CVC3
Public Member Functions

CVC3::BitvectorProofRules Class Reference

#include <bitvector_proof_rules.h>

Inherited by CVC3::BitvectorTheoremProducer.

List of all members.

Public Member Functions


Detailed Description

Definition at line 33 of file bitvector_proof_rules.h.


Constructor & Destructor Documentation

virtual CVC3::BitvectorProofRules::~BitvectorProofRules ( ) [inline, virtual]

Definition at line 36 of file bitvector_proof_rules.h.


Member Function Documentation

virtual Theorem CVC3::BitvectorProofRules::bitvectorFalseRule ( const Theorem thm) [pure virtual]
Parameters:
thminput theorem: (e1[i]<=>e2[i])<=>false
Returns:
(e1=e2)<=>false

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitvectorTrueRule ( const Theorem thm) [pure virtual]
Parameters:
thminput theorem: (~e1[i]<=>e2[i])<=>true
Returns:
(e1!=e2)<=>true

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitBlastEqnRule ( const Expr e,
const Expr f 
) [pure virtual]

t1=t2 ==> AND_i(t1[i:i] = t2[i:i])

Parameters:
eis a Expr(t1=t2)
fis the resulting expression AND_i(t1[i:i] = t2[i:i]) is passed to the rule for efficiency.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitBlastDisEqnRule ( const Theorem e,
const Expr f 
) [pure virtual]

t1/=t2 ==> OR_i(NOT t1[i]<=>t2[i])

Parameters:
eis a Theorem(t1/=t2)
fis the resulting expression OR_i(NOT t1[i]<=>t2[i]), passed to the rule for efficiency.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::signExtendRule ( const Expr e) [pure virtual]

sign extend the input SX(e) appropriately

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::padBVLTRule ( const Expr e,
int  len 
) [pure virtual]

Pad the kids of BVLT/BVLE to make their length equal.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::padBVSLTRule ( const Expr e,
int  len 
) [pure virtual]

Sign Extend the kids of BVSLT/BVSLE to make their length equal.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::signBVLTRule ( const Expr e,
const Theorem topBit0,
const Theorem topBit1 
) [pure virtual]

input: e0 <=(s) e1. output depends on whether the topbits(MSB) of e0 and e1 are constants. If they are constants then optimizations are done, otherwise the following rule is implemented.

e0 <=(s) e1 <==> (e0[n-1] AND NOT e1[n-1]) OR (e0[n-1] AND e1[n-1] AND e1[n-2:0] <= e0[n-2:0]) OR (NOT e0[n-1] AND NOT e1[n-1] AND e0[n-2:0] <= e1[n-2:0])

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::notBVEQ1Rule ( const Expr e) [pure virtual]

NOT(e[0][0] = e[0][1]) <==> e[0][0] = ~e[0][1]

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::notBVLTRule ( const Expr e) [pure virtual]

NOT(e[0][0] < e[0][1]) <==> (e[0][1] <= e[0][0]), NOT(e[0][0] <= e[0][1]) <==> (e[0][1] < e[0][0])

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::lhsEqRhsIneqn ( const Expr e,
int  kind 
) [pure virtual]

if(lhs==rhs) then we have (lhs < rhs <==> false),(lhs <= rhs <==> true)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::zeroLeq ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvConstIneqn ( const Expr e,
int  kind 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::generalIneqn ( const Expr e,
const Theorem e0,
const Theorem e1,
int  kind 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bitExtractAllToConstEq ( std::vector< Theorem > &  thms) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bitExtractToExtract ( const Theorem thm) [pure virtual]

t[i] ==> t[i:i] = 0bin1 or NOT t[i] ==> t[i:i] = 0bin0

Parameters:
thmis a Theorem(t[i]) or Theorem(NOT t[i]), where t[i] is BOOLEXTRACT(t, i).

