use of com.sri.ai.expresso.core.ExtensionalIndexExpressionsSet in project aic-expresso by aic-sri-international.
the class BruteForceFunctionTheory method getSingleVariableConstraintQuantifierEliminatorStepSolver.
@Override
public ExpressionLiteralSplitterStepSolver getSingleVariableConstraintQuantifierEliminatorStepSolver(AssociativeCommutativeGroup group, SingleVariableConstraint constraint, Expression body, Context context) {
Expression variable = constraint.getVariable();
Expression type = GrinderUtil.getTypeExpression(variable, context);
Expression indexExpression = IndexExpressions.makeIndexExpression(variable, type);
ExtensionalIndexExpressionsSet indexExpressionsSet = new ExtensionalIndexExpressionsSet(indexExpression);
MultiIndexQuantifierEliminator quantifierEliminator = new BruteForceMultiIndexQuantifierEliminator(context.getTheory().getTopRewriter());
Expression solution = quantifierEliminator.solve(group, indexExpressionsSet, constraint, body, context);
return new ConstantExpressionStepSolver(solution);
}
use of com.sri.ai.expresso.core.ExtensionalIndexExpressionsSet in project aic-expresso by aic-sri-international.
the class AssignmentsIterator method makeMapFromVariablesToIteratorMakersFrom.
private static Map<Expression, NullaryFunction<Iterator<Expression>>> makeMapFromVariablesToIteratorMakersFrom(IndexExpressionsSet indexExpressionsSet, Registry registry) {
Map<Expression, NullaryFunction<Iterator<Expression>>> fromVariableToIteratorMaker = map();
ExtensionalIndexExpressionsSet extensionalIndexExpressionsSet;
try {
extensionalIndexExpressionsSet = (ExtensionalIndexExpressionsSet) indexExpressionsSet;
} catch (ClassCastException e) {
throw new Error("AssignmentsIterator defined for extensional index expressions sets only.");
}
for (Expression indexExpression : extensionalIndexExpressionsSet.getList()) {
Expression variable = IndexExpressions.getIndex(indexExpression);
Expression typeDescription = IndexExpressions.getType(indexExpression);
if (typeDescription == null) {
typeDescription = GrinderUtil.getTypeExpression(variable, registry);
}
putVariableAndIteratorMakerIn(fromVariableToIteratorMaker, variable, typeDescription, registry);
}
return fromVariableToIteratorMaker;
}
use of com.sri.ai.expresso.core.ExtensionalIndexExpressionsSet in project aic-expresso by aic-sri-international.
the class AbstractFunctionBasedGroup method makeProblemExpression.
@Override
public Expression makeProblemExpression(Expression index, Expression indexType, Expression constraint, Expression body) {
Expression indexExpression = makeIndexExpression(index, indexType);
IndexExpressionsSet indexExpressionsSet = new ExtensionalIndexExpressionsSet(indexExpression);
DefaultIntensionalMultiSet set = new DefaultIntensionalMultiSet(indexExpressionsSet, body, constraint);
Expression problem = apply(getFunctionString(), set);
return problem;
}
use of com.sri.ai.expresso.core.ExtensionalIndexExpressionsSet in project aic-expresso by aic-sri-international.
the class ExpressoAPIExamples method main.
public static void main(String[] args) {
// Symbols are expressions representing Java values, such as a string,
// a number, a boolean, and even any other objects (Expressions themselves will throw an error, though, to prevent common mistakes)
Expression a = DefaultSymbol.createSymbol("a");
Expression ten = DefaultSymbol.createSymbol(10);
Expression trueValue = DefaultSymbol.createSymbol(true);
Expression object = DefaultSymbol.createSymbol(Car.ferrari);
// Below, we use Util.println to avoid having to write System.out.println.
// Util has lots and lots and lots of very useful methods that eliminate boring Java chores.
// We definitely recommend studying it carefully!
// To easily write just "println" and have it work, write "println" and use Ctrl-1 to be offered the option
// of statically importing Util.println.
// You can statically import an identifier in Eclipse by placing the cursor on it and pressing Shift-Ctrl-M in Windows.
println("a : " + a);
println("ten : " + ten);
println("trueValue: " + trueValue);
println("object : " + object);
// It is easier to remember to make symbols using Expressions.makeSymbol:
// 'Expressions' is a class with lots of useful static methods for working with expressions.
// This of it as the counterpart of 'Util', but for expressions.
// Having many useful expression classes in a single place makes it easier to remember them and access them through code completion.
