From: Thomas Walker Lynch <eknp9n@reasoningtechnology.com>
Date: Thu, 9 Jan 2025 10:44:03 +0000 (+0000)
Subject: moving to use of Object and inheritance to add more specific type, instead of Java... 
X-Git-Url: https://git.reasoningtechnology.com/style/static/git-favicon.png?a=commitdiff_plain;h=c56db095c5abf78a8ff52a8724a96c8e3f3fbacd;p=Ariadne

moving to use of Object and inheritance to add more specific type, instead of Java Generics
---

diff --git a/developer/example/Example_CountingNumber_0 b/developer/example/Example_CountingNumber_0
deleted file mode 100755
index 03434e8..0000000
--- a/developer/example/Example_CountingNumber_0
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_CountingNumber_0
diff --git a/developer/example/Example_CountingNumber_0.class b/developer/example/Example_CountingNumber_0.class
deleted file mode 100644
index 37c012a..0000000
Binary files a/developer/example/Example_CountingNumber_0.class and /dev/null differ
diff --git a/developer/example/Example_IndexTree_4x4 b/developer/example/Example_IndexTree_4x4
deleted file mode 100755
index 66b84a4..0000000
--- a/developer/example/Example_IndexTree_4x4
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_IndexTree_4x4
diff --git a/developer/example/Example_IndexTree_4x4.class b/developer/example/Example_IndexTree_4x4.class
deleted file mode 100644
index fc79e76..0000000
Binary files a/developer/example/Example_IndexTree_4x4.class and /dev/null differ
diff --git a/developer/example/Example_IndexTree_4x4.java b/developer/example/Example_IndexTree_4x4.java
index 79a00af..5f766bd 100644
--- a/developer/example/Example_IndexTree_4x4.java
+++ b/developer/example/Example_IndexTree_4x4.java
@@ -1,46 +1,46 @@
-
 import com.ReasoningTechnology.Ariadne.Ariadne_SRM;
 import com.ReasoningTechnology.Ariadne.Ariadne_SRM_List;
 import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Child_SRM;
 import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Graph;
 import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Node;
 
-import java.math.BigInteger;
-
 public class Example_IndexTree_4x4{
 
   public static void main(String[] args){
 
-    Ariadne_IndexTree_Graph graph = new Ariadne_IndexTree_Graph();
-    Ariadne_SRM<BigInteger[]> root = graph.start();
+    System.out.println("Example_IndexTree_4x4");
+
+    // Initialize graph and start at root
+    Ariadne_IndexTree_Graph graph = Ariadne_IndexTree_Graph.make();
+    Ariadne_IndexTree_Child_SRM root = graph.start();
 
-    BigInteger  label[];
+    System.out.println("root: " + root.read().toString());
+
+    // Variables for traversal
+    Ariadne_IndexTree_Label label = root.read();
     Ariadne_IndexTree_Node node;
-    Ariadne_SRM<BigInteger[]> child_srm;
+    Ariadne_SRM<Ariadne_IndexTree_Label> child_srm;
 
-    // descend 3 more levels
-    label = root.read();
-    System.out.println(label);
+    // Descend 3 more levels
     int i = 1;
     do{
       node = graph.lookup(label);
       child_srm = node.neighbor();
       label = child_srm.read();
-      System.out.println(label);
+      System.out.println("Descend: " + label.toString());
       if(i == 3) break;
       i++;
     }while(true);
-       
-    // move across three more nodes
+
+    // Move across three more nodes
     i = 1;
     do{
       child_srm.step();
       label = child_srm.read();
-      System.out.println(label);
+      System.out.println("Across: " + label.toString());
       if(i == 3) break;
       i++;
     }while(true);
 
   }
 }
-
diff --git a/developer/example/Example_IndexTree_Diagonal_SRM b/developer/example/Example_IndexTree_Diagonal_SRM
deleted file mode 100755
index 5b45c16..0000000
--- a/developer/example/Example_IndexTree_Diagonal_SRM
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_IndexTree_Diagonal_SRM
diff --git a/developer/example/Example_IndexTree_Diagonal_SRM.class b/developer/example/Example_IndexTree_Diagonal_SRM.class
deleted file mode 100644
index 7f9b08e..0000000
Binary files a/developer/example/Example_IndexTree_Diagonal_SRM.class and /dev/null differ
diff --git a/developer/example/Example_SRMI_Array b/developer/example/Example_SRMI_Array
deleted file mode 100755
index 80c5dbd..0000000
--- a/developer/example/Example_SRMI_Array
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_SRMI_Array
diff --git a/developer/example/Example_SRMI_Array.class b/developer/example/Example_SRMI_Array.class
deleted file mode 100644
index c99942c..0000000
Binary files a/developer/example/Example_SRMI_Array.class and /dev/null differ
diff --git a/developer/example/Example_SRM_List b/developer/example/Example_SRM_List
deleted file mode 100755
index e0d48dd..0000000
--- a/developer/example/Example_SRM_List
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_SRM_List
diff --git a/developer/example/Example_SRM_List.class b/developer/example/Example_SRM_List.class
deleted file mode 100644
index 5c8b1bc..0000000
Binary files a/developer/example/Example_SRM_List.class and /dev/null differ
diff --git a/developer/example/IndexTree_Diagonal_SRM.java b/developer/example/IndexTree_Diagonal_SRM.java
index a9a653b..4daa8b3 100644
--- a/developer/example/IndexTree_Diagonal_SRM.java
+++ b/developer/example/IndexTree_Diagonal_SRM.java
@@ -1,3 +1,14 @@
+/*
+An index Tree is infinite.
+
+A tree diagonal consists of
+a) a node descending from each child discovered thus far
+b> a node extending each child list discovered thus far.
+
+Hence, each diagonal extends the tree down one, and over one.
+
+*/
+
 import java.math.BigInteger;
 import java.util.ArrayList;
 import java.util.List;
@@ -5,33 +16,68 @@ import com.ReasoningTechnology.Ariadne.Ariadne_Test;
 import com.ReasoningTechnology.Ariadne.Ariadne_SRM;
 import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Node;
 
