Move the StandardPlugin into a "standard" package along with the ops.

Replace some more cases where null is used with Exceptions.

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/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/ReductionException.java

@@ -1,16 +1,14 @@
 package org.nwapw.abacus.exception;
 
 /**
- * An exception thrown primarily from Tree Value operators and functions,
+ * An exception thrown from TreeReducers.
- * which have to deal with the result of a Reducer as well as the results
- * of Applicable.
  */
-public class EvaluationException extends AbacusException {
+public class ReductionException extends AbacusException {
 
     /**
      * Creates a new EvaluationException with the default string.
      */
-    public EvaluationException() {
+    public ReductionException() {
         this("");
     }
 
@@ -18,7 +16,7 @@ public class EvaluationException extends AbacusException {
      * Creates a new EvaluationError with the given message string.
      * @param message the message string.
      */
-    public EvaluationException(String message) {
+    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/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;
@@ -123,8 +124,8 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
      * @param matches the list of tokens from the source string.
      * @return the construct tree expression.
      */
-    public TreeNode constructRecursive(List<Match<TokenType>> matches) {
+    public TreeNode constructRecursive(List<? extends 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 {
@@ -157,10 +156,9 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             List<TreeNode> children = new ArrayList<>();
             while (!matches.isEmpty() && matches.get(0).getType() != TokenType.INTERNAL_FUNCTION_END) {
                 TreeNode argument = constructRecursive(matches);
-                if (argument == null) return null;
                 children.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) {
@@ -170,16 +168,17 @@ public class ShuntingYardParser implements Parser<Match<TokenType>>, PluginListe
             }
             return node;
         }
-        return null;
+        throw new ParseException("unrecognized token");
     }
 
     @Override
-    public TreeNode constructTree(List<Match<TokenType>> tokens) {
+    public TreeNode constructTree(List<? extends 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/Tokenizer.java

@@ -1,20 +0,0 @@
-package org.nwapw.abacus.parsing;
-
-import java.util.List;
-
-/**
- * Interface that provides the ability to convert a string into a list of tokens.
- *
- * @param <T> the type of the tokens produced.
- */
-public interface Tokenizer<T> {
-
-    /**
-     * Converts a string into tokens.
-     *
-     * @param string the string to convert.
-     * @return the list of tokens, or null on error.
-     */
-    public List<T> tokenizeString(String string);
-
-}

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

@@ -1,50 +0,0 @@
-package org.nwapw.abacus.parsing;
-
-import org.nwapw.abacus.tree.TreeNode;
-
-import java.util.List;
-
-/**
- * TreeBuilder class used to piece together a Tokenizer and
- * Parser of the same kind. This is used to essentially avoid
- * working with any parameters at all, and the generics
- * in this class are used only to ensure the tokenizer and parser
- * are of the same type.
- *
- * @param <T> the type of tokens created by the tokenizer and used by the parser.
- */
-public class TreeBuilder<T> {
-
-    /**
-     * The tokenizer used to convert a string into tokens.
-     */
-    private Tokenizer<T> tokenizer;
-    /**
-     * The parser used to parse a list of tokens into a tree.
-     */
-    private Parser<T> parser;
-
-    /**
-     * Create a new Tree Builder with the given tokenizer and parser
-     *
-     * @param tokenizer the tokenizer to turn strings into tokens
-     * @param parser    the parser to turn tokens into a tree
-     */
-    public TreeBuilder(Tokenizer<T> tokenizer, Parser<T> parser) {
-        this.tokenizer = tokenizer;
-        this.parser = parser;
-    }
-
-    /**
-     * Parse the given string into a tree.
-     *
-     * @param input the string to parse into a tree.
-     * @return the resulting tree.
-     */
-    public TreeNode fromString(String input) {
-        List<T> tokens = tokenizer.tokenizeString(input);
-        if (tokens == null) return null;
-        return parser.constructTree(tokens);
-    }
-
-}

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

@@ -1,12 +1,14 @@
-package org.nwapw.abacus.plugin;
+package org.nwapw.abacus.plugin.standard;
 
 import org.nwapw.abacus.context.MutableEvaluationContext;
 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.TreeNode;
+import org.nwapw.abacus.plugin.NumberImplementation;
-import org.nwapw.abacus.tree.VariableNode;
+import org.nwapw.abacus.plugin.Plugin;
+import org.nwapw.abacus.plugin.PluginManager;
+import org.nwapw.abacus.plugin.standard.operator.*;
 
