This theory handles basic linear arithmetic. More...

#include <theory_arith.h>

Inherits CVC3::Theory.

Inherited by CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

Collaboration diagram for CVC3::TheoryArith:

[legend]

List of all members.

Public Member Functions

TheoryArith (TheoryCore *core, const std::string &name)
~TheoryArith ()
virtual void addMultiplicativeSignSplit (const Theorem &case_split_thm)
virtual bool addPairToArithOrder (const Expr &smaller, const Expr &bigger)
bool isSyntacticRational (const Expr &e, Rational &r)
Return whether e is syntactically identical to a rational constant.
bool isAtomicArithFormula (const Expr &e)
Whether any ite's appear in the arithmetic part of the formula e.
Expr rewriteToDiff (const Expr &e)
Rewrite an atom to look like x - y op c if possible--for smtlib translation.
Theorem canonThm (const Theorem &thm)
Composition of canon(const Expr&) by transitivity: take e0 = e1, canonize e1 to e2, return e0 = e2.
virtual void separateMonomial (const Expr &e, Expr &c, Expr &var)=0
Separate monomial e = c*p1*...*pn into c and 1*p1*...*pn.
virtual void addSharedTerm (const Expr &e)=0
Notify theory of a new shared term.
virtual void assertFact (const Theorem &e)=0
Assert a new fact to the decision procedure.
virtual void refineCounterExample ()=0
Process disequalities from the arrangement for model generation.
virtual void computeModelBasic (const std::vector< Expr > &v)=0
Assign concrete values to basic-type variables in v.
virtual void computeModel (const Expr &e, std::vector< Expr > &vars)=0
Compute the value of a compound variable from the more primitive ones.
virtual void checkSat (bool fullEffort)=0
Check for satisfiability in the theory.
virtual Theorem rewrite (const Expr &e)=0
Theory-specific rewrite rules.
virtual void setup (const Expr &e)=0
Set up the term e for call-backs when e or its children change.
virtual void update (const Theorem &e, const Expr &d)=0
Notify a theory of a new equality.
virtual Theorem solve (const Theorem &e)=0
An optional solver.
virtual void checkAssertEqInvariant (const Theorem &e)=0
A debug check used by the primary solver.
virtual void checkType (const Expr &e)=0
Check that e is a valid Type expr.
virtual Cardinality finiteTypeInfo (Expr &e, Unsigned &n, bool enumerate, bool computeSize)=0
Compute information related to finiteness of types.
virtual void computeType (const Expr &e)=0
Compute and store the type of e.
virtual Type computeBaseType (const Type &t)=0
Compute the base type of the top-level operator of an arbitrary type.
virtual void computeModelTerm (const Expr &e, std::vector< Expr > &v)=0
Add variables from 'e' to 'v' for constructing a concrete model.
virtual Expr computeTypePred (const Type &t, const Expr &e)=0
Theory specific computation of the subtyping predicate for type t applied to the expression e.
virtual Expr computeTCC (const Expr &e)=0
Compute and cache the TCC of e.
virtual ExprStream & print (ExprStream &os, const Expr &e)=0
Theory-specific pretty-printing.
virtual Expr parseExprOp (const Expr &e)=0
Theory-specific parsing implemented by the DP.
Type realType ()
Type intType ()
Type subrangeType (const Expr &l, const Expr &r)
Expr rat (Rational r)
Expr darkShadow (const Expr &lhs, const Expr &rhs)
Construct the dark shadow expression representing lhs <= rhs.
Expr grayShadow (const Expr &v, const Expr &e, const Rational &c1, const Rational &c2)
Construct the gray shadow expression representing c1 <= v - e <= c2.
bool leavesAreNumConst (const Expr &e)

Protected Member Functions

virtual Theorem canon (const Expr &e)=0
Canonize the expression e, assuming all children are canonical.
Theorem canonRec (const Expr &e)
Canonize the expression e recursively.
void printRational (ExprStream &os, const Rational &r, bool printAsReal=false)
Print a rational in SMT-LIB format.
bool isAtomicArithTerm (const Expr &e)
Whether any ite's appear in the arithmetic part of the term e.
Theorem canonSimp (const Expr &e)
simplify leaves and then canonize
bool recursiveCanonSimpCheck (const Expr &e)
helper for checkAssertEqInvariant

Protected Attributes

Type d_realType
Type d_intType
std::vector< int > d_kinds

Detailed Description

This theory handles basic linear arithmetic.

Author: Clark Barrett

Created: Sat Feb 8 14:44:32 2003

Definition at line 70 of file theory_arith.h.

