Add more descriptive message to context exceptions.

Add a NumberRange utility.

.gitignore

@@ -24,7 +24,9 @@ hs_err_pid*
 # Custom Stuff
 # Gradle
 .gradle/*
-build/*
+**/build/*
+**/out/**
+**/.DS_Store
 
 # IntelliJ
 .idea/*

core/src/main/java/org/nwapw/abacus/exception/AbacusException.java

@@ -0,0 +1,9 @@
+package org.nwapw.abacus.exception;
+
+public class AbacusException extends RuntimeException {
+
+    public AbacusException(String baseMessage, String description){
+        super(baseMessage + ((description.equals("")) ? "." : (": " + description)));
+    }
+
+}

core/src/main/java/org/nwapw/abacus/exception/ComputationInterruptedException.java

@@ -1,16 +1,16 @@
-package org.nwapw.abacus.number;
+package org.nwapw.abacus.exception;
 
 /**
  * Exception thrown when the computation is interrupted by
  * the user.
  */
-public class ComputationInterruptedException extends RuntimeException {
+public class ComputationInterruptedException extends AbacusException {
 
     /**
      * Creates a new exception of this type.
      */
     public ComputationInterruptedException() {
-        super("Computation interrupted by user.");
+        super("Computation interrupted", "");
     }
 
 }

core/src/main/java/org/nwapw/abacus/exception/ContextException.java

@@ -0,0 +1,24 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * Exception thrown by the Context in cases where lookup fails
+ * where it should not.
+ */
+public class ContextException extends AbacusException {
+
+    /**
+     * Creates a new ContextException without an extra message.
+     */
+    public ContextException() {
+        this("");
+    }
+
+    /**
+     * Creates a ContextException with the given message.
+     * @param message the message to use.
+     */
+    public ContextException(String message){
+        super("Context exception", message);
+    }
+
+}

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

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

core/src/main/java/org/nwapw/abacus/exception/NumberReducerException.java

@@ -0,0 +1,25 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * Exception thrown by the NumberReducer if something goes wrong when
+ * transforming a parse tree into a single value.
+ */
+public class NumberReducerException extends AbacusException {
+
+    /**
+     * Creates a new NumberReducerException with
+     * no additional message.
+     */
+    public NumberReducerException() {
+        this("");
+    }
+
+    /**
+     * Creates a new NumberReducerException with the given message.
+     * @param message the message.
+     */
+    public NumberReducerException(String message) {
+        super("Error evaluating expression", message);
+    }
+
+}

core/src/main/java/org/nwapw/abacus/exception/ParseException.java

@@ -0,0 +1,23 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * Exception thrown by parsers.
+ */
+public class ParseException extends AbacusException {
+
+    /**
+     * Creates a new ParseException with no additional message.
+     */
+    public ParseException(){
+        this("");
+    }
+
+    /**
+     * Creates a new ParseException with the given additional message.
+     * @param message the message.
+     */
+    public ParseException(String message){
+        super("Failed to parse string", message);
+    }
+
+}

core/src/main/java/org/nwapw/abacus/exception/PromotionException.java

@@ -0,0 +1,24 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * Exception thrown when a promotion fails.
+ */
+public class PromotionException extends AbacusException {
+
+    /**
+     * Creates a new PromotionException with the default message
+     * and no additional information.
+     */
+    public PromotionException() {
+        this("");
+    }
+
+    /**
+     * Creates a new PromotionException with the given additional message.
+     * @param message the additional message to include with the error.
+     */
+    public PromotionException(String message) {
+        super("Failed to promote number instances", message);
+    }
+
+}

core/src/main/java/org/nwapw/abacus/exception/ReductionException.java

@@ -0,0 +1,23 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * An exception thrown from TreeReducers.
+ */
+public class ReductionException extends AbacusException {
+
+    /**
+     * Creates a new EvaluationException with the default string.
+     */
+    public ReductionException() {
+        this("");
+    }
+
+    /**
+     * Creates a new EvaluationError with the given message string.
+     * @param message the message string.
+     */
+    public ReductionException(String message) {
+        super("Evaluation error", message);
+    }
+
+}

core/src/main/java/org/nwapw/abacus/exception/TokenizeException.java

@@ -0,0 +1,23 @@
+package org.nwapw.abacus.exception;
+
+/**
+ * Exception thrown by Lexers when they are unable to tokenize the input string.
+ */
+public class TokenizeException extends AbacusException {
+
+    /**
+     * Create a new tokenize exception with no additional data.
+     */
+    public TokenizeException() {
+        this("");
+    }
+
+    /**
+     * Create a new tokenize exception with the given message.
+     * @param message the message to use.
+     */
+    public TokenizeException(String message){
+        super("Failed to tokenize string", message);
+    }
+
+}

