CVC3
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CVC3::TheoryArith Class Referenceabstract

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:
Collaboration graph

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 ExprStreamprint (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)
 
- Public Member Functions inherited from CVC3::Theory
 Theory (TheoryCore *theoryCore, const std::string &name)
 Whether theory has been used (for smtlib translator)
 
virtual ~Theory (void)
 Destructor.
 
ExprManagergetEM ()
 Access to ExprManager.
 
TheoryCoretheoryCore ()
 Get a pointer to theoryCore.
 
CommonProofRulesgetCommonRules ()
 Get a pointer to common proof rules.
 
const std::string & getName () const
 Get the name of the theory (for debugging purposes)
 
virtual void setUsed ()
 Set the "used" flag on this theory (for smtlib translator)
 
virtual bool theoryUsed ()
 Get whether theory has been used (for smtlib translator)
 
virtual Theorem theoryPreprocess (const Expr &e)
 Theory-specific preprocessing.
 
virtual Theorem simplifyOp (const Expr &e)
 Recursive simplification step.
 
virtual void assertTypePred (const Expr &e, const Theorem &pred)
 Receives all the type predicates for the types of the given theory.
 
virtual Theorem rewriteAtomic (const Expr &e)
 Theory-specific rewrites for atomic formulas.
 
virtual void notifyInconsistent (const Theorem &thm)
 Notification of conflict.
 
virtual void registerAtom (const Expr &e, const Theorem &thm)
 
virtual void registerAtom (const Expr &e)
 Theory-specific registration of atoms.
 
virtual bool inconsistent ()
 Check if the current context is inconsistent.
 
virtual void setInconsistent (const Theorem &e)
 Make the context inconsistent; The formula proved by e must FALSE.
 
virtual void setIncomplete (const std::string &reason)
 Mark the current decision branch as possibly incomplete.
 
virtual Theorem simplify (const Expr &e)
 Simplify a term e and return a Theorem(e==e')
 
Expr simplifyExpr (const Expr &e)
 Simplify a term e w.r.t. the current context.
 
virtual void enqueueFact (const Theorem &e)
 Submit a derived fact to the core from a decision procedure.
 
virtual void enqueueSE (const Theorem &e)
 Check if the current context is inconsistent.
 
virtual void assertEqualities (const Theorem &e)
 Handle new equalities (usually asserted through addFact)
 
virtual Expr parseExpr (const Expr &e)
 Parse the generic expression.
 
virtual void assignValue (const Expr &t, const Expr &val)
 Assigns t a concrete value val. Used in model generation.
 
virtual void assignValue (const Theorem &thm)
 Record a derived assignment to a variable (LHS).
 
void registerKinds (Theory *theory, std::vector< int > &kinds)
 Register new kinds with the given theory.
 
void unregisterKinds (Theory *theory, std::vector< int > &kinds)
 Unregister kinds for a theory.
 
void registerTheory (Theory *theory, std::vector< int > &kinds, bool hasSolver=false)
 Register a new theory.
 
void unregisterTheory (Theory *theory, std::vector< int > &kinds, bool hasSolver)
 Unregister a theory.
 
int getNumTheories ()
 Return the number of registered theories.
 
bool hasTheory (int kind)
 Test whether a kind maps to any theory.
 
TheorytheoryOf (int kind)
 Return the theory associated with a kind.
 
TheorytheoryOf (const Type &e)
 Return the theory associated with a type.
 
TheorytheoryOf (const Expr &e)
 Return the theory associated with an Expr.
 
Theorem find (const Expr &e)
 Return the theorem that e is equal to its find.
 
const TheoremfindRef (const Expr &e)
 Return the find as a reference: expr must have a find.
 
Theorem findReduce (const Expr &e)
 Return find-reduced version of e.
 
bool findReduced (const Expr &e)
 Return true iff e is find-reduced.
 
Expr findExpr (const Expr &e)
 Return the find of e, or e if it has no find.
 
Expr getTCC (const Expr &e)
 Compute the TCC of e, or the subtyping predicate, if e is a type.
 
Type getBaseType (const Expr &e)
 Compute (or look up in cache) the base type of e and return the result.
 