 import java.util.ArrayList;
 import java.util.HashMap;
@@ -20,93 +22,27 @@ public class StandardPlugin extends Plugin {
     /**
      * The set operator.
      */
-    public final TreeValueOperator opSet = new TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+    public static final TreeValueOperator OP_SET = new OperatorSet();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, TreeNode[] params) {
-            return params.length == 2 && params[0] instanceof VariableNode;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, TreeNode[] params) {
-            String assignTo = ((VariableNode) params[0]).getVariable();
-            NumberInterface value = params[1].reduce(context.getInheritedReducer());
-            context.setVariable(assignTo, value);
-            return value;
-        }
-    };
     /**
      * The define operator.
      */
-    public final TreeValueOperator opDefine = new TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+    public final TreeValueOperator OP_DEFINE = new OperatorDefine();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, TreeNode[] params) {
-            return params.length == 2 && params[0] instanceof VariableNode;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, TreeNode[] params) {
-            String assignTo = ((VariableNode) params[0]).getVariable();
-            context.setDefinition(assignTo, params[1]);
-            return params[1].reduce(context.getInheritedReducer());
-        }
-    };
     /**
      * The addition operator, +
      */
-    public static final NumberOperator OP_ADD = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+    public static final NumberOperator OP_ADD = new OperatorAdd();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return params[0].add(params[1]);
-        }
-    };
     /**
      * The subtraction operator, -
      */
-    public static final NumberOperator OP_SUBTRACT = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+    public static final NumberOperator OP_SUBTRACT = new OperatorSubtract();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return params[0].subtract(params[1]);
-
-        }
-    };
     /**
      * The negation operator, -
      */
-    public static final NumberOperator OP_NEGATE = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.UNARY_PREFIX, 0) {
+    public static final NumberOperator OP_NEGATE = new OperatorNegate();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 1;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return params[0].negate();
-        }
-    };
     /**
      * The multiplication operator, *
      */
-    public static final NumberOperator OP_MULTIPLY = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
+    public static final NumberOperator OP_MULTIPLY = new OperatorMultiply();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return params[0].multiply(params[1]);
-        }
-    };
     /**
      * The implementation for double-based naive numbers.
      */
@@ -161,96 +97,19 @@ public class StandardPlugin extends Plugin {
     /**
      * The division operator, /
      */
-    public static final NumberOperator OP_DIVIDE = new NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
+    public static final NumberOperator OP_DIVIDE = new OperatorDivide();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2 && params[1].compareTo(context.getInheritedNumberImplementation().instanceForString(Integer.toString(0))) != 0;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return params[0].divide(params[1]);
-        }
-    };
     /**
      * The factorial operator, !
      */
-    public static final NumberOperator OP_FACTORIAL = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0) {
+    public static final NumberOperator OP_FACTORIAL = new OperatorFactorial();
-        //private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 1
-                    && params[0].fractionalPart().compareTo(context.getInheritedNumberImplementation().instanceForString("0")) == 0
-                    && params[0].signum() >= 0;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            NumberImplementation implementation = context.getInheritedNumberImplementation();
-            if (params[0].signum() == 0) {
-                return implementation.instanceForString("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.
-            while ((multiplier = multiplier.subtract(one)).signum() == 1) {
-                factorial = factorial.multiply(multiplier);
-            }
-            return factorial;
-                /*if(!storedList.containsKey(params[0].getClass())){
-                    storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
-                    storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
-                    storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
-                }*/
-        }
-    };
     /**
      * The permutation operator.
      */
-    public static final NumberOperator OP_NPR = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
+    public static final NumberOperator OP_NPR = new OperatorNpr();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2 && params[0].fractionalPart().signum() == 0
-                    && params[1].fractionalPart().signum() == 0;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            NumberImplementation implementation = context.getInheritedNumberImplementation();
-            if (params[0].compareTo(params[1]) < 0 ||
-                    params[0].signum() < 0 ||
-                    (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(implementation.instanceForString("2"));
-            if (remainingMultiplications.compareTo(halfway) > 0) {
-                remainingMultiplications = params[0].subtract(remainingMultiplications);
-            }
-            while (remainingMultiplications.signum() > 0) {
-                total = total.multiply(multiplyBy);
-                remainingMultiplications = remainingMultiplications.subtract(implementation.instanceForString("1"));
-                multiplyBy = multiplyBy.subtract(implementation.instanceForString("1"));
-            }
-            return total;
-        }
-    };
     /**
      * The combination operator.
      */
-    public static final NumberOperator OP_NCR = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
+    public static final NumberOperator OP_NCR = new OperatorNcr();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            return params.length == 2 && params[0].fractionalPart().signum() == 0
-                    && params[1].fractionalPart().signum() == 0;
-        }
-
-        @Override
-        public NumberInterface applyInternal(MutableEvaluationContext context, NumberInterface[] params) {
-            return OP_NPR.apply(context, params).divide(OP_FACTORIAL.apply(context, params[1]));
-        }
-    };
     /**
      * The absolute value function, abs(-3) = 3
      */
@@ -332,7 +191,7 @@ 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;
@@ -363,34 +222,7 @@ public class StandardPlugin extends Plugin {
     /**
      * The caret / pow operator, ^
      */
-    public static final NumberOperator OP_CARET = new NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2) {
+    public static final NumberOperator OP_CARET = new OperatorCaret();
-        @Override
-        public boolean matchesParams(MutableEvaluationContext context, NumberInterface[] params) {
-            NumberInterface zero = context.getInheritedNumberImplementation().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(MutableEvaluationContext context, NumberInterface[] params) {
-            NumberImplementation implementation = context.getInheritedNumberImplementation();
-            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(context, params[1]).compareTo(implementation.instanceForString(Integer.toString(Integer.MAX_VALUE))) < 0
-                    && FUNCTION_ABS.apply(context, params[1]).compareTo(implementation.instanceForString("1")) >= 0) {
-                NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
-                return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(context, newParams));
-            }
-            return FUNCTION_EXP.apply(context, FUNCTION_LN.apply(context, FUNCTION_ABS.apply(context, params[0])).multiply(params[1]));
-        }
-    };
     /**
      * The square root function.
      */
@@ -715,7 +547,7 @@ 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 {
@@ -756,8 +588,8 @@ public class StandardPlugin extends Plugin {
         registerOperator("^", OP_CARET);
         registerOperator("!", OP_FACTORIAL);
 