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

@@ -1,25 +0,0 @@
-package org.nwapw.abacus.function;
-
-/**
- * An exception thrown primarily from Tree Value operators and functions,
- * which have to deal with the result of a Reducer as well as the results
- * of Applicable.
- */
-public class EvaluationException extends RuntimeException {
-
-    /**
-     * Creates a new EvaluationException with the default string.
-     */
-    public EvaluationException() {
-        super("Error evaluating expression.");
-    }
-
-    /**
-     * Creates a new EvaluationError with the given message string.
-     * @param message the message string.
-     */
-    public EvaluationException(String message) {
-        super(message);
-    }
-
-}

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

@@ -1,9 +1,11 @@
 package org.nwapw.abacus.number;
 
+import org.nwapw.abacus.exception.ComputationInterruptedException;
+
 /**
  * An interface used to represent a number.
  */
-public abstract class NumberInterface {
+public abstract class NumberInterface implements Comparable<NumberInterface> {
 
     /**
      * Check if the thread was interrupted and
@@ -156,14 +158,6 @@ public abstract class NumberInterface {
         return intPowInternal(exponent);
     }
 
-    /**
-     * Compares this number to another.
-     *
-     * @param number the number to compare to.
-     * @return same as Integer.compare();
-     */
-    public abstract int compareTo(NumberInterface number);
-
     /**
      * Same as Math.signum().
      *
@@ -244,4 +238,16 @@ public abstract class NumberInterface {
      */
     public abstract NumberInterface getMaxError();
 
+    /**
+     * Returns a NumberRangeBuilder object, which is used to create a range.
+     * The reason that this returns a builder and not an actual range is that
+     * the NumberRange needs to promote values passed to it, which
+     * requires an abacus instance.
+     * @param other the value at the bottom of the range.
+     * @return the resulting range builder.
+     */
+    public NumberRangeBuilder rangeTo(NumberInterface other){
+        return new NumberRangeBuilder(this, other);
+    }
+
 }

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

@@ -1,5 +1,6 @@
 package org.nwapw.abacus.parsing;
 
+import org.nwapw.abacus.exception.TokenizeException;
 import org.nwapw.abacus.lexing.Lexer;
 import org.nwapw.abacus.lexing.pattern.Match;
 import org.nwapw.abacus.lexing.pattern.Pattern;
@@ -42,7 +43,9 @@ public class LexerTokenizer implements Tokenizer<Match<TokenType>>, PluginListen
 
     @Override
     public List<Match<TokenType>> tokenizeString(String string) {
-        return lexer.lexAll(string, 0, TOKEN_SORTER);
+        List<Match<TokenType>> tokens = lexer.lexAll(string, 0, TOKEN_SORTER);
+        if(tokens == null) throw new TokenizeException();
+        return tokens;
     }
 
     @Override

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

@@ -1,5 +1,6 @@
 package org.nwapw.abacus.parsing;
 
+import org.nwapw.abacus.exception.ParseException;
 import org.nwapw.abacus.function.Operator;
 import org.nwapw.abacus.function.OperatorAssociativity;
 import org.nwapw.abacus.function.OperatorType;
@@ -99,7 +100,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
                 while (!tokenStack.empty() && tokenStack.peek().getType() != TokenType.OPEN_PARENTH) {
                     output.add(tokenStack.pop());
                 }
-                if (tokenStack.empty()) return null;
+                if (tokenStack.empty()) throw new ParseException("mismatched parentheses");
                 if (matchType == TokenType.CLOSE_PARENTH) {
                     tokenStack.pop();
                 }
@@ -111,7 +112,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             if (!(newMatchType == TokenType.OP ||
                     newMatchType == TokenType.TREE_VALUE_OP ||
                     newMatchType == TokenType.FUNCTION ||
-                    newMatchType == TokenType.TREE_VALUE_FUNCTION)) return null;
+                    newMatchType == TokenType.TREE_VALUE_FUNCTION)) throw new ParseException("mismatched parentheses");
             output.add(tokenStack.pop());
         }
         return output;
@@ -124,7 +125,7 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
      * @return the construct tree expression.
      */
     public TreeNode constructRecursive(List<Match<TokenType>> matches) {
-        if (matches.size() == 0) return null;
+        if (matches.size() == 0) throw new ParseException("no tokens left in input");
         Match<TokenType> match = matches.remove(0);
         TokenType matchType = match.getType();
         if (matchType == TokenType.OP || matchType == TokenType.TREE_VALUE_OP) {
@@ -133,7 +134,6 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             if (type == OperatorType.BINARY_INFIX) {
                 TreeNode right = constructRecursive(matches);
                 TreeNode left = constructRecursive(matches);
-                if (left == null || right == null) return null;
                 if (matchType == TokenType.OP) {
                     return new NumberBinaryNode(operator, left, right);
                 } else {
@@ -141,7 +141,6 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
                 }
             } else {
                 TreeNode applyTo = constructRecursive(matches);
-                if (applyTo == null) return null;
                 if (matchType == TokenType.OP) {
                     return new NumberUnaryNode(operator, applyTo);
                 } else {
@@ -154,31 +153,32 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             return new VariableNode(match.getContent());
         } else if (matchType == TokenType.FUNCTION || matchType == TokenType.TREE_VALUE_FUNCTION) {
             String functionName = match.getContent();
-            CallNode node;
+            List<TreeNode> children = new ArrayList<>();
-            if (matchType == TokenType.FUNCTION) {
-                node = new FunctionNode(functionName);
-            } else {
-                node = new TreeValueFunctionNode(functionName);
-            }
             while (!matches.isEmpty() && matches.get(0).getType() != TokenType.INTERNAL_FUNCTION_END) {
                 TreeNode argument = constructRecursive(matches);
-                if (argument == null) return null;
+                children.add(0, argument);
-                node.getChildren().add(0, argument);
             }
-            if (matches.isEmpty()) return null;
+            if (matches.isEmpty()) throw new ParseException("incorrectly formatted function call");
             matches.remove(0);
+            CallNode node;
+            if (matchType == TokenType.FUNCTION) {
+                node = new FunctionNode(functionName, children);
+            } else {
+                node = new TreeValueFunctionNode(functionName, children);
+            }
             return node;
         }
-        return null;
+        throw new ParseException("unrecognized token");
     }
 
