sbv 0.9.3 → 0.9.4
raw patch · 4 files changed
+118/−11 lines, 4 files
Files
- Data/SBV/Examples/Polynomials/Polynomials.hs +78/−0
- Data/SBV/TestSuite/Polynomials/Polynomials.hs +25/−0
- SBVUnitTest/SBVUnitTest.hs +12/−10
- sbv.cabal +3/−1
+ Data/SBV/Examples/Polynomials/Polynomials.hs view
@@ -0,0 +1,78 @@+-----------------------------------------------------------------------------+-- |+-- Module : Data.SBV.Examples.Polynomials.Polynomials+-- Copyright : (c) Levent Erkok+-- License : BSD3+-- Maintainer : erkokl@gmail.com+-- Stability : experimental+-- Portability : portable+--+-- Simple usage of polynomials over GF(2^n), using Rijndael's+-- finite field: <http://en.wikipedia.org/wiki/Finite_field_arithmetic#Rijndael.27s_finite_field>+--+-- The functions available are:+--+-- [/pMult/] GF(2^n) Multiplication+--+-- [/pDiv/] GF(2^n) Division+--+-- [/pMod/] GF(2^n) Modulus+--+-- [/pDivMod/] GF(2^n) Division/Modulus, packed together+--+-- Note that addition in GF(2^n) is simply `xor`, so no custom function is provided.+-----------------------------------------------------------------------------++module Data.SBV.Examples.Polynomials.Polynomials where++import Data.SBV++-- | Helper synonym for representing GF(2^8); which are merely 8-bit unsigned words. Largest+-- term in such a polynomial has degree 7.+type GF28 = SWord8++-- | Multiplication in Rijndael's field; usual polynomial multiplication followed by reduction+-- by the irreducible polynomial. The irreducible used by Rijndael's field is the polynomial+-- @x^8 + x^4 + x^3 + x + 1@, which we write by giving it's /exponents/ in SBV.+-- See: <http://en.wikipedia.org/wiki/Finite_field_arithmetic#Rijndael.27s_finite_field>.+-- Note that the irreducible itself is not in GF28! It has a degree of 8.+--+-- NB. You can use the 'showPoly' function to print polynomials nicely, as a mathematician would write.+(<*>) :: GF28 -> GF28 -> GF28+a <*> b = pMult (a, b, [8, 4, 3, 1, 0])++-- | States that the unit polynomial @1@, is the unit element+multUnit :: GF28 -> SBool+multUnit x = (x <*> unit) .== x+ where unit = polynomial [0] -- x@0++-- | States that multiplication is commutative+multComm :: GF28 -> GF28 -> SBool+multComm x y = (x <*> y) .== (y <*> x)++-- | States that multiplication is associative, note that associativity+-- proofs are notoriously hard for SAT/SMT solvers+multAssoc :: GF28 -> GF28 -> GF28 -> SBool+multAssoc x y z = ((x <*> y) <*> z) .== (x <*> (y <*> z))++-- | States that the usual multiplication rule holds over GF(2^n) polynomials+-- Checks:+--+-- @+-- if (a, b) = x `pDivMod` y then x = y `pMult` a + b+-- @+--+-- being careful about @y = 0@. When divisor is 0, then quotient is+-- defined to be 0 and the remainder is the numerator.+-- (Note that addition is simply `xor` in GF(2^8).)+polyDivMod :: GF28 -> GF28 -> SBool+polyDivMod x y = ite (y .== 0) ((0, x) .== (a, b)) (x .== y <*> a `xor` b)+ where (a, b) = x `pDivMod` y++-- | Queries+testGF28 :: IO ()+testGF28 = do+ print =<< prove multUnit+ print =<< prove multComm+ -- print =<< prove multAssoc -- takes too long; see above note..+ print =<< prove polyDivMod
+ Data/SBV/TestSuite/Polynomials/Polynomials.hs view
