0:

- Most of existing code should work with no changes.
- Old code relying on some features might require extra imports,
since we no longer export some functionality directly from
`Data.SBV`

. This was done in order to reduce the number of exported items to avoid extra clutter. - Old optimization features are removed, as the new and much improved capabilities should be used instead.

The next two bullets cover new features in SBV regarding optimization, based on the capabilities of the z3 SMT solver. With this release SBV gains the capability optimize objectives, and solve MaxSAT problems; by appropriately employing the corresponding capabilities in z3. A good review of these features as implemented by Z3, and thus what is available in SBV is given in this paper: http://www.easychair.org/publications/download/Z

*-*Maximal*Satisfaction*with_Z3SBV now allows for real or integral valued metrics. Goals can be lexicographically (default), independently, or pareto-front optimized. Currently, only the z3 backend supports optimization routines.

Optimization can be done over bit-vector, real, and integer goals. The relevant functions are:

`- `minimize`: Minimize a given arithmetic goal - `maximize`: Minimize a given arithmetic goal`

For instance, a call of the form

`minimize "name-of-goal" $ x + 2*y`

Minimizes the arithmetic goal x+2*y, where x and y can be bit-vectors, reals, or integers. Such goals will be lexicographically optimized, i.e., in the order given. If there are multiple goals, then user can also ask for independent optimization results, or pareto-fronts.

Once the objectives are given, a top level call to

`optimize`

(similar to`prove`

and`sat`

) performs the optimization.SBV now implements soft-asserts. A soft assertion is a hint to the SMT solver that we would like a particular condition to hold if

*possible*. That is, if there is a solution satisfying it, then we would like it to hold. However, if the set of constraints is unsatisfiable, then a soft-assertion can be violated by incurring a user-given numeric penalty to satisfy the remaining constraints. The solver then tries to minimize the penalty, i.e., satisfy as many of the soft-asserts as possible such that the total penalty for those that are not satisfied is minimized.Note that

`assertSoft`

works well with optimization goals (minimize/maximize etc.), and are most useful when we are optimizing a metric and thus some of the constraints can be relaxed with a penalty to obtain a good solution.SBV no longer provides the old optimization routines, based on iterative and quantifier based methods. Those methods were rarely used, and are now superseded by the above mechanism. If the old code is needed, please contact for help: They can be resurrected in your own code if absolutely necessary.

(NB. This feature is deprecated in 7.0, see above for its replacement.) SBV now implements tactics, which allow the user to navigate the proof process. This is an advanced feature that most users will have no need of, but can become handy when dealing with complicated problems. Users can, for instance, implement case-splitting in a proof to guide the underlying solver through. Here is the list of tactics implemented:

`- `CaseSplit` : Case-split, with implicit coverage. Bool says whether we should be verbose. - `CheckCaseVacuity` : Should the case-splits be checked for vacuity? (Default: True.) - `ParallelCase` : Run case-splits in parallel. (Default: Sequential.) - `CheckConstrVacuity`: Should constraints be checked for vacuity? (Default: False.) - `StopAfter` : Time-out given to solver, in seconds. - `CheckUsing` : Invoke with check-sat-using command, instead of check-sat - `UseLogic` : Use this logic, a custom one can be specified too - `UseSolver` : Use this solver (z3, yices, etc.) - `OptimizePriority` : Specify priority for optimization: Lexicographic (default), Independent, or Pareto.`

Name-space clean-up. The following modules are no longer automatically exported from Data.SBV:

`- `Data.SBV.Tools.ExpectedValue` (computing with expected values) - `Data.SBV.Tools.GenTest` (test case generation) - `Data.SBV.Tools.Polynomial` (polynomial arithmetic, CRCs etc.) - `Data.SBV.Tools.STree` (full symbolic binary trees)`

To use the functionality of these modules, users must now explicitly import the corresponding module. Not other changes should be needed other than the explicit import.

Changed the signatures of:

`isSatisfiableInCurrentPath :: SBool -> Symbolic Bool svIsSatisfiableInCurrentPath :: SVal -> Symbolic Bool`

to:

`isSatisfiableInCurrentPath :: SBool -> Symbolic (Maybe SatResult) svIsSatisfiableInCurrentPath :: SVal -> Symbolic (Maybe SatResult)`

which returns the result in case of SAT. This is more useful than before. This is backwards-compatibility breaking, but is more useful. (Requested by Jared Ziegler.)

Add instance

`Provable (Symbolic ())`

, which simply stands for returning true for proof/sat purposes. This allows for simpler coding, as constrain/minimize/maximize calls (which return unit) can now be directly sat/prove processed, without needing a final call to return at the end.Add type synonym

`Goal`

(for`Symbolic ()`

), in order to simplify type signaturesSBV now properly adds check-sat commands and other directives in debugging output.

- New examples:
- Data.SBV.Examples.Optimization.LinearOpt: Simple linear-optimization example.
- Data.SBV.Examples.Optimization.Production: Scheduling machines in a shop
- Data.SBV.Examples.Optimization.VM: Scheduling virtual-machines in a data-center

### Version 5.15, 2017-01-30

- Bump up dependency on CrackNum >= 1.9, to get access to hexadecimal floats.
- Improve time/tracking-print code. Thanks to Iavor Diatchki for the patch.

### Version 5.14, 2017-01-12

Bump up QuickCheck dependency to >= 2.9.2 to avoid the following quick-check bug http://github.com/nick8325/quickcheck/issues/113, which transitively impacted the quick-check as implemented by SBV.

Generalize casts between integral-floats, using the rounding mode round-nearest-ties-to-even. Previously calls to sFromIntegral did not support conversion to floats since it needed a rounding mode. But it does make sense to support them with the default mode. If a different mode is needed, use the function 'toSFloat' as before, which takes an explicit rounding mode.

### Version 5.13, 2016-10-29

Fix broken links, thanks to Stephan Renatus for the patch.

Code generation: Create directory path if it does not exist. Thanks to Robert Dockins for the patch.

Generalize the type of sFromIntegral, dropping the Bits requirement. In turn, this allowed us to remove sIntegerToSReal, since sFromIntegral can be used instead.

Add support for sRealToSInteger. (Essentially the floor function for SReal.)

Several space-leaks fixed for better performance. Patch contributed by Robert Dockins.

Improved Random instance for Rational. Thanks to Joe Leslie-Hurd for the idea.

### Version 5.12, 2016-06-06

Fix GHC8.0 compliation issues, and warning clean-up. Thanks to Adam Foltzer for the bulk of the work and Tom Sydney Kerckhove for the initial patch for 8.0 compatibility.

Minor fix to printing models with floats when the base is 2/16, making sure the alignment is done properly accommodating for the crackNum output.

Wait for external process to die on exception, to avoid spawning zombies. Thanks to Daniel Wagner for the patch.