// As with 'Util', we often import its methods statically.
a = makeSymbol("a");
ten = makeSymbol(10);
trueValue = makeSymbol(true);
object = makeSymbol(Car.ferrari);
println("a : " + a);
println("ten : " + ten);
println("trueValue: " + trueValue);
println("object : " + object);
// The second most important type of expressions are function applications.
// They consist of a functor (an expression representing a function, typically a symbol) applied to zero or more arguments:
Expression f = makeSymbol("f");
Expression g = makeSymbol("g");
Expression fATen = new DefaultFunctionApplication(f, list(a, ten));
Expression gOnNothing = new DefaultFunctionApplication(g, list());
println("function f applied to a and ten: " + fATen);
println("function g applied to nothing: " + gOnNothing);
// It is much easier to use Expressions.apply:
fATen = apply(f, a, ten);
gOnNothing = apply(g);
println("function f applied to a and ten: " + fATen);
println("function g applied to nothing: " + gOnNothing);
// Naturally, function applications can be applied to any expression, including other function applications:
Expression gFATen = apply(g, apply(f, a, ten));
println("function g applied to function f applied to a and ten: " + gFATen);
// If we do not create symbols for Java values, apply does it automatically for us:
gFATen = apply("g", apply("f", "a", 10));
println("function g applied to function f applied to a and ten: " + gFATen);
// Some operators are output in special infix notation for readability:
// again not creating symbols first
Expression twoPlusTwoPlusThree = apply("+", 2, 2, 3);
println("two plus two plus three: " + twoPlusTwoPlusThree);
Expression arithmetic1 = apply("*", 2, apply("+", 2, 3));
Expression arithmetic2 = apply("+", 2, apply("*", 2, 3));
println("Arithmetic gets printed while respecting usual precedence rules by using parentheses: " + arithmetic1);
println("Arithmetic gets printed while respecting usual precedence rules by using parentheses: " + arithmetic2);
// Same for logic:
Expression logic1 = apply("and", "p", apply("or", "q", "r"));
Expression logic2 = apply("or", "p", apply("and", "q", "r"));
println("Same for logic: " + logic1);
println("Same for logic: " + logic2);
// It is not good practice to use separate strings for referring to the same operators.
// In the future, we may decide to change the string associated to an operator
// and have that string used in many places would make that hard to effect.
// FunctorConstants is a class with lots of static fields for operator strings:
arithmetic1 = apply(FunctorConstants.TIMES, 2, apply(FunctorConstants.PLUS, 2, 3));
logic1 = apply(FunctorConstants.AND, "p", apply(FunctorConstants.OR, "q", "r"));
// Functor constants can also be statically imported:
arithmetic1 = apply(TIMES, 2, apply(PLUS, 2, 3));
logic1 = apply(AND, "p", apply(OR, "q", "r"));
// We can access the functor and arguments of a function application:
println("The functor of " + gFATen + " is " + gFATen.getFunctor());
println("The second argument of " + fATen + " is " + fATen.get(1));
// returns a List<Expression>
println("All arguments of " + fATen + " are " + fATen.getArguments());
// We can also set new functors or arguments.
// IMPORTANT: expressions are IMMUTABLE, so this creates a new expression,
// although it does re-use the unchanged parts.
Expression newArgument = gFATen.set(0, a);
println("Changed first argument of " + gFATen + " to " + a + " and obtained " + newArgument);
println("Original expression continues the same, since they are immutable: " + gFATen);
// getFunctor returns a symbol, so to check if it is, for example, "f", we need
// to write expression.getFunctor().equals(makeSymbol("f"))
// which is too long.
// Instead, we can use 'hasFunctor'
println(fATen + " has functor \"f\": " + fATen.hasFunctor("f"));
// Finally, we can parse expressions for strings.
// BUT we should never use that to construct expressions if we have the sub-expressions already represented as Java objects.
// For example, don't do this: parse("f(" + a + ", " + b + ")");
// Instead, use apply("f", a, b);
ten = parse("10");
trueValue = parse("true");
fATen = parse("f(a,10)");
arithmetic1 = parse("2*(2 + 3)");
arithmetic2 = parse("2+(2 * 3)");
println(ten);
println(trueValue);
println(fATen);
println(arithmetic1);
println(arithmetic2);
// Another important type of expression is sets.
// There are two dimensions for sets: they can be uni- or multi-sets, and they can be extensionally or intensionally defined.
//
// A uni-set has at most one instance of each element in it. This is the typical mathematical set.
// A multi-set may have multiple instances of the same element in it.
// For example, the multi-set {1,2,2,3} is distinct from multi-set {1,2,2,2,3}.
// In Expresso, we use double-brackets for denoting multi-sets: {{ 1, 2, 2, 3 }}.