     @Override
     public TreeNode constructTree(List<Match<TokenType>> tokens) {
+        if (tokens.isEmpty()) throw new ParseException("no input tokens");
         tokens = intoPostfix(new ArrayList<>(tokens));
-        if (tokens == null) return null;
         Collections.reverse(tokens);
         TreeNode constructedTree = constructRecursive(tokens);
-        return tokens.size() == 0 ? constructedTree : null;
+        if(tokens.size() == 0) return constructedTree;
+        throw new ParseException("could not parse all input");
     }
 
     @Override

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

@@ -42,9 +42,7 @@ public class TreeBuilder<T> {
      * @return the resulting tree.
      */
     public TreeNode fromString(String input) {
-        List<T> tokens = tokenizer.tokenizeString(input);
+        return parser.constructTree(tokenizer.tokenizeString(input));
-        if (tokens == null) return null;
-        return parser.constructTree(tokens);
     }
 
 }

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

@@ -141,6 +141,7 @@ public class PluginManager {
         registeredNumberImplementations.put(name, implementation);
         interfaceImplementationNames.put(implementation.getImplementation(), name);
         interfaceImplementations.put(implementation.getImplementation(), implementation);
+        cachedPi.put(implementation.getImplementation(), implementation.instanceForPi());
     }
 
     /**
@@ -218,10 +219,6 @@ public class PluginManager {
                 break;
             }
         }
-        if (toReturn == null) {
-            toReturn = new Documentation(name, "", "", "", type);
-            registerDocumentation(toReturn);
-        }
         return toReturn;
     }
 
@@ -252,14 +249,7 @@ public class PluginManager {
      * @return pi
      */
     public NumberInterface piFor(Class<? extends NumberInterface> forClass) {
-        if (cachedPi.containsKey(forClass)) return cachedPi.get(forClass);
+        return cachedPi.get(forClass);
-        NumberImplementation implementation = interfaceImplementationFor(forClass);
-        NumberInterface generatedPi = null;
-        if (implementation != null) {
-            generatedPi = implementation.instanceForPi();
-        }
-        cachedPi.put(forClass, generatedPi);
-        return generatedPi;
     }
 
     /**

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

@@ -29,8 +29,7 @@ public class StandardPlugin extends Plugin {
         @Override
         public NumberInterface applyInternal(MutableEvaluationContext context, TreeNode[] params) {
             String assignTo = ((VariableNode) params[0]).getVariable();
-            NumberInterface value = params[1].reduce(context.getReducer());
+            NumberInterface value = params[1].reduce(context.getInheritedReducer());
-            if(value == null) throw new EvaluationException();
             context.setVariable(assignTo, value);
             return value;
         }
@@ -48,9 +47,7 @@ public class StandardPlugin extends Plugin {
         public NumberInterface applyInternal(MutableEvaluationContext context, TreeNode[] params) {
             String assignTo = ((VariableNode) params[0]).getVariable();
             context.setDefinition(assignTo, params[1]);
-            NumberInterface value = params[1].reduce(context.getReducer());
+            return params[1].reduce(context.getInheritedReducer());
-            if(value == null) throw new EvaluationException();
-            return value;
         }
     };
     /**
@@ -335,7 +332,7 @@ public class StandardPlugin extends Plugin {
             //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 = implementation.instanceForString("1"), b = a, c = a;
+            NumberInterface a = implementation.instanceForString("1"), b = a, c;
             NumberInterface sum = implementation.instanceForString("0");
             NumberInterface one = implementation.instanceForString("1");
             int n = 0;
@@ -696,8 +693,7 @@ public class StandardPlugin extends Plugin {
      * @param n              non-negative integer.
      * @return a number of numClass with value n factorial.
      */
-    public static NumberInterface factorial(NumberImplementation implementation, int n) {
+    synchronized 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"));
@@ -719,7 +715,7 @@ public class StandardPlugin extends Plugin {
      * @return the value of the series
      */
     private static NumberInterface sinTaylor(MutableEvaluationContext context, NumberInterface x) {
-        NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
+        NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm, sum = x;
         NumberInterface maxError = x.getMaxError();
         int n = 1;
         do {