Fix hash-consed arrays: Previously we were caching based only on elements, which is not sufficient as you can have conflicts differing only on the address type, but same contents. Thanks to Brian Huffman for reporting and the corresponding patch.

### Version 5.11, 2016-01-15

Fix documentation issue; no functional changes

### Version 5.10, 2016-01-14

Documentation: Fix a bunch of dead http links. Thanks to Andres Sicard-Ramirez for reporting.

Additions to the Dynamic API:

- svSetBit : set a given bit
- svBlastLE, svBlastBE : Bit-blast to big/little endian
- svWordFromLE, svWordFromBE: Unblast from big/little endian
- svAddConstant : Add a constant to an SVal
- svIncrement, svDecrement : Add/subtract 1 from an SVal

### Version 5.9, 2016-01-05

Default definition for 'symbolicMerge', which allows types that are instances of 'Generic' to have an automatically derivable merge (i.e., ite) instance. Thanks to Christian Conkle for the patch.

Add support for "non-model-vars," where we can now tell SBV not to take into account certain variables from a model-building perspective. This comes handy in doing an

`allSat`

calls where there might be witness variables that we do not care the uniqueness for. See "Data/SBV/Examples/Misc/Auxiliary.hs" for an example, and the discussion in https://github.com/LeventErkok/sbv/issues/208 for motivation.Yices interface: If Reals are used, then pick the logic QF

*UFLRA, instead of QF*AUFLIA. Unfortunately, logic selection remains tricky since the SMTLib story for logic selection is rather messy. Other solvers are not impacted by this change.

### Version 5.8, 2016-01-01

- Fix some typos
- Add 'svEnumFromThenTo' to the Dynamic interface, allowing dynamic construction of [x, y .. z] and [x .. y] when the involved values are concrete.
- Add 'svExp' to the Dynamic interface, implementing exponentiation

### Version 5.7, 2015-12-21

- Export
`HasKind(..)`

from the Dynamic interface. Thanks to Adam Foltzer for the patch. - More careful handling of SMT-Lib reserved names.
- Update tested version of MathSAT to 5.3.9
- Generalize
`sShiftLeft`

/`sShiftRight`

/`sRotateLeft`

/`sRotateRight`

to work with signed shift/rotate amounts, where negative values revert the direction. Similar generalizations are also done for the dynamic variants.

### Version 5.6, 2015-12-06

- Minor changes to how we print models:
- Align by the type
- Always print the type (previously we were skipping for Bool)
- Rework how SBV properties are quick-checked; much more usable and robust
- Provide a function
`sbvQuickCheck`

, which is essentially the same as quickCheck, except it also returns a boolean. Useful for the programmable API. (The dynamic version is called`svQuickCheck`

.) - Several changes/additions in support of the sbvPlugin development:
- Data.SBV.Dynamic: Define/export
`svFloat`

/`svDouble`

/`sReal`

/`sNumerator`

/`sDenominator`

- Data.SBV.Internals: Export constructors of
`Result`

,`SMTModel`

, and the function`showModel`

- Simplify how Uninterpreted-types are internally represented.

### Version 5.5, 2015-11-10

This is essentially the same release as 5.4 below, except to allow SBV compile with GHC 7.8 series. Thanks to Adam Foltzer for the patch.

### Version 5.4, 2015-11-09

Add 'sAssert', which allows users to pepper their code with boolean conditions, much like the usual ASSERT calls. Note that the semantics of an 'sAssert' is that it is a NOOP, i.e., it simply returns its final argument. Use in coordination with 'safe' and 'safeWith', see below.

Implement 'safe' and 'safeWith', which statically determine all calls to 'sAssert' being safe to execute. Any violations will be flagged.

SBV->C: Translate 'sAssert' calls to dynamic checks in the generated C code. If this is not desired, use the 'cgIgnoreSAssert' function to turn it off.

Add 'isSafe': Which converts a 'SafeResult' to a 'Bool', when we are only interested in a boolean result.

Add Data/SBV/Examples/Misc/NoDiv0 to demonstrate the use of the 'safe' function.

### Version 5.3, 2015-10-20

Main point of this release to make SBV compile with GHC 7.8 again, to accommodate mainly for Cryptol. As Cryptol moves to GHC >= 7.10, we intend to remove the "compatibility" changes again. Thanks to Adam Foltzer for the patch.

Minor mods to how bitvector equality/inequality are translated to SMTLib. No user visible impact.

### Version 5.2, 2015-10-12

Regression on 5.1: Fix a minor bug in base 2/16 printing where uninterpreted constants were not handled correctly.

### Version 5.1, 2015-10-10

fpMin, fpMax: If these functions receive +0/-0 as their two arguments, i.e., both zeros but alternating signs in any order, then SMTLib requires the output to be nondeterministicly chosen. Previously, we fixed this result as +0 following the interpretation in Z3, but Z3 recently changed and now incorporates the nondeterministic output. SBV similarly changed to allow for non-determinism here.

Change the types of the following Floating-point operations:

`* sFloatAsSWord32, sFloatAsSWord32, blastSFloat, blastSDouble`

These were previously coded as relations, since NaN values were not representable in the target domain uniquely. While it was OK, it was hard to use them. We now simply implement these as functions, and they are underspecified if the inputs are NaNs: In those cases, we simply get a symbolic output. The new types are:

- sFloatAsSWord32 :: SFloat -> SWord32
- sDoubleAsSWord64 :: SDouble -> SWord64
- blastSFloat :: SFloat -> (SBool, [SBool], [SBool])
- blastSDouble :: SDouble -> (SBool, [SBool], [SBool])

MathSAT backend: Use the SMTLib interpretation of fp.min/fp.max by passing the "-theory.fp.minmax

*zero*mode=4" argument explicitly.Fix a bug in hash-consing of floating-point constants, where we were confusing +0 and -0 since we were using them as keys into the map though they compare equal. We now explicitly keep track of the negative-zero status to make sure this confusion does not arise. Note that this bug only exhibited itself in rare occurrences of both constants being present in a benchmark; a true corner case. Note that @NaN@ values are also interesting in this context: Since NaN /= NaN, we never hash-cons floating point constants that have the value NaN. But that is actually OK; it is a bit wasteful in case you have a lot of NaN constants around, but there is no soundness issue: We just waste a little bit of space.

Remove the functions

`allSatWithAny`

and`allSatWithAll`

. These two variants do*not*make sense when run with multiple solvers, as they internally sequentialize the solutions due to the nature of`allSat`

. Not really needed anyhow; so removed. The variants`satWithAny/All`

and`proveWithAny/All`

are still available.Export SMTLibVersion from the library, forgotten export needed by Cryptol. Thanks to Adam Foltzer for the patch.