Constructor & Destructor Documentation

CVC3::TheoryArith::TheoryArith	(	TheoryCore *	core,
		const std::string &	name
	)		`[inline]`

Definition at line 98 of file theory_arith.h.

CVC3::TheoryArith::~TheoryArith ( ) [inline]

Definition at line 100 of file theory_arith.h.

Member Function Documentation

virtual Theorem CVC3::TheoryArith::canon ( const Expr & e ) [protected, pure virtual]

Canonize the expression e, assuming all children are canonical.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

Referenced by canonThm().

Theorem TheoryArith::canonRec ( const Expr & e ) [protected]

Canonize the expression e recursively.

Definition at line 31 of file theory_arith.cpp.

References CVC3::Expr::arity(), CVC3::Theorem::getLHS(), and CVC3::Theorem::getRHS().

void TheoryArith::printRational	(	ExprStream &	os,
		const Rational &	r,
		bool	printAsReal = `false`
	)		`[protected]`

Print a rational in SMT-LIB format.

Definition at line 54 of file theory_arith.cpp.

References DebugAssert, CVC3::Rational::getDenominator(), CVC3::Rational::getNumerator(), CVC3::Rational::isInteger(), CVC3::ExprStream::lang(), CVC3::push(), CVC3::SMTLIB_LANG, CVC3::space(), CVC3::SPASS_LANG, and CVC3::Rational::toString().

Referenced by CVC3::TheoryArithOld::print(), CVC3::TheoryArithNew::print(), and CVC3::TheoryArith3::print().

bool TheoryArith::isAtomicArithTerm ( const Expr & e ) [protected]

Whether any ite's appear in the arithmetic part of the term e.

Definition at line 115 of file theory_arith.cpp.

References CVC3::Expr::arity(), CVC3::DIVIDE, CVC3::Expr::getKind(), CVC3::INTDIV, ITE, CVC3::MINUS, CVC3::MOD, CVC3::MULT, CVC3::PLUS, CVC3::POW, RATIONAL_EXPR, and CVC3::UMINUS.

Theorem TheoryArith::canonSimp ( const Expr & e ) [protected]

simplify leaves and then canonize

Definition at line 257 of file theory_arith.cpp.

References CVC3::Expr::arity(), DebugAssert, CVC3::Theorem::getLHS(), and CVC3::Theorem::getRHS().

Referenced by CVC3::TheoryArithOld::checkAssertEqInvariant(), CVC3::TheoryArith3::checkAssertEqInvariant(), CVC3::TheoryArithNew::update(), and CVC3::TheoryArith3::update().

bool TheoryArith::recursiveCanonSimpCheck ( const Expr & e ) [protected]

helper for checkAssertEqInvariant

Definition at line 283 of file theory_arith.cpp.

References CVC3::Expr::begin(), CVC3::Expr::end(), and CVC3::Expr::hasFind().

Referenced by CVC3::TheoryArithOld::checkAssertEqInvariant(), and CVC3::TheoryArith3::checkAssertEqInvariant().

virtual void CVC3::TheoryArith::addMultiplicativeSignSplit ( const Theorem & case_split_thm ) [inline, virtual]

Reimplemented in CVC3::TheoryArithOld.

Definition at line 102 of file theory_arith.h.

virtual bool CVC3::TheoryArith::addPairToArithOrder	(	const Expr &	smaller,
		const Expr &	bigger
	)		`[inline, virtual]`

Record that smaller should be smaller than bigger in the variable order. Should be implemented in decision procedures that support it.

Reimplemented in CVC3::TheoryArithOld.

Definition at line 108 of file theory_arith.h.

bool TheoryArith::isSyntacticRational	(	const Expr &	e,
		Rational &	r
	)

Return whether e is syntactically identical to a rational constant.

Definition at line 157 of file theory_arith.cpp.

References CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::isDivide(), CVC3::Expr::isRational(), CVC3::isUMinus(), and CVC3::REAL_CONST.

bool TheoryArith::isAtomicArithFormula ( const Expr & e )

Whether any ite's appear in the arithmetic part of the formula e.

Definition at line 143 of file theory_arith.cpp.

References EQ, CVC3::GE, CVC3::Expr::getKind(), CVC3::GT, CVC3::LE, and CVC3::LT.

Expr TheoryArith::rewriteToDiff ( const Expr & e )

Rewrite an atom to look like x - y op c if possible--for smtlib translation.

Definition at line 189 of file theory_arith.cpp.