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

@@ -68,6 +68,7 @@ class Abacus(val configuration: Configuration) {
         pluginManager.reload()
         with(mutableContext) {
             numberImplementation = pluginManager.numberImplementationFor(configuration.numberImplementation)
+                    ?: StandardPlugin.IMPLEMENTATION_NAIVE
             clearVariables()
             clearDefinitions()
         }
@@ -87,7 +88,7 @@ class Abacus(val configuration: Configuration) {
      * @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)
+    fun parseString(input: String): TreeNode = treeBuilder.fromString(input)
     /**
      * Evaluates the given tree.
      *

core/src/main/kotlin/org/nwapw/abacus/context/ChainSearchDelegate.kt

@@ -1,5 +1,6 @@
 package org.nwapw.abacus.context
 
+import org.nwapw.abacus.exception.ContextException
 import kotlin.reflect.KProperty
 
 /**
@@ -16,14 +17,14 @@ import kotlin.reflect.KProperty
  */
 class ChainSearchDelegate<out V>(private val valueGetter: EvaluationContext.() -> V?) {
 
-    operator fun getValue(selfRef: Any, property: KProperty<*>): V? {
+    operator fun getValue(selfRef: Any, property: KProperty<*>): V {
-        var currentRef = selfRef as? EvaluationContext ?: return null
+        var currentRef = selfRef as EvaluationContext
         var returnedValue = currentRef.valueGetter()
         while (returnedValue == null) {
             currentRef = currentRef.parent ?: break
             returnedValue = currentRef.valueGetter()
         }
-        return returnedValue
+        return returnedValue ?: throw ContextException("context chain does not contain value")
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/context/EvaluationContext.kt

@@ -43,13 +43,13 @@ open class EvaluationContext(val parent: EvaluationContext? = null,
     /**
      * The implementation inherited from this context's parent.
      */
-    val inheritedNumberImplementation: NumberImplementation?
+    val inheritedNumberImplementation: NumberImplementation
-            by ChainSearchDelegate { numberImplementation}
+            by ChainSearchDelegate { numberImplementation }
 
     /**
      * The reducer inherited from this context's parent.
      */
-    val inheritedReducer: Reducer<NumberInterface>?
+    val inheritedReducer: Reducer<NumberInterface>
             by ChainSearchDelegate { reducer }
 
     /**

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

@@ -1,7 +1,7 @@
 package org.nwapw.abacus.function.applicable
 
 import org.nwapw.abacus.context.MutableEvaluationContext
-import org.nwapw.abacus.function.DomainException
+import org.nwapw.abacus.exception.DomainException
 
 /**
  * A class that can be applied to arguments.
@@ -36,7 +36,8 @@ interface Applicable<in T : Any, out O : Any> {
      * @return the result of the operation, or null if parameters do not match.
      */
     fun apply(context: MutableEvaluationContext, vararg params: T): O {
-        if (!matchesParams(context, params)) throw DomainException()
+        if (!matchesParams(context, params))
+            throw DomainException("parameters do not match function requirements.")
         return applyInternal(context, params)
     }
 

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

@@ -0,0 +1,28 @@
+package org.nwapw.abacus.number
+
+import org.nwapw.abacus.Abacus
+
+/**
+ * A closed range designed specifically for [NumberInterface]
+ *
+ * Besides providing the usual functionality of a [ClosedRange], this range
+ * also handles promotion - that is, it's safe to use it with numbers of different
+ * implementations, even as starting and ending points.
+ *
+ * @property abacus the abacus instance used for promotion.
+ * @property start the starting point of the range.
+ * @property endInclusive the ending point of the range.
+ */
+class NumberRange(val abacus: Abacus,
+                  override val start: NumberInterface,
+                  override val endInclusive: NumberInterface): ClosedRange<NumberInterface> {
+
+    override operator fun contains(value: NumberInterface): Boolean {
+        val promotionResult = abacus.promotionManager.promote(start, endInclusive, value)
+        val newStart = promotionResult.items[0]
+        val newEnd = promotionResult.items[1]
+        val newValue = promotionResult.items[2]
+        return newValue >= newStart && newValue <= newEnd
+    }
+
+}

