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AIMA-Java Core Algorithms from the book Artificial Intelligence a Modern Approach 3rd Ed.
package aima.core.logic.fol;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;
import aima.core.logic.fol.parsing.ast.FOLNode;
import aima.core.logic.fol.parsing.ast.Function;
import aima.core.logic.fol.parsing.ast.Term;
import aima.core.logic.fol.parsing.ast.Variable;
/**
* Artificial Intelligence A Modern Approach (3rd Edition): Figure 9.1, page
* 328.
*
*
*
* function UNIFY(x, y, theta) returns a substitution to make x and y identical
* inputs: x, a variable, constant, list, or compound
* y, a variable, constant, list, or compound
* theta, the substitution built up so far (optional, defaults to empty)
*
* if theta = failure then return failure
* else if x = y the return theta
* else if VARIABLE?(x) then return UNIVY-VAR(x, y, theta)
* else if VARIABLE?(y) then return UNIFY-VAR(y, x, theta)
* else if COMPOUND?(x) and COMPOUND?(y) then
* return UNIFY(x.ARGS, y.ARGS, UNIFY(x.OP, y.OP, theta))
* else if LIST?(x) and LIST?(y) then
* return UNIFY(x.REST, y.REST, UNIFY(x.FIRST, y.FIRST, theta))
* else return failure
*
* ---------------------------------------------------------------------------------------------------
*
* function UNIFY-VAR(var, x, theta) returns a substitution
*
* if {var/val} E theta then return UNIFY(val, x, theta)
* else if {x/val} E theta then return UNIFY(var, val, theta)
* else if OCCUR-CHECK?(var, x) then return failure
* else return add {var/x} to theta
*
*
* Figure 9.1 The unification algorithm. The algorithm works by comparing the
* structures of the inputs, elements by element. The substitution theta that is
* the argument to UNIFY is built up along the way and is used to make sure that
* later comparisons are consistent with bindings that were established earlier.
* In a compound expression, such as F(A, B), the OP field picks out the
* function symbol F and the ARGS field picks out the argument list (A, B).
*
* @author Ciaran O'Reilly
* @author Ravi Mohan
* @author Mike Stampone
*
*/
public class Unifier {
//
private static SubstVisitor _substVisitor = new SubstVisitor();
public Unifier() {
}
/**
* Returns a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a failure to
* unify.
*
* @param x
* a variable, constant, list, or compound
* @param y
* a variable, constant, list, or compound
*
* @return a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a
* failure to unify.
*/
public Map unify(FOLNode x, FOLNode y) {
return unify(x, y, new LinkedHashMap());
}
/**
* Returns a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a failure to
* unify.
*
* @param x
* a variable, constant, list, or compound
* @param y
* a variable, constant, list, or compound
* @param theta
* the substitution built up so far
*
* @return a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a
* failure to unify.
*/
public Map unify(FOLNode x, FOLNode y,
Map theta) {
// if theta = failure then return failure
if (theta == null) {
return null;
} else if (x.equals(y)) {
// else if x = y then return theta
return theta;
} else if (x instanceof Variable) {
// else if VARIABLE?(x) then return UNIVY-VAR(x, y, theta)
return unifyVar((Variable) x, y, theta);
} else if (y instanceof Variable) {
// else if VARIABLE?(y) then return UNIFY-VAR(y, x, theta)
return unifyVar((Variable) y, x, theta);
} else if (isCompound(x) && isCompound(y)) {
// else if COMPOUND?(x) and COMPOUND?(y) then
// return UNIFY(x.ARGS, y.ARGS, UNIFY(x.OP, y.OP, theta))
return unify(args(x), args(y), unifyOps(op(x), op(y), theta));
} else {
// else return failure
return null;
}
}
/**
* Returns a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a failure to
* unify.
*
* @param x
* a variable, constant, list, or compound
* @param y
* a variable, constant, list, or compound
* @param theta
* the substitution built up so far
*
* @return a Map representing the substitution (i.e. a set
* of variable/term pairs) or null which is used to indicate a
* failure to unify.
*/
// else if LIST?(x) and LIST?(y) then
// return UNIFY(x.REST, y.REST, UNIFY(x.FIRST, y.FIRST, theta))
public Map unify(List x,
List y, Map theta) {
if (theta == null) {
return null;
} else if (x.size() != y.size()) {
return null;
} else if (x.size() == 0 && y.size() == 0) {
return theta;
} else if (x.size() == 1 && y.size() == 1) {
return unify(x.get(0), y.get(0), theta);
} else {
return unify(x.subList(1, x.size()), y.subList(1, y.size()),
unify(x.get(0), y.get(0), theta));
}
}
//
// PROTECTED METHODS
//
// Note: You can subclass and override this method in order
// to re-implement the OCCUR-CHECK?() to always
// return false if you want that to be the default
// behavior, as is the case with Prolog.
// Note: Implementation is based on unify-bug.pdf document by Peter Norvig:
// http://norvig.com/unify-bug.pdf
protected boolean occurCheck(Map theta, Variable var,
FOLNode x) {
// ((equal var x) t)
if (var.equals(x)) {
return true;
// ((bound? x subst)
} else if (theta.containsKey(x)) {
// (occurs-in? var (lookup x subst) subst))
return occurCheck(theta, var, theta.get(x));
// ((consp x) (or (occurs-in? var (first x) subst) (occurs-in? var
// (rest x) subst)))
} else if (x instanceof Function) {
// (or (occurs-in? var (first x) subst) (occurs-in? var (rest x)
// subst)))
Function fx = (Function) x;
for (Term fxt : fx.getArgs()) {
if (occurCheck(theta, var, fxt)) {
return true;
}
}
}
return false;
}
//
// PRIVATE METHODS
//
/**
*
* function UNIFY-VAR(var, x, theta) returns a substitution
* inputs: var, a variable
* x, any expression
* theta, the substitution built up so far
*
*/
private Map unifyVar(Variable var, FOLNode x,
Map theta) {
if (!Term.class.isInstance(x)) {
return null;
} else if (theta.keySet().contains(var)) {
// if {var/val} E theta then return UNIFY(val, x, theta)
return unify(theta.get(var), x, theta);
} else if (theta.keySet().contains(x)) {
// else if {x/val} E theta then return UNIFY(var, val, theta)
return unify(var, theta.get(x), theta);
} else if (occurCheck(theta, var, x)) {
// else if OCCUR-CHECK?(var, x) then return failure
return null;
} else {
// else return add {var/x} to theta
cascadeSubstitution(theta, var, (Term) x);
return theta;
}
}
private Map unifyOps(String x, String y,
Map theta) {
if (theta == null) {
return null;
} else if (x.equals(y)) {
return theta;
} else {
return null;
}
}
private List args(FOLNode x) {
return x.getArgs();
}
private String op(FOLNode x) {
return x.getSymbolicName();
}
private boolean isCompound(FOLNode x) {
return x.isCompound();
}
// See:
// http://logic.stanford.edu/classes/cs157/2008/miscellaneous/faq.html#jump165
// for need for this.
private Map cascadeSubstitution(Map theta,
Variable var, Term x) {
theta.put(var, x);
for (Variable v : theta.keySet()) {
theta.put(v, _substVisitor.subst(theta, theta.get(v)));
}
// Ensure Function Terms are correctly updates by passing over them
// again. Fix for testBadCascadeSubstitution_LCL418_1()
for (Variable v : theta.keySet()) {
Term t = theta.get(v);
if (t instanceof Function) {
theta.put(v, _substVisitor.subst(theta, t));
}
}
return theta;
}
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