References CVC3::Expr::arity(), DebugAssert, EQ, CVC3::GE, CVC3::Expr::getKind(), CVC3::Expr::getRational(), CVC3::GT, CVC3::isRational(), CVC3::LE, CVC3::LT, CVC3::MULT, CVC3::PLUS, and RATIONAL_EXPR.

Theorem CVC3::TheoryArith::canonThm ( const Theorem & thm ) [inline]

Composition of canon(const Expr&) by transitivity: take e0 = e1, canonize e1 to e2, return e0 = e2.

Definition at line 120 of file theory_arith.h.

References canon(), CVC3::Theorem::getRHS(), and CVC3::Theory::transitivityRule().

Referenced by CVC3::TheoryArithNew::substAndCanonizeModTableaux(), and CVC3::TheoryArithNew::substAndCanonizeTableaux().

virtual void CVC3::TheoryArith::separateMonomial	(	const Expr &	e,
		Expr &	c,
		Expr &	var
	)		`[pure virtual]`

Separate monomial e = c*p1*...*pn into c and 1*p1*...*pn.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::addSharedTerm ( const Expr & e ) [pure virtual]

Notify theory of a new shared term.

When a term e associated with theory i occurs as a child of an expression associated with theory j, the framework calls i->addSharedTerm(e) and j->addSharedTerm(e)

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::assertFact ( const Theorem & e ) [pure virtual]

Assert a new fact to the decision procedure.

Each fact that makes it into the core framework is assigned to exactly one theory: the theory associated with that fact. assertFact is called to inform the theory that a new fact has been assigned to the theory.

Implements CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::refineCounterExample ( ) [pure virtual]

Process disequalities from the arrangement for model generation.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::computeModelBasic ( const std::vector< Expr > & v ) [pure virtual]

Assign concrete values to basic-type variables in v.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::computeModel	(	const Expr &	e,
		std::vector< Expr > &	vars
	)		`[pure virtual]`

Compute the value of a compound variable from the more primitive ones.

The more primitive variables for e are already assigned concrete values, and are available through getModelValue().

The new value for e must be assigned using assignValue() method.

Parameters:

e	is the compound type expression to assign a value;
vars	are the variables actually assigned. Normally, 'e' is the only element of vars. However, e.g. in the case of uninterpreted functions, assigning 'f' means assigning all relevant applications of 'f' to constant values (f(0), f(5), etc.). Such applications might not be known before the model is constructed (they may be of the form f(x), f(y+z), etc., where x,y,z are still unassigned).

Populating 'vars' is an opportunity for a DP to change the set of top-level "variables" to assign, if needed. In particular, it may drop 'e' from the model entirely, if it is already a concrete value by itself.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::checkSat ( bool fullEffort ) [pure virtual]

Check for satisfiability in the theory.

Parameters:

fullEffort when it is false, checkSat can do as much or as little work as it likes, though simple inferences and checks for consistency should be done to increase efficiency. If fullEffort is true, checkSat must check whether the set of facts given by assertFact together with the arrangement of shared terms (provided by addSharedTerm) induced by the global find database equivalence relation are satisfiable. If satisfiable, checkSat does nothing.

If satisfiability can be acheived by merging some of the shared terms, a new fact must be enqueued using enqueueFact (this fact need not be a literal). If there is no way to make things satisfiable, setInconsistent must be called.

Implements CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Theorem CVC3::TheoryArith::rewrite ( const Expr & e ) [pure virtual]

Theory-specific rewrite rules.

By default, rewrite just returns a reflexive theorem stating that the input expression is equivalent to itself. However, rewrite is allowed to return any theorem which describes how the input expression is equivalent to some new expression. rewrite should be used to perform simplifications, normalization, and any other preprocessing on theory-specific expressions that needs to be done.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::setup ( const Expr & e ) [pure virtual]

Set up the term e for call-backs when e or its children change.

setup is called once for each expression associated with the theory. It is typically used to setup theory-specific data for an expression and to add call-back information for use with update.

See also:: update

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::update	(	const Theorem &	e,
		const Expr &	d
	)		`[pure virtual]`

Notify a theory of a new equality.

update is a call-back used by the notify mechanism of the core theory. It works as follows. When an equation t1 = t2 makes it into the core framework, the two find equivalence classes for t1 and t2 are merged. The result is that t2 is the new equivalence class representative and t1 is no longer an equivalence class representative. When this happens, the notify list of t1 is traversed. Notify list entries consist of a theory and an expression d. For each entry (i,d), i->update(e, d) is called, where e is the theorem corresponding to the equality t1=t2.