-public class IndexTree_Diagonal_SRM extends Ariadne_SRM<List<BigInteger[]>>{
+public class IndexTree_Diagonal_SRM extends Ariadne_SRM_Label>{
+
+  // Static
+  //
+
+  public static IndexTree_Diagonal_SRM make(){
+    return new IndexTree_Diagonal_SRM();
+  }
 
-  // Instance data
-  private final List<BigInteger[]> list_of__unopened_node;
-  private final List<List<BigInteger[]>> list_of__opened_incomplete_child_list;
-  private final List<BigInteger[]> read_list;
+  //Instance data
+  //
+
+  private final List<Ariadne_Label> list_of__unopened_node;
+  // each node has a child list,  this is a list of child lists
+  private final List<List<Ariadne_IndexTree_Label>> list_of__opened_incomplete_child_list;
+  // Each diagonal is a list of nodes, referenced by their label
+  private final List<Ariadne_Label> read_list;
+
+  // Constructor(s)
+  //
 
-  // Constructor
   protected IndexTree_Diagonal_SRM(){
-    this.list_of__unopened_node = new ArrayList<>();
-    this.list_of__opened_incomplete_child_list = new ArrayList<>();
-    this.read_list = new ArrayList<>();
+    list_of__unopened_node = new ArrayList<>();
+    list_of__opened_incomplete_child_list = new ArrayList<>();
+    read_list = new ArrayList<>();
     enqueue_root();
   }
 
-  // Static factory method
-  public static IndexTree_Diagonal_SRM make(){
-    return new IndexTree_Diagonal_SRM();
+  // Implementation of instance interface.
+  //
+
+  private void enqueue_root(){
+    Ariadne_IndexTree_Label root_label = Ariadne_IndexTree_Label.root();
+    read_list.add(root_label);
+
+    Ariadne_IndexTree_Node root_node = lookup(root_label);
+    if( !fetch_child_labels(root_node).isEmpty() ){
+      list_of__unopened_node.add(root_label);
+    }
   }
 
-  @Override
-  public List<BigInteger[]> read(){
+  // lol! This can not be done on an infinite list!
+  private List<BigInteger[]> fetch_child_labels(Ariadne_IndexTree_Node node){
+    List<BigInteger[]> child_labels = new ArrayList<>();
+    if(node != null){
+      IndexTree_Diagonal_SRM child_srm = node.neighbor();
+      if( child_srm.can_read() ){
+        do{
+          child_labels.add(child_srm.read());
+          if( !srm.can_step ) break;
+          child_srm.step();
+        }while(true);
+      }
+    }
+    return child_labels;
+  }
+
+  @Override public List<BigInteger[]> read(){
     return read_list;
   }
 
-  @Override
-  public void step(){
+  @Override public void step(){
     read_list.clear();
 
     // Process unopened nodes
@@ -64,32 +110,9 @@ public class IndexTree_Diagonal_SRM extends Ariadne_SRM<List<BigInteger[]>>{
     }
   }
 
-  private void enqueue_root(){
-    BigInteger[] root_label = new BigInteger[0];
-    read_list.add(root_label);
-
-    Ariadne_IndexTree_Node root_node = lookup(root_label);
-    if( !fetch_child_labels(root_node).isEmpty() ){
-      list_of__unopened_node.add(root_label);
-    }
-  }
-
   private Ariadne_IndexTree_Node lookup(BigInteger[] label){
     // Perform a lookup to retrieve the node corresponding to the label
     return Ariadne_IndexTree_Node.make(label);
   }
 
-  private List<BigInteger[]> fetch_child_labels(Ariadne_IndexTree_Node node){
-    List<BigInteger[]> child_labels = new ArrayList<>();
-
-    if(node != null){
-      Ariadne_SRM<BigInteger[]> neighbor_srm = node.neighbor();
-      while( neighbor_srm.can_step() ){
-        child_labels.add(neighbor_srm.read());
-        neighbor_srm.step();
-      }
-    }
-
-    return child_labels;
-  }
 }
diff --git a/developer/example/hold/CountingNumber.java b/developer/example/hold/CountingNumber.java
deleted file mode 100644
index f4f41cf..0000000
--- a/developer/example/hold/CountingNumber.java
+++ /dev/null
@@ -1,79 +0,0 @@
-import com.ReasoningTechnology.Ariadne.Ariadne_SRM;
-import com.ReasoningTechnology.Ariadne.Ariadne_Test;
-import java.math.BigInteger;
-
-public class CountingNumber extends Ariadne_SRM<BigInteger> {
-
-  private static final Ariadne_Test test = Ariadne_Test.make( "Ariadne_SRM<BigInteger>::" );
-
-  public static CountingNumber make(){
-    return new CountingNumber( null );
-  }
-
-  public static CountingNumber make( BigInteger maximum ){
-    return new CountingNumber( maximum );
-  }
-
-  private final Topology _topology;
-  private BigInteger i;
-  private BigInteger maximum;
-  private Location location;
-  private Runnable step_behavior;
-
-  protected CountingNumber( BigInteger maximum ){
-    this.maximum = maximum;
-    this.i = BigInteger.ONE;
-    this.location = Location.LEFTMOST;
-
-    if( maximum == null ){
-      _topology = Topology.INFINITE_RIGHT;
-      step_behavior = this::step_infinite_right;
-    } else {
-      _topology = Topology.SEGMENT;
-      step_behavior = this::step_segment;
-    }
-
-    test.print( "CountingNumber initialized with topology: " + _topology + ", initial value: " + i );
-  }
-
-  @Override
-  public Topology topology(){
-    return _topology;
-  }
-
-  @Override
-  public Location location(){
-    return location;
-  }
-
-  @Override
-  public BigInteger read(){
-    return i;
-  }
-
-  @Override
-  public void step(){
-    step_behavior.run();
-  }
-
-  private void step_segment(){
-    i = i.add( BigInteger.ONE );
-    if( i.equals( maximum ) ){
-      location = Location.RIGHTMOST;
-      step_behavior = this::step_from_rightmost;
-    }else if( location == Location.LEFTMOST ){
-      location = Location.INTERIM;
-    }
-    test.print( " after step_segment, new read() value: " + i );
-  }
-
-  private void step_infinite_right(){
-    i = i.add( BigInteger.ONE );
-    test.print( " after step_infinite_right, new read() value: " + i );
-  }
-
-  private void step_from_rightmost(){
-    throw new UnsupportedOperationException( "CountingNumber::step can not step from RIGHTMOST." );
-  }
-
-}
diff --git a/developer/example/hold/Example_IndexTree_0 b/developer/example/hold/Example_IndexTree_0
deleted file mode 100755
index f6eac3c..0000000
--- a/developer/example/hold/Example_IndexTree_0
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_IndexTree_0
diff --git a/developer/example/hold/Example_IndexTree_0.java b/developer/example/hold/Example_IndexTree_0.java
deleted file mode 100644
index 296b499..0000000
--- a/developer/example/hold/Example_IndexTree_0.java
+++ /dev/null
@@ -1,53 +0,0 @@
-import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Child_SRM;
-import com.ReasoningTechnology.Ariadne.Ariadne_IndexTree_Node;
-import java.math.BigInteger;
-
-public class Example_IndexTree_0{
-
-  public static void traverse_index_tree(){
-    System.out.println("Starting Index Tree Traversal:");
-
-    Ariadne_IndexTree_Node root_node = Ariadne_IndexTree_Node.make(new BigInteger[0]);
-    System.out.println("Root Node: " + format_label(root_node.label()));
-
-    Ariadne_IndexTree_Node current_node = root_node;
-    int depth_count = 0;
-    do{
-      Ariadne_IndexTree_Child_SRM depth_srm = current_node.neighbor();
-      BigInteger[] depth_label = depth_srm.read();
-      System.out.println("Step " + (depth_count + 1) + " Down: " + format_label(depth_label));
-      current_node = Ariadne_IndexTree_Node.make(depth_label);
-
-      // precise loop termination
-      if(depth_count == 3) break; 
-      depth_count++;
-    }while(true);
-
-    Ariadne_IndexTree_Child_SRM child_srm = current_node.neighbor();
-    int child_count = 0;
-    do{
-      BigInteger[] child_label = child_srm.read();
-      System.out.println("Step " + (child_count + 1) + " Across: " + format_label(child_label));
-
-      // precise loop termination
-      if(child_count == 3) break; // Mid-loop test for inclusive bound
-      child_count++;
-      child_srm.step();
-    }while(true);
-  }
-
-  private static String format_label(BigInteger[] label){
-    if(label.length == 0) return "[]";
-    StringBuilder formatted = new StringBuilder("[");
-    for(int i = 0 ;i < label.length ;i++){
-      formatted.append(label[i].toString());
-      if(i < label.length - 1) formatted.append(" ,");
-    }
-    formatted.append("]");
-    return formatted.toString();
-  }
-
-  public static void main(String[] args){
-    traverse_index_tree();
-  }
-}
diff --git a/developer/example/hold/Example_IndexTree_Diagonal_SRM b/developer/example/hold/Example_IndexTree_Diagonal_SRM
deleted file mode 100755
index 5b45c16..0000000
--- a/developer/example/hold/Example_IndexTree_Diagonal_SRM
+++ /dev/null
@@ -1,2 +0,0 @@
-#!/bin/bash
-java Example_IndexTree_Diagonal_SRM
diff --git "a/developer/javac\360\237\226\211/Ariadne_Graph.java" "b/developer/javac\360\237\226\211/Ariadne_Graph.java"
index 51cbfd2..769eeda 100644
--- "a/developer/javac\360\237\226\211/Ariadne_Graph.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_Graph.java"
@@ -1,5 +1,5 @@
 /*
-  User defines a graph by implementing this interface.  For the build tool, the defined
+  User defines a graph by implementing this interface. For the build tool, the defined
   graph is dynamically loaded.
 
   Generally labels are returned and passed around. Only `lookup` returns a Node.
@@ -10,12 +10,10 @@
 
 package com.ReasoningTechnology.Ariadne;
 
-public interface Ariadne_Graph<TLabel> {
+public interface Ariadne_Graph {
 
-  // returns list of TLabel
-  Ariadne_SRM<TLabel> start();
+  Ariadne_SRM start();
 
-  // lookup a Node by label
-  Ariadne_Node<TLabel> lookup(TLabel label);
+  Ariadne_Node lookup(Ariadne_Label label);
 
 }
diff --git "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Child_SRM.java" "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Child_SRM.java"
index 6dbec47..bbe68e8 100644
--- "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Child_SRM.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Child_SRM.java"
@@ -1,47 +1,81 @@
 package com.ReasoningTechnology.Ariadne;
 
-import java.math.BigInteger;
+public class Ariadne_IndexTree_Child_SRM extends Ariadne_SRM_Label {
 
-public class Ariadne_IndexTree_Child_SRM extends Ariadne_SRMI<BigInteger[]>{
-
-  // Static
-  public static Ariadne_IndexTree_Child_SRM make(BigInteger[] initial_label){
-    return new Ariadne_IndexTree_Child_SRM( initial_label );
+  public static Ariadne_IndexTree_Child_SRM make( Ariadne_IndexTree_Label first_child_label ){
+    return new Ariadne_IndexTree_Child_SRM( first_child_label );
   }
 
-  // Instance data
-  private BigInteger[] label;
+  private final Ariadne_IndexTree_Label label;
+
+  protected Ariadne_IndexTree_Child_SRM( Ariadne_IndexTree_Label first_child_label ){
+    this.label = first_child_label.copy();
 
-  // Constructor
-  protected Ariadne_IndexTree_Child_SRM(BigInteger[] initial_label){
-    super();
+    if( label == null ){
+      set_topology( topo_null );
+      return;
+    }
 
-    if( initial_label == null || initial_label.length == 0 ){
-      throw new IllegalArgumentException( "Initial label must not be null or empty." );
+    if( label.isEmpty() ){
+      set_topology( topo_rightmost );
+      return;
     }
 
-    this.label = initial_label;
     set_topology( topo_infinite_right );
   }
 
-  // Infinite right topology
-  private final TopoIface<BigInteger[]> topo_infinite_right = new TopoIface<BigInteger[]>(){
+  private final TopoIface topo_null = new TopoIface(){
+    @Override public boolean can_read(){
+      return false;
+    }
+    @Override public Object read(){
+      throw new UnsupportedOperationException( "Cannot read from NULL topology." );
+    }
+    @Override public boolean can_step(){
+      return false;
+    }
+    @Override public void step(){
+      throw new UnsupportedOperationException( "Cannot step from NULL topology." );
+    }
+    @Override public Topology topology(){
+      return Topology.NULL;
+    }
+  };
+
+  private final TopoIface topo_infinite_right = new TopoIface(){
     @Override public boolean can_read(){
       return true;
     }
-    @Override public BigInteger[] read(){
+    @Override public Object read(){
       return label;
     }
     @Override public boolean can_step(){
       return true;
     }
     @Override public void step(){
-      increment();
-      label[label.length - 1] = index();
+      label.inc_across();
     }
     @Override public Topology topology(){
       return Topology.INFINITE;
     }
   };
-}
 
+  private final TopoIface topo_rightmost = new TopoIface(){
+    @Override public boolean can_read(){
+      return true;
+    }
+    @Override public Object read(){
+      return label;
+    }
+    @Override public boolean can_step(){
+      return false;
+    }
+    @Override public void step(){
+      throw new UnsupportedOperationException( "Cannot step from RIGHTMOST topology." );
+    }
+    @Override public Topology topology(){
+      return Topology.RIGHTMOST;
+    }
+  };
+
+}
diff --git "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Graph.java" "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Graph.java"
index 5924bb4..034d604 100644
--- "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Graph.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Graph.java"
@@ -1,16 +1,19 @@
 package com.ReasoningTechnology.Ariadne;
 
-import java.math.BigInteger;
+public class Ariadne_IndexTree_Graph{
 
-public class Ariadne_IndexTree_Graph implements Ariadne_Graph<BigInteger[]>{
+  public static Ariadne_IndexTree_Graph make(){
+    return new Ariadne_IndexTree_Graph();
+  }
+  protected Ariadne_IndexTree_Graph(){
+  }
 
-  @Override
   public Ariadne_IndexTree_Child_SRM start(){
-    return Ariadne_IndexTree_Child_SRM.make(new BigInteger[0]);
+    Ariadne_IndexTree_Label root_label = Ariadne_IndexTree_Label.root();
+    return Ariadne_IndexTree_Child_SRM.make(root_label);
   }
 
-  @Override
-  public Ariadne_IndexTree_Node lookup(BigInteger[] label){
+  Ariadne_IndexTree_Node lookup(Ariadne_IndexTree_Label label){
     return Ariadne_IndexTree_Node.make(label);
   }
 
diff --git "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Label.java" "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Label.java"
new file mode 100644
index 0000000..8abb146
--- /dev/null
+++ "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Label.java"
@@ -0,0 +1,81 @@
+/*
+  Implementation of Ariadne_Label for BigInteger array-based labels.
+*/
+
+package com.ReasoningTechnology.Ariadne;
+
+import java.math.BigInteger;
+import java.util.Arrays;
+
+public class Ariadne_IndexTree_Label implements Ariadne_Label{
+
+  // Owned by class
+  //
+
+  public static Ariadne_IndexTree_Label make(BigInteger[] array){
+    return new Ariadne_IndexTree_Label(array);
+  }
+
+  public static Ariadne_IndexTree_Label root(){
+    return new Ariadne_IndexTree_Label(new BigInteger[0]);
+  }
+
+  // Instance data
+  //
+
+  private BigInteger[] value;
+
+  // Constructor
+  //
+
+  private Ariadne_IndexTree_Label(BigInteger[] array){
+    this.value = array.clone();
+  }
+
+  // Instance interface implementation
+  //
+
+  @Override public boolean isEmpty(){
+    return value == null;
+  }
+
+  @Override public String toString(){
+    return Arrays.toString(value);
+  }
+
+  @Override public Ariadne_IndexTree_Label copy(){
+    return new Ariadne_IndexTree_Label(value);
+  }
+
+  // Increment last element by one, modifying in place
+  public void inc_across(){
+    if(value == null || value.length == 0){
+      throw new UnsupportedOperationException("Cannot increment across an empty array.");
+    }
+    value[value.length - 1] = value[value.length - 1].add(BigInteger.ONE);
+  }
+
+  // Append a zero element, modifying in place
+  public void inc_down(){
+    if(value == null){
+      throw new UnsupportedOperationException("Cannot append to a null array.");
+    }
+    BigInteger[] newValue = Arrays.copyOf(value, value.length + 1);
+    newValue[newValue.length - 1] = BigInteger.ZERO;
+    value = newValue;
+  }
+
+  // Good object citizenship
+  //
+  
+  @Override public boolean equals(Object o){
+    if(this == o) return true;
+    if( o == null || getClass() != o.getClass() ) return false;
+    Ariadne_IndexTree_Label that = (Ariadne_IndexTree_Label) o;
+    return Arrays.equals(value, that.value);
+  }
+
+  @Override public int hashCode(){
+    return Arrays.hashCode(value);
+  }
+}
diff --git "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Node.java" "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Node.java"
index ceb1739..314ab6b 100644
--- "a/developer/javac\360\237\226\211/Ariadne_IndexTree_Node.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_IndexTree_Node.java"
@@ -1,33 +1,23 @@
 package com.ReasoningTechnology.Ariadne;
-
-import java.math.BigInteger;
 import java.util.Arrays;
 
-public class Ariadne_IndexTree_Node extends Ariadne_Node<BigInteger[]>{
+public class Ariadne_IndexTree_Node extends Ariadne_Node{
 
-  public static Ariadne_IndexTree_Node make(BigInteger[] label){
+  public static Ariadne_IndexTree_Node make(Ariadne_IndexTree_Label label){
     return new Ariadne_IndexTree_Node(label);
   }
 
-  private final BigInteger[] first_child_label;
+  private final Ariadne_IndexTree_Label first_child_label;
  
-  public Ariadne_IndexTree_Node(BigInteger[] label){
+  public Ariadne_IndexTree_Node(Ariadne_IndexTree_Label label){
     super(label);
-    this.first_child_label = new BigInteger[label.length + 1];
-    System.arraycopy(label, 0, this.first_child_label, 0, label.length);
-    this.first_child_label[label.length] = BigInteger.ZERO;
+    first_child_label = label.copy();
+    first_child_label.inc_down();
   }
 
-  @Override
+  //  public Ariadne_IndexTree_Child_SRM neighbor(){
   public Ariadne_IndexTree_Child_SRM neighbor(){
     return Ariadne_IndexTree_Child_SRM.make(first_child_label);
   }
 
-  @Override
-  public String toString(){
-    return 
-      "<" 
-      + String.join("," ,Arrays.stream(label()).map(BigInteger::toString).toArray(String[]::new)) 
-      + ">";
-  }
 }
diff --git "a/developer/javac\360\237\226\211/Ariadne_Label.java" "b/developer/javac\360\237\226\211/Ariadne_Label.java"
index c97f0a3..a4bb823 100644
--- "a/developer/javac\360\237\226\211/Ariadne_Label.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_Label.java"
@@ -1,54 +1,10 @@
-package com.ReasoningTechnology.Ariadne;
-
-
 
 /*
-  A value for the node.label property.
-
-  This is a wrapper for a String. We can't instead use an alias by extending
-  String, because String is a JavaScript 'final' type.
-
+  Base interface for labels used in the Ariadne library.
 */
-public class Ariadne_Label{
-
-  // owned by class
-
-
-  // data owned by instance
-
-    private final String value;
-
-  // constructors
-
-
-  private Ariadne_Label(String s){
-    this.value = s;
-  }
-
-  Ariadne_Label make(String s){
-    return  new Ariadne_Label(s);
-  }
-
-  public boolean isEmpty(){
-    return value.isEmpty();
-  }
-
-  @Override
-  public String toString(){
-    return value;
-  }
-
-  @Override
-  public boolean equals(Object o){
-    if(this == o) return true;
-    if( o == null || getClass() != o.getClass() ) return false;
-    Ariadne_Label label = (Ariadne_Label)o;
-    return value.equals( label.value );
-  }
-
-  @Override
-  public int hashCode(){
-    return value.hashCode();
-  }
-
+package com.ReasoningTechnology.Ariadne;
+public interface Ariadne_Label {
+  boolean isEmpty();
+  Ariadne_Label copy();
+  @Override String toString();
 }
diff --git "a/developer/javac\360\237\226\211/Ariadne_Label_String.java" "b/developer/javac\360\237\226\211/Ariadne_Label_String.java"
new file mode 100644
index 0000000..2212b94
--- /dev/null
+++ "b/developer/javac\360\237\226\211/Ariadne_Label_String.java"
@@ -0,0 +1,45 @@
+/*
+  Implementation of Ariadne_Label for string-based labels.
+*/
+package com.ReasoningTechnology.Ariadne;
+
+public class Ariadne_Label_String implements Ariadne_Label {
+
+  // Owned by class
+  public static Ariadne_Label_String make(String s) {
+    return new Ariadne_Label_String(s);
+  }
+
+  // Instance data
+  private final String value;
+
+  // Constructor
+  private Ariadne_Label_String(String s) {
+    this.value = s;
+  }
+
+  // Instance interface implementation
+  @Override public boolean isEmpty() {
+    return value.isEmpty();
+  }
+
+  @Override public String toString() {
+    return value;
+  }
+
+  @Override public Ariadne_Label copy() {
+    return new Ariadne_Label_String(value);
+  }
+
+  // Good object citizenship
+  @Override public boolean equals(Object o) {
+    if (this == o) return true;
+    if (o == null || getClass() != o.getClass()) return false;
+    Ariadne_Label_String that = (Ariadne_Label_String) o;
+    return value.equals(that.value);
+  }
+
+  @Override public int hashCode() {
+    return value.hashCode();
+  }
+}
diff --git "a/developer/javac\360\237\226\211/Ariadne_Node.java" "b/developer/javac\360\237\226\211/Ariadne_Node.java"
index f3a05dd..732b0a7 100644
--- "a/developer/javac\360\237\226\211/Ariadne_Node.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_Node.java"
@@ -31,52 +31,77 @@ package com.ReasoningTechnology.Ariadne;
 import java.util.HashMap;
 import java.util.HashSet;
 
-public class Ariadne_Node<TLabel> extends HashMap<String, Object>{
+public class Ariadne_Node extends HashMap<String, Object>{
 
   // Owned by the class
-  public static <TLabel> Ariadne_Node<TLabel> make(TLabel label){
-    return new Ariadne_Node<>(label);
+  public static Ariadne_Node make(Ariadne_Label label){
+    return new Ariadne_Node(label);
   }
 
   // Data owned by the instance
-  private final TLabel label;
-  private final HashSet<Ariadne_Token> markSet;
+  private final Ariadne_Label label;
+  private final HashSet<Ariadne_Token> mark_set;
   private static final String NEIGHBOR_PROPERTY_NAME = "neighbor_property";
 
   // Constructors
-  protected Ariadne_Node(TLabel label){
-    super();
+  protected Ariadne_Node(Ariadne_Label label){
     this.label = label;
-    this.markSet = new HashSet<>();
+    this.mark_set = new HashSet<>();
   }
 
   // Instance interface
-  public TLabel label(){
+  public Ariadne_Label label(){
     return this.label;
   }
 
-  public Ariadne_SRM<TLabel> neighbor(){
-    throw new UnsupportedOperationException("Neighbor is not implemented in the base class.");
+  public Ariadne_SRM_Label neighbor(){
+    throw new UnsupportedOperationException("Ariadne_Node::neighbor not implemented in the base class.");
   }
 
   public void mark(Ariadne_Token token){
-    markSet.add(token);
+    mark_set.add(token);
   }
 
   public boolean hasMark(Ariadne_Token token){
-    return markSet.contains(token);
+    return mark_set.contains(token);
   }
 
   public void removeMark(Ariadne_Token token){
-    markSet.remove(token);
+    mark_set.remove(token);
   }
 
+
   // Object interface
-  @Override
-  public String toString(){
-    return "Ariadne_Node{"
-           + "label=" + label
-           + " ,markSet=" + markSet
-           + "}";
+  @Override public String toString(){
+    StringBuilder output = new StringBuilder();
+
+    // Node representation
+    if( label == null ){
+      output.append( "Node()" );
+    }else{
+      output
+        .append( "Node(" )
+        .append( label.toString() )
+        .append( ")" )
+        ;
+    }
+
+    // Marks representation
+    if( !mark_set.isEmpty() ){
+      Ariadne_SRM_Set srm = Ariadne_SRM_Set.make(mark_set);
+      output.append( " Mark(" );
+
+      do{
+        output.append( srm.read().toString() );
+        if( !srm.can_step() ) break;
+        output.append( ", " );
+        srm.step();
+      }while(true);
+
+      output.append( ")" );
+    }
+
+    return output.toString();
   }
+
 }
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRM.java" "b/developer/javac\360\237\226\211/Ariadne_SRM.java"
index b5cbd5a..462c9df 100644
--- "a/developer/javac\360\237\226\211/Ariadne_SRM.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_SRM.java"
@@ -8,7 +8,10 @@
 */
 package com.ReasoningTechnology.Ariadne;
 
-public class Ariadne_SRM<T>{
+public class Ariadne_SRM{
+
+  // static
+  //
 
   public enum Topology{
     NULL
@@ -16,18 +19,23 @@ public class Ariadne_SRM<T>{
     ,SEGMENT
     ,RIGHTMOST
     ,INFINITE
-    ;
   }
 
-  public static <TElement> Ariadne_SRM<TElement> make(){
-    return new Ariadne_SRM<>();
+  public static make(){
+    return new Ariadne_SRM
   }
 
-  protected TopoIface<T> current_topology;
-  public final TopoIface<T> not_mounted = new NotMounted();
+  // instance data
+  //
+
+  protected TopoIface current_topology;
+  public final TopoIface not_mounted = new NotMounted();
+
+  // constructor(s)
+  //
 
   protected Ariadne_SRM(){
-    set_topology(not_mounted);
+    set_topology( not_mounted );
   }
 
   public boolean is_mounted(){
@@ -36,54 +44,59 @@ public class Ariadne_SRM<T>{
       && current_topology != not_mounted;
   }
 
-  // Interface for interacting with a tape.
-  protected interface TopoIface<T>{
+  // Implementation of instance interface.
+
+  protected interface TopoIface{
     boolean can_read();
-    T read();
+    Object read();
     boolean can_step();
     void step();
     Topology topology();
   }
 
-  // Initially the tape has not been mounted so it can not be interacted with.
-  protected class NotMounted implements TopoIface<T>{
-    public boolean can_read(){
+  // Initially, the tape has not been mounted.
+  protected class NotMounted implements TopoIface{
+    @Override public boolean can_read(){
       return false;
     }
-    public T read(){
+    @Override public Object read(){
       throw new UnsupportedOperationException("Ariadne_SRM::NotMounted::read.");
     }
-    public boolean can_step(){
+    @Override public boolean can_step(){
       return false;
     }
-    public void step(){
+    @Override public void step(){
       throw new UnsupportedOperationException("Ariadne_SRM::NotMounted::step.");
     }
-    public Topology topology(){
+    @Override public Topology topology(){
       throw new UnsupportedOperationException("Ariadne_SRM::NotMounted::topology.");
     }
   }
 
-  // sets the tape access methods to be used
-  protected void set_topology(TopoIface<T> new_topology){
+  // Sets the tape access methods to be used.
+  protected void set_topology(TopoIface new_topology){
     current_topology = new_topology;
   }
 
   public boolean can_read(){
     return current_topology.can_read();
   }
-  public T read(){
+
+  public Object read(){
     return current_topology.read();
   }
+
   public boolean can_step(){
     return current_topology.can_step();
   }
+
   public void step(){
     current_topology.step();
   }
+
   public Topology topology(){
     return current_topology.topology();
   }
 
 }
- 
+
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRMI.java" "b/developer/javac\360\237\226\211/Ariadne_SRMI.java"
index ffecd86..4bb120a 100644
--- "a/developer/javac\360\237\226\211/Ariadne_SRMI.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_SRMI.java"
@@ -6,7 +6,7 @@ Ariadne_SRM with index
 package com.ReasoningTechnology.Ariadne;
 import java.math.BigInteger;
 
-public abstract class Ariadne_SRMI<T> extends Ariadne_SRM<T>{
+public abstract class Ariadne_SRMI extends Ariadne_SRM{
 
   private BigInteger current_index;
 
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRMI_Array.java" "b/developer/javac\360\237\226\211/Ariadne_SRMI_Array.java"
index a0c75c3..9027594 100644
--- "a/developer/javac\360\237\226\211/Ariadne_SRMI_Array.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_SRMI_Array.java"
@@ -3,22 +3,22 @@ package com.ReasoningTechnology.Ariadne;
 import java.math.BigInteger;
 import java.util.List;
 
-public class Ariadne_SRMI_Array<T> extends Ariadne_SRMI<T>{
+public class Ariadne_SRMI_Array extends Ariadne_SRMI{
 
   // Static methods
-  public static <T> Ariadne_SRMI_Array<T> make(List<T> array){
-    return new Ariadne_SRMI_Array<>( array );
+  public static  Ariadne_SRMI_Array make(List array){
+    return new Ariadne_SRMI_Array( array );
   }
 
   // Instance data
-  private final List<T> array;
+  private final List array;
 
-  private final TopoIface<T> topo_null = new TopoNull();
-  private final TopoIface<T> topo_segment = new TopoSegment();
-  private final TopoIface<T> topo_rightmost = new TopoRightmost();
+  private final TopoIface topo_null = new TopoNull();
+  private final TopoIface topo_segment = new TopoSegment();
+  private final TopoIface topo_rightmost = new TopoRightmost();
 
   // Constructor
-  protected Ariadne_SRMI_Array(List<T> array){
+  protected Ariadne_SRMI_Array(List array){
     super();
     this.array = array;
 
@@ -36,13 +36,13 @@ public class Ariadne_SRMI_Array<T> extends Ariadne_SRMI<T>{
   }
 
   // TopoNull
-  private class TopoNull implements TopoIface<T>{
+  private class TopoNull implements TopoIface{
     @Override
     public boolean can_read(){
       return false;
     }
     @Override
-    public T read(){
+    public Object read(){
       throw new UnsupportedOperationException( "Cannot read from NULL topo." );
     }
     @Override
@@ -60,13 +60,13 @@ public class Ariadne_SRMI_Array<T> extends Ariadne_SRMI<T>{
   }
 
   // TopoSegment
-  private class TopoSegment implements TopoIface<T>{
+  private class TopoSegment implements TopoIface{
     @Override
     public boolean can_read(){
       return true;
     }
     @Override
-    public T read(){
+    public Object read(){
       return array.get( index().intValueExact() );
     }
     @Override
@@ -86,13 +86,13 @@ public class Ariadne_SRMI_Array<T> extends Ariadne_SRMI<T>{
   }
 
   // TopoRightmost
-  private class TopoRightmost implements TopoIface<T>{
+  private class TopoRightmost implements TopoIface{
     @Override
     public boolean can_read(){
       return true;
     }
     @Override
-    public T read(){
+    public Object read(){
       return array.get( index().intValueExact() );
     }
     @Override
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRM_Label.java" "b/developer/javac\360\237\226\211/Ariadne_SRM_Label.java"
new file mode 100644
index 0000000..b69e3e1
--- /dev/null
+++ "b/developer/javac\360\237\226\211/Ariadne_SRM_Label.java"
@@ -0,0 +1,13 @@
+package com.ReasoningTechnology.Ariadne;
+
+public class Ariadne_SRM_Label extends Ariadne_SRM {
+
+  public static Ariadne_SRM_Label make(){
+    return new Ariadne_SRM_Label();
+  }
+
+  @Override public Ariadne_Label read(){
+    return (Ariadne_Label)super.read();
+  }
+
+}
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRM_List.java" "b/developer/javac\360\237\226\211/Ariadne_SRM_List.java"
index 061b3ca..2974af5 100644
--- "a/developer/javac\360\237\226\211/Ariadne_SRM_List.java"
+++ "b/developer/javac\360\237\226\211/Ariadne_SRM_List.java"
@@ -8,22 +8,22 @@ package com.ReasoningTechnology.Ariadne;
 import java.util.List;
 import java.util.ListIterator;
 
-public class Ariadne_SRM_List<T> extends Ariadne_SRM<T>{
+public class Ariadne_SRM_List extends Ariadne_SRM{
 
   // Static methods
-  public static <T> Ariadne_SRM_List<T> make(List<T> list){
-    return new Ariadne_SRM_List<>(list);
+  public static  Ariadne_SRM_List make(List list){
+    return new Ariadne_SRM_List(list);
   }
 
-  private List<T> list;  // The attached linked list
-  private ListIterator<T> iterator;  // Iterator for traversal
-  private T read_value;  // Stores the current cell value
+  private List list;  // The attached linked list
+  private ListIterator iterator;  // Iterator for traversal
+  private Object read_value;  // Stores the current cell value
 
-  private final TopoIface<T> topo_null = new TopoNull();
-  private final TopoIface<T> topo_segment = new TopoSegment();
-  private final TopoIface<T> topo_rightmost = new TopoRightmost();
+  private final TopoIface topo_null = new TopoNull();
+  private final TopoIface topo_segment = new TopoSegment();
+  private final TopoIface topo_rightmost = new TopoRightmost();
 
-  protected Ariadne_SRM_List(List<T> list){
+  protected Ariadne_SRM_List(List list){
     this.list = list;
 
     if( list == null || list.isEmpty() ){
@@ -43,11 +43,11 @@ public class Ariadne_SRM_List<T> extends Ariadne_SRM<T>{
     set_topology(topo_segment);
   }
 
-  private class TopoNull implements TopoIface<T>{
+  private class TopoNull implements TopoIface{
     @Override public boolean can_read(){
       return false;
     }
-    @Override public T read(){
+    @Override public Object read(){
       throw new UnsupportedOperationException( "Cannot read from NULL topo." );
     }
     @Override public boolean can_step(){
@@ -61,11 +61,11 @@ public class Ariadne_SRM_List<T> extends Ariadne_SRM<T>{
     }
   }
 
-  private class TopoSegment implements TopoIface<T>{
+  private class TopoSegment implements TopoIface{
     @Override public boolean can_read(){
       return true;
     }
-    @Override public T read(){
+    @Override public Object read(){
       return read_value;
     }
     @Override public boolean can_step(){
@@ -80,11 +80,11 @@ public class Ariadne_SRM_List<T> extends Ariadne_SRM<T>{
     }
   }
 
-  private class TopoRightmost implements TopoIface<T>{
+  private class TopoRightmost implements TopoIface{
     @Override public boolean can_read(){
       return true;
     }
-    @Override public T read(){
+    @Override public Object read(){
       return read_value;
     }
     @Override public boolean can_step(){
diff --git "a/developer/javac\360\237\226\211/Ariadne_SRM_Set.java" "b/developer/javac\360\237\226\211/Ariadne_SRM_Set.java"
new file mode 100644
index 0000000..8ec5ad0
--- /dev/null
+++ "b/developer/javac\360\237\226\211/Ariadne_SRM_Set.java"
@@ -0,0 +1,18 @@
+package com.ReasoningTechnology.Ariadne;
+
+import java.util.ArrayList;
+import java.util.Set;
+
+public class Ariadne_SRM_Set extends Ariadne_SRMI_Array{
+
+  // Static factory method
+  public static  Ariadne_SRM_Set make(Set set){
+    return new Ariadne_SRM_Set( set );
+  }
+
+  // Constructor
+  protected Ariadne_SRM_Set(Set set){
+    super( new ArrayList(set) );
+  }
+
+}