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractRewrite ( const Expr x) [pure virtual]

t[i] <=> t[i:i][0] (to use rewriter for simplifying t[i:i])

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractConstant ( const Expr x,
int  i 
) [pure virtual]
Parameters:
xis bitvector constant
iis extracted bitposition
Returns:

\[ \frac{}{\mathrm{BOOLEXTRACT(x,i)} \iff \mathrm{TRUE}} \]

, if bitposition has a 1;

\[ \frac{}{\mathrm{BOOLEXTRACT(x,i)} \iff \mathrm{FALSE}} \]

, if the bitposition has a 0

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractConcatenation ( const Expr x,
int  i 
) [pure virtual]
Parameters:
xis bitvector binary concatenation
iis extracted bitposition
Returns:

\[ \frac{}{(t_{[m]}@q_{[n]})[i] \iff (q_{[n]})[i]} \]

, where

\[ 0 \geq i \geq n-1 \]

, another case of boolextract over concatenation is:

\[\frac{}{(t_{[m]}@q_{[n]})[i] \iff (t_{[m]})[i-n]} \]

, where

\[ n \geq i \geq m+n-1 \]

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractConstBVMult ( const Expr t,
int  i 
) [pure virtual]
Parameters:
tis bitvector binary BVMULT. x[0] must be BVCONST
iis extracted bitposition
Returns:
bitblast of BVMULT

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractBVMult ( const Expr t,
int  i 
) [pure virtual]
Parameters:
t: input1 is bitvector binary BVMULT. t[0] must not be BVCONST
i: input2 is extracted bitposition
Returns:
bitblast of BVMULT

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractExtraction ( const Expr x,
int  i 
) [pure virtual]
Parameters:
xis bitvector extraction e[k:j]
iis extracted bitposition
Returns:

\[ \frac{}{(t_{[n]}[k:j])[i] \iff (t_{[n]})[i+j]} \]

, where

\[ 0 \geq j \geq k < n, 0 \geq i < k-j \]

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractBVPlus ( const std::vector< Theorem > &  t1,
const std::vector< Theorem > &  t2,
const Expr bvPlusTerm,
int  i 
) [pure virtual]
Parameters:
t1is vector of bitblasts of t, from bit i-1 to 0
t2is vector of bitblasts of q, from bit i-1 to 0
bvPlusTermis BVPLUS term: BVPLUS(n,t,q)
iis extracted bitposition
Returns:
The base case is:

\[ \frac{}{(\mathrm{BVPLUS}(n,t,q))[0] \iff t[0] \oplus q[0]} \]

, when

\[ 0 < i \leq n-1 \]

, we have

\[ \frac{}{(\mathrm{BVPLUS}(n,t,q))[i] \iff t[i] \oplus q[i] \oplus c(t,q,i)} \]

, where c(t,q,i) is the carry generated by the addition of bits from 0 to i-1

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractBVPlusPreComputed ( const Theorem t1_i,
const Theorem t2_i,
const Expr bvPlusTerm,
int  bitPos,
int  precomputed 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvPlusAssociativityRule ( const Expr bvPlusTerm) [pure virtual]
Parameters:
bvPlusTerm: input1 is bvPlusTerm, a BVPLUS term with arity > 2
Returns:
: output is iff-Theorem: bvPlusTerm <==> outputTerm, where outputTerm is an equivalent BINARY bvplus.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractNot ( const Expr x,
int  i 
) [pure virtual]
Parameters:
x: input1 is bitwise NEGATION
i: input2 is extracted bitposition
Returns:

\[ \frac{}{(\sim t_{[n]})[i] \iff \neg (t_{[n]}[i])} \]

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractBitwise ( const Expr x,
int  i,
int  kind 
) [pure virtual]

Extract from bitwise AND, OR, or XOR.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractFixedLeftShift ( const Expr x,
int  i 
) [pure virtual]
Parameters:
x: input1 is bitvector FIXED SHIFT

\[ e_{[n]} \ll k \]

i: input2 is extracted bitposition
Returns:

\[\frac{}{(e_{[n]} \ll k)[i] \iff \mathrm{FALSE}} \]

, if 0 <= i < k. however, if k <= i < n then, result is

\[\frac{}{(e_{[n]} \ll k)[i] \iff e_{[n]}[i]} \]