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

@@ -0,0 +1,24 @@
+package org.nwapw.abacus.number
+
+import org.nwapw.abacus.Abacus
+
+/**
+ * A utility class for creating [NumberRange] instances.
+ *
+ * Unlike a regular [ClosedRange], a NumberRange must have a third parameter,
+ * which is the [Abacus] instance that is used for promotion. However, the ".." operator
+ * is infix, and can only take two parameters. The solution is, instead of returning instances
+ * of NumberRange directly, to return a builder, which then provides a [with] infix function
+ * to attach it to an instance of Abacus.
+ * @property start the beginning of the range.
+ * @property endInclusive the end of the range.
+ */
+class NumberRangeBuilder(private val start: NumberInterface, private val endInclusive: NumberInterface) {
+
+    /**
+     * Generate a [NumberRange] with the given instance of [abacus].
+     * @return a new range with the given instance of Abacus.
+     */
+    infix fun with(abacus: Abacus) = NumberRange(abacus, start, endInclusive)
+
+}

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

@@ -1,6 +1,7 @@
 package org.nwapw.abacus.number
 
 import org.nwapw.abacus.Abacus
+import org.nwapw.abacus.exception.PromotionException
 import org.nwapw.abacus.plugin.NumberImplementation
 import org.nwapw.abacus.plugin.PluginListener
 import org.nwapw.abacus.plugin.PluginManager
@@ -37,21 +38,6 @@ class PromotionManager(val abacus: Abacus) : PluginListener {
         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
@@ -60,22 +46,30 @@ class PromotionManager(val abacus: Abacus) : PluginListener {
      * @param numbers the numbers to promote.
      * @return the resulting promotion result.
      */
-    fun promote(vararg numbers: NumberInterface): PromotionResult? {
+    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)
+            else computePaths[pluginManager.interfaceImplementationFor(it.javaClass) to highestPriority]
-                    ?.promote(it) ?: return null
+                    ?.promote(it) ?: throw PromotionException()
         }.toTypedArray(), promotedTo = highestPriority)
     }
 
-    override fun onLoad(manager: PluginManager?) {
+    override fun onLoad(manager: PluginManager) {
-
+        val implementations = manager.allNumberImplementations.map { manager.numberImplementationFor(it) }
+        for(first in implementations) {
+            for(second in implementations) {
+                val promoteFrom = if(second.priority > first.priority) first else second
+                val promoteTo = if(second.priority > first.priority) second else first
+                val path = computePathBetween(promoteFrom, promoteTo)
+                computePaths[promoteFrom to promoteTo] = path
+            }
+        }
     }
 
-    override fun onUnload(manager: PluginManager?) {
+    override fun onUnload(manager: PluginManager) {
         computePaths.clear()
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/BinaryNode.kt

@@ -11,10 +11,10 @@ package org.nwapw.abacus.tree
  * @param left the left node.
  * @param right the right node.
  */
-abstract class BinaryNode(val operation: String, val left: TreeNode? = null, val right: TreeNode?) : TreeNode() {
+abstract class BinaryNode(val operation: String, val left: TreeNode, val right: TreeNode) : TreeNode() {
 
     override fun toString(): String {
-        return "(" + (left?.toString() ?: "null") + operation + (right?.toString() ?: "null") + ")"
+        return "(" + left.toString() + operation + right.toString() + ")"
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/tree/CallNode.kt

@@ -7,13 +7,9 @@ package org.nwapw.abacus.tree
  * to extend this functionality.
  *
  * @param callTo the name of the things being called.
+ * @param children the children of this node.
  */
-abstract class CallNode(val callTo: String) : TreeNode() {
+abstract class CallNode(val callTo: String, val children: List<TreeNode>) : TreeNode() {
-
-    /**
-     * The list of children this node has.
-     */
-    val children: MutableList<TreeNode> = mutableListOf()
 
     override fun toString(): String {
         val buffer = StringBuffer()

core/src/main/kotlin/org/nwapw/abacus/tree/EvaluationResult.kt

@@ -3,4 +3,4 @@ package org.nwapw.abacus.tree
 import org.nwapw.abacus.context.MutableEvaluationContext
 import org.nwapw.abacus.number.NumberInterface
 
-data class EvaluationResult(val value: NumberInterface?, val resultingContext: MutableEvaluationContext)
+data class EvaluationResult(val value: NumberInterface, val resultingContext: MutableEvaluationContext)

core/src/main/kotlin/org/nwapw/abacus/tree/FunctionNode.kt

@@ -8,10 +8,10 @@ package org.nwapw.abacus.tree
  *
  * @param function the function string.
  */
-class FunctionNode(function: String) : CallNode(function) {
+class FunctionNode(function: String, children: List<TreeNode>) : CallNode(function, children) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
-        val children = Array<Any>(children.size, { children[it].reduce(reducer) ?: return null; })
+        val children = Array<Any>(children.size, { children[it].reduce(reducer) })
         return reducer.reduceNode(this, *children)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/NumberBinaryNode.kt