Slightly modify model-outputs so the variables are aligned vertically. (Only matters if we have model-variable names that are of differing length.)

Move to Travis-CI "docker" based infrastructure for builds

Enable local builds to use the Herbie plugin. Currently SBV does not have any expressions that can benefit from Herbie, but it is nice to have this support in general.

### Version 5.0, 2015-09-22

Note: This is a backwards-compatibility breaking release, see below for details.

SBV now requires GHC 7.10.1 or newer to be compiled, taking advantage of newer features/bug-fixes in GHC. If you really need SBV to compile with older GHCs, please get in touch.

SBV no longer supports SMTLib1. We now exclusively use SMTLib2 for communicating with backend solvers. Strictly speaking, this means some loss in functionality: Uninterpreted-function models that we supported via Yices-1 are no longer available. In practice this facility was not really used, and required a very old version of Yices that was no longer supported by SRI and has lacked in other features. So, in reality this change should hardly matter for end-users.

Added function "label", which is useful in emitting comments around expressions. It is essentially a no-op, but does generate a comment with the given text in the SMT-Lib and C output, for diagnostic purposes.

Added "sFromIntegral": Conversions from all integral types (SInteger, SWord/SInts) between each other. Similar to the "fromIntegral" function of Haskell. These generate simple casts when used in code-generation to C, and thus are very efficient.

SBV no longer supports the functions sBranch/sAssert, as we realized these functions can cause soundness issues under certain conditions. While the triggering scenarios are not common use-cases for these functions, we are opting for safety, and thus removing support. See http://github.com/LeventErkok/sbv/issues/180 for details; and see below for the new function 'isSatisfiableInCurrentPath'.

A new function 'isSatisfiableInCurrentPath' is added, which checks for satisfiability during a symbolic simulation run. This function can be used as the basis of sBranch/sAssert like functionality if needed. The difference is that this is a much lower level call, and also exposes the fact that the result is in the 'Symbolic' monad (which avoids the soundness issue). Of course, the new type makes it less useful as it will not be a drop-in replacement for if-then-else like structure. Intended to be used by tools built on top of SBV, as opposed to end-users.

SBV no longer implements the 'SignCast' class, as its functionality is replaced by the 'sFromIntegral' function. Programs using the functions 'signCast' and 'unsignCast' should simply replace both with calls to 'sFromIntegral'. (Note that extra type-annotations might be necessary, similar to the uses of the 'fromIntegral' function in Haskell.)

Backend solver related changes:

Yices: Upgraded to work with Yices release 2.4.1. Note that earlier versions of Yices are

*not*supported.Boolector: Upgraded to work with new Boolector release 2.0.7. Note that earlier versions of Boolector are

*not*supported.MathSAT: Upgraded to work with latest release 5.3.7. Note that earlier versions of MathSAT are

*not*supported (due to a buffering issue in MathSAT itself.)MathSAT: Enabled floating-point support in MathSAT.

New examples:

Add Data.SBV.Examples.Puzzles.Birthday, which solves the Cheryl-Birthday problem that went viral in April 2015. Turns out really easy to solve for SMT, but the formalization of the problem is still interesting as an exercise in formal reasoning.

Add Data.SBV.Examples.Puzzles.SendMoreMoney, which solves the classic send + more = money problem. Really a trivial example, but included since it is pretty much the hello-world for basic constraint solving.

Add Data.SBV.Examples.Puzzles.Fish, which solves a typical logic puzzle; finding the unique solution to a set of assertions made about a bunch of people, their pets, beverage choices, etc. Not particularly interesting, but could be fun to play around with for modeling purposes.

Add Data.SBV.Examples.BitPrecise.MultMask, which demonstrates the use of the bitvector solver to an interesting bit-shuffling problem.

Rework floating-point arithmetic, and add missing floating-point operations:

- fpRem : remainder
- fpRoundToIntegral: truncating round
- fpMin : min
- fpMax : max
- fpIsEqualObject : FP equality as object (i.e., NaN equals NaN, +0 does not equal -0, etc.)

This brings SBV up-to par with everything supported by the SMT-Lib FP theory.

Add the IEEEFloatConvertable class, which provides conversions to/from Floats and other types. (i.e., value conversions from all other types to Floats and Doubles; and back.)

Add SWord32/SWord64 to/from SFloat/SDouble conversions, as bit-pattern reinterpretation; using the IEEE754 interchange format. The functions are: sWord32AsSFloat, sWord64AsSDouble, sFloatAsSWord32, sDoubleAsSWord64. Note that the sWord32AsSFloat and sWord64ToSDouble are regular functions, but sFloatToSWord32 and sDoubleToSWord64 are "relations", since NaN values are not uniquely convertable.

Add 'sExtractBits', which takes a list of indices to extract bits from, essentially equivalent to 'map sTestBit'.

Rename a set of symbolic functions for consistency. Here are the old/new names:

- sbvTestBit --> sTestBit
- sbvPopCount --> sPopCount
- sbvShiftLeft --> sShiftLeft
- sbvShiftRight --> sShiftRight
- sbvRotateLeft --> sRotateLeft
- sbvRotateRight --> sRotateRight
- sbvSignedShiftArithRight --> sSignedShiftArithRight

Rename all FP recognizers to be in sync with FP operations. Here are the old/new names:

- isNormalFP --> fpIsNormal
- isSubnormalFP --> fpIsSubnormal
- isZeroFP --> fpIsZero
- isInfiniteFP --> fpIsInfinite
- isNaNFP --> fpIsNaN
- isNegativeFP --> fpIsNegative
- isPositiveFP --> fpIsPositive
- isNegativeZeroFP --> fpIsNegativeZero
- isPositiveZeroFP --> fpIsPositiveZero
- isPointFP --> fpIsPoint

Lots of other work around floating-point, test cases, reorg, etc.

Introduce shorter variants for rounding modes: sRNE, sRNA, sRTP, sRTN, sRTZ; aliases for sRoundNearestTiesToEven, sRoundNearestTiesToAway, sRoundTowardPositive, sRoundTowardNegative, and sRoundTowardZero; respectively.

### Version 4.4, 2015-04-13

Hook-up crackNum package; so counter-examples involving floats and doubles can be printed in detail when the printBase is chosen to be 2 or 16. (With base 10, we still get the simple output.)

`` Prelude Data.SBV> satWith z3{printBase=2} $ \x -> x .== (2::SFloat) Satisfiable. Model: s0 = 2.0 :: Float 3 2 1 0 1 09876543 21098765432109876543210 S ---E8--- ----------F23---------- Binary: 0 10000000 00000000000000000000000 Hex: 4000 0000 Precision: SP Sign: Positive Exponent: 1 (Stored: 128, Bias: 127) Value: +2.0 (NORMAL)`

`Change how we print type info; for models insted of SType just print Type (i.e., for SWord8, instead print Word8) which makes more sense and is more consistent. This change should be mostly relevant as how we see the counter-example output.