-        registerTreeValueOperator("=", opSet);
+        registerTreeValueOperator("=", OP_SET);
-        registerTreeValueOperator(":=", opDefine);
+        registerTreeValueOperator(":=", OP_DEFINE);
 
         registerOperator("nPr", OP_NPR);
         registerOperator("nCr", OP_NCR);

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

@@ -8,7 +8,7 @@ import org.nwapw.abacus.parsing.LexerTokenizer
 import org.nwapw.abacus.parsing.ShuntingYardParser
 import org.nwapw.abacus.parsing.TreeBuilder
 import org.nwapw.abacus.plugin.PluginManager
-import org.nwapw.abacus.plugin.StandardPlugin
+import org.nwapw.abacus.plugin.standard.StandardPlugin
 import org.nwapw.abacus.tree.EvaluationResult
 import org.nwapw.abacus.tree.NumberReducer
 import org.nwapw.abacus.tree.TreeNode
@@ -88,7 +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/number/NumberInterface.kt

@@ -1,253 +1,268 @@
-package org.nwapw.abacus.number;
+package org.nwapw.abacus.number
-
+
-import org.nwapw.abacus.exception.ComputationInterruptedException;
+import org.nwapw.abacus.exception.ComputationInterruptedException
-
+
-/**
+abstract class NumberInterface: Comparable<NumberInterface> {
- * An interface used to represent a number.
+
- */
+    /**
-public abstract class NumberInterface implements Comparable<NumberInterface> {
+     * Check if the thread was interrupted and
-
+     * throw an exception to end the computation.
-    /**
+     */
-     * Check if the thread was interrupted and
+    private fun checkInterrupted(){
-     * throw an exception to end the computation.
+        if(Thread.currentThread().isInterrupted)
-     */
+            throw ComputationInterruptedException()
-    private static void checkInterrupted() {
+    }
-        if (Thread.currentThread().isInterrupted())
+
-            throw new ComputationInterruptedException();
+    /**
-    }
+     * Returns the integer representation of this number, discarding any fractional part,
-
+     * if int can hold the value.
-    /**
+     *
-     * The maximum precision to which this number operates.
+     * @return the integer value of this number.
-     *
+     */
-     * @return the precision.
+    abstract fun intValue(): Int
-     */
+    /**
-    public abstract int getMaxPrecision();
+     * Same as Math.signum().
-
+     *
-    /**
+     * @return 1 if this number is positive, -1 if this number is negative, 0 if this number is 0.
-     * Multiplies this number by another, returning
+     */
-     * a new number instance.
+    abstract fun signum(): Int
-     *
+
-     * @param multiplier the multiplier
+    /**
-     * @return the result of the multiplication.
+     * The maximum precision to which this number operates.
-     */
+     */
-    protected abstract NumberInterface multiplyInternal(NumberInterface multiplier);
+    abstract val maxPrecision: Int
-
+    /**
-    /**
+     * Returns the smallest error this instance can tolerate depending
-     * Multiplies this number by another, returning
+     * on its precision and value.
-     * a new number instance. Also, checks if the
+     */
-     * thread has been interrupted, and if so, throws
+    abstract val maxError: NumberInterface
-     * an exception.
+
-     *
+    /**
-     * @param multiplier the multiplier
+     * Adds this number to another, returning
-     * @return the result of the multiplication.
+     * a new number instance.
-     */
+     *
-    public final NumberInterface multiply(NumberInterface multiplier) {
+     * @param summand the summand
-        checkInterrupted();
+     * @return the result of the summation.
-        return multiplyInternal(multiplier);
+     */
-    }
+    abstract fun addInternal(summand: NumberInterface): NumberInterface
-
+    /**
-    /**
+     * Subtracts another number from this number,
-     * Divides this number by another, returning
+     * a new number instance.
-     * a new number instance.
+     *
-     *
+     * @param subtrahend the subtrahend.
-     * @param divisor the divisor
+     * @return the result of the subtraction.
-     * @return the result of the division.
+     */
-     */
+    abstract fun subtractInternal(subtrahend: NumberInterface): NumberInterface
-    protected abstract NumberInterface divideInternal(NumberInterface divisor);
+    /**
-
+     * Multiplies this number by another, returning
-    /**
+     * a new number instance.
-     * Divides this number by another, returning
+     *
-     * a new number instance. Also, checks if the
+     * @param multiplier the multiplier
-     * thread has been interrupted, and if so, throws
+     * @return the result of the multiplication.
-     * an exception.
+     */
-     *
+    abstract fun multiplyInternal(multiplier: NumberInterface): NumberInterface
-     * @param divisor the divisor
+    /**
-     * @return the result of the division.
+     * Divides this number by another, returning
-     */
+     * a new number instance.
-    public final NumberInterface divide(NumberInterface divisor) {
+     *
-        checkInterrupted();
+     * @param divisor the divisor
-        return divideInternal(divisor);
+     * @return the result of the division.
-    }
+     */
-
+    abstract fun divideInternal(divisor: NumberInterface): NumberInterface
-    /**
+    /**
-     * Adds this number to another, returning
+     * Returns a new instance of this number with
-     * a new number instance.
+     * the sign flipped.
-     *
+     *
-     * @param summand the summand
+     * @return the new instance.
-     * @return the result of the summation.
+     */
-     */
+    abstract fun negateInternal(): NumberInterface
-    protected abstract NumberInterface addInternal(NumberInterface summand);
+    /**
-