@@ -10,12 +10,12 @@ package org.nwapw.abacus.tree
  * @param left the left child of this node.
  * @param right the right child of this node.
  */
-class NumberBinaryNode(operation: String, left: TreeNode?, right: TreeNode?)
+class NumberBinaryNode(operation: String, left: TreeNode, right: TreeNode)
     : BinaryNode(operation, left, right) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
-        val left = left?.reduce(reducer) ?: return null
+        val left = left.reduce(reducer)
-        val right = right?.reduce(reducer) ?: return null
+        val right = right.reduce(reducer)
         return reducer.reduceNode(this, left, right)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/NumberNode.kt

@@ -10,7 +10,7 @@ package org.nwapw.abacus.tree
  */
 class NumberNode(val number: String) : TreeNode() {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
         return reducer.reduceNode(this)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/NumberReducer.kt

@@ -2,6 +2,8 @@ package org.nwapw.abacus.tree
 
 import org.nwapw.abacus.Abacus
 import org.nwapw.abacus.context.EvaluationContext
+import org.nwapw.abacus.exception.NumberReducerException
+import org.nwapw.abacus.exception.ReductionException
 import org.nwapw.abacus.number.NumberInterface
 
 class NumberReducer(val abacus: Abacus, context: EvaluationContext) : Reducer<NumberInterface> {
@@ -12,18 +14,18 @@ class NumberReducer(val abacus: Abacus, context: EvaluationContext) : Reducer<Nu
         this.context.reducer = this
     }
 
-    override fun reduceNode(treeNode: TreeNode, vararg children: Any): NumberInterface? {
+    override fun reduceNode(treeNode: TreeNode, vararg children: Any): NumberInterface {
         val promotionManager = abacus.promotionManager
         return when(treeNode){
             is NumberNode -> {
-                context.inheritedNumberImplementation?.instanceForString(treeNode.number)
+                context.inheritedNumberImplementation.instanceForString(treeNode.number)
             }
             is VariableNode -> {
                 val variable = context.getVariable(treeNode.variable)
                 if(variable != null) return variable
                 val definition = context.getDefinition(treeNode.variable)
                 if(definition != null) return definition.reduce(this)
-                null
+                throw NumberReducerException("variable is not defined.")
             }
             is NumberUnaryNode -> {
                 val child = children[0] as NumberInterface
@@ -34,29 +36,29 @@ class NumberReducer(val abacus: Abacus, context: EvaluationContext) : Reducer<Nu
             is NumberBinaryNode -> {
                 val left = children[0] as NumberInterface
                 val right = children[1] as NumberInterface
-                val promotionResult = promotionManager.promote(left, right) ?: return null
+                val promotionResult = promotionManager.promote(left, right)
                 context.numberImplementation = promotionResult.promotedTo
                 abacus.pluginManager.operatorFor(treeNode.operation).apply(context, *promotionResult.items)
             }
             is FunctionNode -> {
                 val promotionResult = promotionManager
-                        .promote(*children.map { it as NumberInterface }.toTypedArray()) ?: return null
+                        .promote(*children.map { it as NumberInterface }.toTypedArray())
                 context.numberImplementation = promotionResult.promotedTo
                 abacus.pluginManager.functionFor(treeNode.callTo).apply(context, *promotionResult.items)
             }
             is TreeValueUnaryNode -> {
                 abacus.pluginManager.treeValueOperatorFor(treeNode.operation)
-                        .apply(context, treeNode.applyTo ?: return null)
+                        .apply(context, treeNode.applyTo)
             }
             is TreeValueBinaryNode -> {
                 abacus.pluginManager.treeValueOperatorFor(treeNode.operation)
-                        .apply(context, treeNode.left ?: return null, treeNode.right ?: return null)
+                        .apply(context, treeNode.left, treeNode.right)
             }
             is TreeValueFunctionNode -> {
                 abacus.pluginManager.treeValueFunctionFor(treeNode.callTo)
                         .apply(context, *treeNode.children.toTypedArray())
             }
-            else -> null
+            else -> throw ReductionException("unrecognized tree node.")
         }
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/NumberUnaryNode.kt

@@ -8,11 +8,11 @@ package org.nwapw.abacus.tree
  * @param operation the operation this node performs.
  * @param child the child this node should be applied to.
  */
-class NumberUnaryNode(operation: String, child: TreeNode?)
+class NumberUnaryNode(operation: String, child: TreeNode)
     : UnaryNode(operation, child) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
-        val child = applyTo?.reduce(reducer) ?: return null
+        val child = applyTo.reduce(reducer)
         return reducer.reduceNode(this, child)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/Reducer.kt

@@ -14,6 +14,6 @@ interface Reducer<out T> {
      * @param treeNode the tree node to reduce.
      * @param children the list of children, of type T.
      */
-    fun reduceNode(treeNode: TreeNode, vararg children: Any): T?
+    fun reduceNode(treeNode: TreeNode, vararg children: Any): T
 