Fix long standing bug #75, where we now support arrays with Boolean source/targets. This is not a very commonly used case, but by letting the solver pick the logic, we now allow arrays to be uniformly supported.

### Version 4.3, 2015-04-10

Introduce Data.SBV.Dynamic, by Brian Huffman. This is mostly an internal reorg of the SBV codebase, and end-users should not be impacted by the changes. The introduction of the Dynamic SBV variant (i.e., one that does not mandate a phantom type as in "SBV Word8" etc. allows library writers more flexibility as they deal with arbitrary bit-vector sizes. The main customer of these changes are the Cryptol language and the associated toolset, but other developers building on top of SBV can find it useful as well. NB: The "strongly-typed" aspect of SBV is still the main way end-users should interact with SBV, and nothing changed in that respect!

Add symbolic variants of floating-point rounding-modes for convenience

Rename toSReal to sIntegerToSReal, which captures the intent more clearly

Code clean-up: remove mbMinBound/mbMaxBound thus allowing less calls to unliteral. Contributed by Brian Huffman.

Introduce FP conversion functions:

- Between SReal and SFloat/SDouble
- fpToSReal
- sRealToSFloat
- sRealToSDouble

- Between SWord32 and SFloat
- sWord32ToSFloat
- sFloatToSWord32

- Between SWord64 and SDouble. (Relational, due to non-unique NaNs)
- sWord64ToSDouble

- sDoubleToSWord64
- From float to sign/exponent/mantissa fields: (Relational, due to non-unique NaNs)
- blastSFloat
- blastSDouble

- Between SReal and SFloat/SDouble
Rework floating point classifiers. Remove isSNaN and isFPPoint (both renamed), and add the following new recognizers:

- isNormalFP
- isSubnormalFP
- isZeroFP
- isInfiniteFP
- isNaNFP
- isNegativeFP
- isPositiveFP
- isNegativeZeroFP
- isPositiveZeroFP
- isPointFP (corresponds to a real number, i.e., neither NaN nor infinity)

Re-implement sbvTestBit, by Brian Huffman. This version is much faster at large word sizes, as it avoids the costly mask generation.

Code changes to suppress warnings with GHC7.10. General clean-up.

### Version 4.2, 2015-03-17

Add exponentiation (.^). Thanks to Daniel Wagner for contributing the code!

Better handling of SBV

*$SOLVER*OPTIONS, in particular keeping track of proper quoting in environment variables. Thanks to Adam Foltzer for the patch!Silence some hlint/ghci warnings. Thanks to Trevor Elliott for the patch!

Haddock documentation fixes, improvements, etc.

Change ABC default option string to %blast; "&sweep -C 5000; &syn4; &cec -s -m -C 2000" which seems to give good results. Use SBV

*ABC*OPTIONS environment variable (or via abc.rc file and a combination of SBV*ABC*OPTIONS) to experiment.

### Version 4.1, 2015-03-06

Add support for the ABC solver from Berkeley. Thanks to Adam Foltzer for the required infrastructure! See: http://www.eecs.berkeley.edu/~alanmi/abc/ And Alan Mishchenko for adding infrastructure to ABC to work with SBV.

Upgrade the Boolector connection to use a SMT-Lib2 based interaction. NB. You need at least Boolector 2.0.6 installed!

Tracking changes in the SMT-Lib floating-point theory. If you are using symbolic floating-point types (i.e., SFloat and SDouble), then you should upgrade to this version and also get a very latest (unstable) Z3 release. See http://smtlib.cs.uiowa.edu/theories-FloatingPoint.shtml for details.

Introduce a new class, 'RoundingFloat', which supports floating-point operations with arbitrary rounding-modes. Note that Haskell only allows RoundNearestTiesToAway, but with SBV, we get all 5 IEEE754 rounding-modes and all the basic operations ('fpAdd', 'fpMul', 'fpDiv', etc.) with these modes.

Allow Floating-Point RoundingMode to be symbolic as well

Improve the example "Data/SBV/Examples/Misc/Floating.hs" to include rounding-mode based addition example.

Changes required to make SBV compile with GHC 7.10; mostly around instance NFData declarations. Thanks to Iavor Diatchki for the patch.

Export a few extra symbols from the Internals module (mainly for Cryptol usage.)

### Version 4.0, 2015-01-22

This release mainly contains contributions from Brian Huffman, allowing end-users to define new symbolic types, such as Word4, that SBV does not natively support. When GHC gets type-level literals, we shall most likely incorporate arbitrary bit-sized vectors and ints using this mechanism, but in the interim, this release provides a means for the users to introduce individual instances.

- Modifications to support arbitrary bit-sized vectors; These changes have been contributed by Brian Huffman of Galois.. Thanks Brian.
- A new example "Data/SBV/Examples/Misc/Word4.hs" showing how users can add new symbolic types.
- Support for rotate-left/rotate-right with variable rotation amounts. (From Brian Huffman.)

### Version 3.5, 2015-01-15

This release is mainly adding support for enumerated types in Haskell being translated to their symbolic counterparts; instead of going completely uninterpreted.

- Keep track of data-type details for uninterpreted sorts.
- Rework the U2Bridge example to use enumerated types.
- The "Uninterpreted" name no longer makes sense with this change, so rework the relevant names to ensure proper internal naming.
- Add Data/SBV/Examples/Misc/Enumerate.hs as an example for demonstrating how enumerations are translated.
- Fix a long-standing bug in the implementation of select when translated as SMT-Lib tables. (Github issue #103.) Thanks to Brian Huffman for reporting.

### Version 3.4, 2014-12-21

This release is mainly addressing floating-point changes in SMT-Lib.

Track changes in the QF_FPA logic standard; new constants and alike. If you are using the floating-point logic, then you need a relatively new version of Z3 installed (4.3.3 or newer).

Add unary-negation as an explicit operator. Previously, we merely used the "0-x" semantics; but with floating point, this does not hold as 0-0 is 0, and is not -0! (Note that negative-zero is a valid floating point value, that is different than positive-zero; yet it compares equal to it. Sigh..)

Similarly, add abs as a native method; to make sure we map it to fp.abs for floating point values.

Test suite improvements

### Version 3.3, 2014-12-05

Implement 'safe' and 'safeWith', which statically determine all calls to 'sAssert' being safe to execute. This way, users can pepper their programs with liberal calls to 'sAssert' and check they are all safe in one go without further worry.

Robustify the interface to external solvers, by making sure we catch cases where the external solver might exist but not be runnable (library dependency missing, for example). It is impossible to be absolutely foolproof, but we now catch a few more cases and fail gracefully.