+     * Raises this number to an integer power.
-    /**
+     *
-     * Adds this number to another, returning
+     * @param exponent the exponent to which to take the number.
-     * a new number instance. Also, checks if the
+     * @return the resulting value.
-     * thread has been interrupted, and if so, throws
+     */
-     * an exception.
+    abstract fun intPowInternal(pow: Int): NumberInterface
-     *
+    /**
-     * @param summand the summand
+     * Returns the least integer greater than or equal to the number.
-     * @return the result of the summation.
+     *
-     */
+     * @return the least integer greater or equal to the number, if int can hold the value.
-    public final NumberInterface add(NumberInterface summand) {
+     */
-        checkInterrupted();
+    abstract fun ceilingInternal(): NumberInterface
-        return addInternal(summand);
+    /**
-    }
+     * Return the greatest integer less than or equal to the number.
-
+     *
-    /**
+     * @return the greatest integer smaller or equal the number.
-     * Subtracts another number from this number,
+     */
-     * a new number instance.
+    abstract fun floorInternal(): NumberInterface
-     *
+    /**
-     * @param subtrahend the subtrahend.
+     * Returns the fractional part of the number.
-     * @return the result of the subtraction.
+     *
-     */
+     * @return the fractional part of the number.
-    protected abstract NumberInterface subtractInternal(NumberInterface subtrahend);
+     */
-
+    abstract fun fractionalPartInternal(): NumberInterface
-    /**
+
-     * Subtracts another number from this number,
+    /**
-     * a new number instance. Also, checks if the
+     * Adds this number to another, returning
-     * thread has been interrupted, and if so, throws
+     * a new number instance. Also, checks if the
-     * an exception.
+     * thread has been interrupted, and if so, throws
-     *
+     * an exception.
-     * @param subtrahend the subtrahend.
+     *
-     * @return the result of the subtraction.
+     * @param summand the summand
-     */
+     * @return the result of the summation.
-    public final NumberInterface subtract(NumberInterface subtrahend) {
+     */
-        checkInterrupted();
+    fun add(summand: NumberInterface): NumberInterface {
-        return subtractInternal(subtrahend);
+        checkInterrupted()
-    }
+        return addInternal(summand)
-
+    }
-    /**
+
-     * Returns a new instance of this number with
+    /**
-     * the sign flipped.
+     * Subtracts another number from this number,
-     *
+     * a new number instance. Also, checks if the
-     * @return the new instance.
+     * thread has been interrupted, and if so, throws
-     */
+     * an exception.
-    protected abstract NumberInterface negateInternal();
+     *
-
+     * @param subtrahend the subtrahend.
-
+     * @return the result of the subtraction.
-    /**
+     */
-     * Returns a new instance of this number with
+    fun subtract(subtrahend: NumberInterface): NumberInterface {
-     * the sign flipped. Also, checks if the
+        checkInterrupted()
-     * thread has been interrupted, and if so, throws
+        return subtractInternal(subtrahend)
-     * an exception.
+    }
-     *
+
-     * @return the new instance.
+    /**
-     */
+     * Multiplies this number by another, returning
-    public final NumberInterface negate() {
+     * a new number instance. Also, checks if the
-        checkInterrupted();
+     * thread has been interrupted, and if so, throws
-        return negateInternal();
+     * an exception.
-    }
+     *
-
+     * @param multiplier the multiplier
-    /**
+     * @return the result of the multiplication.
-     * Raises this number to an integer power.
+     */
-     *
+    fun multiply(multiplier: NumberInterface): NumberInterface {
-     * @param exponent the exponent to which to take the number.
+        checkInterrupted()
-     * @return the resulting value.
+        return multiplyInternal(multiplier)
-     */
+    }
-    protected abstract NumberInterface intPowInternal(int exponent);
+
-
+    /**
-    /**
+     * Divides this number by another, returning
-     * Raises this number to an integer power. Also, checks if the
+     * a new number instance. Also, checks if the
-     * thread has been interrupted, and if so, throws
+     * thread has been interrupted, and if so, throws
-     * an exception.
+     * an exception.
-     *
+     *
-     * @param exponent the exponent to which to take the number.
+     * @param divisor the divisor
-     * @return the resulting value.
+     * @return the result of the division.
-     */
+     */
-    public final NumberInterface intPow(int exponent) {
+    fun divide(divisor: NumberInterface): NumberInterface {
-        checkInterrupted();
+        checkInterrupted()
-        return intPowInternal(exponent);
+        return divideInternal(divisor)
-    }
+    }
-
+
-    /**
+    /**
-     * Same as Math.signum().
+     * Returns a new instance of this number with
-     *
+     * the sign flipped. Also, checks if the
-     * @return 1 if this number is positive, -1 if this number is negative, 0 if this number is 0.
+     * thread has been interrupted, and if so, throws
-     */
+     * an exception.
-    public abstract int signum();
+     *
-
+     * @return the new instance.
-    /**
+     */
-     * Returns the least integer greater than or equal to the number.
+    fun negate(): NumberInterface {
-     *
+        checkInterrupted()
-     * @return the least integer greater or equal to the number, if int can hold the value.
+        return negateInternal()
-     */
+    }
-    protected abstract NumberInterface ceilingInternal();
