SMT Based Verification: Symbolic Haskell theorem prover using SMT solving.

Version on this page:5.12
LTS Haskell 22.17:10.2@rev:1
Stackage Nightly 2024-04-20:10.9
Latest on Hackage:10.9

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BSD-3-Clause licensed by Levent Erkok
Maintained by Levent Erkok ([email protected])
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Module documentation for 5.12

SBV: SMT Based Verification in Haskell

Hackage version Build Status

Please see:


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 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 exponentation

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 vilations 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 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 customor 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
  • 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)
  • Reimplement 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: 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 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 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!
  • New backend solvers:
    • SBV now supports MathSAT from Fondazione Bruno Kessler and DISI-University of Trento. See:
  • 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
  • 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.
  • 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:
    • 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.)
  • 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 New York University and the University of Iowa. 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: 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:

Version 2.3, 2012-07-20

  • Maintanence 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: 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

  • Maintanence 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 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.


  • 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


  • 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 detalied below: 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 woraround 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


  • 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


  • 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.


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


  • Changes to make it compile with GHC 7.4.1.

Version 0.9.24, 2011-12-28


  • 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 satisfable. 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.


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


  • Bump up random package dependency to (from


  • 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


  • 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.


  • 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:


  • 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


  • 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


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

Version 0.9.18, 2011-04-07


  • 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.


  • 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


  • Simplify and reorganize the test suite


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

Version 0.9.16, 2011-03-28


  • Further optimizations on Bits instance of SBV


  • 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


  • 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

  • Reimplement 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.


  • 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 multipler 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