Start implementing the canvas to draw graphs.

Replace some more cases where null is used with Exceptions.

build.gradle

@@ -1,5 +1,5 @@
 buildscript {
-    ext.kotlin_version = '1.1.3'
+    ext.kotlin_version = '1.1.4-3'
     ext.dokka_version = '0.9.15'
 
     repositories {
@@ -19,7 +19,7 @@ subprojects {
     apply plugin: 'org.jetbrains.dokka'
 
     repositories {
-        mavenCentral()
+        jcenter()
     }
 
     dependencies {

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/number/NumberInterface.java

@@ -238,4 +238,16 @@ public abstract class NumberInterface implements Comparable<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 {
@@ -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) {
+        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/StandardPlugin.java

@@ -332,7 +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;
@@ -715,7 +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

@@ -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/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/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

@@ -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/build.gradle

@@ -2,7 +2,14 @@ apply plugin: 'application'
 
 dependencies {
     compile 'com.moandjiezana.toml:toml4j:0.7.1'
+    compile 'org.jetbrains.kotlinx:kotlinx-coroutines-core:0.18'
     compile project(':core')
 }
 
+kotlin {
+    experimental {
+        coroutines "enable"
+    }
+}
+
 mainClassName = 'org.nwapw.abacus.fx.AbacusApplication'

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

@@ -13,11 +13,8 @@ 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;
@@ -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();

fx/src/main/kotlin/org/nwapw/abacus/fx/graphing/Graph.kt

@@ -0,0 +1,121 @@
+package org.nwapw.abacus.fx.graphing
+
+import kotlinx.coroutines.experimental.CommonPool
+import kotlinx.coroutines.experimental.async
+import kotlinx.coroutines.experimental.runBlocking
+import org.nwapw.abacus.Abacus
+import org.nwapw.abacus.config.Configuration
+import org.nwapw.abacus.context.EvaluationContext
+import org.nwapw.abacus.context.MutableEvaluationContext
+import org.nwapw.abacus.number.NaiveNumber
+import org.nwapw.abacus.number.NumberInterface
+import org.nwapw.abacus.number.NumberRange
+import org.nwapw.abacus.plugin.StandardPlugin
+import org.nwapw.abacus.tree.TreeNode
+
+/**
+ * A class that holds information about a graph.
+ *
+ * Graph that uses an instance of [Abacus] to generate graphs of an
+ * [expression]. Continuous graphing on large expressions is expensive,
+ * and therefore the method of graphing is discrete. The graph class
+ * uses the [pointExpression] to generate inputs until an input is outside
+ * the function's domain. In both the expressions, the [inputVariable] and
+ * [pointInputVariable] are used, respectively, in order to either pass in
+ * the x-coordinate or the number of the input value being generated.
+ *
+ * @property abacus the abacus instance to use to evaluate expressions.
+ * @property domain the domain used in computation.
+ * @property range the range used for displaying the output.
+ * @property inputVariable the variable which is substituted for the input x-coordinate.
+ * @property pointInputVariable the variable which is substituted for the number of the input point being generated.
+ */
+class Graph(val abacus: Abacus,
+            var domain: NumberRange, var range: NumberRange,
+            var inputVariable: String = "x", var pointInputVariable: String = "n") {
+
+    /**
+     * Property used for storing the parsed version of the [expression]
+     */
+    private var expressionTree: TreeNode? = null
+    /**
+     * Property used for storing the parsed version of the [pointExpression]
+     */
+    private var pointExpressionTree: TreeNode? = null
+
+    /**
+     * The expression being graphed.
+     */
+    var expression: String? = null
+        set(value) {
+            field = value
+            expressionTree = abacus.parseString(value ?: return)
+        }
+    /**
+     * The expression being used to generate points.
+     */
+    var pointExpression: String? = null
+        set(value) {
+            field = value
+            pointExpressionTree = abacus.parseString(value ?: return)
+        }
+
+    /**
+     * Evaluates a parsed expression [tree] with the given input [values] of indeterminate type.
+     * This is is an asynchronous operation using coroutines, and for every input
+     * value a new sub-context is created. The [contextModifier] function is executed
+     * on each new sub-context, and is expected to use the input value to modify the context
+     * state so that the evaluation of the expression produces a correct result.
+     *
+     * @param T the type of input values.
+     * @param tree the tree to evaluate.
+     * @param values the values to plug into the expression.
+     * @param contextModifier the function that plugs values into the context.
+     * @return the list of outputs.
+     */
+    fun <T> evaluateWith(tree: TreeNode, values: List<T>,
+                         contextModifier: MutableEvaluationContext.(T) -> Unit) = runBlocking {
+        values.map {
+            val context = abacus.context.mutableSubInstance()
+            context.contextModifier(it)
+            async(CommonPool) { abacus.evaluateTreeWithContext(tree, context) }
+        }.map { it.await() }
+    }
+
+    /**
+     * Extension function that calls [evaluateWith] with the current list.
+     * @param T the type of the values in the list.
+     * @param tree the tree node to evaluate.
+     * @param contextModifier the function that plugs values into the context.
+     * @return the list of outputs.
+     */
+    fun <T> List<T>.evaluateWith(tree: TreeNode,
+                                 contextModifier: MutableEvaluationContext.(T) -> Unit ) =
+            evaluateWith(tree, this, contextModifier)
+
+    /**
+     * Uses the [pointExpression] and [pointInputVariable] to generate
+     * a set of points as inputs for the actual expression. These points are generated
+     * as long as they are within the [domain].
+     * @return the list of generated input values.
+     */
+    fun generateInputs(): List<NumberInterface> =
+            generateSequence(1) {
+                it + 1
+            }.map {
+                val context = abacus.context.mutableSubInstance()
+                context.setVariable(pointInputVariable,
+                        context.inheritedNumberImplementation!!.instanceForString(it.toString()))
+                abacus.evaluateTreeWithContext(pointExpressionTree!!, context).value
+            }.takeWhile { it in domain }.toList()
+
+    /**
+     * Uses the [expression] and [inputVariable] to generate
+     * a set of outputs from the given set of [inputs].
+     * @return the list of generated points.
+     */
+    fun generateOutputs(inputs: List<NumberInterface>): List<Pair<NumberInterface, NumberInterface>> =
+            inputs.evaluateWith(expressionTree!!) {
+                setVariable(inputVariable, it)
+            }.mapIndexed { index, (value) -> inputs[index] to value }
+}

fx/src/main/kotlin/org/nwapw/abacus/fx/graphing/GraphCanvas.kt

@@ -0,0 +1,39 @@
+package org.nwapw.abacus.fx.graphing
+
+import javafx.beans.value.ChangeListener
+import javafx.scene.canvas.Canvas
+
+/**
+ * A canvas that renders a graph.
+ *
+ * The GraphCanvas uses the provided [Graph] instance in order to draw the outputs on itself.
+ * @param graph the graph used to render.
+ */
+class GraphCanvas(graph: Graph): Canvas() {
+
+    /**
+     * The graph that is currently being used to generate inputs / outputs.
+     * The redraw is triggered if this graph is reset.
+     */
+    var graph: Graph = graph
+        set(value) {
+            field = value
+            redraw()
+        }
+
+    init {
+        val redrawListener = ChangeListener<Number> { _, _, _ -> redraw() }
+        widthProperty().addListener(redrawListener)
+        heightProperty().addListener(redrawListener)
+        redraw()
+    }
+
+    /**
+     * Redraws the graph onto the canvas.
+     */
+    fun redraw() {
+        val graphicsContext = graphicsContext2D
+        val outputs = graph.generateOutputs(graph.generateInputs())
+    }
+
+}