+
-
+    /**
-    /**
+     * Raises this number to an integer power. Also, checks if the
-     * Returns the least integer greater than or equal to the number.
+     * thread has been interrupted, and if so, throws
-     * Also, checks if the thread has been interrupted, and if so, throws
+     * an exception.
-     * an exception.
+     *
-     *
+     * @param exponent the exponent to which to take the number.
-     * @return the least integer bigger or equal to the number.
+     * @return the resulting value.
-     */
+     */
-    public final NumberInterface ceiling() {
+    fun intPow(exponent: Int): NumberInterface {
-        checkInterrupted();
+        checkInterrupted()
-        return ceilingInternal();
+        return intPowInternal(exponent)
-    }
+    }
-
+
-    /**
+    /**
-     * Return the greatest integer less than or equal to the number.
+     * Returns the least integer greater than or equal to the number.
-     *
+     * Also, checks if the thread has been interrupted, and if so, throws
-     * @return the greatest integer smaller or equal the number.
+     * an exception.
-     */
+     *
-    protected abstract NumberInterface floorInternal();
+     * @return the least integer bigger or equal to the number.
-
+     */
-    /**
+    fun ceiling(): NumberInterface {
-     * Return the greatest integer less than or equal to the number.
+        checkInterrupted()
-     * Also, checks if the thread has been interrupted, and if so, throws
+        return ceilingInternal()
-     * an exception.
+    }
-     *
+
-     * @return the greatest int smaller than or equal to the number.
+    /**
-     */
+     * Return the greatest integer less than or equal to the number.
-    public final NumberInterface floor() {
+     * Also, checks if the thread has been interrupted, and if so, throws
-        checkInterrupted();
+     * an exception.
-        return floorInternal();
+     *
-    }
+     * @return the greatest int smaller than or equal to the number.
-
+     */
-    /**
+    fun floor(): NumberInterface {
-     * Returns the fractional part of the number.
+        checkInterrupted()
-     *
+        return floorInternal()
-     * @return the fractional part of the number.
+    }
-     */
+
-    protected abstract NumberInterface fractionalPartInternal();
+    /**
-
+     * Returns the fractional part of the number, specifically x - floor(x).
-    /**
+     * Also, checks if the thread has been interrupted,
-     * Returns the fractional part of the number, specifically x - floor(x).
+     * and if so, throws an exception.
-     * Also, checks if the thread has been interrupted,
+     *
-     * and if so, throws an exception.
+     * @return the fractional part of the number.
-     *
+     */
-     * @return the fractional part of the number.
+    fun fractionalPart(): NumberInterface {
-     */
+        checkInterrupted()
-    public final NumberInterface fractionalPart() {
+        return fractionalPartInternal()
-        checkInterrupted();
+    }
-        return fractionalPartInternal();
+
-    }
+    /**
-
+     * 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
-     * Returns the integer representation of this number, discarding any fractional part,
+     * the NumberRange needs to promote values passed to it, which
-     * if int can hold the value.
+     * requires an abacus instance.
-     *
+     * @param other the value at the bottom of the range.
-     * @return the integer value of this number.
+     * @return the resulting range builder.
-     */
+     */
-    public abstract int intValue();
+    operator fun rangeTo(other: NumberInterface) = NumberRangeBuilder(this, other)
-
+
-    /**
+    /**
-     * Returns the smallest error this instance can tolerate depending
+     * Plus operator overloaded to allow "nice" looking math.
-     * on its precision and value.
+     * @param other the value to add to this number.
-     *
+     * @return the result of the addition.
-     * @return the smallest error that should be permitted in calculations.
+     */
-     */
+    operator fun plus(other: NumberInterface) = add(other)
-    public abstract NumberInterface getMaxError();
+    /**
-
+     * Minus operator overloaded to allow "nice" looking math.
-    /**
+     * @param other the value to subtract to this number.
-     * Returns a NumberRangeBuilder object, which is used to create a range.
+     * @return the result of the subtraction.
-     * The reason that this returns a builder and not an actual range is that
+     */
-     * the NumberRange needs to promote values passed to it, which
+    operator fun minus(other: NumberInterface) = subtract(other)
-     * requires an abacus instance.
+    /**
-     * @param other the value at the bottom of the range.
+     * Times operator overloaded to allow "nice" looking math.
-     * @return the resulting range builder.
+     * @param other the value to multiply this number by.
-     */
+     * @return the result of the multiplication.
-    public NumberRangeBuilder rangeTo(NumberInterface other){
+     */
-        return new NumberRangeBuilder(this, other);
+    operator fun times(other: NumberInterface) = multiply(other)
-    }
+    /**
-
+     * Divide operator overloaded to allow "nice" looking math.
-}
+     * @param other the value to divide this number by.
+     * @return the result of the division.
+     */
+    operator fun div(other: NumberInterface) = divide(other)
+    /**
+     * The plus operator.
+     * @return this number.
+     */
+    operator fun unaryPlus() = this
+    /**
+     * The minus operator.
+     * @return the negative of this number.
+     */
+    operator fun unaryMinus() = negate()
+
+}