To add the entry (i,d) to a term t1's notify list, a call must be made to t1.addNotify(i,d). This is typically done in setup.

See also:: setup

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Theorem CVC3::TheoryArith::solve ( const Theorem & e ) [pure virtual]

An optional solver.

The solve method can be used to implement a Shostak-style solver. Since solvers do not in general combine, the following technique is used. One theory is designated as the primary solver (in our case, it is the theory of arithmetic). For each equation that enters the core framework, the primary solver is called to ensure that the equation is in solved form with respect to the primary theory.

After the primary solver, the solver for the theory associated with the equation is called. This solver can do whatever it likes, as long as the result is still in solved form with respect to the primary solver. This is a slight generalization of what is described in my (Clark)'s PhD thesis.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::checkAssertEqInvariant ( const Theorem & e ) [pure virtual]

A debug check used by the primary solver.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::checkType ( const Expr & e ) [pure virtual]

Check that e is a valid Type expr.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Cardinality CVC3::TheoryArith::finiteTypeInfo	(	Expr &	e,
		Unsigned &	n,
		bool	enumerate,
		bool	computeSize
	)		`[pure virtual]`

Compute information related to finiteness of types.

Used by the TypeComputer defined in TheoryCore (theories should not call this funtion directly -- they should use the methods in Type instead). Each theory should implement this if it contains any types that could be non-infinite.

1. Returns Cardinality of the type (finite, infinite, or unknown) 2. If cardinality = finite and enumerate is true, sets e to the nth element of the type if it can sets e to NULL if n is out of bounds or if unable to compute nth element 3. If cardinality = finite and computeSize is true, sets n to the size of the type if it can sets n to 0 otherwise

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::computeType ( const Expr & e ) [pure virtual]

Compute and store the type of e.

Parameters:

e	is the expression whose type is computed.

This function computes the type of the top-level operator of e, and recurses into children using getType(), if necessary.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Type CVC3::TheoryArith::computeBaseType ( const Type & tp ) [pure virtual]

Compute the base type of the top-level operator of an arbitrary type.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual void CVC3::TheoryArith::computeModelTerm	(	const Expr &	e,
		std::vector< Expr > &	v
	)		`[pure virtual]`

Add variables from 'e' to 'v' for constructing a concrete model.

If e is already of primitive type, do NOT add it to v.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Expr CVC3::TheoryArith::computeTypePred	(	const Type &	t,
		const Expr &	e
	)		`[pure virtual]`

Theory specific computation of the subtyping predicate for type t applied to the expression e.

By default returns true. Each theory needs to compute subtype predicates for the types associated with it. So, for example, the theory of records will take a record type [# f1: T1, f2: T2 #] and an expression e and will return the subtyping predicate for e, namely: computeTypePred(T1, e.f1) AND computeTypePred(T2, e.f2)

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Expr CVC3::TheoryArith::computeTCC ( const Expr & e ) [pure virtual]

Compute and cache the TCC of e.

Parameters:

e	is an expression (term or formula). This function computes the TCC of e which is true iff the expression is defined.

This function computes the TCC or predicate of the top-level operator of e, and recurses into children using getTCC(), if necessary.

The default implementation is to compute TCCs recursively for all children, and return their conjunction.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual ExprStream& CVC3::TheoryArith::print	(	ExprStream &	os,
		const Expr &	e
	)		`[pure virtual]`

Theory-specific pretty-printing.

By default, print the top node in AST, and resume pretty-printing the children. The same call e.print(os) can be used in DP-specific printers to use AST printing for the given node. In fact, it is strongly recommended to add e.print(os) as the default for all the cases/kinds that are not handled by the particular pretty-printer.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

virtual Expr CVC3::TheoryArith::parseExprOp ( const Expr & e ) [pure virtual]

Theory-specific parsing implemented by the DP.

Reimplemented from CVC3::Theory.

Implemented in CVC3::TheoryArith3, CVC3::TheoryArithNew, and CVC3::TheoryArithOld.

Type CVC3::TheoryArith::realType ( ) [inline]

Definition at line 152 of file theory_arith.h.

References d_realType.

Referenced by CVC3::TheoryArithOld::computeBaseType(), CVC3::TheoryArithNew::computeBaseType(), CVC3::TheoryArith3::computeBaseType(), CVC3::ArithTheoremProducerOld::realType(), CVC3::ArithTheoremProducer3::realType(), CVC3::ArithTheoremProducer::realType(), and CVC3::Translator::zeroVar().

Type CVC3::TheoryArith::intType ( ) [inline]

Definition at line 153 of file theory_arith.h.