### Version 3.2, 2014-11-18

Implement 'sAssert'. This adds conditional symbolic simulation, by ensuring arbitrary boolean conditions hold during simulation; similar to ASSERT calls in other languages. Note that failures will be detected at symbolic-simulation time, i.e., each assert will generate a call to the external solver to ensure that the condition is never violated. If violation is possible the user will get an error, indicating the failure conditions.

Also implement 'sAssertCont' which allows for a programmatic way to extract/display results for consumers of 'sAssert'. While the latter simply calls 'error' in case of an assertion violation, the 'sAssertCont' variant takes a continuation which can be used to program how the results should be interpreted/displayed. (This is useful for libraries built on top of SBV.) Note that the type of the continuation is such that execution should still stop, i.e., once an assertion violation is detected, symbolic simulation will never continue.

Rework/simplify the 'Mergeable' class to make sure 'sBranch' is sufficiently lazy in case of structural merges. The original implementation was only lazy at the Word instance, but not at lists/tuples etc. Thanks to Brian Huffman for reporting this bug.

Add a few constant-folding optimizations for 'sDiv' and 'sRem'

Boolector: Modify output parser to conform to the new Boolector output format. This means that you need at least v2.0.0 of Boolector installed if you want to use that particular solver.

Fix long-standing translation bug regarding boolean Ord class comparisons. (i.e., 'False > True' etc.) While Haskell allows for this, SMT-Lib does not; and hence we have to be careful in translating. Thanks to Brian Huffman for reporting.

C code generation: Correctly translate square-root and fusedMA functions to C.

### Version 3.1, 2014-07-12

NB: GHC 7.8.1 and 7.8.2 has a serious bug https://ghc.haskell.org/trac/ghc/ticket/9078 that causes SBV to crash under heavy/repeated calls. The bug is addressed in GHC 7.8.3; so upgrading to GHC 7.8.3 is essential for using SBV!

New features/bug-fixes in v3.1:

- Using multiple-SMT solvers in parallel:
- Added functions that let the user run multiple solvers, using asynchronous threads. All results can be obtained (proveWithAll, proveWithAny, satWithAll), or SBV can return the fastest result (satWithAny, allSatWithAll, allSatWithAny). These functions are good for playing with multiple-solvers, especially on machines with multiple-cores.
- Add function: sbvAvailableSolvers; which returns the list of solvers currently available, as installed on the machine we are running. (Not the list that SBV supports, but those that are actually available at run-time.) This function is useful with the multi-solve API.

- Implement sBranch:
- sBranch is a variant of 'ite' that consults the external SMT solver to see if a given branch condition is satisfiable before evaluating it. This can make certain otherwise recursive and thus not-symbolically-terminating inputs amenable to symbolic simulation, if termination can be established this way. Needless to say, this problem is always decidable as far as SBV programs are concerned, but it does not mean the decision procedure is cheap! Use with care.
- sBranchTimeOut config parameter can be used to curtail long runs when sBranch is used. Of course, if time-out happens, SBV will assume the branch is feasible, in which case symbolic-termination may come back to bite you.)

- New API:
- Add predicate 'isSNaN' which allows testing 'SFloat'/'SDouble' values for nan-ness. This is similar to the Prelude function 'isNaN', except the Prelude version requires a RealFrac instance, which unfortunately is not currently implementable for cases. (Requires trigonometric functions etc.) Thus, we provide 'isSNaN' separately (along with the already existing 'isFPPoint') to simplify reasoning with floating-point.

- Examples:
- Add Data/SBV/Examples/Misc/SBranch.hs, to illustrate the use of sBranch.

- Bug fixes:
- Fix pipe-blocking issue, which exhibited itself in the presence of large numbers of variables (> 10K or so). See github issue #86. Thanks to Philipp Meyer for the fine report.

- Misc:
- Add missing SFloat/SDouble instances for SatModel class
- Explicitly support KBool as a kind, separating it from "KUnbounded False 1". Thanks to Brian Huffman for contributing the changes. This should have no user-visible impact, but comes in handy for internal reasons.

### Version 3.0, 2014-02-16

- Support for floating-point numbers:
- Preliminary support for IEEE-floating point arithmetic, introducing
the types
`SFloat`

and`SDouble`

. The support is still quite new, and Z3 is the only solver that currently features a solver for this logic. Likely to have bugs, both at the SBV level, and at the Z3 level; so any bug reports are welcome!

- Preliminary support for IEEE-floating point arithmetic, introducing
the types
- New backend solvers:
- SBV now supports MathSAT from Fondazione Bruno Kessler and DISI-University of Trento. See: http://mathsat.fbk.eu/

- Support all-sat calls in the presence of uninterpreted sorts:
- Implement better support for
`allSat`

in the presence of uninterpreted sorts. Previously, SBV simply rejected running`allSat`

queries in the presence of uninterpreted sorts, since it was not possible to generate a refuting model. The model returned by the SMT solver is simply not usable, since it names constants that is not visible in a subsequent run. Eric Seidel came up with the idea that we can actually compute equivalence classes based on a produced model, and assert the constraint that the new model should disallow the previously found equivalence classes instead. The idea seems to work well in practice, and there is also an example program demonstrating the functionality: Examples/Uninterpreted/UISortAllSat.hs

- Implement better support for
- Programmable model extraction improvements:
- Add functions
`getModelDictionary`

and`getModelDictionaries`

, which provide low-level access to models returned from SMT solvers. Former for`sat`

and`prove`

calls, latter for`allSat`

calls. Together with the exported utils from the`Data.SBV.Internals`

module, this should allow for expert users to dissect the models returned and do fancier programming on top of SBV. - Add
`getModelValue`

,`getModelValues`

,`getModelUninterpretedValue`

, and`getModelUninterpretedValues`

; which further aid in model value extraction.

- Add functions
- Other:
- Allow users to specify the SMT-Lib logic to use, if necessary. SBV will still pick the logic automatically, but users can now override that choice. Comes in handy when playing with custom logics.

- Bug fixes:
- Address allsat-laziness issue (#78 in github issue tracker). Essentially, simplify how all-sat is called so we can avoid calling the solver for solutions that are not needed. Thanks to Eric Seidel for reporting.

- Examples:
- Add Data/SBV/Examples/Misc/ModelExtract.hs as a simple example for programmable model extraction and usage.
- Add Data/SBV/Examples/Misc/Floating.hs for some FP examples.
- Use the AUFLIA logic in Examples.Existentials.Diophantine which helps z3 complete the proof quickly. (The BV logics take too long for this problem.)

### Version 2.10, 2013-03-22

- Add support for the Boolector SMT solver
- See: http://fmv.jku.at/boolector/
- Use
`import Data.SBV.Bridge.Boolector`

to use Boolector from SBV - Boolector supports QF_BV (with an without arrays). In the last SMT-Lib competition it won both bit-vector categories. It is definitely worth trying it out for bitvector problems.