 }

core/src/main/kotlin/org/nwapw/abacus/tree/TreeNode.kt

@@ -5,6 +5,6 @@ package org.nwapw.abacus.tree
  */
 abstract class TreeNode {
 
-    abstract fun <T : Any> reduce(reducer: Reducer<T>): T?
+    abstract fun <T : Any> reduce(reducer: Reducer<T>): T
 
 }

core/src/main/kotlin/org/nwapw/abacus/tree/TreeValueBinaryNode.kt

@@ -11,10 +11,10 @@ package org.nwapw.abacus.tree
  * @param left the left child of this node.
  * @param right the right child of this node.
  */
-class TreeValueBinaryNode(operation: String, left: TreeNode?, right: TreeNode?)
+class TreeValueBinaryNode(operation: String, left: TreeNode, right: TreeNode)
     : BinaryNode(operation, left, right) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
         return reducer.reduceNode(this)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/TreeValueFunctionNode.kt

@@ -7,9 +7,9 @@ package org.nwapw.abacus.tree
  * is mostly to help the reducer. Besides that, this class also does not
  * even attempt to reduce its children.
  */
-class TreeValueFunctionNode(name: String) : CallNode(name) {
+class TreeValueFunctionNode(name: String, children: List<TreeNode>) : CallNode(name, children) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
         return reducer.reduceNode(this)
     }
 

core/src/main/kotlin/org/nwapw/abacus/tree/TreeValueUnaryNode.kt

@@ -9,11 +9,11 @@ package org.nwapw.abacus.tree
  * @param operation the operation this node performs.
  * @param child the node the operation should be applied to.
  */
-class TreeValueUnaryNode(operation: String, child: TreeNode?)
+class TreeValueUnaryNode(operation: String, child: TreeNode)
     : UnaryNode(operation, child) {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
-        return reducer.reduceNode(this);
+        return reducer.reduceNode(this)
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/tree/UnaryNode.kt

@@ -9,10 +9,10 @@ package org.nwapw.abacus.tree
  * @param operation the operation applied to the given node.
  * @param applyTo the node to which the operation will be applied.
  */
-abstract class UnaryNode(val operation: String, val applyTo: TreeNode? = null) : TreeNode() {
+abstract class UnaryNode(val operation: String, val applyTo: TreeNode) : TreeNode() {
 
     override fun toString(): String {
-        return "(" + (applyTo?.toString() ?: "null") + ")" + operation
+        return "(" + applyTo.toString() + ")" + operation
     }
 
 }

core/src/main/kotlin/org/nwapw/abacus/tree/VariableNode.kt

@@ -10,7 +10,7 @@ package org.nwapw.abacus.tree
  */
 class VariableNode(val variable: String) : TreeNode() {
 
-    override fun <T : Any> reduce(reducer: Reducer<T>): T? {
+    override fun <T : Any> reduce(reducer: Reducer<T>): T {
         return reducer.reduceNode(this)
     }
 

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

@@ -5,7 +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.exception.DomainException;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.plugin.StandardPlugin;
 import org.nwapw.abacus.tree.TreeNode;
@@ -22,7 +22,6 @@ public class CalculationTests {
 
     private void testOutput(String input, String parseOutput, String output) {
         TreeNode parsedTree = abacus.parseString(input);
-        Assert.assertNotNull(parsedTree);
         Assert.assertEquals(parsedTree.toString(), parseOutput);
         NumberInterface result = abacus.evaluateTree(parsedTree).getValue();
         Assert.assertNotNull(result);
@@ -31,7 +30,6 @@ public class CalculationTests {
 
     private void testDomainException(String input, String parseOutput) {
         TreeNode parsedTree = abacus.parseString(input);
-        Assert.assertNotNull(parsedTree);
         Assert.assertEquals(parsedTree.toString(), parseOutput);
         try {
             abacus.evaluateTree(parsedTree);

