diff --git a/src/org/nwapw/abacus/lexing/Lexer.java b/src/org/nwapw/abacus/lexing/Lexer.java
new file mode 100644
index 0000000..94457a1
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/Lexer.java
@@ -0,0 +1,68 @@
+package org.nwapw.abacus.lexing;
+
+import org.nwapw.abacus.lexing.pattern.EndNode;
+import org.nwapw.abacus.lexing.pattern.Match;
+import org.nwapw.abacus.lexing.pattern.Pattern;
+import org.nwapw.abacus.lexing.pattern.PatternNode;
+
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.HashSet;
+
+public class Lexer<T> {
+
+    private ArrayList<Pattern<T>> patterns;
+
+    public Lexer(){
+        patterns = new ArrayList<>();
+    }
+
+    public void register(String pattern, T id){
+        Pattern<T> compiledPattern = new Pattern<>(pattern, id);
+        if(compiledPattern.getHead() != null) patterns.add(compiledPattern);
+    }
+
+    public Match<T> lexOne(String from, int startAt, Comparator<T> compare){
+        ArrayList<Match<T>> matches = new ArrayList<>();
+        HashSet<PatternNode<T>> currentSet = new HashSet<>();
+        HashSet<PatternNode<T>> futureSet = new HashSet<>();
+        int index = startAt;
+        for(Pattern<T> pattern : patterns){
+            pattern.getHead().addInto(currentSet);
+        }
+        while(!currentSet.isEmpty()){
+            for(PatternNode<T> node : currentSet){
+                if(index < from.length() && node.matches(from.charAt(index))) {
+                    node.addOutputsInto(futureSet);
+                } else if(node instanceof EndNode){
+                    matches.add(new Match<>(startAt, index, ((EndNode<T>) node).getPatternId()));
+                }
+            }
+
+            HashSet<PatternNode<T>> tmp = currentSet;
+            currentSet = futureSet;
+            futureSet = tmp;
+            futureSet.clear();
+
+            index++;
+        }
+        matches.sort((a, b) -> compare.compare(a.getType(), b.getType()));
+        if(compare != null) {
+            matches.sort(Comparator.comparingInt(a -> a.getTo() - a.getFrom()));
+        }
+        return matches.isEmpty() ? null : matches.get(matches.size() - 1);
+    }
+
+    public ArrayList<Match<T>> lexAll(String from, int startAt, Comparator<T> compare){
+        int index = startAt;
+        ArrayList<Match<T>> matches = new ArrayList<>();
+        Match<T> lastMatch = null;
+        while((lastMatch = lexOne(from, index, compare)) != null && index < from.length()){
+            if(lastMatch.getTo() == lastMatch.getFrom()) return null;
+            matches.add(lastMatch);
+            index += lastMatch.getTo() - lastMatch.getFrom();
+        }
+        return matches;
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/AnyNode.java b/src/org/nwapw/abacus/lexing/pattern/AnyNode.java
new file mode 100644
index 0000000..1cfa635
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/AnyNode.java
@@ -0,0 +1,10 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class AnyNode<T> extends PatternNode<T> {
+
+    @Override
+    public boolean matches(char other) {
+        return true;
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/EndNode.java b/src/org/nwapw/abacus/lexing/pattern/EndNode.java
new file mode 100644
index 0000000..d8e621d
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/EndNode.java
@@ -0,0 +1,15 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class EndNode<T> extends PatternNode<T> {
+
+    private T patternId;
+
+    public EndNode(T patternId){
+        this.patternId = patternId;
+    }
+
+    public T getPatternId(){
+        return patternId;
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/LinkNode.java b/src/org/nwapw/abacus/lexing/pattern/LinkNode.java
new file mode 100644
index 0000000..460c418
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/LinkNode.java
@@ -0,0 +1,13 @@
+package org.nwapw.abacus.lexing.pattern;
+
+import java.util.ArrayList;
+import java.util.Collection;
+
+public class LinkNode<T> extends PatternNode<T> {
+
+    @Override
+    public void addInto(Collection<PatternNode<T>> into) {
+        addOutputsInto(into);
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/Match.java b/src/org/nwapw/abacus/lexing/pattern/Match.java
new file mode 100644
index 0000000..06e0b27
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/Match.java
@@ -0,0 +1,26 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class Match<T> {
