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noti0na1 · Nov 20, 2016 · 0bef09f · 0bef09f
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diff --git a/README.md b/README.md
@@ -1,9 +1,11 @@
 # LambdaCalculus-java
 Lambda calculus implemented in Java
 
+See examples in [com.notnl.lambda.examples](https://github.com/noti0na1/LambdaCalculus-java/tree/master/src/com/notnl/lambda/example)
+
 What is Lambda Calculus: https://en.wikipedia.org/wiki/Lambda_calculus
 
-See examples in [com.notnl.lambda.examples](https://github.com/noti0na1/LambdaCalculus-java/tree/master/src/com/notnl/lambda/example)
+More materials: [A Tutorial Introduction to the Lambda Calculus](www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf)
 
 //TODO 
 

diff --git a/src/com/notnl/lambda/Application.java b/src/com/notnl/lambda/Application.java
@@ -20,29 +20,30 @@
 import java.util.Set;
 
 /**
- * Created by noti0 on 2016/11/18.
+ * An application
+ * apply a function with certain argument
  */
 public class Application extends Expression {
 
     private Expression function;
 
-    private Expression arguement;
+    private Expression argument;
 
     /**
      * @param function
-     * @param arguement
+     * @param argument
      */
-    public Application(Expression function, Expression arguement) {
+    public Application(Expression function, Expression argument) {
         this.function = function;
-        this.arguement = arguement;
+        this.argument = argument;
     }
 
     /**
      * @return
      */
     @Override
     public boolean reducible() {
-        return this.function.reducible() || this.arguement.reducible() || this.function instanceof Function;
+        return this.function.reducible() || this.argument.reducible() || this.function instanceof Function;
     }
 
     /**
@@ -51,12 +52,12 @@ public boolean reducible() {
     @Override
     public Expression reduce() {
         if (this.function.reducible()) {
-            return new Application(this.function.reduce(), this.arguement);
-        } else if (this.arguement.reducible()) {
-            return new Application(this.function, this.arguement.reduce());
+            return new Application(this.function.reduce(), this.argument);
+        } else if (this.argument.reducible()) {
+            return new Application(this.function, this.argument.reduce());
         } else if (this.function instanceof Function) {
             Function fun = (Function) this.getFunction();
-            return subst(fun.getBody(), fun.getName(), this.getArguement());
+            return subst(fun.getBody(), fun.getName(), this.getargument());
         }
         return this;
     }
@@ -90,15 +91,15 @@ public void setFunction(Expression function) {
     /**
      * @return
      */
-    public Expression getArguement() {
-        return arguement;
+    public Expression getargument() {
+        return argument;
     }
 
     /**
-     * @param arguement
+     * @param argument
      */
-    public void setArguement(Expression arguement) {
-        this.arguement = arguement;
+    public void setargument(Expression argument) {
+        this.argument = argument;
     }
 
     /**
@@ -113,15 +114,17 @@ public String toString() {
             apply.append(this.function.toString());
         }
         apply.append(' ');
-        if (this.arguement instanceof Variable) {
-            apply.append(this.arguement);
+        if (this.argument instanceof Variable) {
+            apply.append(this.argument);
         } else {
-            apply.append('(').append(this.arguement).append(')');
+            apply.append('(').append(this.argument).append(')');
         }
         return apply.toString();
     }
 
     /**
+     * substitute variable in expression with replacement
+     *
      * @param expr
      * @param name
      * @param repl
@@ -138,7 +141,7 @@ private static Expression subst(Expression expr, Variable name, Expression repl)
             Application app = (Application) expr;
             return new Application(
                     subst(app.getFunction(), name, repl),
-                    subst(app.getArguement(), name, repl));
+                    subst(app.getargument(), name, repl));
         } else if (expr instanceof Function) {
             Function fun = (Function) expr;
             Set<Variable> fvs = freeVariables(repl);
@@ -152,6 +155,8 @@ private static Expression subst(Expression expr, Variable name, Expression repl)
     }
 
     /**
+     * get unique name
+     *
      * @param name
      * @param usedNames
      * @return
@@ -165,6 +170,8 @@ private static Variable uniqueName(Variable name, Set<Variable> usedNames) {
     }
 
     /**
+     * get all free variables
+     *
      * @param expr
      * @return
      */
@@ -176,7 +183,7 @@ private static Set<Variable> freeVariables(Expression expr) {
         } else if (expr instanceof Application) {
             Application app = (Application) expr;
             vars = freeVariables(app.getFunction());
-            vars.addAll(freeVariables(app.getArguement()));
+            vars.addAll(freeVariables(app.getargument()));
         } else if (expr instanceof Function) {
             Function fun = (Function) expr;
             vars = freeVariables(fun.getBody());

diff --git a/src/com/notnl/lambda/Expression.java b/src/com/notnl/lambda/Expression.java
@@ -17,27 +17,34 @@
 package com.notnl.lambda;
 