// {{ }} denotes the empty multi-set.
// The singleton uni-set with an empty set in it is denoted { {} }.
// You need a space between the brackets to avoid them being parsed as a double bracket.
//
// An extensionally defined set is an explicit enumeration of its elements: {1, 2, 3}, {{1, 2, 2, 3}}, {}, {{ }}.
// An intensionally defined set is defined by a condition: { (on I in Integer) I^2 : I > 3 and I <= 100 }, for example,
// which is equal to { 16, 25, 36, ..., 10000 }.
// The general form of an intensionally defined set (or, less precisely but more succinctly, an intensional set) is
// { (on Index1 in Index1Domain, Index2 in Index2Domain, ..., Index_n in Index_nDomain) Head : Condition }
// We can also have intensionally defined multi-sets using double brackets.
// Here are some ways of constructing sets:
a = makeSymbol("a");
Expression b = makeSymbol("b");
Expression c = makeSymbol("c");
Expression d = makeSymbol("d");
Expression extensionalUniSet = ExtensionalSets.makeUniSet(a, b, c, d);
Expression extensionalMultiSet = ExtensionalSets.makeMultiSet(a, b, c, d);
println(extensionalUniSet);
println(extensionalMultiSet);
// Creating an intensionally defined set programmatically (as opposed to parsing a string description of it)
// is a bit of work (this will be shown below).
// Here's an example of parsing one:
Expression intensionalUniSet = parse("{ ( on P in People, F in Foods ) eats(P, F) : not (P = Rodrigo and F = shrimp) }");
println(intensionalUniSet);
// Here's how to do it from scratch, but see next the way we typically actually do it.
Expression p = makeSymbol("P");
Expression people = makeSymbol("People");
f = makeSymbol("F");
Expression foods = makeSymbol("Foods");
IndexExpressionsSet indices = new ExtensionalIndexExpressionsSet(apply(IN, p, people), apply(IN, f, foods));
// The "extensional" in ExtensionalIndexExpressionsSet means that the list/set of indices is extensionally defined,
// even though they will be the indices of an intensionally defined set.
intensionalUniSet = // IntensionalSet.intensionalUniSet, or simply intensionalUniSet, also works
IntensionalSet.makeUniSet(indices, apply("eats", p, f), apply(NOT, apply(AND, Equality.make(p, "Rodrigo"), Equality.make(f, "shrimp"))));
// Note that Equality.make(p, "Rodrigo") is the same as apply(FunctorConstants.EQUAL, p, "Rodrigo").
// We often have 'make' methods for many operators: And.make, Or.make and so on.
// packages in com.sri.ai.expresso.grinder.sgdpllt.library have many such operator-specific classes.
println(intensionalUniSet);
// When writing code on sets, we typically are modifying an existing set expression, so we can re-use its parts,
// by using special part-replacement methods.
// This requires the variable to implement the IntensionalSet interface, though.
// IMPORTANT: expressions are IMMUTABLE, so setCondition and other part-replacement methods return a NEW expression,
// although the parts not replaced are re-used.
IntensionalSet intensionalSetCast = (IntensionalSet) intensionalUniSet;
Expression noCondition = intensionalSetCast.setCondition(makeSymbol(true));
println("Set with no condition: " + noCondition);
Expression headSaysLoveInsteadOfEats = intensionalSetCast.setHead(apply("loves", p, f));
println("Set with new head: " + headSaysLoveInsteadOfEats);
Expression withNewIndices = intensionalSetCast.setIndexExpressions(new ExtensionalIndexExpressionsSet(apply(IN, p, people), apply(IN, f, foods), apply(IN, "D", "Days")));
println("Set with new indices: " + withNewIndices);
// summations and products are just function applications of FunctorConstants.SUM and FunctorConstants.PRODUCT on intensional multi-sets.
// sum( {{ (on Indices) Head : Condition }} ) represents the summation (in Latex notation) sum_{Indices : Condition} Head
Expression summation = apply(SUM, intensionalSetCast);
println(summation);
Expression product = apply(PRODUCT, intensionalSetCast);
println(product);
///// Evaluating expressions
// The above code shows how to deal with the syntax of expressions.
// Evaluating expressions requires knowing about the semantics, that is, to what functions each operator corresponds to ("+" to addition, etc).
// This is provided by a theory, which for now it suffices to know is a collection of methods for evaluating expressions
// according to an interpretation to some symbols.
Theory theory = new CompoundTheory(new EqualityTheory(false, true), new DifferenceArithmeticTheory(false, false), new LinearRealArithmeticTheory(false, false), new TupleTheory(), new PropositionalTheory());
// Because this evaluation is symbolic, evaluated expressions may involve free variables.