+
+    private int from;
+    private int to;
+    private T type;
+
+    public Match(int from, int to, T type){
+        this.from = from;
+        this.to = to;
+        this.type = type;
+    }
+
+    public int getFrom() {
+        return from;
+    }
+
+    public int getTo() {
+        return to;
+    }
+
+    public T getType() {
+        return type;
+    }
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/Pattern.java b/src/org/nwapw/abacus/lexing/pattern/Pattern.java
new file mode 100644
index 0000000..4d40d77
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/Pattern.java
@@ -0,0 +1,172 @@
+package org.nwapw.abacus.lexing.pattern;
+
+import java.util.Collection;
+import java.util.HashMap;
+import java.util.Stack;
+import java.util.function.Function;
+
+public class Pattern<T> {
+
+    private T id;
+    private PatternNode<T> head;
+    private String source;
+    private int index;
+
+    private HashMap<Character, Function<PatternChain<T>, PatternChain<T>>> operations =
+            new HashMap<Character, Function<PatternChain<T>, PatternChain<T>>>() {{
+                put('+', Pattern.this::transformPlus);
+                put('*', Pattern.this::transformStar);
+                put('?', Pattern.this::transformQuestion);
+            }};
+
+    private PatternChain<T> transformPlus(PatternChain<T> chain){
+        chain.tail.outputStates.add(chain.head);
+        return chain;
+    }
+
+    private PatternChain<T> transformStar(PatternChain<T> chain){
+        LinkNode<T> newTail = new LinkNode<>();
+        LinkNode<T> newHead = new LinkNode<>();
+        newHead.outputStates.add(chain.head);
+        newHead.outputStates.add(newTail);
+        chain.tail.outputStates.add(newTail);
+        newTail.outputStates.add(newHead);
+        chain.head = newHead;
+        chain.tail = newTail;
+        return chain;
+    }
+
+    private PatternChain<T> transformQuestion(PatternChain<T> chain){
+        LinkNode<T> newTail = new LinkNode<>();
+        LinkNode<T> newHead = new LinkNode<>();
+        newHead.outputStates.add(chain.head);
+        newHead.outputStates.add(newTail);
+        chain.tail.outputStates.add(newTail);
+        chain.head = newHead;
+        chain.tail = newTail;
+        return chain;
+    }
+
+    private PatternChain<T> combineChains(Collection<PatternChain<T>> collection){
+        LinkNode<T> head = new LinkNode<>();
+        LinkNode<T> tail = new LinkNode<>();
+        PatternChain<T> newChain = new PatternChain<>(head, tail);
+        for(PatternChain<T> chain : collection){
+            head.outputStates.add(chain.head);
+            chain.tail.outputStates.add(tail);
+        }
+        return newChain;
+    }
+
+    private PatternChain<T> parseValue(){
+        if(index >= source.length()) return null;
+        if(source.charAt(index) == '\\'){
+            if(++index >= source.length()) return null;
+        }
+        return new PatternChain<>(new ValueNode<>(source.charAt(index++)));
+    }
+
+    private PatternChain<T> parseOr(){
+        Stack<PatternChain<T>> orStack = new Stack<>();
+        index++;
+        while(index < source.length() && source.charAt(index) != ']'){
+            if(source.charAt(index) == '-'){
+                index++;
+                if(orStack.empty() || orStack.peek().tail.range() == '\0') return null;
+                PatternChain<T> bottomRange = orStack.pop();
+                PatternChain<T> topRange = parseValue();
+                if(topRange == null || topRange.tail.range() == '\0') return null;
+
+                orStack.push(new PatternChain<>(new RangeNode<>(bottomRange.tail.range(), topRange.tail.range())));
+            } else {
+                PatternChain<T> newChain = parseValue();
+                if(newChain == null) return null;
+                orStack.push(newChain);
+            }
+        }
+        if(index++ >= source.length()) return null;
+        return (orStack.size() == 1) ? orStack.pop() : combineChains(orStack);
+    }
+
+    private PatternChain<T> parseSegment(boolean isSubsegment){
+        if(index >= source.length() || ((source.charAt(index) != '(') && isSubsegment)) return null;
+        if(isSubsegment) index++;
+
+        Stack<PatternChain<T>> orChain = new Stack<>();
+        PatternChain<T> fullChain = new PatternChain<>();
+        PatternChain<T> currentChain = null;