core/src/main/kotlin/org/nwapw/abacus/parsing/Parser.kt

@@ -1,16 +1,17 @@
-package org.nwapw.abacus.parsing;
+package org.nwapw.abacus.parsing
 
-import org.nwapw.abacus.tree.TreeNode;
+import org.nwapw.abacus.tree.TreeNode
-
-import java.util.List;
 
 /**
- * An itnerface that provides the ability to convert a list of tokens
+ * Converter from tokens into a parse tree.
+ *
+ * An interface that provides the ability to convert a list of tokens
  * into a parse tree.
  *
  * @param <T> the type of tokens accepted by this parser.
  */
-public interface Parser<T> {
+
+interface Parser<in T> {
 
     /**
      * Constructs a tree out of the given tokens.
@@ -18,5 +19,6 @@ public interface Parser<T> {
      * @param tokens the tokens to construct a tree from.
      * @return the constructed tree, or null on error.
      */
-    public TreeNode constructTree(List<T> tokens);
+    fun constructTree(tokens: List<T>): TreeNode
-}
+
+}

core/src/main/kotlin/org/nwapw/abacus/parsing/Tokenizer.kt

@@ -0,0 +1,21 @@
+package org.nwapw.abacus.parsing
+
+/**
+ * Converter from string to tokens.
+ *
+ * Interface that converts a string into a list
+ * of tokens of a certain type.
+ *
+ * @param <T> the type of the tokens produced.
+ */
+interface Tokenizer<out T> {
+
+    /**
+     * Converts a string into tokens.
+     *
+     * @param string the string to convert.
+     * @return the list of tokens, or null on error.
+     */
+    fun tokenizeString(string: String):  List<T>
+
+}

core/src/main/kotlin/org/nwapw/abacus/parsing/TreeBuilder.kt

@@ -0,0 +1,26 @@
+package org.nwapw.abacus.parsing
+
+import org.nwapw.abacus.tree.TreeNode
+
+/**
+ * Class to combine a [Tokenizer] and a [Parser]
+ *
+ * TreeBuilder class used to piece together a Tokenizer and
+ * Parser of the same kind. This is used to essentially avoid
+ * working with any parameters at all, and the generics
+ * in this class are used only to ensure the tokenizer and parser
+ * are of the same type.
+ *
+ * @param <T> the type of tokens created by the tokenizer and used by the parser.
+ */
+class TreeBuilder<T>(private val tokenizer: Tokenizer<T>, private val parser: Parser<T>) {
+
+    /**
+     * Parses the given [string] into a tree.
+     *
+     * @param string the string to parse into a tree.
+     * @return the resulting tree.
+     */
+    fun fromString(string: String): TreeNode = parser.constructTree(tokenizer.tokenizeString(string))
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorAdd.kt