- Changes to the library:
- Generalize types of
`allDifferent`

and`allEqual`

to take arbitrary EqSymbolic values. (Previously was just over SBV values.) - Add
`inRange`

predicate, which checks if a value is bounded within two others. - Add
`sElem`

predicate, which checks for symbolic membership - Add
`fullAdder`

: Returns the carry-over as a separate boolean bit. - Add
`fullMultiplier`

: Returns both the lower and higher bits resulting from multiplication. - Use the SMT-Lib Bool sort to represent SBool, instead of bit-vectors of length 1. While this is an under-the-hood mechanism that should be user-transparent, it turns out that one can no longer write axioms that return booleans in a direct way due to this translation. This change makes it easier to write axioms that utilize booleans as there is now a 1-to-1 match. (Suggested by Thomas DuBuisson.)

- Generalize types of
- Solvers changes:
- Z3: Update to the new parameter naming schema of Z3. This implies that you need to have a really recent version of Z3 installed, something in the Z3-4.3 series.

- Examples:
- Add Examples/Uninterpreted/Shannon.hs: Demonstrating Shannon expansion, boolean derivatives, etc.

- Bug-fixes:
- Gracefully handle the case if the backend-SMT solver does not put anything in stdout. (Reported by Thomas DuBuisson.)
- Handle uninterpreted sort values, if they happen to be only created via function calls, as opposed to being inputs. (Reported by Thomas DuBuisson.)

### Version 2.9, 2013-01-02

- Add support for the CVC4 SMT solver from Stanford: http://cvc4.cs.stanford.edu/web/
NB. Z3 remains the default solver for SBV. To use CVC4, use the
*With variants of the interface (i.e., proveWith, satWith, ..) by passing cvc4 as the solver argument. (Similarly, use 'yices' as the argument for the*With functions for invoking yices.) - Latest release of Yices calls the SMT-Lib based solver executable yices-smt. Updated the default value of the executable to have this name for ease of use.
- Add an extra boolean flag to compileToSMTLib and generateSMTBenchmarks functions to control if the translation should keep the query as is (for SAT cases), or negate it (for PROVE cases). Previously, this value was hard-coded to do the PROVE case only.
Add bridge modules, to simplify use of different solvers. You can now say:

`import Data.SBV.Bridge.CVC4 import Data.SBV.Bridge.Yices import Data.SBV.Bridge.Z3`

to pick the appropriate default solver. if you simply 'import Data.SBV', then you will get the default SMT solver, which is currently Z3. The value 'defaultSMTSolver' refers to z3 (currently), and 'sbvCurrentSolver' refers to the chosen solver as determined by the imported module. (The latter is useful for modifying options to the SMT solver in an solver-agnostic way.)

- Various improvements to Z3 model parsing routines.
- New web page for SBV: http://leventerkok.github.com/sbv/ is now online.

### Version 2.8, 2012-11-29

- Rename the SNum class to SIntegral, and make it index over regular types. This makes it much more useful, simplifying coding of polymorphic symbolic functions over integral types, which is the common case.
- Add the functions:
- sbvShiftLeft
- sbvShiftRight which can accommodate unsigned symbolic shift amounts. Note that one cannot use the Haskell shiftL/shiftR functions from the Bits class since they are hard-wired to take 'Int' values as the shift amounts only.
- Add a new function 'sbvArithShiftRight', which is the same as a shift-right, except it uses the MSB of the input as the bit to fill in (instead of always filling in with 0 bits). Note that this is the same as shiftRight for signed values, but differs from a shiftRight when the input is unsigned. (There is no Haskell analogue of this function, as Haskell shiftR is always arithmetic for signed types and logical for unsigned ones.) This variant is designed for use cases when one uses the underlying unsigned SMT-Lib representation to implement custom signed operations, for instance.
- Several typo fixes.

### Version 2.7, 2012-10-21

- Add missing QuickCheck instance for SReal
- When dealing with concrete SReals, make sure to operate only on exact algebraic reals on the Haskell side, leaving true algebraic reals (i.e., those that are roots of polynomials that cannot be expressed as a rational) symbolic. This avoids issues with functions that we cannot implement directly on the Haskell side, like exact square-roots.
- Documentation tweaks, typo fixes etc.
- Rename BVDivisible class to SDivisible; since SInteger is also an instance of this class, and SDivisible is a more appropriate name to start with. Also add sQuot and sRem methods; along with sDivMod, sDiv, and sMod, with usual semantics.
- Improve test suite, adding many constant-folding tests and start using cabal based tests (--enable-tests option.)

### Versions 2.4, 2.5, and 2.6: Around mid October 2012

- Workaround issues related hackage compilation, in particular to the problem with the new containers package release, which does provide an NFData instance for sequences.
- Add explicit Num requirements when necessary, as the Bits class no longer does this.
- Remove dependency on the hackage package strict-concurrency, as hackage can no longer compile it due to some dependency mismatch.
- Add forgotten Real class instance for the type 'AlgReal'
- Stop putting bounds on hackage dependencies, as they cause more trouble then they actually help. (See the discussion here: http://www.haskell.org/pipermail/haskell-cafe/2012-July/102352.html.)

### Version 2.3, 2012-07-20

- Maintenance release, no new features.
- Tweak cabal dependencies to avoid using packages that are newer
than those that come with ghc-7.4.2. Apparently this is a no-no
that breaks many things, see the discussion in this thread:
http://www.haskell.org/pipermail/haskell-cafe/2012-July/102352.html
In particular, the use of containers >= 0.5 is
*not*OK until we have a version of GHC that comes with that version.

### Version 2.2, 2012-07-17

- Maintenance release, no new features.
- Update cabal dependencies, in particular fix the regression with respect to latest version of the containers package.

### Version 2.1, 2012-05-24

- Library:
- Add support for uninterpreted sorts, together with user defined domain axioms. See Data.SBV.Examples.Uninterpreted.Sort and Data.SBV.Examples.Uninterpreted.Deduce for basic examples of this feature.
- Add support for C code-generation with SReals. The user picks one of 3 possible C types for the SReal type: CgFloat, CgDouble or CgLongDouble, using the function cgSRealType. Naturally, the resulting C program will suffer a loss of precision, as it will be subject to IEE-754 rounding as implied by the underlying type.
- Add toSReal :: SInteger -> SReal, which can be used to promote symbolic integers to reals. Comes handy in mixed integer/real computations.

- Examples:
- Recast the dog-cat-mouse example to use the solver over reals.
- Add Data.SBV.Examples.Uninterpreted.Sort, and Data.SBV.Examples.Uninterpreted.Deduce for illustrating uninterpreted sorts and axioms.