+        while (index < source.length() && source.charAt(index) != ')'){
+            char currentChar = source.charAt(index);
+            if(operations.containsKey(currentChar)){
+                if(currentChain == null) return null;
+
+                currentChain = operations.get(currentChar).apply(currentChain);
+                fullChain.append(currentChain);
+                currentChain = null;
+                index++;
+            } else if(currentChar == '|'){
+                if(currentChain == null) return null;
+
+                fullChain.append(currentChain);
+                orChain.push(fullChain);
+                currentChain = null;
+                fullChain = new PatternChain<>();
+                if(++index >= source.length()) return null;
+            } else if(currentChar == '('){
+                if(currentChain != null) {
+                    fullChain.append(currentChain);
+                }
+
+                currentChain = parseSegment(true);
+                if(currentChain == null) return null;
+            } else if(currentChar == '['){
+                if(currentChain != null){
+                    fullChain.append(currentChain);
+                }
+                currentChain = parseOr();
+                if(currentChain == null) return null;
+            } else if(currentChar == '.'){
+                if(currentChain != null){
+                    fullChain.append(currentChain);
+                }
+                currentChain = new PatternChain<>(new AnyNode<>());
+                index++;
+            } else {
+                if(currentChain != null){
+                    fullChain.append(currentChain);
+                }
+                currentChain = parseValue();
+                if(currentChain == null) return null;
+            }
+        }
+
+        if(!(!isSubsegment || (index < source.length() && source.charAt(index) == ')'))) return null;
+        if(isSubsegment) index++;
+
+        if(currentChain != null) fullChain.append(currentChain);
+        if(!orChain.empty()){
+            orChain.push(fullChain);
+            fullChain = combineChains(orChain);
+        }
+
+        return fullChain;
+    }
+
+    public Pattern(String from, T id){
+        this.id = id;
+        index = 0;
+        source = from;
+
+        PatternChain<T> chain = parseSegment(false);
+        if(chain == null) {
+            head = null;
+        } else {
+            chain.append(new EndNode<>(id));
+            head = chain.head;
+        }
+    }
+
+    public PatternNode<T> getHead() {
+        return head;
+    }
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/PatternChain.java b/src/org/nwapw/abacus/lexing/pattern/PatternChain.java
new file mode 100644
index 0000000..aad9be5
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/PatternChain.java
@@ -0,0 +1,40 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class PatternChain<T> {
+
+    public PatternNode<T> head;
+    public PatternNode<T> tail;
+
+    public PatternChain(PatternNode<T> head, PatternNode<T> tail){
+        this.head = head;
+        this.tail = tail;
+    }
+
+    public PatternChain(PatternNode<T> node){
+        this(node, node);
+    }
+
+    public PatternChain(){
+        this(null);
+    }
+
+    public void append(PatternChain<T> other){
+        if(other.head == null || tail == null) {
+            this.head = other.head;
+            this.tail = other.tail;
+        } else {
+            tail.outputStates.add(other.head);
+            tail = other.tail;
+        }
+    }
+
+    public void append(PatternNode<T> node){
+        if(tail == null){
+            head = tail = node;
+        } else {
+            tail.outputStates.add(node);
+            tail = node;
+        }
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/PatternNode.java b/src/org/nwapw/abacus/lexing/pattern/PatternNode.java
new file mode 100644
index 0000000..4c0908a
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/PatternNode.java
@@ -0,0 +1,31 @@
+package org.nwapw.abacus.lexing.pattern;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.HashSet;
+
+public class PatternNode<T> {
+
+    protected HashSet<PatternNode<T>> outputStates;
+
+    public PatternNode(){
+        outputStates = new HashSet<>();
+    }
+
+    public boolean matches(char other){
+        return false;