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractFixedRightShift ( const Expr x,
int  i 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bitExtractBVSHL ( const Expr x,
int  i 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bitExtractBVLSHR ( const Expr x,
int  i 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bitExtractBVASHR ( const Expr x,
int  i 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::zeroPaddingRule ( const Expr e,
int  r 
) [pure virtual]
Parameters:
e: input1 is bitvector term
r: input2 is extracted bitposition
Returns:
we check if r > bvlength(e). if yes, then return BOOLEXTRACT(e,r) <==> FALSE; else raise soundness exception. (Note: this rule is used in BVPLUS bitblast function)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitExtractSXRule ( const Expr e,
int  i 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::eqConst ( const Expr e) [pure virtual]

c1=c2 <=> TRUE/FALSE (equality of constant bitvectors)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::eqToBits ( const Theorem eq) [pure virtual]

|- c1=c2 ==> |- AND(c1[i:i] = c2[i:i]) - expanding equalities into bits

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::leftShiftToConcat ( const Expr e) [pure virtual]

t<<n = c @ 0bin00...00, takes e == (t<<n)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::constWidthLeftShiftToConcat ( const Expr e) [pure virtual]

t<<n = c @ 0bin00...00, takes e == (t<<n)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rightShiftToConcat ( const Expr e) [pure virtual]

t>>m = 0bin00...00 @ t[bvlength-1:m], takes e == (t>>n)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvshlToConcat ( const Expr e) [pure virtual]

BVSHL(t,c) = t[n-c,0] @ 0bin00...00.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvshlSplit ( const Expr e) [pure virtual]

BVSHL(t,c) = IF (c = 0) THEN t ELSE IF (c = 1) ...

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvlshrToConcat ( const Expr e) [pure virtual]

BVLSHR(t,c) = 0bin00...00 @ t[n-1,c].

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvShiftZero ( const Expr e) [pure virtual]

Any shift over a zero = 0.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvashrToConcat ( const Expr e) [pure virtual]

BVASHR(t,c) = SX(t[n-1,c], n-1)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rewriteXNOR ( const Expr e) [pure virtual]

a XNOR b <=> (~a & ~b) | (a & b)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rewriteNAND ( const Expr e) [pure virtual]

a NAND b <=> ~(a & b)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rewriteNOR ( const Expr e) [pure virtual]

a NOR b <=> ~(a | b)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rewriteBVCOMP ( const Expr e) [pure virtual]

BVCOMP(a,b) <=> ITE(a=b,0bin1,0bin0)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::rewriteBVSub ( const Expr e) [pure virtual]

a - b <=> a + (-b)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::constMultToPlus ( const Expr e) [pure virtual]

k*t = BVPLUS(n, <sum of shifts of t>) -- translation of k*t to BVPLUS

If k = 2^m, return k*t = t@0...0

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvplusZeroConcatRule ( const Expr e) [pure virtual]

0bin0...0 @ BVPLUS(n, args) = BVPLUS(n+k, args)

provided that m+ceil(log2(l)) <= n, where k is the size of the 0bin0...0, m is the max. length of each argument, and l is the number of arguments.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::zeroCoeffBVMult ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::oneCoeffBVMult ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::flipBVMult ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::padBVPlus ( const Expr e) [pure virtual]

Make args the same length as the result (zero-extend)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::padBVMult ( const Expr e) [pure virtual]

Make args the same length as the result (zero-extend)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvConstMultAssocRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvMultAssocRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvMultDistRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::flattenBVPlus ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::combineLikeTermsRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::lhsMinusRhsRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::extractBVMult ( const Expr e) [pure virtual]

(x *[n] y)[m:k] = (x *[m+1] y)[m:k], where m < n

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractBVPlus ( const Expr e) [pure virtual]

(x +[n] y)[m:k] = (x +[m+1] y)[m:k], where m < n

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::iteExtractRule ( const Expr e) [pure virtual]

ite(c,t1,t2)[i:j] <=> ite(c,t1[i:j],t2[i:j])

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::iteBVnegRule ( const Expr e) [pure virtual]