### Version 2.0, 2012-05-10

This is a major release of SBV, adding support for symbolic algebraic reals: SReal. See http://en.wikipedia.org/wiki/Algebraic_number for details. In brief, algebraic reals are solutions to univariate polynomials with rational coefficients. The arithmetic on algebraic reals is precise, with no approximation errors. Note that algebraic reals are a proper subset of all reals, in particular transcendental numbers are not representable in this way. (For instance, "sqrt 2" is algebraic, but pi, e are not.) However, algebraic reals is a superset of rationals, so SBV now also supports symbolic rationals as well.

You *should* use Z3 v4.0 when working with real numbers. While the interface will
work with older versions of Z3 (or other SMT solvers in general), it uses Z3
root-obj construct to retrieve and query algebraic reals.

While SReal values have infinite precision, printing such values is not trivial since we might need an infinite number of digits if the result happens to be irrational. The user controls printing precision, by specifying how many digits after the decimal point should be printed. The default number of decimal digits to print is 10. (See the 'printRealPrec' field of SMT-solver configuration.)

The acronym SBV used to stand for Symbolic Bit Vectors. However, SBV has grown beyond bit-vectors, especially with the addition of support for SInteger and SReal types and other code-generation utilities. Therefore, "SMT Based Verification" is now a better fit for the expansion of the acronym SBV.

Other notable changes in the library:

- Add functions s[TYPE] and s[TYPE]s for each symbolic type we support (i.e., sBool, sBools, sWord8, sWord8s, etc.), to create symbolic variables of the right kind. Strictly speaking these are just synonyms for 'free' and 'mapM free' (plural versions), so they are not adding any additional power. Except, they are specialized at their respective types, and might be easier to remember.
- Add function solve, which is merely a synonym for (return . bAnd), but it simplifies expressing problems.
- Add class SNum, which simplifies writing polymorphic code over symbolic values
- Increase haddock coverage metrics
- Major code refactoring around symbolic kinds
- SMTLib2: Emit ":produce-models" call before setting the logic, as required by the SMT-Lib2 standard. [Patch provided by arrowdodger on github, thanks!]

Bugs fixed:

[Performance] Use a much simpler default definition for "select": While the older version (based on binary search on the bits of the indexer) was correct, it created unnecessarily big expressions. Since SBV does not have a notion of concrete subwords, the binary-search trick was not bringing any advantage in any case. Instead, we now simply use a linear walk over the elements.

Examples:

- Change dog-cat-mouse example to use SInteger for the counts
- Add merge-sort example: Data.SBV.Examples.BitPrecise.MergeSort
- Add diophantine solver example: Data.SBV.Examples.Existentials.Diophantine

### Version 1.4, 2012-05-10

Interim release for test purposes

### Version 1.3, 2012-02-25

Workaround cabal/hackage issue, functionally the same as release 1.2 below

### Version 1.2, 2012-02-25

Library:

- Add a hook so users can add custom script segments for SMT solvers. The new "solverTweaks" field in the SMTConfig data-type can be used for this purpose. The need for this came about due to the need to workaround a Z3 v3.2 issue detailed below: http://stackoverflow.com/questions/9426420/soundness-issue-with-integer-bv-mixed-benchmarks As a consequence, mixed Integer/BV problems can cause soundness issues in Z3 and does in SBV. Unfortunately, it is too severe for SBV to add the workaround option, as it slows down the solver as a side effect as well. Thus, we are making this optionally available if/when needed. (Note that the work-around should not be necessary with Z3 v3.3; which is not released yet.)
- Other minor clean-up

### Version 1.1, 2012-02-14

Library:

- Rename bitValue to sbvTestBit
- Add sbvPopCount
- Add a custom implementation of 'popCount' for the Bits class instance of SBV (GHC >= 7.4.1 only)
- Add 'sbvCheckSolverInstallation', which can be used to check that the given solver is installed and good to go.
- Add 'generateSMTBenchmarks', simplifying the generation of SMTLib benchmarks for offline sharing.

### Version 1.0, 2012-02-13

Library:

- Z3 is now the "default" SMT solver. Yices is still available, but has to be specifically selected. (Use satWith, allSatWith, proveWith, etc.)
- Better handling of the pConstrain probability threshold for test case generation and quickCheck purposes.
- Add 'renderTest', which accompanies 'genTest' to render test vectors as Haskell/C/Forte program segments.
- Add 'expectedValue' which can compute the expected value of a symbolic value under the given constraints. Useful for statistical analysis and probability computations.
- When saturating provable values, use forAll
*for proofs and forSome*for sat/allSat. (Previously we were allways using forAll_, which is not incorrect but less intuitive.) - add function: extractModels :: SatModel a => AllSatResult -> [a] which simplifies accessing allSat results greatly.

Code-generation:

add "cgGenerateMakefile" which allows the user to choose if SBV should generate a Makefile. (default: True)

Other

Changes to make it compile with GHC 7.4.1.

### Version 0.9.24, 2011-12-28

Library:

- Add "forSome," analogous to "forAll." (The name "exists" would've been better, but it's already taken.) This is not as useful as one might think as forAll and forSome do not nest, as an inner application of one pushes its argument to a Predicate, making the outer one useless, but it is nonetheless useful by itself.
- Add a "Modelable" class, which simplifies model extraction.
- Add support for quick-check at the "Symbolic SBool" level. Previously SBV only allowed functions returning SBool to be quick-checked, which forced a certain style of coding. In particular with the addition of quantifiers, the new coding style mostly puts the top-level expressions in the Symbolic monad, which were not quick-checkable before. With new support, the quickCheck, prove, sat, and allSat commands are all interchangeable with obvious meanings.
- Add support for concrete test case generation, see the genTest function.
- Improve optimize routines and add support for iterative optimization.
- Add "constrain", simplifying conjunctive constraints, especially useful for adding constraints at variable generation time via forall/exists. Note that the interpretation of such constraints is different for genTest and quickCheck functions, where constraints will be used for appropriately filtering acceptable test values in those two cases.
- Add "pConstrain", which probabilistically adds constraints. This is useful for quickCheck and genTest functions for filtering acceptable test values. (Calls to pConstrain will be rejected for sat/prove calls.)
- Add "isVacuous" which can be used to check that the constraints added via constrain are satisfiable. This is useful to prevent vacuous passes, i.e., when a proof is not just passing because the constraints imposed are inconsistent. (Also added accompanying isVacuousWith.)
- Add "free" and "free
*", analogous to "forall/forall*" and "exists/exists_" The difference is that free behaves universally in a proof context, while it behaves existentially in a sat context. This allows us to express properties more succinctly, since the intended semantics is usually this way depending on the context. (i.e., in a proof, we want our variables universal, in a sat call existential.) Of course, exists/forall are still available when mixed quantifiers are needed, or when the user wants to be explicit about the quantifiers.