+    }
+
+    public char range(){
+        return '\0';
+    }
+
+    public void addInto(Collection<PatternNode<T>> into){
+        into.add(this);
+    }
+
+    public void addOutputsInto(Collection<PatternNode<T>> into){
+        outputStates.forEach(e -> e.addInto(into));
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/RangeNode.java b/src/org/nwapw/abacus/lexing/pattern/RangeNode.java
new file mode 100644
index 0000000..4ff9e5b
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/RangeNode.java
@@ -0,0 +1,18 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class RangeNode<T> extends PatternNode<T> {
+
+    private char from;
+    private char to;
+
+    public RangeNode(char from, char to){
+        this.from = from;
+        this.to = to;
+    }
+
+    @Override
+    public boolean matches(char other) {
+        return other >= from && other <= to;
+    }
+
+}
diff --git a/src/org/nwapw/abacus/lexing/pattern/ValueNode.java b/src/org/nwapw/abacus/lexing/pattern/ValueNode.java
new file mode 100644
index 0000000..855f805
--- /dev/null
+++ b/src/org/nwapw/abacus/lexing/pattern/ValueNode.java
@@ -0,0 +1,20 @@
+package org.nwapw.abacus.lexing.pattern;
+
+public class ValueNode<T> extends PatternNode<T> {
+
+    private char value;
+
+    public ValueNode(char value){
+        this.value = value;
+    }
+
+    @Override
+    public boolean matches(char other) {
+        return other == value;
+    }
+
+    @Override
+    public char range() {
+        return value;
+    }
+}
diff --git a/src/org/nwapw/abacus/tree/NumberNode.java b/src/org/nwapw/abacus/tree/NumberNode.java
new file mode 100644
index 0000000..1ad6da5
--- /dev/null
+++ b/src/org/nwapw/abacus/tree/NumberNode.java
@@ -0,0 +1,25 @@
+package org.nwapw.abacus.tree;
+
+import org.nwapw.abacus.number.NaiveNumber;
+import org.nwapw.abacus.number.NumberInterface;
+
+public class NumberNode extends TreeNode {
+
+    private NumberInterface number;
+
+    public NumberNode(){
+        number = null;
+    }
+
+    public NumberNode(double value){
+        number = new NaiveNumber(value);
+    }
+
+    public NumberNode(String value){
+        this(Double.parseDouble(value));
+    }
+
+    public NumberInterface getNumber() {
+        return number;
+    }
+}
diff --git a/src/org/nwapw/abacus/tree/OpNode.java b/src/org/nwapw/abacus/tree/OpNode.java
new file mode 100644
index 0000000..0fcdaed
--- /dev/null
+++ b/src/org/nwapw/abacus/tree/OpNode.java
@@ -0,0 +1,38 @@
+package org.nwapw.abacus.tree;
+
+public class OpNode extends TreeNode {
+
+    private String operation;
+    private TreeNode left;
+    private TreeNode right;
+
+    public OpNode(String operation){
+        this(operation, null, null);
+    }
+
+    public OpNode(String operation, TreeNode left, TreeNode right){
+        this.operation = operation;
+        this.left = left;
+        this.right = right;
+    }
+
+    public String getOperation() {
+        return operation;
+    }
+
+    public TreeNode getLeft() {
+        return left;
+    }
+
+    public void setLeft(TreeNode left) {
+        this.left = left;
+    }
+
+    public TreeNode getRight() {
+        return right;
+    }
+
+    public void setRight(TreeNode right) {
+        this.right = right;
+    }
+}
diff --git a/src/org/nwapw/abacus/tree/OperatorAssociativity.java b/src/org/nwapw/abacus/tree/OperatorAssociativity.java
new file mode 100644
index 0000000..78b633b
--- /dev/null
+++ b/src/org/nwapw/abacus/tree/OperatorAssociativity.java
@@ -0,0 +1,5 @@
+package org.nwapw.abacus.tree;
+
+public enum OperatorAssociativity {
+    LEFT, RIGHT
+}
diff --git a/src/org/nwapw/abacus/tree/TokenType.java b/src/org/nwapw/abacus/tree/TokenType.java
new file mode 100644
index 0000000..e0d7d97
--- /dev/null
+++ b/src/org/nwapw/abacus/tree/TokenType.java
@@ -0,0 +1,13 @@
+package org.nwapw.abacus.tree;
+
+public enum TokenType {
+
+    ANY(0), OP(1), NUM(2), WORD(3), OPEN_PARENTH(4), CLOSE_PARENTH(5);
+
+    public final int priority;
+
+    TokenType(int priority){
+        this.priority = priority;
+    }
+
+}
diff --git a/src/org/nwapw/abacus/tree/TreeNode.java b/src/org/nwapw/abacus/tree/TreeNode.java
new file mode 100644
index 0000000..6581826
--- /dev/null
+++ b/src/org/nwapw/abacus/tree/TreeNode.java
@@ -0,0 +1,103 @@
+package org.nwapw.abacus.tree;
+
+import org.nwapw.abacus.lexing.Lexer;
+import org.nwapw.abacus.lexing.pattern.Match;
