Adding Automatic Inference Reasoners

Beside the input sequent, reasoners of this type does not have any extra input and automatically applies an inference rule to the input sequent. As an example, consider the following inference rule (called IMP_R).

$\frac{H, P \vdash Q}{H \vdash P \limp Q}$

IMP_R

Declare the Reasoner

• Create a new plug-in project, e.g. org.eventb.contributors.seqprover.implinference. Deselect the plug-in options for "Generating an activator" and "Contribution to the UI".

• Add dependency on the project org.eventb.core.seqprover

• Add an extension for org.eventb.core.seqprover.reasoners for our implication rewrite reasoner, e.g.

<extension point="org.eventb.core.seqprover.reasoners">
  <reasoner
    class="org.eventb.internal.contributors.seqprover.implinference.AutoInference"
    id="autoInference"
    name="%autoInferenceName"/>
</extension>

(add the key autoInferenceName to the plugin.properties accordingly).

• We will use Tom to implement the reasoner class itself.

Implement the Reasoner

The following steps is for implementing the reasoner using Tom.

• Create a package within the src folder of the project with the name org.eventb.internal.contributors.seqprover.implinference.

• Create a Tom file within the newly created package with the name AutoInference.t.

• The content of the Tom file looks like this.

package org.eventb.internal.contributors.seqprover.implinference;

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import java.util.Set;
import java.util.HashSet;

import org.eventb.core.ast.AssociativeExpression;
import org.eventb.core.ast.AssociativePredicate;
import org.eventb.core.ast.AtomicExpression;
import org.eventb.core.ast.BinaryExpression;
import org.eventb.core.ast.BinaryPredicate;
import org.eventb.core.ast.BoolExpression;
import org.eventb.core.ast.BoundIdentDecl;
import org.eventb.core.ast.BoundIdentifier;
import org.eventb.core.ast.DefaultFilter;
import org.eventb.core.ast.Expression;
import org.eventb.core.ast.Formula;
import org.eventb.core.ast.FormulaFactory;
import org.eventb.core.ast.FreeIdentifier;
import org.eventb.core.ast.Identifier;
import org.eventb.core.ast.IntegerLiteral;
import org.eventb.core.ast.IPosition;
import org.eventb.core.ast.LiteralPredicate;
import org.eventb.core.ast.PowerSetType;
import org.eventb.core.ast.Predicate;
import org.eventb.core.ast.ProductType;
import org.eventb.core.ast.QuantifiedExpression;
import org.eventb.core.ast.QuantifiedPredicate;
import org.eventb.core.ast.RelationalPredicate;
import org.eventb.core.ast.SetExtension;
import org.eventb.core.ast.SimplePredicate;
import org.eventb.core.ast.Type;
import org.eventb.core.ast.UnaryExpression;
import org.eventb.core.ast.UnaryPredicate;
import org.eventb.core.seqprover.eventbExtensions.Tactics;
import org.eventb.core.seqprover.IProverSequent;
import org.eventb.core.seqprover.IHypAction;
import org.eventb.core.seqprover.ProverFactory;
import org.eventb.core.seqprover.SequentProver;
import org.eventb.core.seqprover.IProofRule.IAntecedent;
import org.eventb.core.seqprover.eventbExtensions.Lib;
import org.eventb.core.seqprover.eventbExtensions.Tactics;
import org.eventb.internal.core.seqprover.eventbExtensions.AbstractAutoInference;

/**
 * Basic implementation for "automatic implication inference"
 */
@SuppressWarnings("unused")
public class AutoInference extends AbstractAutoInference {

  %include {Formula.tom}
	
  public String getReasonerID() {
    return "org.eventb.contributors.seqprover.implinference.autoInference";
  }
	
  @Override
  protected String getDisplayName() {
    return "Automatic deduction";
  }

  @Override
  protected IAntecedent[] getAntecedents(IProverSequent seq) {
    Predicate goal = seq.goal();
	
    Predicate P = null;
    Predicate Q = null;
    %match (Predicate goal) {

      /**
       * Deduction: 
       *           H, P |- Q
       *         -----------
       *          H |- P => Q
       */
      Limp(PP, QQ) -> {
        P = `PP;
        Q = `QQ;
      }

    }

    if (P == null)
      return null;
	
    // There will be 1 antecidents
    IAntecedent[] antecidents = new IAntecedent[1];

    // Added hypothesis P
    Set<Predicate> addedHyps = new HashSet<Predicate>(1);
    addedHyps.add(P);
    // Select the new hypothesis P
    IHypAction hypAction = ProverFactory.makeSelectHypAction(addedHyps);
    antecidents[0] = ProverFactory.makeAntecedent(Q, addedHyps, hypAction);

    return antecidents;
  }
	
}

• The implementation is based on org.eventb.internal.core.seqprover.eventbExtensions.AbstractAutoInference. (For the moment, the class is internal within the project and subjected to be changed. Clients can make a copy of this class to develop their own implementation).

• Clients need to implement first the two methods to return the reasoner id, getReasonerID(), and return the display name, getDisplayName().

• Moreover, clients need to implement the method for getting the actual antecedents getAntecedents(IProverSequent seq)
  • The input of the method is the sequent.
  • The method return the list of antecedents to implement the inference rule.
  • Tom is used here to do pattern matching. In our case, match the goal with $P \limp Q$.
  • Methods for construct hypothesis actions, antecedent, etc. can be found in class org.eventb.core.seqprover.ProverFactory.

Setting up Tom

• Create a file named build-tom.xml within your project. The content of the file looks like this.

<project name="org.eventb.contributors.seqprover.implrewrites" default="tom" basedir=".">
  <description>
    Generates derived files in the Sequent Prover.
  </description>

  <property name="src" location="src" />

  <property name="org.eventb.core.ast.home" location="../org.eventb.core.ast" />
  <import file="${org.eventb.core.ast.home}/tom/tom-task.xml"/>

  <property name="inference.src"
      location="${src}/org/eventb/internal/contributors/seqprover/implinference" />

  <target name="init" description="Create the initial time stamp">
    <tstamp />
  </target>

  <target name="tom" depends="init"
      description="Launch tom for all files">
    <tom config="${tom.home}/Tom.xml"
        srcdir="${src}"
        destdir="${src}"
        options="-I ${org.eventb.core.ast.home}/tom --static"
        pretty="true"
        optimize="true">
      <include name="**/*.t" />
    </tom>
  </target>
	
  <target name="clean" description="clean up">
    <delete file="${inference.src}/AutoInference.java" />
  </target>
	
</project>