~ite(c,t1,t2) <=> ite(c,~t1,~t2)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvuminusBVConst ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvuminusBVMult ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvuminusBVUminus ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvuminusVar ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvmultBVUminus ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvuminusToBVPlus ( const Expr e) [pure virtual]

-t <==> ~t+1

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvuminusBVPlus ( const Expr e) [pure virtual]

-(c1*t1+...+cn*tn) <==> (-(c1*t1)+...+-(cn*tn))

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractConst ( const Expr e) [pure virtual]

c1[i:j] = c (extraction from a constant bitvector)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractWhole ( const Expr e) [pure virtual]

t[n-1:0] = t for n-bit t

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractExtract ( const Expr e) [pure virtual]

t[i:j][k:l] = t[k+j:l+j] (eliminate double extraction)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractConcat ( const Expr e) [pure virtual]

(t1 @ t2)[i:j] = t1[...] @ t2[...] (push extraction through concat)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractAnd ( const Expr e) [pure virtual]

(t1 & t2)[i:j] = t1[i:j] & t2[i:j] (push extraction through OR)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractOr ( const Expr e) [pure virtual]

(t1 | t2)[i:j] = t1[i:j] | t2[i:j] (push extraction through AND)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractNeg ( const Expr e) [pure virtual]

(~t)[i:j] = ~(t[i:j]) (push extraction through NEG)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::extractBitwise ( const Expr e,
int  kind,
const std::string &  name 
) [pure virtual]

Auxiliary function: (t1 op t2)[i:j] = t1[i:j] op t2[i:j].

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negConst ( const Expr e) [pure virtual]

~c1 = c (bit-wise negation of a constant bitvector)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negConcat ( const Expr e) [pure virtual]

~(t1@...@tn) = (~t1)@...@(~tn) -- push negation through concat

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negNeg ( const Expr e) [pure virtual]

~(~t) = t -- eliminate double negation

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negElim ( const Expr e) [pure virtual]

~t = -1*t + 1 -- eliminate negation

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negBVand ( const Expr e) [pure virtual]

~(t1 & t2) <=> ~t1 | ~t2 -- DeMorgan's Laws

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negBVor ( const Expr e) [pure virtual]

~(t1 | t2) <=> ~t1 & ~t2 -- DeMorgan's Laws

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negBVxor ( const Expr e) [pure virtual]

~(t1 xor t2) = ~t1 xor t2

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::negBVxnor ( const Expr e) [pure virtual]

~(t1 xnor t2) = t1 xor t2

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitwiseConst ( const Expr e,
const std::vector< int > &  idxs,
int  kind 
) [pure virtual]

Combine constants in bitwise AND, OR, XOR.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitwiseConcat ( const Expr e,
int  kind 
) [pure virtual]

Lifts concatenation above bitwise operators.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitwiseFlatten ( const Expr e,
int  kind 
) [pure virtual]

Flatten bitwise operation.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitwiseConstElim ( const Expr e,
int  idx,
int  kind 
) [pure virtual]

Simplify bitwise operator containing a constant child.

Parameters:
eis the bit-wise expr
idxis the index of the constant bitvector
kindis the kind of e

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::concatConst ( const Expr e) [pure virtual]

c1@c2@...@cn = c (concatenation of constant bitvectors)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::concatFlatten ( const Expr e) [pure virtual]

Flatten one level of nested concatenation, e.g.: x@(y@z)@w = x@y@z@w.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::concatMergeExtract ( const Expr e) [pure virtual]

Merge n-ary concat. of adjacent extractions: x[15:8]@x[7:0] = x[15:0].