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

@@ -0,0 +1,97 @@
+package org.nwapw.abacus.tests;
+
+import org.junit.Assert;
+import org.junit.BeforeClass;
+import org.junit.Test;
+import org.nwapw.abacus.Abacus;
+import org.nwapw.abacus.config.Configuration;
+import org.nwapw.abacus.number.NaiveNumber;
+import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.number.NumberRange;
+import org.nwapw.abacus.number.PreciseNumber;
+import org.nwapw.abacus.plugin.StandardPlugin;
+
+import java.util.function.Function;
+
+public class RangeTests {
+
+    private static Abacus abacus = new Abacus(new Configuration( "precise", new String[]{}));
+    private static Function<NumberInterface, NumberInterface> naivePromotion = i -> new NaiveNumber((i.toString()));
+    private static Function<NumberInterface, NumberInterface> precisePromotion = i -> new PreciseNumber((i.toString()));
+
+    @BeforeClass
+    public static void prepareTests() {
+        abacus.getPluginManager().addInstantiated(new StandardPlugin(abacus.getPluginManager()));
+        abacus.reload();
+    }
+
+    public static NumberRange naiveRange(String bottom, String top) {
+        return new NaiveNumber(bottom).rangeTo(new NaiveNumber(top)).with(abacus);
+    }
+
+    @Test
+    public void testNaiveRange(){
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertTrue(range.getStart().toString().startsWith("0"));
+        Assert.assertTrue(range.getEndInclusive().toString().startsWith("10"));
+    }
+
+    @Test
+    public void testNaiveRangeBelow() {
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertFalse(range.contains(new NaiveNumber("-10")));
+    }
+
+    @Test
+    public void testNaiveRangeAbove() {
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertFalse(range.contains(new NaiveNumber("20")));
+    }
+
+    @Test
+    public void testNaiveRangeJustWithinBottom() {
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertTrue(range.contains(new NaiveNumber("0")));
+    }
+
+    @Test
+    public void testNaiveRangeJustWithinTop() {
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertTrue(range.contains(new NaiveNumber("10")));
+    }
+
+    @Test
+    public void testNaiveRangeWithin() {
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertTrue(range.contains(new NaiveNumber("5")));
+    }
+
+    public static void addTestPromotionPaths() {
+        StandardPlugin.IMPLEMENTATION_NAIVE.getPromotionPaths().put("precise", precisePromotion);
+        StandardPlugin.IMPLEMENTATION_PRECISE.getPromotionPaths().put("naive", naivePromotion);
+        abacus.reload();
+    }
+
+    public static void removeTestPromotionPaths() {
+        StandardPlugin.IMPLEMENTATION_NAIVE.getPromotionPaths().remove("precise");
+        StandardPlugin.IMPLEMENTATION_NAIVE.getPromotionPaths().remove("naive");
+        abacus.reload();
+    }
+
+    @Test
+    public void testPromotionWithin() {
+        addTestPromotionPaths();
+        NumberRange range = naiveRange("0", "10");
+        Assert.assertTrue(range.contains(new PreciseNumber("5")));
+        removeTestPromotionPaths();
+    }
+
+    @Test
+    public void testPromotionOutside(){
+        addTestPromotionPaths();
+        NumberRange range = naiveRange("0","10");
+        Assert.assertFalse(range.contains(new PreciseNumber("20")));
+        removeTestPromotionPaths();
+    }
+
+}

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

@@ -12,9 +12,9 @@ import javafx.util.Callback;
 import javafx.util.StringConverter;
 import org.nwapw.abacus.Abacus;
 import org.nwapw.abacus.config.Configuration;
+import org.nwapw.abacus.exception.AbacusException;
 import org.nwapw.abacus.function.Documentation;
 import org.nwapw.abacus.function.DocumentationType;
-import org.nwapw.abacus.function.DomainException;
 import org.nwapw.abacus.number.*;
 import org.nwapw.abacus.plugin.ClassFinder;
 import org.nwapw.abacus.plugin.PluginListener;
@@ -142,21 +142,13 @@ public class AbacusController implements PluginListener {
         private String attemptCalculation() {
             try {
                 TreeNode constructedTree = abacus.parseString(inputField.getText());
-                if (constructedTree == null) {
-                    return ERR_SYNTAX;
-                }
                 EvaluationResult result = abacus.evaluateTree(constructedTree);
                 NumberInterface evaluatedNumber = result.getValue();
-                if (evaluatedNumber == null) {
-                    return ERR_EVAL;
-                }
                 String resultingString = evaluatedNumber.toString();
                 historyData.add(new HistoryModel(inputField.getText(), constructedTree.toString(), resultingString));
                 abacus.applyToContext(result.getResultingContext());
                 return resultingString;
-            } catch (ComputationInterruptedException exception) {
+            } catch (AbacusException exception) {
-                return ERR_STOP;
-            } catch (DomainException exception) {
                 return exception.getMessage();
             } catch (RuntimeException exception) {
                 exception.printStackTrace();
@@ -363,7 +355,12 @@ public class AbacusController implements PluginListener {
             enabledPlugins.add(plugin);
         }
         PluginManager pluginManager = abacus.getPluginManager();
-        functionList.addAll(manager.getAllFunctions().stream().map(name -> pluginManager.documentationFor(name, DocumentationType.FUNCTION))
+        functionList.addAll(manager.getAllFunctions().stream().map(name -> {
+            Documentation documentationInstance = pluginManager.documentationFor(name, DocumentationType.FUNCTION);
+            if(documentationInstance == null)
+                documentationInstance = new Documentation(name, "", "", "", DocumentationType.FUNCTION);
+            return documentationInstance;
+        })
                 .collect(Collectors.toCollection(ArrayList::new)));
         functionList.addAll(manager.getAllTreeValueFunctions().stream().map(name -> pluginManager.documentationFor(name, DocumentationType.TREE_VALUE_FUNCTION))
                 .collect(Collectors.toCollection(ArrayList::new)));