@@ -0,0 +1,21 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The addition operator.
+ *
+ * This is a standard operator that simply performs addition.
+ */
+class OperatorAdd: NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params[0] + params[1]
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorCaret.kt

@@ -0,0 +1,38 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.plugin.standard.StandardPlugin.*
+
+/**
+ * The power operator.
+ *
+ * This is a standard operator that brings one number to the power of the other.
+ */
+class OperatorCaret: NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2
+                    && !(params[0].signum() == 0 && params[1].signum() == 0)
+                    && !(params[0].signum() == -1 && params[1].fractionalPart().signum() != 0)
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>): NumberInterface {
+        val implementation = context.inheritedNumberImplementation
+        if (params[0].signum() == 0)
+            return implementation.instanceForString("0")
+        else if (params[1].signum() == 0)
+            return implementation.instanceForString("1")
+        //Detect integer bases:
+        if (params[0].fractionalPart().signum() == 0
+                && FUNCTION_ABS.apply(context, params[1]) < implementation.instanceForString(Integer.toString(Integer.MAX_VALUE))
+                && FUNCTION_ABS.apply(context, params[1]) >= implementation.instanceForString("1")) {
+            val newParams = arrayOf(params[0], params[1].fractionalPart())
+            return params[0].intPow(params[1].floor().intValue()) * applyInternal(context, newParams)
+        }
+        return FUNCTION_EXP.apply(context, FUNCTION_LN.apply(context, FUNCTION_ABS.apply(context, params[0])) * params[1])
+    }
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorDefine.kt

@@ -0,0 +1,28 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.function.TreeValueOperator
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.tree.TreeNode
+import org.nwapw.abacus.tree.VariableNode
+
+/**
+ * The definition operator.
+ *
+ * This is a standard operator that creates a definition - something that doesn't capture variable values
+ * when it's created, but rather the variables themselves, and changes when the variables it uses change.
+ */
+class OperatorDefine: TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out TreeNode>) =
+            params.size == 2 && params[0] is VariableNode
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out TreeNode>): NumberInterface {
+        val assignTo = (params[0] as VariableNode).variable
+        context.setDefinition(assignTo, params[1])
+        return params[1].reduce(context.inheritedReducer)
+    }
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorDivide.kt

@@ -0,0 +1,21 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The division operator.
+ *
+ * This is a standard operator that simply performs division.
+ */
+class OperatorDivide: NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params[0] / params[1]
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorFactorial.kt

@@ -0,0 +1,37 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The factorial operator.
+ *
+ * This is a standard operator that simply evaluates the factorial of a number.
+ */
+class OperatorFactorial: NumberOperator(OperatorAssociativity.LEFT, OperatorType.UNARY_POSTFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+        params.size == 1
+                && params[0].fractionalPart().signum() == 0
+                && params[0].signum() >= 0
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>): NumberInterface {
+        val implementation = context.inheritedNumberImplementation
+        val one = implementation.instanceForString("1")
+        if (params[0].signum() == 0) {
+            return one
+        }
+        var factorial = params[0]
+        var multiplier = params[0] - one
+        //It is necessary to later prevent calls of factorial on anything but non-negative integers.
+        while (multiplier.signum() == 1) {
+            factorial *= multiplier
+            multiplier -= one
+        }
+        return factorial
+    }
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorMultiply.kt

@@ -0,0 +1,21 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The multiplication operator.
+ *
+ * This is a standard operator that simply performs multiplication.
+ */
+class OperatorMultiply: NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params[0] * params[1]
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorNcr.kt

@@ -0,0 +1,25 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.plugin.standard.StandardPlugin.*
+
+/**
+ * The "N choose R" operator.
+ *
+ * This is a standard operator that returns the number of possible combinations, regardless of order,
+ * of a certain size can be taken out of a pool of a bigger size.
+ */
+class OperatorNcr: NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2 && params[0].fractionalPart().signum() == 0
+                    && params[1].fractionalPart().signum() == 0
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            OP_NPR.apply(context, *params) / OP_FACTORIAL.apply(context, params[1])
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorNegate.kt

@@ -0,0 +1,22 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The negation operator.
+ *
+ * This is a standard operator that negates a number.
+ */
+class OperatorNegate: NumberOperator(OperatorAssociativity.LEFT, OperatorType.UNARY_PREFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 1
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            -params[0]
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorNpr.kt