Examples

Add Data/SBV/Examples/Puzzles/Coins.hs. (Shows the usage of "constrain".)

Dependencies

Bump up random package dependency to 1.0.1.1 (from 1.0.0.2)

Internal

- Major reorganization of files to and build infrastructure to decrease build times and better layout
- Get rid of custom Setup.hs, just use simple build. The extra work was not worth the complexity.

### Version 0.9.23, 2011-12-05

Library:

- Add support for SInteger, the type of signed unbounded integer values. SBV can now prove theorems about unbounded numbers, following the semantics of Haskell Integer type. (Requires z3 to be used as the backend solver.)
- Add functions 'optimize', 'maximize', and 'minimize' that can be used to find optimal solutions to given constraints with respect to a given cost function.
- Add 'cgUninterpret', which simplifies code generation when we want to use an alternate definition in the target language (i.e., C). This is important for efficient code generation, when we want to take advantage of native libraries available in the target platform.

Other:

Change getModel to return a tuple in the success case, where the first component is a boolean indicating whether the model is "potential." This is used to indicate that the solver actually returned "unknown" for the problem and the model might therefore be bogus. Note that we did not need this before since we only supported bounded bit-vectors, which has a decidable theory. With the addition of unbounded Integers and quantifiers, the solvers can now return unknown. This should still be rare in practice, but can happen with the use of non-linear constructs. (i.e., multiplication of two variables.)

### Version 0.9.22, 2011-11-13

The major change in this release is the support for quantifiers. The
SBV library *no* longer assumes all variables are universals in a proof,
(and correspondingly existential in a sat) call. Instead, the user
marks free-variables appropriately using forall/exists functions, and the
solver translates them accordingly. Note that this is a non-backwards
compatible change in sat calls, as the semantics of formulas is essentially
changing. While this is unfortunate, it is more uniform and simpler to understand
in general.

This release also adds support for the Z3 solver, which is the main SMT-solver used for solving formulas involving quantifiers. More formally, we use the new AUFBV/ABV/UFBV logics when quantifiers are involved. Also, the communication with Z3 is now done via SMT-Lib2 format. Eventually the SMTLib1 connection will be severed.

The other main change is the support for C code generation with uninterpreted functions enabling users to interface with external C functions defined elsewhere. See below for details.

Other changes:

Code:

- Change getModel, so it returns an Either value to indicate something went wrong; instead of throwing an error
- Add support for computing CRCs directly (without needing polynomial division).

Code generation:

- Add "cgGenerateDriver" function, which can be used to turn on/off driver program generation. Default is to generate a driver. (Issue "cgGenerateDriver False" to skip the driver.) For a library, a driver will be generated if any of the constituent parts has a driver. Otherwise it will be skipped.
- Fix a bug in C code generation where "Not" over booleans were incorrectly getting translated due to need for masking.
- Add support for compilation with uninterpreted functions. Users can now specify the corresponding C code and SBV will simply call the "native" functions instead of generating it. This enables interfacing with other C programs. See the functions: cgAddPrototype, cgAddDecl, cgAddLDFlags

Examples:

- Add CRC polynomial generation example via existentials
- Add USB CRC code generation example, both via polynomials and using the internal CRC functionality

### Version 0.9.21, 2011-08-05

Code generation:

- Allow for inclusion of user makefiles
- Allow for CCFLAGS to be set by the user
- Other minor clean-up

### Version 0.9.20, 2011-06-05

Regression on 0.9.19; add missing file to cabal

### Version 0.9.19, 2011-06-05

- Add SignCast class for conversion between signed/unsigned quantities for same-sized bit-vectors
- Add full-binary trees that can be indexed symbolically (STree). The advantage of this type is that the reads and writes take logarithmic time. Suitable for implementing faster symbolic look-up.
- Expose HasSignAndSize class through Data.SBV.Internals
- Many minor improvements, file re-orgs

Examples:

- Add sentence-counting example
- Add an implementation of RC4

### Version 0.9.18, 2011-04-07

Code:

- Re-engineer code-generation, and compilation to C. In particular, allow arrays of inputs to be specified, both as function arguments and output reference values.
- Add support for generation of generation of C-libraries, allowing code generation for a set of functions that work together.

Examples:

- Update code-generation examples to use the new API.
- Include a library-generation example for doing 128-bit AES encryption

### Version 0.9.17, 2011-03-29

Code:

Simplify and reorganize the test suite

Examples:

Improve AES decryption example, by using table-lookups in InvMixColumns.

### Version 0.9.16, 2011-03-28

Code:

Further optimizations on Bits instance of SBV

Examples:

Add AES algorithm as an example, showing how encryption algorithms are particularly suitable for use with the code-generator

### Version 0.9.15, 2011-03-24

Bug fixes:

- Fix rotateL/rotateR instances on concrete words. Previous versions was bogus since it relied on the Integer instance, which does the wrong thing after normalization.
- Fix conversion of signed numbers from bits, previous version did not handle twos complement layout correctly

Testing:

Add a sleuth of concrete test cases on arithmetic to catch bugs. (There are many of them, ~30K, but they run quickly.)

### Version 0.9.14, 2011-03-19

Re-implement sharing using Stable names, inspired by the Data.Reify techniques. This avoids tricks with unsafe memory stashing, and hence is safe. Thus, issues with respect to CAFs are now resolved.

### Version 0.9.13, 2011-03-16

Bug fixes:

Make sure SBool short-cut evaluations are done as early as possible, as these help with coding recursion-depth based algorithms, when dealing with symbolic termination issues.

Examples:

- Add fibonacci code-generation example, original code by Lee Pike.
- Add a GCD code-generation/verification example

### Version 0.9.12, 2011-03-10

New features:

- Add support for compilation to C
- Add a mechanism for offline saving of SMT-Lib files

Bug fixes:

- Output naming bug, reported by Josef Svenningsson
- Specification bug in Legatos multiplier example

### Version 0.9.11, 2011-02-16

Make ghc-7.0 happy, minor re-org on the cabal file/Setup.hs

### Version 0.9.10, 2011-02-15

- Integrate commits from Iavor: Generalize SBVs to keep track the integer directly without resorting to different leaf types
- Remove the unnecessary CLC instruction from the Legato example
- More tests

### Version 0.9.9, 2011-01-23

- Support for user-defined SMT-Lib axioms to be specified for uninterpreted constants/functions
- Move to using doctest style inline tests

### Version 0.9.8, 2011-01-22

- Better support for uninterpreted-functions
- Support counter-examples with SArrays
- Ladner-Fischer scheme example
- Documentation updates

### Version 0.9.7, 2011-01-18

First stable public hackage release

### Versions 0.0.0 - 0.9.6, Mid 2010 through early 2011

- Basic infrastructure, design exploration