+
+import java.util.*;
+
+public abstract class TreeNode {
+
+    private static Lexer<TokenType> lexer = new Lexer<TokenType>(){{
+        register(".", TokenType.ANY);
+        register("\\+|-|\\*|/|^", TokenType.OP);
+        register("[0-9]+(\\.[0-9]+)?", TokenType.NUM);
+        register("[a-zA-Z]+", TokenType.WORD);
+        register("\\(", TokenType.OPEN_PARENTH);
+        register("\\)", TokenType.CLOSE_PARENTH);
+    }};
+    private static HashMap<String, Integer> precedenceMap = new HashMap<String, Integer>(){{
+        put("+", 0);
+        put("-", 0);
+        put("*", 1);
+        put("/", 1);
+        put("^", 2);
+    }};
+    private static HashMap<String, OperatorAssociativity> associativityMap =
+            new HashMap<String, OperatorAssociativity>() {{
+                put("+", OperatorAssociativity.LEFT);
+                put("-", OperatorAssociativity.LEFT);
+                put("*", OperatorAssociativity.LEFT);
+                put("/", OperatorAssociativity.LEFT);
+                put("^", OperatorAssociativity.RIGHT);
+            }};
+
+    private static Comparator<TokenType> tokenSorter = Comparator.comparingInt(e -> e.priority);
+
+    public static ArrayList<Match<TokenType>> tokenize(String string){
+        return lexer.lexAll(string, 0, tokenSorter);
+    }
+
+    public static ArrayList<Match<TokenType>> intoPostfix(String source, ArrayList<Match<TokenType>> from){
+        ArrayList<Match<TokenType>> output = new ArrayList<>();
+        Stack<Match<TokenType>> tokenStack = new Stack<>();
+        while(!from.isEmpty()){
+            Match<TokenType> match = from.remove(0);
+            if(match.getType() == TokenType.NUM) {
+                output.add(match);
+            } else if(match.getType() == TokenType.OP){
+                String tokenString = source.substring(match.getFrom(), match.getTo());
+                int precedence = precedenceMap.get(tokenString);
+                OperatorAssociativity associativity = associativityMap.get(tokenString);
+
+                while(!tokenStack.empty()) {
+                    Match<TokenType> otherMatch = tokenStack.peek();
+                    if(otherMatch.getType() != TokenType.OP) break;
+
+                    int otherPrecdence = precedenceMap.get(source.substring(otherMatch.getFrom(), otherMatch.getTo()));
+                    if(otherPrecdence < precedence ||
+                            (associativity == OperatorAssociativity.RIGHT && otherPrecdence == precedence)) {
+                        break;
+                    }
+                    output.add(tokenStack.pop());
+                }
+                tokenStack.push(match);
+            } else if(match.getType() == TokenType.OPEN_PARENTH){
+                tokenStack.push(match);
+            } else if(match.getType() == TokenType.CLOSE_PARENTH){
+                while(!tokenStack.empty() && tokenStack.peek().getType() != TokenType.OPEN_PARENTH){
+                    output.add(tokenStack.pop());
+                }
+                if(tokenStack.empty()) return null;
+                tokenStack.pop();
+            }
+        }
+        while(!tokenStack.empty()){
+            if(!(tokenStack.peek().getType() == TokenType.OP)) return null;
+            output.add(tokenStack.pop());
+        }
+        return output;
+    }
+
+    public static TreeNode fromStringRecursive(String source, ArrayList<Match<TokenType>> matches){
+        if(matches.size() == 0) return null;
+        Match<TokenType> match = matches.remove(0);
+        if(match.getType() == TokenType.OP){
+            TreeNode right = fromStringRecursive(source, matches);
+            TreeNode left = fromStringRecursive(source, matches);
+            if(left == null || right == null) return null;
+            else return new OpNode(source.substring(match.getFrom(), match.getTo()), left, right);
+        } else if(match.getType() == TokenType.NUM){
+            return new NumberNode(Double.parseDouble(source.substring(match.getFrom(), match.getTo())));
+        }
+        return null;
+    }
+
+    public static TreeNode fromString(String string){
+        ArrayList<Match<TokenType>> matches = intoPostfix(string, tokenize(string));
+        if(matches == null) return null;
+
+        Collections.reverse(matches);
+        return fromStringRecursive(string, matches);
+    }
+
+}