@@ -0,0 +1,25 @@+-----------------------------------------------------------------------------+-- |+-- Module : Data.SBV.TestSuite.Polynomials.Polynomials+-- Copyright : (c) Levent Erkok+-- License : BSD3+-- Maintainer : erkokl@gmail.com+-- Stability : experimental+-- Portability : portable+--+-- Test suite for Data.SBV.Examples.Polynomials.Polynomials+-----------------------------------------------------------------------------++module Data.SBV.TestSuite.Polynomials.Polynomials(testSuite) where++import Data.SBV+import Data.SBV.Internals+import Data.SBV.Examples.Polynomials.Polynomials++-- Test suite+testSuite :: SBVTestSuite+testSuite = mkTestSuite $ \_ -> test [+ "polynomial-1" ~: assert =<< isTheorem multUnit+ , "polynomial-2" ~: assert =<< isTheorem multComm+ , "polynomial-3" ~: assert =<< isTheorem polyDivMod+ ]
SBVUnitTest/SBVUnitTest.hs view
@@ -39,16 +39,17 @@ import qualified Data.SBV.TestSuite.CRC.GenPoly as T12(testSuite) import qualified Data.SBV.TestSuite.CRC.Parity as T13(testSuite) import qualified Data.SBV.TestSuite.CRC.USB5 as T14(testSuite)-import qualified Data.SBV.TestSuite.PrefixSum.PrefixSum as T15(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.DogCatMouse as T16(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.MagicSquare as T17(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.NQueens as T18(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.PowerSet as T19(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.Sudoku as T20(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.Temperature as T21(testSuite)-import qualified Data.SBV.TestSuite.Puzzles.U2Bridge as T22(testSuite)-import qualified Data.SBV.TestSuite.Uninterpreted.AUF as T23(testSuite)-import qualified Data.SBV.TestSuite.Uninterpreted.Uninterpreted as T24(testSuite)+import qualified Data.SBV.TestSuite.Polynomials.Polynomials as T15(testSuite)+import qualified Data.SBV.TestSuite.PrefixSum.PrefixSum as T16(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.DogCatMouse as T17(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.MagicSquare as T18(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.NQueens as T19(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.PowerSet as T20(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.Sudoku as T21(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.Temperature as T22(testSuite)+import qualified Data.SBV.TestSuite.Puzzles.U2Bridge as T23(testSuite)+import qualified Data.SBV.TestSuite.Uninterpreted.AUF as T24(testSuite)+import qualified Data.SBV.TestSuite.Uninterpreted.Uninterpreted as T25(testSuite) testCollection :: [SBVTestSuite] testCollection = [@@ -58,6 +59,7 @@ , T13.testSuite, T14.testSuite, T15.testSuite, T16.testSuite , T17.testSuite, T18.testSuite, T19.testSuite, T20.testSuite , T21.testSuite, T22.testSuite, T23.testSuite, T24.testSuite+ , T25.testSuite ] -- No user serviceable parts below..
sbv.cabal view
@@ -1,5 +1,5 @@ Name: sbv-Version: 0.9.3+Version: 0.9.4 Category: Formal Methods, Theorem Provers, Bit vectors, Symbolic Computation, Math Synopsis: Symbolic Bit Vectors: Prove bit-precise program properties using SMT solvers. Description: Adds support for symbolic bit vectors, allowing formal models of bit-precise@@ -42,6 +42,7 @@ , Data.SBV.Internals , Data.SBV.Examples.BitPrecise.BitTricks , Data.SBV.Examples.BitPrecise.Legato+ , Data.SBV.Examples.Polynomials.Polynomials , Data.SBV.Examples.Puzzles.DogCatMouse , Data.SBV.Examples.Puzzles.MagicSquare , Data.SBV.Examples.Puzzles.NQueens@@ -93,6 +94,7 @@ , Data.SBV.TestSuite.CRC.Parity , Data.SBV.TestSuite.CRC.USB5 , Data.SBV.TestSuite.PrefixSum.PrefixSum+ , Data.SBV.TestSuite.Polynomials.Polynomials , Data.SBV.TestSuite.Puzzles.DogCatMouse , Data.SBV.TestSuite.Puzzles.MagicSquare , Data.SBV.TestSuite.Puzzles.NQueens