@@ -0,0 +1,42 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The "N pick R" operator.
+ *
+ * his is a standard operator that returns the number of possible combinations
+ * of a certain size can be taken out of a pool of a bigger size.
+ */
+class OperatorNpr: NumberOperator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2 && params[0].fractionalPart().signum() == 0
+                    && params[1].fractionalPart().signum() == 0
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>): NumberInterface {
+        val implementation = context.inheritedNumberImplementation
+        if (params[0] < params[1] ||
+                params[0].signum() < 0 ||
+                params[0].signum() == 0 && params[1].signum() != 0)
+            return implementation.instanceForString("0")
+        var total = implementation.instanceForString("1")
+        var multiplyBy = params[0]
+        var remainingMultiplications = params[1]
+        val halfway = params[0] / implementation.instanceForString("2")
+        if (remainingMultiplications > halfway) {
+            remainingMultiplications = params[0] - remainingMultiplications
+        }
+        while (remainingMultiplications.signum() > 0) {
+            total *= multiplyBy
+            remainingMultiplications -= implementation.instanceForString("1")
+            multiplyBy -= implementation.instanceForString("1")
+        }
+        return total
+    }
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorSet.kt

@@ -0,0 +1,28 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.function.TreeValueOperator
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.tree.TreeNode
+import org.nwapw.abacus.tree.VariableNode
+
+/**
+ * The set operator.
+ *
+ * This is a standard operator that assigns a value to a variable name.
+ */
+class OperatorSet: TreeValueOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out TreeNode>) =
+            params.size == 2 && params[0] is VariableNode
+
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out TreeNode>): NumberInterface {
+        val assignTo = (params[0] as VariableNode).variable
+        val value = params[1].reduce(context.inheritedReducer)
+        context.setVariable(assignTo, value)
+        return value
+    }
+
+}

core/src/main/kotlin/org/nwapw/abacus/plugin/standard/operator/OperatorSubtract.kt

@@ -0,0 +1,21 @@
+package org.nwapw.abacus.plugin.standard.operator
+
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.function.NumberOperator
+import org.nwapw.abacus.function.OperatorAssociativity
+import org.nwapw.abacus.function.OperatorType
+import org.nwapw.abacus.number.NumberInterface
+
+/**
+ * The subtraction operator.
+ *
+ * This is a standard operator that performs subtraction.
+ */
+class OperatorSubtract: NumberOperator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0) {
+
+    override fun matchesParams(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params.size == 2
+    override fun applyInternal(context: MutableEvaluationContext, params: Array<out NumberInterface>) =
+            params[0] - params[1]
+
+}

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

@@ -2,7 +2,8 @@ package org.nwapw.abacus.tree
 
 import org.nwapw.abacus.Abacus
 import org.nwapw.abacus.context.EvaluationContext
-import org.nwapw.abacus.exception.EvaluationException
+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> {
@@ -17,15 +18,14 @@ class NumberReducer(val abacus: Abacus, context: EvaluationContext) : Reducer<Nu
         val promotionManager = abacus.promotionManager
         return when(treeNode){
             is NumberNode -> {
-                context.inheritedNumberImplementation?.instanceForString(treeNode.number)
+                context.inheritedNumberImplementation.instanceForString(treeNode.number)
-                        ?: throw EvaluationException("no number implementation selected.")
             }
             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)
-                throw EvaluationException("variable is not defined.")
+                throw NumberReducerException("variable is not defined.")
             }
             is NumberUnaryNode -> {
                 val child = children[0] as NumberInterface
@@ -58,7 +58,7 @@ class NumberReducer(val abacus: Abacus, context: EvaluationContext) : Reducer<Nu
                 abacus.pluginManager.treeValueFunctionFor(treeNode.callTo)
                         .apply(context, *treeNode.children.toTypedArray())
             }
-            else -> throw EvaluationException("unrecognized tree node.")
+            else -> throw ReductionException("unrecognized tree node.")
         }
     }
 

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

@@ -7,7 +7,7 @@ import org.nwapw.abacus.Abacus;
 import org.nwapw.abacus.config.Configuration;
 import org.nwapw.abacus.exception.DomainException;
 import org.nwapw.abacus.number.NumberInterface;
-import org.nwapw.abacus.plugin.StandardPlugin;
+import org.nwapw.abacus.plugin.standard.StandardPlugin;
 import org.nwapw.abacus.tree.TreeNode;
 
 public class CalculationTests {
@@ -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

@@ -9,7 +9,7 @@ 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 org.nwapw.abacus.plugin.standard.StandardPlugin;
 
 import java.util.function.Function;
 

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

@@ -13,16 +13,13 @@ 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.exception.ComputationInterruptedException;
 import org.nwapw.abacus.function.Documentation;
 import org.nwapw.abacus.function.DocumentationType;
-import org.nwapw.abacus.exception.DomainException;
-import org.nwapw.abacus.exception.EvaluationException;
 import org.nwapw.abacus.number.*;
 import org.nwapw.abacus.plugin.ClassFinder;
 import org.nwapw.abacus.plugin.PluginListener;
 import org.nwapw.abacus.plugin.PluginManager;
-import org.nwapw.abacus.plugin.StandardPlugin;
+import org.nwapw.abacus.plugin.standard.StandardPlugin;
 import org.nwapw.abacus.tree.EvaluationResult;
 import org.nwapw.abacus.tree.TreeNode;
 
@@ -145,9 +142,6 @@ 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();
                 String resultingString = evaluatedNumber.toString();