// In this case, the result of the evaluation will be a simplified expression that
// is equivalent to the original expression for all possible assignments to the free variables.
// For example, X + 0*Y is evaluate to X because, for any assignment to (X,Y), X + 0*Y = X.
// true context: all assignments to free variables are of interest
Context context = new TrueContext(theory);
// We will later see how we can use contexts that restrict the free variable assignments of interest.
// Now that we have a theory and a context, we can evaluate expressions:
println("1 + 0*X + 1 = " + theory.evaluate(parse("1 + 1"), context));
evaluate(new String[] { "1 + 1", "2", "X + 1 + 1", "X + 2", "sum({{ (on I in 1..10) I }})", "55", "product({{ (on I in 1..5) 2 : I != 3 and I != 5 }})", "8" }, theory, context);
// now let us assume we have a free variable J which is an integer
// Contexts are, like expressions, also IMMUTABLE:
Context context2 = context.extendWithSymbolsAndTypes("J", "Integer");
// However, here we just want to use the same variable 'context' all along, so we keep the updated context in it:
context = context2;
// Because we store the reference to the modified context in the same variable, we lose the reference to the original one,
// but, if we wanted, we could keep contexts in a stack, for example,
// so that we could always easily revert back to a previous context if needed.
evaluate(new String[] { "X + 1 + 1 + J", "X + 2 + J", "sum({{ (on I in 1..10) I : I != J }})", "if J > 0 then if J <= 10 then -1 * J + 55 else 55 else 55" }, theory, context);
// now let us assume we have a free variable J which is an integer
// The context is also a boolean formula (a constraint)
// Current, its value is "true", but we can conjoin it with a literal J < 0
context = context.conjoin(parse("J < 0"));
evaluate(new String[] { "J < 1", "true", // J is irrelevant because it is out of the range of I
"sum({{ (on I in 1..1000) I : I != J }})", // J is irrelevant because it is out of the range of I
"500500" }, theory, context);
// we now add another symbol and constraint
context = context.extendWithSymbolsAndTypes("K", "Integer");
context = context.conjoin(parse("K > 0"));
evaluate(new String[] { "J < K", "true" }, theory, context);
// Obtaining all free variables in an expression.
// In order to obtain all free variables appearing in an expression
// (and therefore excluding quantified variables (for all X, there exists X) and set indices ({ (on Z in Real) Z }))
// we must traverse the expression and select its sub-expressions that are variables.
// However, we need to know what a variable is.
// It is not enough to say that any symbol is a variable, because "1" and "true" are symbols, but not variables.
// It is not enough to say that any symbols that is an identifier (starting with an alphabet letter) is a variable,
// because we may have uniquely named constants such as "john" and "bob" that are not to be treated as variables
// (we want "john = bob" to be evaluated to "false", and if they were variable, this would not happen.
// The way Expresso deals with this question is by letting the user define a predicate in the context that
// encoded what a uniquely named constant is, and considering any other symbol to be considered a variable.
// By default, Expresso follows the Prolog convention of capitalized variables: X is a variable, x is not.
// Note how this takes "Real" to be a variable!
context = new TrueContext();
Expression expression = parse("X + f(g(x, Y, 1, true, false, 10, bob, john, there exists Z in Real : 10, { (on W in Real) 1 } ))");
Set<Expression> variablesInExpression = Expressions.freeVariables(expression, context);
// outputs [X, Y]
println("variables in " + expression + " by Prolog standard: " + variablesInExpression);
// More recently, we have adopted the practice of not caring about capitalization.
// This means that we may, for example, defined uniquely named constants to be any symbols that are not in a given set of variables.
Set<Expression> allVariables = set(parse("x"), parse("X"), parse("Y"), parse("Z"), parse("W"));
context = context.setIsUniquelyNamedConstantPredicate(new UniquelyNamedConstantAreAllSymbolsNotIn(allVariables));
variablesInExpression = Expressions.freeVariables(expression, context);
println("variables in " + expression + " if all variables is " + allVariables + ": " + // outputs [x, X, Y]
variablesInExpression);
// Sometimes, it is useful to replace subexpressions in a given expression by another subexpression:
expression = parse("f(f(f(X))) + X");
Expression valueOfX = parse("10");
Expression replacementOfFirstOccurrenceOnly = expression.replaceFirstOccurrence(parse("X"), valueOfX, context);
println("Replacing only the first occurrence of X by its value gives " + replacementOfFirstOccurrenceOnly);
Expression replacementOfAllOccurrences = expression.replaceAllOccurrences(parse("X"), valueOfX, context);
println("Replacing all occurrences of X by its value gives " + replacementOfAllOccurrences);
// There are a LOT of variants of these functions in Expression (not Expressions),
// including some very flexible ones that allow the user to provide a function for determining the replacement.