 /**
- * Created by noti0 on 2016/11/18.
+ * An Expression
  */
 public abstract class Expression {
 
     /**
+     * return if it can be reduced
+     *
      * @return
      */
     public abstract boolean reducible();
 
     /**
+     * reduce it for one step
+     *
      * @return
      */
     public abstract Expression reduce();
 
     /**
+     * fully reduce it
+     * caution: this may cause infinite loop
+     *
      * @return
      */
     public abstract Expression deepReduce();
 
     /**
-     *
+     * display reduce steps
      */
     public void printReduceSteps() {
         System.out.println(this.toString());
@@ -47,7 +54,9 @@ public void printReduceSteps() {
     }
 
     /**
-     * @param n
+     * display certain reduce steps
+     *
+     * @param n number of steps
      */
     public void printReduceSteps(int n) {
         if (n == 0) {

diff --git a/src/com/notnl/lambda/Function.java b/src/com/notnl/lambda/Function.java
@@ -17,7 +17,7 @@
 package com.notnl.lambda;
 
 /**
- *
+ * A lambda function
  */
 public class Function extends Expression {
 

diff --git a/src/com/notnl/lambda/Lambda.java b/src/com/notnl/lambda/Lambda.java
@@ -17,11 +17,13 @@
 package com.notnl.lambda;
 
 /**
- * Created by noti0 on 2016/11/18.
+ * A useful class to create lambda expression
  */
 public class Lambda {
 
     /**
+     * create a variable
+     *
      * @param name
      * @return
      */
@@ -30,6 +32,8 @@ public static Variable var(String name) {
     }
 
     /**
+     * create a lambda function
+     *
      * @param name
      * @param body
      * @return
@@ -39,6 +43,8 @@ public static Function lambda(String name, String body) {
     }
 
     /**
+     * create a lambda function
+     *
      * @param name
      * @param body
      * @return
@@ -48,6 +54,8 @@ public static Function lambda(String name, Expression body) {
     }
 
     /**
+     * create a lambda function
+     *
      * @param name
      * @param body
      * @return
@@ -57,6 +65,8 @@ public static Function lambda(Variable name, Expression body) {
     }
 
     /**
+     * create a lambda function
+     *
      * @param name
      * @param body
      * @return
@@ -75,6 +85,8 @@ public static Function lambda(Variable name, Expression body) {
     }
 
     /**
+     * create a lambda function
+     *
      * @param name
      * @param body
      * @return
@@ -84,38 +96,46 @@ public static Function lambda(Variable name, Expression body) {
     }
 
     /**
+     * apply a function with argument
+     *
      * @param function
-     * @param arguement
+     * @param argument
      * @return
      */
-    public static Application apply(String function, String arguement) {
-        return new Application(new Variable(function), new Variable(arguement));
+    public static Application apply(String function, String argument) {
+        return new Application(new Variable(function), new Variable(argument));
     }
 
     /**
+     * apply a function with argument
+     *
      * @param function
-     * @param arguement
+     * @param argument
      * @return
      */
-    public static Application apply(String function, Expression arguement) {
-        return new Application(new Variable(function), arguement);
+    public static Application apply(String function, Expression argument) {
+        return new Application(new Variable(function), argument);
     }
 
     /**
+     * apply a function with argument
+     *
      * @param function
-     * @param arguement
+     * @param argument
      * @return
      */
-    public static Application apply(Expression function, String arguement) {
-        return new Application(function, new Variable(arguement));
+    public static Application apply(Expression function, String argument) {
+        return new Application(function, new Variable(argument));
     }
 
     /**
+     * apply a function with argument
+     *
      * @param function
-     * @param arguement
+     * @param argument
      * @return
      */
-    public static Application apply(Expression function, Expression arguement) {
-        return new Application(function, arguement);
+    public static Application apply(Expression function, Expression argument) {
+        return new Application(function, argument);
     }
 }
diff --git a/src/com/notnl/lambda/Variable.java b/src/com/notnl/lambda/Variable.java
@@ -17,7 +17,8 @@
 package com.notnl.lambda;
 
 /**
- * Created by noti0 on 2016/11/18.
+ * A variable
+ * its name should be String
  */
 public class Variable extends Expression {
-Original file line number
+Diff line change
@@ Expand Up / @@ -17,7 +17,7 @@ @@
     package com.notnl.lambda;
     /**
-     *
+     * A lambda function
      */
     public class Function extends Expression {
@@ Expand Down @@