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvplusConst ( const Expr e) [pure virtual]

BVPLUS(n, c1,c2,...,cn) = c (bit-vector plus of constant bitvectors)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvmultConst ( const Expr e) [pure virtual]

n*c1 = c, where n >= 0 (multiplication of a constant bitvector by a non-negative constant)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::typePredBit ( const Expr e) [pure virtual]

|- t=0 OR t=1 for any 1-bit bitvector t

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::expandTypePred ( const Theorem tp) [pure virtual]

Expand the type predicate wrapper (compute the actual type predicate)

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::isolate_var ( const Expr e) [pure virtual]

isolate a variable with coefficient = 1 on the Lhs of an

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::liftConcatBVMult ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::canonBVMult ( const Expr e) [pure virtual]

canonize BVMult expressions in order to get one coefficient

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::liftConcatBVPlus ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::canonBVPlus ( const Expr e) [pure virtual]

canonize BVPlus expressions in order to get just one

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::canonBVUMinus ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::processExtract ( const Theorem e,
bool &  solvedForm 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::canonBVEQ ( const Expr e,
int  maxEffort = 3 
) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::distributive_rule ( const Expr e) [pure virtual]

apply the distributive rule on the BVMULT expression e

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::BVMult_order_subterms ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::MarkNonSolvableEq ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::zeroExtendRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::repeatRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::rotlRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::rotrRule ( const Expr e) [pure virtual]
virtual Theorem CVC3::BitvectorProofRules::bvUDivConst ( const Expr divExpr) [pure virtual]

Divide a with b unsigned and return the bit-vector constant result

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvUDivTheorem ( const Expr divExpr) [pure virtual]

Rewrite a/b with a fresh variable d and add the constraints to make it be a divider.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvURemConst ( const Expr remExpr) [pure virtual]

Divide a with b unsigned and return the bit-vector constant result

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvURemRewrite ( const Expr divExpr) [pure virtual]

Rewrite ab in terms of a/b, i.e. a - a/b

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvSDivRewrite ( const Expr sDivExpr) [pure virtual]

Rewrite the signed divide in terms of the unsigned one.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvSRemRewrite ( const Expr sRemExpr) [pure virtual]

Rewrite the signed remainder in terms of the unsigned one.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bvSModRewrite ( const Expr sModExpr) [pure virtual]

Rewrite the signed mod in terms of the unsigned one.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitblastBVMult ( const std::vector< Theorem > &  a_bits,
const std::vector< Theorem > &  b_bits,
const Expr a_times_b,
std::vector< Theorem > &  output_bits 
) [pure virtual]

Bit-blast the multiplication a_times_b given the bits in a_bits and b_bits. The resulting output bits will be in the vector output_bits. The return value is a theorem saying there is no overflow for this multiplication. (TODO, it's just an empty theorem for now).

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::bitblastBVPlus ( const std::vector< Theorem > &  a_bits,
const std::vector< Theorem > &  b_bits,
const Expr a_plus_b,
std::vector< Theorem > &  output_bits 
) [pure virtual]

Bit-blast the sum a_times_b given the bits in a_bits and b_bits. The resulting output bits will be in the vector output_bits. The return value is a theorem saying there is no overflow for this sum. (TODO, it's just an empty theorem for now).

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::zeroBVOR ( const Expr orEqZero) [pure virtual]

Rewrite x_1 x_2 x_n = 0 into x_1 = 0 x_2 = 0 x_n = 0.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::oneBVAND ( const Expr andEqOne) [pure virtual]

Rewrite x_1 x_2 x_n = 1^n into x_1 = 1^n x_2 = 1^n x_n = 1^n.

Implemented in CVC3::BitvectorTheoremProducer.

virtual Theorem CVC3::BitvectorProofRules::constEq ( const Expr eq) [pure virtual]

Equalities over constants go to true/false.

Implemented in CVC3::BitvectorTheoremProducer.

virtual bool CVC3::BitvectorProofRules::solveExtractOverlapApplies ( const Expr eq) [pure virtual]

Returns true if equation is of the form x[i:j] = x[k:l], where the extracted segments overlap, i.e. i > j >= k > l or k > i >= l > j.

Implemented in CVC3::BitvectorTheoremProducer.

Referenced by CVC3::TheoryBitvector::solve().

virtual Theorem CVC3::BitvectorProofRules::solveExtractOverlap ( const Expr eq) [pure virtual]

Returns the theorem that simplifies the equality of two overlapping extracts over the same term.

Implemented in CVC3::BitvectorTheoremProducer.

Referenced by CVC3::TheoryBitvector::solve().


The documentation for this class was generated from the following file: