Merge branch 'master' into no-null

Add variables implemented via Tree Value Operators.

core/src/main/java/org/nwapw/abacus/Abacus.java

@@ -1,135 +0,0 @@
-package org.nwapw.abacus;
-
-import org.nwapw.abacus.config.Configuration;
-import org.nwapw.abacus.number.NumberInterface;
-import org.nwapw.abacus.parsing.LexerTokenizer;
-import org.nwapw.abacus.parsing.ShuntingYardParser;
-import org.nwapw.abacus.parsing.TreeBuilder;
-import org.nwapw.abacus.plugin.NumberImplementation;
-import org.nwapw.abacus.plugin.PluginManager;
-import org.nwapw.abacus.plugin.StandardPlugin;
-import org.nwapw.abacus.tree.NumberReducer;
-import org.nwapw.abacus.tree.TreeNode;
-
-/**
- * The main calculator class. This is responsible
- * for piecing together all of the components, allowing
- * their interaction with each other.
- */
-public class Abacus {
-
-    /**
-     * The default number implementation to be used if no other one is available / selected.
-     */
-    public static final NumberImplementation DEFAULT_IMPLEMENTATION = StandardPlugin.IMPLEMENTATION_NAIVE;
-
-    /**
-     * The plugin manager responsible for
-     * loading and unloading plugins,
-     * and getting functions from them.
-     */
-    private PluginManager pluginManager;
-    /**
-     * The reducer used to evaluate the tree.
-     */
-    private NumberReducer numberReducer;
-    /**
-     * The configuration loaded from a file.
-     */
-    private Configuration configuration;
-    /**
-     * The tree builder used to construct a tree
-     * from a string.
-     */
-    private TreeBuilder treeBuilder;
-
-    /**
-     * Creates a new instance of the Abacus calculator.
-     *
-     * @param configuration the configuration object for this Abacus instance.
-     */
-    public Abacus(Configuration configuration) {
-        pluginManager = new PluginManager(this);
-        numberReducer = new NumberReducer(this);
-        this.configuration = new Configuration(configuration);
-        LexerTokenizer lexerTokenizer = new LexerTokenizer();
-        ShuntingYardParser shuntingYardParser = new ShuntingYardParser();
-        treeBuilder = new TreeBuilder<>(lexerTokenizer, shuntingYardParser);
-
-        pluginManager.addListener(shuntingYardParser);
-        pluginManager.addListener(lexerTokenizer);
-    }
-
-    /**
-     * Gets the current tree builder.
-     *
-     * @return the main tree builder in this abacus instance.
-     */
-    public TreeBuilder getTreeBuilder() {
-        return treeBuilder;
-    }
-
-    /**
-     * Gets the current plugin manager,
-     *
-     * @return the plugin manager in this abacus instance.
-     */
-    public PluginManager getPluginManager() {
-        return pluginManager;
-    }
-
-    /**
-     * Get the reducer that is responsible for transforming
-     * an expression into a number.
-     *
-     * @return the number reducer in this abacus instance.
-     */
-    public NumberReducer getNumberReducer() {
-        return numberReducer;
-    }
-
-    /**
-     * Gets the configuration object associated with this instance.
-     *
-     * @return the configuration object.
-     */
-    public Configuration getConfiguration() {
-        return configuration;
-    }
-
-    /**
-     * Parses a string into a tree structure using the main
-     * tree builder.
-     *
-     * @param input the input string to parse
-     * @return the resulting tree, null if the tree builder or the produced tree are null.
-     */
-    public TreeNode parseString(String input) {
-        return treeBuilder.fromString(input);
-    }
-
-    /**
-     * Evaluates the given tree using the main
-     * number reducer.
-     *
-     * @param tree the tree to reduce, must not be null.
-     * @return the resulting number, or null of the reduction failed.
-     */
-    public NumberInterface evaluateTree(TreeNode tree) {
-        return tree.reduce(numberReducer);
-    }
-
-    /**
-     * Creates a number from a string.
-     *
-     * @param numberString the string to create the number from.
-     * @return the resulting number.
-     */
-    public NumberInterface numberFromString(String numberString) {
-        NumberImplementation toInstantiate =
-                pluginManager.numberImplementationFor(configuration.getNumberImplementation());
-        if (toInstantiate == null) toInstantiate = DEFAULT_IMPLEMENTATION;
-
-        return toInstantiate.instanceForString(numberString);
-    }
-}

core/src/main/java/org/nwapw/abacus/function/DomainException.java

@@ -0,0 +1,24 @@
+package org.nwapw.abacus.function;
+
+/**
+ * Exception thrown if the function parameters do not match
+ * requirements.
+ */
+public class DomainException extends RuntimeException {
+
+    /**
+     * Creates a new DomainException.
+     * @param reason the reason for which the exception is thrown.
+     */
+    public DomainException(String reason) {
+        super(reason);
+    }
+
+    /**
+     * Creates a new DomainException with a default message.
+     */
+    public DomainException(){
+        this("Domain Error");
+    }
+
+}

core/src/main/java/org/nwapw/abacus/number/NaiveNumber.java

@@ -114,15 +114,6 @@ public class NaiveNumber extends NumberInterface {
         return (int) value;
     }
 
-    @Override
-    public NumberInterface promoteToInternal(Class<? extends NumberInterface> toClass) {
-        if (toClass == this.getClass()) return this;
-        else if (toClass == PreciseNumber.class) {
-            return new PreciseNumber(Double.toString(value));
-        }
-        return null;
-    }
-
     public String toString() {
         double shiftBy = Math.pow(10, 10);
         return Double.toString(Math.round(value * shiftBy) / shiftBy);

core/src/main/java/org/nwapw/abacus/number/NumberInterface.java

@@ -236,29 +236,6 @@ public abstract class NumberInterface {
      */
     public abstract int intValue();
 
-    /**
-     * Promotes this class to another number class.
-     *
-     * @param toClass the class to promote to.
-     * @return the resulting new instance.
-     */
-    @Deprecated
-    protected abstract NumberInterface promoteToInternal(Class<? extends NumberInterface> toClass);
-
-    /**
-     * Promotes this class to another number class. Also, checks if the
-     * thread has been interrupted, and if so, throws
-     * an exception.
-     *
-     * @param toClass the class to promote to.
-     * @return the resulting new instance.
-     */
-    @Deprecated
-    public final NumberInterface promoteTo(Class<? extends NumberInterface> toClass) {
-        checkInterrupted();
-        return promoteToInternal(toClass);
-    }
-
     /**
      * Returns the smallest error this instance can tolerate depending
      * on its precision and value.

core/src/main/java/org/nwapw/abacus/number/PreciseNumber.java

@@ -152,14 +152,6 @@ public class PreciseNumber extends NumberInterface {
         return new PreciseNumber(value.negate());
     }
 
-    @Override
-    public NumberInterface promoteToInternal(Class<? extends NumberInterface> toClass) {
-        if (toClass == this.getClass()) {
-            return this;
-        }
-        return null;
-    }
-
     @Override
     public String toString() {
         return value.round(outputContext).toString();

core/src/main/java/org/nwapw/abacus/parsing/LexerTokenizer.java

@@ -50,13 +50,13 @@ public class LexerTokenizer implements Tokenizer<Match<TokenType>>, PluginListen
         for (String operator : manager.getAllOperators()) {
             lexer.register(Pattern.sanitize(operator), TokenType.OP);
         }
-        for (String operator : manager.getAllTreeValueOperators()){
+        for (String operator : manager.getAllTreeValueOperators()) {
             lexer.register(Pattern.sanitize(operator), TokenType.TREE_VALUE_OP);
         }
         for (String function : manager.getAllFunctions()) {
             lexer.register(Pattern.sanitize(function), TokenType.FUNCTION);
         }
-        for (String function : manager.getAllTreeValueFunctions()){
+        for (String function : manager.getAllTreeValueFunctions()) {
             lexer.register(Pattern.sanitize(function), TokenType.TREE_VALUE_FUNCTION);
         }
     }
@@ -66,13 +66,13 @@ public class LexerTokenizer implements Tokenizer<Match<TokenType>>, PluginListen
         for (String operator : manager.getAllOperators()) {
             lexer.unregister(Pattern.sanitize(operator), TokenType.OP);
         }
-        for (String operator : manager.getAllTreeValueOperators()){
+        for (String operator : manager.getAllTreeValueOperators()) {
             lexer.unregister(Pattern.sanitize(operator), TokenType.TREE_VALUE_OP);
         }
         for (String function : manager.getAllFunctions()) {
             lexer.unregister(Pattern.sanitize(function), TokenType.FUNCTION);
         }
-        for (String function : manager.getAllTreeValueFunctions()){
+        for (String function : manager.getAllTreeValueFunctions()) {
             lexer.unregister(Pattern.sanitize(function), TokenType.TREE_VALUE_FUNCTION);
         }
     }

core/src/main/java/org/nwapw/abacus/parsing/ShuntingYardParser.java

@@ -134,7 +134,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
                 TreeNode right = constructRecursive(matches);
                 TreeNode left = constructRecursive(matches);
                 if (left == null || right == null) return null;
-                if(matchType == TokenType.OP) {
+                if (matchType == TokenType.OP) {
                     return new NumberBinaryNode(operator, left, right);
                 } else {
                     return new TreeValueBinaryNode(operator, left, right);
@@ -142,7 +142,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             } else {
                 TreeNode applyTo = constructRecursive(matches);
                 if (applyTo == null) return null;
-                if(matchType == TokenType.OP){
+                if (matchType == TokenType.OP) {
                     return new NumberUnaryNode(operator, applyTo);
                 } else {
                     return new TreeValueUnaryNode(operator, applyTo);
@@ -155,7 +155,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
         } else if (matchType == TokenType.FUNCTION || matchType == TokenType.TREE_VALUE_FUNCTION) {
             String functionName = match.getContent();
             CallNode node;
-            if(matchType == TokenType.FUNCTION){
+            if (matchType == TokenType.FUNCTION) {
                 node = new FunctionNode(functionName);
             } else {
                 node = new TreeValueFunctionNode(functionName);

core/src/main/java/org/nwapw/abacus/plugin/NumberImplementation.java

@@ -14,7 +14,7 @@ public abstract class NumberImplementation {
     /**
      * The list of paths through which this implementation can be promoted.
      */
-    private Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> promotionPaths;
+    private Map<String, Function<NumberInterface, NumberInterface>> promotionPaths;
     /**
      * The implementation class for this implementation.
      */
@@ -41,7 +41,7 @@ public abstract class NumberImplementation {
      *
      * @return the map of documentation paths.
      */
-    public final Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> getPromotionPaths() {
+    public final Map<String, Function<NumberInterface, NumberInterface>> getPromotionPaths() {
         return promotionPaths;
     }
 

core/src/main/java/org/nwapw/abacus/plugin/Plugin.java

@@ -2,6 +2,7 @@ package org.nwapw.abacus.plugin;
 
 import org.nwapw.abacus.function.*;
 import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.variables.VariableDatabase;
 
 /**
  * A plugin class that can be externally implemented and loaded via the
@@ -219,4 +220,12 @@ public abstract class Plugin {
      */
     public abstract void onDisable();
 
+    /**
+     * Get the variable database.
+     * @return the variable database.
+     */
+    public final VariableDatabase getVariableDatabase(){
+        return manager.getVariableDatabase();
+    }
+
 }

core/src/main/java/org/nwapw/abacus/plugin/PluginManager.java

@@ -3,6 +3,7 @@ package org.nwapw.abacus.plugin;
 import org.nwapw.abacus.Abacus;
 import org.nwapw.abacus.function.*;
 import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.variables.VariableDatabase;
 
 import java.lang.reflect.InvocationTargetException;
 import java.util.HashMap;
@@ -49,10 +50,13 @@ public class PluginManager {
      */
     private Set<Documentation> registeredDocumentation;
     /**
-     * The list of number implementations that have been
-     * found by their implementation class.
+     * The list of number implementation names.
      */
-    private Map<Class<? extends NumberInterface>, NumberImplementation> cachedInterfaceImplementations;
+    private Map<Class<? extends NumberInterface>, String> interfaceImplementationNames;
+    /**
+     * The list of number implementations.
+     */
+    private Map<Class<? extends NumberInterface>, NumberImplementation> interfaceImplementations;
     /**
      * The pi values for each implementation class that have already been computer.
      */
@@ -82,7 +86,8 @@ public class PluginManager {
         registeredTreeValueOperators = new HashMap<>();
         registeredNumberImplementations = new HashMap<>();
         registeredDocumentation = new HashSet<>();
-        cachedInterfaceImplementations = new HashMap<>();
+        interfaceImplementations = new HashMap<>();
+        interfaceImplementationNames = new HashMap<>();
         cachedPi = new HashMap<>();
         listeners = new HashSet<>();
     }
@@ -135,6 +140,8 @@ public class PluginManager {
      */
     public void registerNumberImplementation(String name, NumberImplementation implementation) {
         registeredNumberImplementations.put(name, implementation);
+        interfaceImplementationNames.put(implementation.getImplementation(), name);
+        interfaceImplementations.put(implementation.getImplementation(), implementation);
     }
 
     /**
@@ -226,17 +233,17 @@ public class PluginManager {
      * @return the implementation.
      */
     public NumberImplementation interfaceImplementationFor(Class<? extends NumberInterface> name) {
-        if (cachedInterfaceImplementations.containsKey(name)) return cachedInterfaceImplementations.get(name);
-        NumberImplementation toReturn = null;
-        for (String key : registeredNumberImplementations.keySet()) {
-            NumberImplementation implementation = registeredNumberImplementations.get(key);
-            if (implementation.getImplementation() == name) {
-                toReturn = implementation;
-                break;
-            }
-        }
-        cachedInterfaceImplementations.put(name, toReturn);
-        return toReturn;
+        return interfaceImplementations.get(name);
+    }
+
+    /**
+     * Gets the number implementation name for the given implementation class.
+     *
+     * @param name the class for which to find the implementation name.
+     * @return the implementation name.
+     */
+    public String interfaceImplementationNameFor(Class<? extends NumberInterface> name) {
+        return interfaceImplementationNames.get(name);
     }
 
     /**
@@ -329,7 +336,8 @@ public class PluginManager {
         registeredTreeValueOperators.clear();
         registeredNumberImplementations.clear();
         registeredDocumentation.clear();
-        cachedInterfaceImplementations.clear();
+        interfaceImplementationNames.clear();
+        interfaceImplementations.clear();
         cachedPi.clear();
         listeners.forEach(e -> e.onUnload(this));
     }
@@ -414,4 +422,12 @@ public class PluginManager {
     public Set<Class<?>> getLoadedPluginClasses() {
         return loadedPluginClasses;
     }
+
+    /**
+     * Gets the variable database.
+     * @return the database.
+     */
+    public VariableDatabase getVariableDatabase(){
+        return abacus.getVariableDatabase();
+    }
 }

core/src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java

@@ -1,13 +1,17 @@
 package org.nwapw.abacus.plugin;
 
+import org.jetbrains.annotations.NotNull;
+import org.jetbrains.annotations.Nullable;
 import org.nwapw.abacus.function.*;
 import org.nwapw.abacus.number.NaiveNumber;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.number.PreciseNumber;
+import org.nwapw.abacus.tree.Reducer;
+import org.nwapw.abacus.tree.TreeNode;
+import org.nwapw.abacus.tree.VariableNode;
 
 import java.util.ArrayList;
 import java.util.HashMap;
-import java.util.function.BiFunction;
 
 /**
  * The plugin providing standard functions such as addition and subtraction to
@@ -15,17 +19,51 @@ import java.util.function.BiFunction;
  */
 public class StandardPlugin extends Plugin {
 
+    /**
+     * The set operator.
+     */
+    public final TreeValueOperator opSet = new TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+        @Override
+        public boolean matchesParams(NumberImplementation implementation, TreeNode[] params) {
+            return params.length == 2 && params[0] instanceof VariableNode;
+        }
+
+        @Override
+        public NumberInterface applyWithReducerInternal(NumberImplementation implementation, Reducer<? extends NumberInterface> reducer, TreeNode[] params) {
+            String assignTo = ((VariableNode) params[0]).getVariable();
+            NumberInterface value = params[1].reduce(reducer);
+            getVariableDatabase().getVariables().put(assignTo, value);
+            return value;
+        }
+    };
+    /**
+     * The define operator.
+     */
+    public final TreeValueOperator opDefine = new TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+        @Override
+        public boolean matchesParams(NumberImplementation implementation, TreeNode[] params) {
+            return params.length == 2 && params[0] instanceof VariableNode;
+        }
+
+        @Nullable
+        @Override
+        public NumberInterface applyWithReducerInternal(NumberImplementation implementation, Reducer<? extends NumberInterface> reducer, TreeNode[] params) {
+            String assignTo = ((VariableNode) params[0]).getVariable();
+            getVariableDatabase().getDefinitions().put(assignTo, params[1]);
+            return params[1].reduce(reducer);
+        }
+    };
     /**
      * The addition operator, +
      */
     public static final NumberOperator OP_ADD = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].add(params[1]);
         }
     };
@@ -34,12 +72,12 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberOperator OP_SUBTRACT = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].subtract(params[1]);
 
         }
@@ -49,12 +87,12 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberOperator OP_NEGATE = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.UNARY_PREFIX, 0) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].negate();
         }
     };
@@ -63,12 +101,12 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberOperator OP_MULTIPLY = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].multiply(params[1]);
         }
     };
@@ -86,20 +124,6 @@ public class StandardPlugin extends Plugin {
             return new NaiveNumber(Math.PI);
         }
     };
-    /**
-     * The square root function.
-     */
-    public static final NumberFunction FUNCTION_SQRT = new NumberFunction() {
-        @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1;
-        }
-
-        @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return OP_CARET.apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
-        }
-    };
     /**
      * The implementation for the infinite-precision BigDecimal.
      */
@@ -111,7 +135,7 @@ public class StandardPlugin extends Plugin {
 
         @Override
         public NumberInterface instanceForPi() {
-            NumberInterface C = FUNCTION_SQRT.apply(new PreciseNumber("10005")).multiply(new PreciseNumber("426880"));
+            NumberInterface C = FUNCTION_SQRT.apply(this, new PreciseNumber("10005")).multiply(new PreciseNumber("426880"));
             NumberInterface M = PreciseNumber.ONE;
             NumberInterface L = new PreciseNumber("13591409");
             NumberInterface X = M;
@@ -136,21 +160,17 @@ public class StandardPlugin extends Plugin {
             return C.divide(sum);
         }
     };
-    /**
-     * Stores objects of NumberInterface with integer values for reuse.
-     */
-    private final static HashMap<Class<? extends NumberInterface>, HashMap<Integer, NumberInterface>> integerValues = new HashMap<>();
     /**
      * The division operator, /
      */
     public static final NumberOperator OP_DIVIDE = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 2 && params[1].compareTo(fromInt(params[0].getClass(), 0)) != 0;
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 2 && params[1].compareTo(implementation.instanceForString(Integer.toString(0))) != 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].divide(params[1]);
         }
     };
@@ -160,18 +180,18 @@ public class StandardPlugin extends Plugin {
     public static final NumberOperator OP_FACTORIAL = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0) {
         //private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1
-                    && params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
+                    && params[0].fractionalPart().compareTo(implementation.instanceForString("0")) == 0
                     && params[0].signum() >= 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             if (params[0].signum() == 0) {
-                return fromInt(params[0].getClass(), 1);
+                return implementation.instanceForString("1");
             }
-            NumberInterface one = fromInt(params[0].getClass(), 1);
+            NumberInterface one = implementation.instanceForString("1");
             NumberInterface factorial = params[0];
             NumberInterface multiplier = params[0];
             //It is necessary to later prevent calls of factorial on anything but non-negative integers.
@@ -191,27 +211,27 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberOperator OP_NPR = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2 && params[0].fractionalPart().signum() == 0
                     && params[1].fractionalPart().signum() == 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             if (params[0].compareTo(params[1]) < 0 ||
                     params[0].signum() < 0 ||
-                    (params[0].signum() == 0 && params[1].signum() != 0)) return fromInt(params[0].getClass(), 0);
-            NumberInterface total = fromInt(params[0].getClass(), 1);
+                    (params[0].signum() == 0 && params[1].signum() != 0)) return implementation.instanceForString("0");
+            NumberInterface total = implementation.instanceForString("1");
             NumberInterface multiplyBy = params[0];
             NumberInterface remainingMultiplications = params[1];
-            NumberInterface halfway = params[0].divide(fromInt(params[0].getClass(), 2));
+            NumberInterface halfway = params[0].divide(implementation.instanceForString("2"));
             if (remainingMultiplications.compareTo(halfway) > 0) {
                 remainingMultiplications = params[0].subtract(remainingMultiplications);
             }
             while (remainingMultiplications.signum() > 0) {
                 total = total.multiply(multiplyBy);
-                remainingMultiplications = remainingMultiplications.subtract(fromInt(params[0].getClass(), 1));
-                multiplyBy = multiplyBy.subtract(fromInt(params[0].getClass(), 1));
+                remainingMultiplications = remainingMultiplications.subtract(implementation.instanceForString("1"));
+                multiplyBy = multiplyBy.subtract(implementation.instanceForString("1"));
             }
             return total;
         }
@@ -221,14 +241,14 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberOperator OP_NCR = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2 && params[0].fractionalPart().signum() == 0
                     && params[1].fractionalPart().signum() == 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return OP_NPR.apply(params).divide(OP_FACTORIAL.apply(params[1]));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return OP_NPR.apply(implementation, params).divide(OP_FACTORIAL.apply(implementation, params[1]));
         }
     };
     /**
@@ -236,13 +256,13 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberFunction FUNCTION_ABS = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return params[0].multiply(fromInt(params[0].getClass(), params[0].signum()));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return params[0].multiply(implementation.instanceForString(Integer.toString(params[0].signum())));
         }
     };
     /**
@@ -250,25 +270,25 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberFunction FUNCTION_LN = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && params[0].compareTo(fromInt(params[0].getClass(), 0)) > 0;
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 1 && params[0].compareTo(implementation.instanceForString("0")) > 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             NumberInterface param = params[0];
-            NumberInterface one = fromInt(param.getClass(), 1);
+            NumberInterface one = implementation.instanceForString("1");
             int powersOf2 = 0;
-            while (FUNCTION_ABS.apply(param.subtract(one)).compareTo(new NaiveNumber(0.1).promoteTo(param.getClass())) >= 0) {
+            while (FUNCTION_ABS.apply(implementation, param.subtract(one)).compareTo(implementation.instanceForString(".1")) >= 0) {
                 if (param.subtract(one).signum() == 1) {
-                    param = param.divide(fromInt(param.getClass(), 2));
+                    param = param.divide(implementation.instanceForString("2"));
                     powersOf2++;
                     if (param.subtract(one).signum() != 1) {
                         break;
                         //No infinite loop for you.
                     }
                 } else {
-                    param = param.multiply(fromInt(param.getClass(), 2));
+                    param = param.multiply(implementation.instanceForString("2"));
                     powersOf2--;
                     if (param.subtract(one).signum() != -1) {
                         break;
@@ -276,7 +296,7 @@ public class StandardPlugin extends Plugin {
                     }
                 }
             }
-            return getLog2(param).multiply(fromInt(param.getClass(), powersOf2)).add(getLogPartialSum(param));
+            return getLog2(implementation, param).multiply(implementation.instanceForString(Integer.toString(powersOf2))).add(getLogPartialSum(implementation, param));
         }
 
         /**
@@ -285,16 +305,16 @@ public class StandardPlugin extends Plugin {
          * @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
          * @return the partial sum.
          */
-        private NumberInterface getLogPartialSum(NumberInterface x) {
+        private NumberInterface getLogPartialSum(NumberImplementation implementation, NumberInterface x) {
 
             NumberInterface maxError = x.getMaxError();
-            x = x.subtract(fromInt(x.getClass(), 1)); //Terms used are for log(x+1).
+            x = x.subtract(implementation.instanceForString("1")); //Terms used are for log(x+1).
             NumberInterface currentNumerator = x, currentTerm = x, sum = x;
             int n = 1;
-            while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
+            while (FUNCTION_ABS.apply(implementation, currentTerm).compareTo(maxError) > 0) {
                 n++;
                 currentNumerator = currentNumerator.multiply(x).negate();
-                currentTerm = currentNumerator.divide(fromInt(x.getClass(), n));
+                currentTerm = currentNumerator.divide(implementation.instanceForString(Integer.toString(n)));
                 sum = sum.add(currentTerm);
             }
             return sum;
@@ -305,21 +325,21 @@ public class StandardPlugin extends Plugin {
          * @param number a number of the same type as the return type. (Used for precision.)
          * @return the value of log(2) with the appropriate precision.
          */
-        private NumberInterface getLog2(NumberInterface number) {
+        private NumberInterface getLog2(NumberImplementation implementation, NumberInterface number) {
             NumberInterface maxError = number.getMaxError();
-            //NumberInterface errorBound = fromInt(number.getClass(), 1);
+            //NumberInterface errorBound = implementation.instanceForString("1");
             //We'll use the series \sigma_{n >= 1) ((1/3^n + 1/4^n) * 1/n)
             //In the following, a=1/3^n, b=1/4^n, c = 1/n.
             //a is also an error bound.
-            NumberInterface a = fromInt(number.getClass(), 1), b = a, c = a;
-            NumberInterface sum = fromInt(number.getClass(), 0);
-            NumberInterface one = fromInt(number.getClass(), 1);
+            NumberInterface a = implementation.instanceForString("1"), b = a, c = a;
+            NumberInterface sum = implementation.instanceForString("0");
+            NumberInterface one = implementation.instanceForString("1");
             int n = 0;
             while (a.compareTo(maxError) >= 1) {
                 n++;
-                a = a.divide(fromInt(number.getClass(), 3));
-                b = b.divide(fromInt(number.getClass(), 4));
-                c = one.divide(fromInt(number.getClass(), n));
+                a = a.divide(implementation.instanceForString("3"));
+                b = b.divide(implementation.instanceForString("4"));
+                c = one.divide(implementation.instanceForString(Integer.toString(n)));
                 sum = sum.add(a.add(b).multiply(c));
             }
             return sum;
@@ -330,44 +350,88 @@ public class StandardPlugin extends Plugin {
      */
     public static final NumberFunction FUNCTION_RAND_INT = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return fromInt(params[0].getClass(), (int) Math.round(Math.random() * params[0].floor().intValue()));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return implementation.instanceForString(Long.toString(Math.round(Math.random() * params[0].floor().intValue())));
         }
     };
-    private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
+    /**
+     * The caret / pow operator, ^
+     */
+    public static final NumberOperator OP_CARET = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2) {
+        @Override
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            NumberInterface zero = implementation.instanceForString("0");
+            return params.length == 2
+                    && !(params[0].compareTo(zero) == 0
+                    && params[1].compareTo(zero) == 0)
+                    && !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(zero) != 0);
+        }
+
+        @Override
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            NumberInterface zero = implementation.instanceForString("0");
+            if (params[0].compareTo(zero) == 0)
+                return zero;
+            else if (params[1].compareTo(zero) == 0)
+                return implementation.instanceForString("1");
+            //Detect integer bases:
+            if (params[0].fractionalPart().compareTo(implementation.instanceForString("0")) == 0
+                    && FUNCTION_ABS.apply(implementation, params[1]).compareTo(implementation.instanceForString(Integer.toString(Integer.MAX_VALUE))) < 0
+                    && FUNCTION_ABS.apply(implementation, params[1]).compareTo(implementation.instanceForString("1")) >= 0) {
+                NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
+                return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(implementation, newParams));
+            }
+            return FUNCTION_EXP.apply(implementation, FUNCTION_LN.apply(implementation, FUNCTION_ABS.apply(implementation, params[0])).multiply(params[1]));
+        }
+    };
+    /**
+     * The square root function.
+     */
+    public static final NumberFunction FUNCTION_SQRT = new NumberFunction() {
+        @Override
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 1;
+        }
+
+        @Override
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return OP_CARET.apply(implementation, params[0], implementation.instanceForString(".5"));
+        }
+    };
+    private static final HashMap<NumberImplementation, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
     /**
      * The exponential function, exp(1) = e^1 = 2.71...
      */
     public static final NumberFunction FUNCTION_EXP = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             NumberInterface maxError = params[0].getMaxError();
             int n = 0;
             if (params[0].signum() < 0) {
                 NumberInterface[] negatedParams = {params[0].negate()};
-                return fromInt(params[0].getClass(), 1).divide(applyInternal(negatedParams));
+                return implementation.instanceForString("1").divide(applyInternal(implementation, negatedParams));
             } else {
                 //We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
                 //right and left refer to lhs and rhs in the above inequality.
-                NumberInterface sum = fromInt(params[0].getClass(), 1);
+                NumberInterface sum = implementation.instanceForString("1");
                 NumberInterface nextNumerator = params[0];
-                NumberInterface left = params[0].multiply(fromInt(params[0].getClass(), 3).intPow(params[0].ceiling().intValue())), right = maxError;
+                NumberInterface left = params[0].multiply(implementation.instanceForString("3").intPow(params[0].ceiling().intValue())), right = maxError;
                 do {
-                    sum = sum.add(nextNumerator.divide(factorial(params[0].getClass(), n + 1)));
+                    sum = sum.add(nextNumerator.divide(factorial(implementation, n + 1)));
                     n++;
                     nextNumerator = nextNumerator.multiply(params[0]);
                     left = left.multiply(params[0]);
-                    NumberInterface nextN = fromInt(params[0].getClass(), n + 1);
+                    NumberInterface nextN = implementation.instanceForString(Integer.toString(n + 1));
                     right = right.multiply(nextN);
                     //System.out.println(left + ", " + right);
                 }
@@ -377,58 +441,28 @@ public class StandardPlugin extends Plugin {
             }
         }
     };
-    /**
-     * The caret / pow operator, ^
-     */
-    public static final NumberOperator OP_CARET = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2) {
-        @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            NumberInterface zero = fromInt(params[0].getClass(), 0);
-            return params.length == 2
-                    && !(params[0].compareTo(zero) == 0
-                    && params[1].compareTo(zero) == 0)
-                    && !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(zero) != 0);
-        }
-
-        @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface zero = fromInt(params[0].getClass(), 0);
-            if (params[0].compareTo(zero) == 0)
-                return zero;
-            else if (params[1].compareTo(zero) == 0)
-                return fromInt(params[0].getClass(), 1);
-            //Detect integer bases:
-            if (params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
-                    && FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
-                    && FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[1].getClass(), 1)) >= 0) {
-                NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
-                return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(newParams));
-            }
-            return FUNCTION_EXP.apply(FUNCTION_LN.apply(FUNCTION_ABS.apply(params[0])).multiply(params[1]));
-        }
-    };
     /**
      * The sine function (the argument is interpreted in radians).
      */
     public final NumberFunction functionSin = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             NumberInterface pi = piFor(params[0].getClass());
-            NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
-            NumberInterface theta = getSmallAngle(params[0], pi);
+            NumberInterface twoPi = pi.multiply(implementation.instanceForString("2"));
+            NumberInterface theta = getSmallAngle(implementation, params[0], pi);
             //System.out.println(theta);
-            if (theta.compareTo(pi.multiply(new NaiveNumber(1.5).promoteTo(twoPi.getClass()))) >= 0) {
+            if (theta.compareTo(pi.multiply(implementation.instanceForString("1.5"))) >= 0) {
                 theta = theta.subtract(twoPi);
-            } else if (theta.compareTo(pi.divide(fromInt(pi.getClass(), 2))) > 0) {
+            } else if (theta.compareTo(pi.divide(implementation.instanceForString("2"))) > 0) {
                 theta = pi.subtract(theta);
             }
             //System.out.println(theta);
-            return sinTaylor(theta);
+            return sinTaylor(implementation, theta);
         }
     };
     /**
@@ -436,13 +470,13 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionCos = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return functionSin.apply(piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return functionSin.apply(implementation, piFor(params[0].getClass()).divide(implementation.instanceForString("2"))
                     .subtract(params[0]));
         }
     };
@@ -451,13 +485,13 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionTan = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return functionSin.apply(params[0]).divide(functionCos.apply(params[0]));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return functionSin.apply(implementation, params[0]).divide(functionCos.apply(implementation, params[0]));
         }
     };
     /**
@@ -465,13 +499,13 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionSec = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return fromInt(params[0].getClass(), 1).divide(functionCos.apply(params[0]));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return implementation.instanceForString("1").divide(functionCos.apply(implementation, params[0]));
         }
     };
     /**
@@ -479,13 +513,13 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionCsc = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return fromInt(params[0].getClass(), 1).divide(functionSin.apply(params[0]));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return implementation.instanceForString("1").divide(functionSin.apply(implementation, params[0]));
         }
     };
     /**
@@ -493,13 +527,13 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionCot = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return functionCos.apply(params[0]).divide(functionSin.apply(params[0]));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return functionCos.apply(implementation, params[0]).divide(functionSin.apply(implementation, params[0]));
         }
     };
 
@@ -508,28 +542,28 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArcsin = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1
-                    && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) <= 0;
+                    && FUNCTION_ABS.apply(implementation, params[0]).compareTo(implementation.instanceForString("1")) <= 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            if (FUNCTION_ABS.apply(params[0]).compareTo(new NaiveNumber(0.8).promoteTo(params[0].getClass())) >= 0) {
-                NumberInterface[] newParams = {FUNCTION_SQRT.apply(fromInt(params[0].getClass(), 1).subtract(params[0].multiply(params[0])))};
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                        .subtract(applyInternal(newParams)).multiply(fromInt(params[0].getClass(), params[0].signum()));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            if (FUNCTION_ABS.apply(implementation, params[0]).compareTo(implementation.instanceForString(".8")) >= 0) {
+                NumberInterface[] newParams = {FUNCTION_SQRT.apply(implementation, implementation.instanceForString("1").subtract(params[0].multiply(params[0])))};
+                return piFor(params[0].getClass()).divide(implementation.instanceForString("2"))
+                        .subtract(applyInternal(implementation, newParams)).multiply(implementation.instanceForString(Integer.toString(params[0].signum())));
             }
             NumberInterface currentTerm = params[0], sum = currentTerm,
-                    multiplier = currentTerm.multiply(currentTerm), summandBound = sum.getMaxError().multiply(fromInt(sum.getClass(), 1).subtract(multiplier)),
-                    power = currentTerm, coefficient = fromInt(params[0].getClass(), 1);
+                    multiplier = currentTerm.multiply(currentTerm), summandBound = sum.getMaxError().multiply(implementation.instanceForString("1").subtract(multiplier)),
+                    power = currentTerm, coefficient = implementation.instanceForString("1");
             int exponent = 1;
-            while (FUNCTION_ABS.apply(currentTerm).compareTo(summandBound) > 0) {
+            while (FUNCTION_ABS.apply(implementation, currentTerm).compareTo(summandBound) > 0) {
                 exponent += 2;
                 power = power.multiply(multiplier);
-                coefficient = coefficient.multiply(fromInt(params[0].getClass(), exponent - 2))
-                        .divide(fromInt(params[0].getClass(), exponent - 1));
-                currentTerm = power.multiply(coefficient).divide(fromInt(power.getClass(), exponent));
+                coefficient = coefficient.multiply(implementation.instanceForString(Integer.toString(exponent - 2)))
+                        .divide(implementation.instanceForString(Integer.toString(exponent - 1)));
+                currentTerm = power.multiply(coefficient).divide(implementation.instanceForString(Integer.toString(exponent)));
                 sum = sum.add(currentTerm);
             }
             return sum;
@@ -541,14 +575,14 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArccos = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) <= 0;
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 1 && FUNCTION_ABS.apply(implementation, params[0]).compareTo(implementation.instanceForString("1")) <= 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                    .subtract(functionArcsin.apply(params));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return piFor(params[0].getClass()).divide(implementation.instanceForString("2"))
+                    .subtract(functionArcsin.apply(implementation, params));
         }
     };
 
@@ -557,14 +591,14 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArccsc = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) >= 0;
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 1 && FUNCTION_ABS.apply(implementation, params[0]).compareTo(implementation.instanceForString("1")) >= 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface[] reciprocalParamArr = {fromInt(params[0].getClass(), 1).divide(params[0])};
-            return functionArcsin.apply(reciprocalParamArr);
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            NumberInterface[] reciprocalParamArr = {implementation.instanceForString("1").divide(params[0])};
+            return functionArcsin.apply(implementation, reciprocalParamArr);
         }
     };
 
@@ -573,14 +607,14 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArcsec = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) >= 0;
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
+            return params.length == 1 && FUNCTION_ABS.apply(implementation, params[0]).compareTo(implementation.instanceForString("1")) >= 0;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface[] reciprocalParamArr = {fromInt(params[0].getClass(), 1).divide(params[0])};
-            return functionArccos.apply(reciprocalParamArr);
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            NumberInterface[] reciprocalParamArr = {implementation.instanceForString("1").divide(params[0])};
+            return functionArccos.apply(implementation, reciprocalParamArr);
         }
     };
 
@@ -589,36 +623,36 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArctan = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             if (params[0].signum() == -1) {
                 NumberInterface[] negatedParams = {params[0].negate()};
-                return applyInternal(negatedParams).negate();
+                return applyInternal(implementation, negatedParams).negate();
             }
-            if (params[0].compareTo(fromInt(params[0].getClass(), 1)) > 0) {
-                NumberInterface[] reciprocalParams = {fromInt(params[0].getClass(), 1).divide(params[0])};
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                        .subtract(applyInternal(reciprocalParams));
+            if (params[0].compareTo(implementation.instanceForString("1")) > 0) {
+                NumberInterface[] reciprocalParams = {implementation.instanceForString("1").divide(params[0])};
+                return piFor(params[0].getClass()).divide(implementation.instanceForString("2"))
+                        .subtract(applyInternal(implementation, reciprocalParams));
             }
-            if (params[0].compareTo(fromInt(params[0].getClass(), 1)) == 0) {
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 4));
+            if (params[0].compareTo(implementation.instanceForString("1")) == 0) {
+                return piFor(params[0].getClass()).divide(implementation.instanceForString("4"));
             }
-            if (params[0].compareTo(new NaiveNumber(0.9).promoteTo(params[0].getClass())) >= 0) {
-                NumberInterface[] newParams = {params[0].multiply(fromInt(params[0].getClass(), 2))
-                        .divide(fromInt(params[0].getClass(), 1).subtract(params[0].multiply(params[0])))};
-                return applyInternal(newParams).divide(fromInt(params[0].getClass(), 2));
+            if (params[0].compareTo(implementation.instanceForString(".9")) >= 0) {
+                NumberInterface[] newParams = {params[0].multiply(implementation.instanceForString("2"))
+                        .divide(implementation.instanceForString("1").subtract(params[0].multiply(params[0])))};
+                return applyInternal(implementation, newParams).divide(implementation.instanceForString("2"));
             }
             NumberInterface currentPower = params[0], currentTerm = currentPower, sum = currentTerm,
                     maxError = params[0].getMaxError(), multiplier = currentPower.multiply(currentPower).negate();
             int n = 1;
-            while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
+            while (FUNCTION_ABS.apply(implementation, currentTerm).compareTo(maxError) > 0) {
                 n += 2;
                 currentPower = currentPower.multiply(multiplier);
-                currentTerm = currentPower.divide(fromInt(currentPower.getClass(), n));
+                currentTerm = currentPower.divide(implementation.instanceForString(Integer.toString(n)));
                 sum = sum.add(currentTerm);
             }
             return sum;
@@ -630,14 +664,14 @@ public class StandardPlugin extends Plugin {
      */
     public final NumberFunction functionArccot = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 1;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
-            return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                    .subtract(functionArctan.apply(params));
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+            return piFor(params[0].getClass()).divide(implementation.instanceForString("2"))
+                    .subtract(functionArctan.apply(implementation, params));
         }
     };
 
@@ -645,40 +679,25 @@ public class StandardPlugin extends Plugin {
         super(manager);
     }
 
-    /**
-     * Returns a partial sum of a series whose terms are given by the nthTermFunction, evaluated at x.
-     *
-     * @param x               the value at which the series is evaluated.
-     * @param nthTermFunction the function that returns the nth term of the series, in the format term(x, n).
-     * @param n               the number of terms in the partial sum.
-     * @return the value of the partial sum that has the same class as x.
-     */
-    private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n) {
-        NumberInterface sum = fromInt(x.getClass(), 0);
-        for (int i = 0; i <= n; i++) {
-            sum = sum.add(nthTermFunction.apply(i, x));
-        }
-        return sum;
-    }
-
     /**
      * A factorial function that uses memoization for each number class; it efficiently
      * computes factorials of non-negative integers.
      *
-     * @param numberClass type of number to return.
-     * @param n           non-negative integer.
+     * @param implementation type of number to return.
+     * @param n              non-negative integer.
      * @return a number of numClass with value n factorial.
      */
-    public static NumberInterface factorial(Class<? extends NumberInterface> numberClass, int n) {
-        if (!FACTORIAL_LISTS.containsKey(numberClass)) {
-            FACTORIAL_LISTS.put(numberClass, new ArrayList<>());
-            FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
-            FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
+    public static NumberInterface factorial(NumberImplementation implementation, int n) {
+
+        if (!FACTORIAL_LISTS.containsKey(implementation)) {
+            FACTORIAL_LISTS.put(implementation, new ArrayList<>());
+            FACTORIAL_LISTS.get(implementation).add(implementation.instanceForString("1"));
+            FACTORIAL_LISTS.get(implementation).add(implementation.instanceForString("1"));
         }
-        ArrayList<NumberInterface> list = FACTORIAL_LISTS.get(numberClass);
+        ArrayList<NumberInterface> list = FACTORIAL_LISTS.get(implementation);
         if (n >= list.size()) {
             while (list.size() < n + 16) {
-                list.add(list.get(list.size() - 1).multiply(fromInt(numberClass, list.size())));
+                list.add(list.get(list.size() - 1).multiply(implementation.instanceForString(Integer.toString(list.size()))));
             }
         }
         return list.get(n);
@@ -690,16 +709,16 @@ public class StandardPlugin extends Plugin {
      * @param x where the series is evaluated.
      * @return the value of the series
      */
-    private static NumberInterface sinTaylor(NumberInterface x) {
+    private static NumberInterface sinTaylor(NumberImplementation implementation, NumberInterface x) {
         NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
         NumberInterface maxError = x.getMaxError();
         int n = 1;
         do {
             n += 2;
             power = power.multiply(multiplier);
-            currentTerm = power.divide(factorial(x.getClass(), n));
+            currentTerm = power.divide(factorial(implementation, n));
             sum = sum.add(currentTerm);
-        } while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0);
+        } while (FUNCTION_ABS.apply(implementation, currentTerm).compareTo(maxError) > 0);
         return sum;
     }
 
@@ -709,33 +728,16 @@ public class StandardPlugin extends Plugin {
      * @param phi an angle (in radians).
      * @return theta in [0, 2pi) that differs from phi by a multiple of 2pi.
      */
-    private static NumberInterface getSmallAngle(NumberInterface phi, NumberInterface pi) {
-        NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
-        NumberInterface theta = FUNCTION_ABS.apply(phi).subtract(twoPi
-                .multiply(FUNCTION_ABS.apply(phi).divide(twoPi).floor())); //Now theta is in [0, 2pi).
+    private static NumberInterface getSmallAngle(NumberImplementation implementation, NumberInterface phi, NumberInterface pi) {
+        NumberInterface twoPi = pi.multiply(implementation.instanceForString("2"));
+        NumberInterface theta = FUNCTION_ABS.apply(implementation, phi).subtract(twoPi
+                .multiply(FUNCTION_ABS.apply(implementation, phi).divide(twoPi).floor())); //Now theta is in [0, 2pi).
         if (phi.signum() < 0) {
             theta = twoPi.subtract(theta);
         }
         return theta;
     }
 
-    /**
-     * Returns a number of class numType with value n.
-     *
-     * @param numType class of number to return.
-     * @param n       value of returned number.
-     * @return numClass instance with value n.
-     */
-    private static NumberInterface fromInt(Class<? extends NumberInterface> numType, int n) {
-        if (!integerValues.containsKey(numType)) {
-            integerValues.put(numType, new HashMap<>());
-        }
-        if (!integerValues.get(numType).containsKey(n)) {
-            integerValues.get(numType).put(n, new NaiveNumber(n).promoteTo(numType));
-        }
-        return integerValues.get(numType).get(n);
-    }
-
     @Override
     public void onEnable() {
         registerNumberImplementation("naive", IMPLEMENTATION_NAIVE);
@@ -749,6 +751,9 @@ public class StandardPlugin extends Plugin {
         registerOperator("^", OP_CARET);
         registerOperator("!", OP_FACTORIAL);
 
+        registerTreeValueOperator("=", opSet);
+        registerTreeValueOperator(":=", opDefine);
+
         registerOperator("nPr", OP_NPR);
         registerOperator("nCr", OP_NCR);
 
@@ -824,6 +829,6 @@ public class StandardPlugin extends Plugin {
 
     @Override
     public void onDisable() {
-
+        FACTORIAL_LISTS.clear();
     }
 }

core/src/main/java/org/nwapw/abacus/tree/NumberReducer.java

@@ -1,8 +1,14 @@
 package org.nwapw.abacus.tree;
 
 import org.nwapw.abacus.Abacus;
-import org.nwapw.abacus.function.*;
+import org.nwapw.abacus.function.NumberFunction;
+import org.nwapw.abacus.function.NumberOperator;
+import org.nwapw.abacus.function.TreeValueFunction;
+import org.nwapw.abacus.function.TreeValueOperator;
 import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.number.PromotionManager;
+import org.nwapw.abacus.number.PromotionResult;
+import org.nwapw.abacus.variables.VariableDatabase;
 
 /**
  * A reducer implementation that turns a tree into a single number.
@@ -26,19 +32,28 @@ public class NumberReducer implements Reducer<NumberInterface> {
 
     @Override
     public NumberInterface reduceNode(TreeNode node, Object... children) {
+        PromotionManager manager = abacus.getPromotionManager();
         if (node instanceof NumberNode) {
-            return abacus.numberFromString(((NumberNode) node).getNumber());
-        } else if(node instanceof VariableNode) {
-            return abacus.numberFromString("0");
+            return abacus.getNumberImplementation().instanceForString(((NumberNode) node).getNumber());
+        } else if (node instanceof VariableNode) {
+            VariableDatabase database = abacus.getVariableDatabase();
+            String name = ((VariableNode) node).getVariable();
+            NumberInterface variable = database.getVariables().get(name);
+            if(variable != null) return variable;
+            TreeNode definition = database.getDefinitions().get(name);
+            if(definition != null) return definition.reduce(this);
+            return abacus.getNumberImplementation().instanceForString("0");
         } else if (node instanceof NumberBinaryNode) {
             NumberInterface left = (NumberInterface) children[0];
             NumberInterface right = (NumberInterface) children[1];
             NumberOperator operator = abacus.getPluginManager().operatorFor(((BinaryNode) node).getOperation());
-            return operator.apply(left, right);
+            PromotionResult result = manager.promote(left, right);
+            if (result == null) return null;
+            return operator.apply(result.getPromotedTo(), result.getItems());
         } else if (node instanceof NumberUnaryNode) {
             NumberInterface child = (NumberInterface) children[0];
             NumberOperator operator = abacus.getPluginManager().operatorFor(((UnaryNode) node).getOperation());
-            return operator.apply(child);
+            return operator.apply(abacus.getPluginManager().interfaceImplementationFor(child.getClass()), child);
         } else if (node instanceof FunctionNode) {
             NumberInterface[] convertedChildren = new NumberInterface[children.length];
             for (int i = 0; i < convertedChildren.length; i++) {
@@ -46,29 +61,31 @@ public class NumberReducer implements Reducer<NumberInterface> {
             }
             NumberFunction function = abacus.getPluginManager().functionFor(((FunctionNode) node).getCallTo());
             if (function == null) return null;
-            return function.apply(convertedChildren);
-        } else if (node instanceof TreeValueFunctionNode){
+            PromotionResult result = manager.promote(convertedChildren);
+            if (result == null) return null;
+            return function.apply(result.getPromotedTo(), result.getItems());
+        } else if (node instanceof TreeValueFunctionNode) {
             CallNode callNode = (CallNode) node;
             TreeNode[] realChildren = new TreeNode[callNode.getChildren().size()];
-            for(int i = 0; i < realChildren.length; i++){
+            for (int i = 0; i < realChildren.length; i++) {
                 realChildren[i] = callNode.getChildren().get(i);
             }
             TreeValueFunction function =
                     abacus.getPluginManager().treeValueFunctionFor(callNode.getCallTo());
-            if(function == null) return null;
-            return function.applyWithReducer(this, realChildren);
+            if (function == null) return null;
+            return function.applyWithReducer(abacus.getNumberImplementation(), this, realChildren);
         } else if (node instanceof TreeValueBinaryNode) {
             BinaryNode binaryNode = (BinaryNode) node;
             TreeValueOperator operator = abacus.getPluginManager()
                     .treeValueOperatorFor(binaryNode.getOperation());
-            if(operator == null) return null;
-            return operator.applyWithReducer(this, binaryNode.getLeft(), binaryNode.getRight());
-        } else if(node instanceof TreeValueUnaryNode) {
+            if (operator == null) return null;
+            return operator.applyWithReducer(abacus.getNumberImplementation(), this, binaryNode.getLeft(), binaryNode.getRight());
+        } else if (node instanceof TreeValueUnaryNode) {
             UnaryNode unaryNode = (UnaryNode) node;
             TreeValueOperator operator = abacus.getPluginManager()
                     .treeValueOperatorFor(unaryNode.getOperation());
-            if(operator == null) return null;
-            return operator.applyWithReducer(this, unaryNode.getApplyTo());
+            if (operator == null) return null;
+            return operator.applyWithReducer(abacus.getNumberImplementation(), this, unaryNode.getApplyTo());
         }
         return null;
     }

core/src/main/kotlin/org/nwapw/abacus/Abacus.kt

@@ -0,0 +1,90 @@
+package org.nwapw.abacus
+
+import org.nwapw.abacus.config.Configuration
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.number.PromotionManager
+import org.nwapw.abacus.parsing.LexerTokenizer
+import org.nwapw.abacus.parsing.ShuntingYardParser
+import org.nwapw.abacus.parsing.TreeBuilder
+import org.nwapw.abacus.plugin.NumberImplementation
+import org.nwapw.abacus.plugin.PluginManager
+import org.nwapw.abacus.plugin.StandardPlugin
+import org.nwapw.abacus.tree.NumberReducer
+import org.nwapw.abacus.tree.TreeNode
+import org.nwapw.abacus.variables.VariableDatabase
+
+/**
+ * Core class to handle all mathematics.
+ *
+ * The main calculator class. This is responsible
+ * for piecing together all of the components, allowing
+ * their interaction with each other.
+ *
+ * @property configuration the configuration to use.
+ */
+class Abacus(val configuration: Configuration) {
+
+    /**
+     * The tokenizer used to convert strings into tokens.
+     */
+    private val tokenizer = LexerTokenizer()
+    /**
+     * Parser the parser used to convert tokens into trees.
+     */
+    private val parser = ShuntingYardParser()
+    /**
+     * The plugin manager used to handle loading and unloading plugins.
+     */
+    val pluginManager = PluginManager(this)
+    /**
+     * The reducer used to turn trees into a single number.
+     */
+    val numberReducer = NumberReducer(this)
+    /**
+     * The tree builder that handles the conversion of strings into trees.
+     */
+    val treeBuilder = TreeBuilder(tokenizer, parser)
+    /**
+     * The promotion manager used to convert between number implementations.
+     */
+    val promotionManager = PromotionManager(this)
+    /**
+     * The database of variable definitions.
+     */
+    val variableDatabase = VariableDatabase(this)
+    /**
+     * The number implementation used by default.
+     */
+    val numberImplementation: NumberImplementation
+        get() {
+            val selectedImplementation =
+                    pluginManager.numberImplementationFor(configuration.numberImplementation)
+            if (selectedImplementation != null) return selectedImplementation
+            return StandardPlugin.IMPLEMENTATION_NAIVE
+        }
+
+    init {
+        pluginManager.addListener(tokenizer)
+        pluginManager.addListener(parser)
+        pluginManager.addListener(promotionManager)
+        pluginManager.addListener(variableDatabase)
+    }
+
+    /**
+     * Parses a string into a tree structure using the main
+     * tree builder.
+     *
+     * @param input the input string to parse
+     * @return the resulting tree, null if the tree builder or the produced tree are null.
+     */
+    fun parseString(input: String): TreeNode? = treeBuilder.fromString(input)
+    /**
+     * Evaluates the given tree using the main
+     * number reducer.
+     *
+     * @param tree the tree to reduce, must not be null.
+     * @return the resulting number, or null of the reduction failed.
+     */
+    fun evaluateTree(tree: TreeNode): NumberInterface? = tree.reduce(numberReducer)
+
+}

core/src/main/kotlin/org/nwapw/abacus/function/applicable/Applicable.kt

@@ -1,5 +1,8 @@
 package org.nwapw.abacus.function.applicable
 
+import org.nwapw.abacus.function.DomainException
+import org.nwapw.abacus.plugin.NumberImplementation
+
 /**
  * A class that can be applied to arguments.
  *
@@ -15,7 +18,7 @@ interface Applicable<in T : Any, out O : Any> {
      * @param params the parameter array to verify for compatibility.
      * @return whether the array can be used with applyInternal.
      */
-    fun matchesParams(params: Array<out T>): Boolean
+    fun matchesParams(implementation: NumberImplementation, params: Array<out T>): Boolean
 
     /**
      * Applies the applicable object to the given parameters,
@@ -23,7 +26,7 @@ interface Applicable<in T : Any, out O : Any> {
      * @param params the parameters to apply to.
      * @return the result of the application.
      */
-    fun applyInternal(params: Array<out T>): O?
+    fun applyInternal(implementation: NumberImplementation, params: Array<out T>): O
 
     /**
      * If the parameters can be used with this applicable, returns
@@ -32,9 +35,9 @@ interface Applicable<in T : Any, out O : Any> {
      * @param params the parameters to apply to.
      * @return the result of the operation, or null if parameters do not match.
      */
-    fun apply(vararg params: T): O? {
-        if (!matchesParams(params)) return null
-        return applyInternal(params)
+    fun apply(implementation: NumberImplementation, vararg params: T): O {
+        if (!matchesParams(implementation, params)) throw DomainException()
+        return applyInternal(implementation, params)
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/function/applicable/ReducerApplicable.kt

@@ -1,5 +1,7 @@
 package org.nwapw.abacus.function.applicable
 
+import org.nwapw.abacus.function.DomainException
+import org.nwapw.abacus.plugin.NumberImplementation
 import org.nwapw.abacus.tree.Reducer
 
 /**
@@ -18,7 +20,7 @@ interface ReducerApplicable<in T : Any, out O : Any, in R : Any> {
      * given parameters.
      * @param params the parameters to check.
      */
-    fun matchesParams(params: Array<out T>): Boolean
+    fun matchesParams(implementation: NumberImplementation, params: Array<out T>): Boolean
 
     /**
      * Applies this applicable to the given arguments, and reducer.
@@ -26,7 +28,7 @@ interface ReducerApplicable<in T : Any, out O : Any, in R : Any> {
      * @param params the arguments to apply to.
      * @return the result of the application.
      */
-    fun applyWithReducerInternal(reducer: Reducer<R>, params: Array<out T>): O?
+    fun applyWithReducerInternal(implementation: NumberImplementation, reducer: Reducer<R>, params: Array<out T>): O
 
     /**
      * Applies this applicable to the given arguments, and reducer,
@@ -35,9 +37,9 @@ interface ReducerApplicable<in T : Any, out O : Any, in R : Any> {
      * @param params the arguments to apply to.
      * @return the result of the application, or null if the arguments are incompatible.
      */
-    fun applyWithReducer(reducer: Reducer<R>, vararg params: T): O? {
-        if (!matchesParams(params)) return null
-        return applyWithReducerInternal(reducer, params)
+    fun applyWithReducer(implementation: NumberImplementation, reducer: Reducer<R>, vararg params: T): O {
+        if (!matchesParams(implementation, params)) throw DomainException()
+        return applyWithReducerInternal(implementation, reducer, params)
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/number/NumberUtils.kt

@@ -0,0 +1,16 @@
+@file:JvmName("NumberUtils")
+package org.nwapw.abacus.number
+
+typealias PromotionFunction = java.util.function.Function<NumberInterface, NumberInterface>
+typealias PromotionPath = List<PromotionFunction>
+typealias NumberClass = Class<NumberInterface>
+
+/**
+ * Promote a number through this path. The functions in this path
+ * are applied in order to the number, and the final result is returned.
+ *
+ * @param from the number to start from.
+ */
+fun PromotionPath.promote(from: NumberInterface): NumberInterface {
+    return fold(from, { current, function -> function.apply(current) })
+}

core/src/main/kotlin/org/nwapw/abacus/number/PromotionManager.kt

@@ -0,0 +1,83 @@
+package org.nwapw.abacus.number
+
+import org.nwapw.abacus.Abacus
+import org.nwapw.abacus.plugin.NumberImplementation
+import org.nwapw.abacus.plugin.PluginListener
+import org.nwapw.abacus.plugin.PluginManager
+import java.util.function.Function
+
+/**
+ * A class that handles promotions based on priority and the
+ * transition paths each implementation provides.
+ *
+ * @property abacus the Abacus instance to use to access other components.
+ */
+class PromotionManager(val abacus: Abacus) : PluginListener {
+
+    /**
+     * The already computed paths
+     */
+    val computePaths = mutableMapOf<Pair<NumberImplementation, NumberImplementation>, PromotionPath?>()
+
+    /**
+     * Computes a path between a starting and an ending implementation.
+     *
+     * @param from the implementation to start from.
+     * @param to the implementation to get to.
+     * @return the resulting promotion path, or null if it is not found
+     */
+    fun computePathBetween(from: NumberImplementation, to: NumberImplementation): PromotionPath? {
+        val fromName = abacus.pluginManager.interfaceImplementationNameFor(from.implementation)
+        val toName = abacus.pluginManager.interfaceImplementationNameFor(to.implementation)
+
+        if(fromName == toName) return listOf(Function { it })
+
+        if(from.promotionPaths.containsKey(toName))
+            return listOf(from.promotionPaths[toName] ?: return null)
+        return null
+    }
+
+    /**
+     * If a path between the given implementations has already been computed, uses
+     * the already calculated path. Otherwise, calls [computePathBetween] to compute a new
+     * path.
+     *
+     * @param from the implementation to start from.
+     * @param to the implementation to get to.
+     * @return the resulting promotion path, or null if it is not found
+     */
+    fun getPathBetween(from: NumberImplementation, to: NumberImplementation): PromotionPath? {
+        return computePaths.computeIfAbsent(from to to, {
+             computePathBetween(it.first, it.second)
+        })
+    }
+
+    /**
+     * Promote all the numbers in the list to the same number implementation, to ensure
+     * they can be used with each other. Finds the highest priority implementation
+     * in the list, and promotes all other numbers to it.
+     *
+     * @param numbers the numbers to promote.
+     * @return the resulting promotion result.
+     */
+    fun promote(vararg numbers: NumberInterface): PromotionResult? {
+        val pluginManager = abacus.pluginManager
+        val implementations = numbers.map { pluginManager.interfaceImplementationFor(it.javaClass) }
+        val highestPriority = implementations.sortedBy { it.priority }.last()
+        return PromotionResult(items = numbers.map {
+            if(it.javaClass == highestPriority.implementation) it
+            else getPathBetween(pluginManager.interfaceImplementationFor(it.javaClass), highestPriority)
+                    ?.promote(it) ?: return null
+        }.toTypedArray(), promotedTo = highestPriority)
+    }
+
+    override fun onLoad(manager: PluginManager?) {
+
+    }
+
+    override fun onUnload(manager: PluginManager?) {
+        computePaths.clear()
+    }
+
+
+}

core/src/main/kotlin/org/nwapw/abacus/number/PromotionResult.kt

@@ -0,0 +1,11 @@
+package org.nwapw.abacus.number
+
+import org.nwapw.abacus.plugin.NumberImplementation
+
+/**
+ * The result of promoting an array of NumberInterfaces.
+ *
+ * @param promotedTo the implementation to which the numbers were promoted.
+ * @param items the items the items resulting from the promotion.
+ */
+data class PromotionResult(val promotedTo: NumberImplementation, val items: Array<NumberInterface>)

core/src/main/kotlin/org/nwapw/abacus/variables/VariableDatabase.kt

@@ -0,0 +1,37 @@
+package org.nwapw.abacus.variables
+
+import org.nwapw.abacus.Abacus
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.plugin.PluginListener
+import org.nwapw.abacus.plugin.PluginManager
+import org.nwapw.abacus.tree.TreeNode
+
+/**
+ * A database for variables and definition.
+ *
+ * The variable database is used to keep track of
+ * variables and definitions throughout the calculator.
+ *
+ * @property abacus the Abacus instance.
+ */
+class VariableDatabase(val abacus: Abacus): PluginListener {
+
+    /**
+     * The variables that are stored in the database.
+     */
+    val variables = mutableMapOf<String, NumberInterface>()
+    /**
+     * The definitions that are stored in the database.
+     */
+    val definitions = mutableMapOf<String, TreeNode>()
+
+    override fun onLoad(manager: PluginManager?) {
+
+    }
+
+    override fun onUnload(manager: PluginManager?) {
+        variables.clear()
+        definitions.clear()
+    }
+
+}

core/src/test/java/org/nwapw/abacus/tests/CalculationTests.java

@@ -5,6 +5,7 @@ import org.junit.BeforeClass;
 import org.junit.Test;
 import org.nwapw.abacus.Abacus;
 import org.nwapw.abacus.config.Configuration;
+import org.nwapw.abacus.function.DomainException;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.plugin.StandardPlugin;
 import org.nwapw.abacus.tree.TreeNode;
@@ -28,11 +29,14 @@ public class CalculationTests {
         Assert.assertTrue(result.toString().startsWith(output));
     }
 
-    private void testEvalError(String input, String parseOutput) {
+    private void testDomainException(String input, String parseOutput) {
         TreeNode parsedTree = abacus.parseString(input);
         Assert.assertNotNull(parsedTree);
         Assert.assertEquals(parsedTree.toString(), parseOutput);
-        Assert.assertNull(abacus.evaluateTree(parsedTree));
+        try {
+            abacus.evaluateTree(parsedTree);
+            Assert.fail("Function did not throw DomainException.");
+        } catch (DomainException e){ }
     }
 
     @Test
@@ -73,7 +77,7 @@ public class CalculationTests {
 
     @Test
     public void testLn() {
-        testEvalError("ln(-1)", "ln((1)`)");
+        testDomainException("ln(-1)", "ln((1)`)");
         testOutput("ln2", "ln(2)", "0.6931471805599453094172321214581765680755");
     }
 
@@ -100,8 +104,8 @@ public class CalculationTests {
         testOutput("2^-1", "(2^(1)`)", "0.5");
         testOutput("2^50", "(2^50)", "112589990684262");
         testOutput("7^(-sqrt2*17)", "(7^((sqrt(2)*17))`)", "4.81354609155297814551845300063563");
-        testEvalError("0^0", "(0^0)");
-        testEvalError("(-13)^.9999", "((13)`^.9999)");
+        testDomainException("0^0", "(0^0)");
+        testDomainException("(-13)^.9999", "((13)`^.9999)");
     }
 
 }

core/src/test/java/org/nwapw/abacus/tests/TokenizerTests.java

@@ -9,6 +9,7 @@ import org.nwapw.abacus.function.*;
 import org.nwapw.abacus.lexing.pattern.Match;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.parsing.LexerTokenizer;
+import org.nwapw.abacus.plugin.NumberImplementation;
 import org.nwapw.abacus.plugin.Plugin;
 import org.nwapw.abacus.tree.TokenType;
 
@@ -20,12 +21,12 @@ public class TokenizerTests {
     private static LexerTokenizer lexerTokenizer = new LexerTokenizer();
     private static NumberFunction subtractFunction = new NumberFunction() {
         @Override
-        public boolean matchesParams(NumberInterface[] params) {
+        public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
             return params.length == 2;
         }
 
         @Override
-        public NumberInterface applyInternal(NumberInterface[] params) {
+        public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
             return params[0].subtract(params[1]);
         }
     };
@@ -36,26 +37,26 @@ public class TokenizerTests {
                     0) {
 
                 @Override
-                public boolean matchesParams(NumberInterface[] params) {
+                public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
                     return true;
                 }
 
                 @Override
-                public NumberInterface applyInternal(NumberInterface[] params) {
-                    return subtractFunction.apply(params);
+                public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+                    return subtractFunction.apply(implementation, params);
                 }
             });
             registerOperator("-", new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,
                     0) {
 
                 @Override
-                public boolean matchesParams(NumberInterface[] params) {
+                public boolean matchesParams(NumberImplementation implementation, NumberInterface[] params) {
                     return true;
                 }
 
                 @Override
-                public NumberInterface applyInternal(NumberInterface[] params) {
-                    return subtractFunction.apply(params);
+                public NumberInterface applyInternal(NumberImplementation implementation, NumberInterface[] params) {
+                    return subtractFunction.apply(implementation, params);
                 }
             });
             registerFunction("subtract", subtractFunction);

docs/_layouts/home.html

@@ -3,7 +3,7 @@
   {% include head.html %}
   <style>
   body {
-    margin-top: 100px;
+    margin-top: 50px;
     color: white;
     text-align: center;
   }
@@ -11,7 +11,13 @@
     font-family: "Source Code Pro"
   }
 
-  img {
+  img#logo {
+    margin: auto;
+    width: 100%;
+    max-width: 100px;
+  }
+
+  img#image_preview {
     margin: auto;
     width: 100%;
     max-width: 432px;
@@ -33,6 +39,7 @@
   }
   </style>
   <body>
+  <img src="https://raw.githubusercontent.com/DanilaFe/abacus/master/image/logo.png" id="logo">
   <h1>Abacus</h1>
   <h2>The programmer's calculator</h2>
   <div id="buttons">
@@ -41,6 +48,6 @@
     <a class="button inverted" href="https://github.com/DanilaFe/abacus">Contribute</a>
     <a class="button inverted" href="https://github.com/DanilaFe/abacus/wiki">Wiki</a>
   </div>
-  <img src="http://i.imgur.com/Min70QY.png" title="source: imgur.com" />
+  <img src="http://i.imgur.com/Min70QY.png" title="source: imgur.com" id="image_preview"/>
   </body>
 </html>

fx/src/main/java/org/nwapw/abacus/fx/AbacusController.java

@@ -14,8 +14,8 @@ import org.nwapw.abacus.Abacus;
 import org.nwapw.abacus.config.Configuration;
 import org.nwapw.abacus.function.Documentation;
 import org.nwapw.abacus.function.DocumentationType;
-import org.nwapw.abacus.number.ComputationInterruptedException;
-import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.function.DomainException;
+import org.nwapw.abacus.number.*;
 import org.nwapw.abacus.plugin.ClassFinder;
 import org.nwapw.abacus.plugin.PluginListener;
 import org.nwapw.abacus.plugin.PluginManager;
@@ -153,6 +153,8 @@ public class AbacusController implements PluginListener {
                 return resultingString;
             } catch (ComputationInterruptedException exception) {
                 return ERR_STOP;
+            } catch (DomainException exception) {
+                return exception.getMessage();
             } catch (RuntimeException exception) {
                 exception.printStackTrace();
                 return ERR_EXCEPTION;