Type getBaseType (const Type &tp)
 Compute the base type from an arbitrary type.
 
Expr getTypePred (const Type &t, const Expr &e)
 Calls the correct theory to compute a type predicate.
 
Theorem updateHelper (const Expr &e)
 Update the children of the term e.
 
void setupCC (const Expr &e)
 Setup a term for congruence closure (must have sig and rep attributes)
 
void updateCC (const Theorem &e, const Expr &d)
 Update a term w.r.t. congruence closure (must be setup with setupCC())
 
Theorem rewriteCC (const Expr &e)
 Rewrite a term w.r.t. congruence closure (must be setup with setupCC())
 
void getModelTerm (const Expr &e, std::vector< Expr > &v)
 Calls the correct theory to get all of the terms that need to be assigned values in the concrete model.
 
Theorem getModelValue (const Expr &e)
 Fetch the concrete assignment to the variable during model generation.
 
void addSplitter (const Expr &e, int priority=0)
 Suggest a splitter to the SearchEngine.
 
void addGlobalLemma (const Theorem &thm, int priority=0)
 Add a global lemma.
 
bool isLeaf (const Expr &e)
 Test if e is an i-leaf term for the current theory.
 
bool isLeafIn (const Expr &e1, const Expr &e2)
 Test if e1 is an i-leaf in e2.
 
bool leavesAreSimp (const Expr &e)
 Test if all i-leaves of e are simplified.
 
Type boolType ()
 Return BOOLEAN type.
 
const ExprfalseExpr ()
 Return FALSE Expr.
 
const ExprtrueExpr ()
 Return TRUE Expr.
 
Expr newVar (const std::string &name, const Type &type)
 Create a new variable given its name and type.
 
Expr newVar (const std::string &name, const Type &type, const Expr &def)
 Create a new named expression given its name, type, and definition.
 
Op newFunction (const std::string &name, const Type &type, bool computeTransClosure)
 Create a new uninterpreted function.
 
Op lookupFunction (const std::string &name, Type *type)
 Look up a function by name.
 
Op newFunction (const std::string &name, const Type &type, const Expr &def)
 Create a new defined function.
 
Expr addBoundVar (const std::string &name, const Type &type)
 Create and add a new bound variable to the stack, for parseExprOp().
 
Expr addBoundVar (const std::string &name, const Type &type, const Expr &def)
 Create and add a new bound named def to the stack, for parseExprOp().
 
Expr lookupVar (const std::string &name, Type *type)
 Lookup variable and return it and its type. Return NULL Expr if it doesn't exist yet.
 
Type newTypeExpr (const std::string &name)
 Create a new uninterpreted type with the given name.
 
Type lookupTypeExpr (const std::string &name)
 Lookup type by name. Return Null if no such type exists.
 
Type newTypeExpr (const std::string &name, const Type &def)
 Create a new type abbreviation with the given name.
 
Type newSubtypeExpr (const Expr &pred, const Expr &witness)
 Create a new subtype expression.
 
Expr resolveID (const std::string &name)
 Resolve an identifier, for use in parseExprOp()
 
void installID (const std::string &name, const Expr &e)
 Install name as a new identifier associated with Expr e.
 
Theorem typePred (const Expr &e)
 Return BOOLEAN type.
 
Theorem reflexivityRule (const Expr &a)
 ==> a == a
 
Theorem symmetryRule (const Theorem &a1_eq_a2)
 a1 == a2 ==> a2 == a1
 
Theorem transitivityRule (const Theorem &a1_eq_a2, const Theorem &a2_eq_a3)
 (a1 == a2) & (a2 == a3) ==> (a1 == a3)
 
Theorem substitutivityRule (const Op &op, const std::vector< Theorem > &thms)
 (c_1 == d_1) & ... & (c_n == d_n) ==> op(c_1,...,c_n) == op(d_1,...,d_n)
 
Theorem substitutivityRule (const Expr &e, const Theorem &t)
 Special case for unary operators.
 
Theorem substitutivityRule (const Expr &e, const Theorem &t1, const Theorem &t2)
 Special case for binary operators.
 
Theorem substitutivityRule (const Expr &e, const std::vector< unsigned > &changed, const std::vector< Theorem > &thms)
 Optimized: only positions which changed are included.
 