// BUG: need to debug
// Here's how to decide if a point is in the convex hull of other two points:
Context convexityContext = context.extendWithSymbolsAndTypes("p", "Real", "p1", "Real", "p2", "Real");
//convexityContext = convexityContext.conjoin(parse("p = 4"));
//convexityContext = convexityContext.conjoin(parse("p1 = 3"));
//convexityContext = convexityContext.conjoin(parse("p2 = 5"));
Expression isInConvexHull = parse("there exists c1 in Real : there exists c2 in Real : " + "0 <= c1 and c1 <= 1 and 0 <= c2 and c2 <= 1 and 4 = c1*3 + c2*5");
Expression result = theory.evaluate(isInConvexHull, convexityContext);
println("4 is in the convex hull of 3 and 5: " + result);
}
use of com.sri.ai.expresso.core.ExtensionalIndexExpressionsSet in project aic-expresso by aic-sri-international.
the class Context method extendWith.
/**
* Extends context with index expressions, taking into account that new contextual variables may collide with existing ones.
* In this case, it renames the incoming variables to unique identifiers and replaces them in the types of remaining
* index expressions. It also renames the variables in a given expressions supposed to be in their scope (for example,
* the head and condition of an intensionally defined set).
* Returns the new context and the index expressions and expression in scope after the renaming.
* @param indexExpressions
* @param expressionInScope
* @return the new context and the index expressions and expression in scope after the renaming
*/
default default Triple<Context, ExtensionalIndexExpressionsSet, Expression> extendWith(ExtensionalIndexExpressionsSet indexExpressions, Expression expressionInScope) {
Triple<Context, ExtensionalIndexExpressionsSet, Expression> result;
if (thereExists(getIndices(indexExpressions), index -> this.containsSymbol(index))) {
// OPTIMIZATION: only kick in this entire procedure when extending with symbol in the context (previous ones could have been dealt with normally).
// the objects to be returned in the triple:
Context newContext = this;
ArrayList<Expression> newIndexExpressionsList = new ArrayList<>(indexExpressions.getList());
Expression newExpressionInScope = expressionInScope;
// Collects all existing symbols to be able to create unique symbols
Set<Expression> alreadyDefined = Util.set();
alreadyDefined.addAll(this.getSymbols());
alreadyDefined.addAll(Expressions.freeSymbols(new DefaultTuple(newIndexExpressionsList), this));
alreadyDefined.addAll(Expressions.freeSymbols(expressionInScope, this));
Predicate<Expression> isAlreadyDefined = e -> alreadyDefined.contains(e);
for (int i = 0; i != newIndexExpressionsList.size(); i++) {
Expression indexExpression = newIndexExpressionsList.get(i);
Symbol index = (Symbol) indexExpression.get(0);
Expression type = indexExpression.get(1);
PairOf<Expression> newIndexAndNewExpressionInScope = Expressions.standardizeApart(index, isAlreadyDefined, newExpressionInScope);
Expression newIndex = newIndexAndNewExpressionInScope.first;
newExpressionInScope = newIndexAndNewExpressionInScope.second;
// type should not contain the index
Expression newIndexExpression = apply(IN, newIndex, type);
newIndexExpressionsList.set(i, newIndexExpression);
alreadyDefined.add(newIndex);
for (int j = i + 1; j != newIndexExpressionsList.size(); j++) {
Expression anotherIndexExpression = newIndexExpressionsList.get(j);
Expression anotherIndex = anotherIndexExpression.get(0);
Expression anotherType = anotherIndexExpression.get(1);
Expression newAnotherType = anotherType.replaceSymbol(index, newIndex, this);
// anotherIndex is a symbols and does not contain index
Expression newAnotherIndexExpression = apply(IN, anotherIndex, newAnotherType);
newIndexExpressionsList.set(j, newAnotherIndexExpression);
}
}
ExtensionalIndexExpressionsSet newIndexExpressions = new ExtensionalIndexExpressionsSet(newIndexExpressionsList);
newContext = newContext.extendWith(newIndexExpressions);
result = triple(newContext, newIndexExpressions, newExpressionInScope);
} else {
// no collision; usual extension and the expressions do not change.
result = triple(extendWith(indexExpressions), indexExpressions, expressionInScope);
}
return result;
}
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