Theorem substitutivityRule (const Expr &e, int changed, const Theorem &thm)
 Optimized: only a single position changed.
 
Theorem iffMP (const Theorem &e1, const Theorem &e1_iff_e2)
 e1 AND (e1 IFF e2) ==> e2
 
Theorem rewriteAnd (const Expr &e)
 ==> AND(e1,e2) IFF [simplified expr]
 
Theorem rewriteOr (const Expr &e)
 ==> OR(e1,...,en) IFF [simplified expr]
 
Theorem rewriteIte (const Expr &e)
 Derived rule for rewriting ITE.
 
Theorem renameExpr (const Expr &e)
 Derived rule to create a new name for an expression.
 

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
 
- Protected Attributes inherited from CVC3::Theory
bool d_theoryUsed
 

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)
protectedpure virtual

Canonize the expression e, assuming all children are canonical.

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

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
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
bool TheoryArith::recursiveCanonSimpCheck ( const Expr e)
protected
virtual void CVC3::TheoryArith::addMultiplicativeSignSplit ( const Theorem case_split_thm)
inlinevirtual

Reimplemented in CVC3::TheoryArithOld.

Definition at line 102 of file theory_arith.h.

virtual bool CVC3::TheoryArith::addPairToArithOrder ( const Expr smaller,
const Expr bigger 
)
inlinevirtual

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

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

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

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

Process disequalities from the arrangement for model generation.

Reimplemented from CVC3::Theory.

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

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

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
eis the compound type expression to assign a value;
varsare 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::TheoryArithOld, CVC3::TheoryArith3, and CVC3::TheoryArithNew.

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

Check for satisfiability in the theory.

Parameters
fullEffortwhen 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::TheoryArithOld, CVC3::TheoryArith3, and CVC3::TheoryArithNew.

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

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

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

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

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

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

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

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

Compute and store the type of e.

Parameters
eis 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::TheoryArithOld, CVC3::TheoryArith3, and CVC3::TheoryArithNew.

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

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

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

virtual Expr CVC3::TheoryArith::computeTCC ( const Expr e)
pure virtual

Compute and cache the TCC of e.

Parameters
eis 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::TheoryArithOld, CVC3::TheoryArith3, and CVC3::TheoryArithNew.

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

virtual Expr CVC3::TheoryArith::parseExprOp ( const Expr e)
pure virtual

Theory-specific parsing implemented by the DP.

Reimplemented from CVC3::Theory.

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

Type CVC3::TheoryArith::realType ( )
inline
Type CVC3::TheoryArith::intType ( )
inline
Type CVC3::TheoryArith::subrangeType ( const Expr l,
const Expr r 
)
inline

Definition at line 154 of file theory_arith.h.

References CVC3::SUBRANGE.

Expr CVC3::TheoryArith::rat ( Rational  r)
inline
Expr CVC3::TheoryArith::darkShadow ( const Expr lhs,
const Expr rhs 
)
inline

Construct the dark shadow expression representing lhs <= rhs.

Definition at line 159 of file theory_arith.h.

References CVC3::DARK_SHADOW.

Referenced by CVC3::ArithTheoremProducer3::darkShadow(), CVC3::ArithTheoremProducerOld::darkShadow(), and CVC3::ArithTheoremProducer::darkShadow().

Expr CVC3::TheoryArith::grayShadow ( const Expr v,
const Expr e,
const Rational c1,
const Rational c2 
)
inline

Construct the gray shadow expression representing c1 <= v - e <= c2.

Alternatively, v = e + i for some i s.t. c1 <= i <= c2

Definition at line 165 of file theory_arith.h.

References CVC3::GRAY_SHADOW, and rat().

Referenced by CVC3::ArithTheoremProducer3::grayShadow(), CVC3::ArithTheoremProducerOld::grayShadow(), and CVC3::ArithTheoremProducer::grayShadow().

bool TheoryArith::leavesAreNumConst ( const Expr e)

Member Data Documentation

Type CVC3::TheoryArith::d_realType
protected
Type CVC3::TheoryArith::d_intType
protected
std::vector<int> CVC3::TheoryArith::d_kinds
protected

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