diff --git a/AlgebraicDataflowArchitectureModel/models/Game.model b/AlgebraicDataflowArchitectureModel/models/Game.model
index 4ad4a36..bc6ae7b 100644
--- a/AlgebraicDataflowArchitectureModel/models/Game.model
+++ b/AlgebraicDataflowArchitectureModel/models/Game.model
@@ -1,19 +1,19 @@
 channel CIO {
-	out force(f:Double, action(x)) == x
+	out force(f:Double, action(x:Double)) == x
 	out time(t:Double, action(x)) == t + 0.01
 	out force(f, e) == x
 	out time(t, e) == t + 0.01
 }
 
 channel CIO2 {
-	out velocity(v:Double, setVel(x)) == x
+	out velocity(v:Double, setVel(x:Double)) == x
 	out velocity(v, e) == x
 }
 
 channel C1 {
 	in force(f, update1(y, m)) == y
 	in mass(m:Double, update1(y, m)) == m
-	out acceleration(a:Double, update1(y, m)) == y / m
+	out acceleration(a: Double, update1(y, m)) == y / m
 }
 
 channel C2 {
diff --git a/AlgebraicDataflowArchitectureModel/models/POS.model b/AlgebraicDataflowArchitectureModel/models/POS.model
index eabfc49..4e61b45 100644
--- a/AlgebraicDataflowArchitectureModel/models/POS.model
+++ b/AlgebraicDataflowArchitectureModel/models/POS.model
@@ -1,5 +1,5 @@
 channel CIO {
-	out payment(p:Int, purchase(x)) == x
+	out payment(p:Int, purchase(x:Int)) == x
 }
 
 channel C1 {
diff --git a/AlgebraicDataflowArchitectureModel/src/models/algebra/Term.java b/AlgebraicDataflowArchitectureModel/src/models/algebra/Term.java
index b6e3ebb..e5bf77d 100644
--- a/AlgebraicDataflowArchitectureModel/src/models/algebra/Term.java
+++ b/AlgebraicDataflowArchitectureModel/src/models/algebra/Term.java
@@ -42,6 +42,10 @@
 		return children.get(n);
 	}
 	
+	public ArrayList<Expression> getChildren() {
+		return children;
+	}
+	
 	public <T extends Expression> HashMap<Position, T> getSubTerms(Class<T> clazz) {
 		HashMap<Position, T> subTerms = new HashMap<>();
 		if (clazz == this.getClass()) {
diff --git a/AlgebraicDataflowArchitectureModel/src/models/dataConstraintModel/DataConstraintModel.java b/AlgebraicDataflowArchitectureModel/src/models/dataConstraintModel/DataConstraintModel.java
index e8b641e..c718d72 100644
--- a/AlgebraicDataflowArchitectureModel/src/models/dataConstraintModel/DataConstraintModel.java
+++ b/AlgebraicDataflowArchitectureModel/src/models/dataConstraintModel/DataConstraintModel.java
@@ -18,7 +18,7 @@
 	public static final Type typeInt = new Type("Int", "int");
 	public static final Type typeFloat = new Type("Float", "float");
 	public static final Type typeDouble = new Type("Double", "double");
-	public static final Type typeList = new Type("List", "List<Integer>");
+	public static final Type typeList = new Type("List", "ArrayList<Integer>");
 	public static final Type typeBoolean = new Type("Bool", "boolean");
 	public static final Symbol add = new Symbol(Parser.ADD, 2, Symbol.Type.INFIX);
 	public static final Symbol mul = new Symbol(Parser.MUL, 2, Symbol.Type.INFIX);;
@@ -38,6 +38,7 @@
 		div.setInverses(new Symbol[] {mul});
 		minus.setInverses(new Symbol[] {minus});
 		cons.setInverses(new Symbol[] {head, body});
+		cons.setSignature(new Type[] {typeList, null, typeList});
 	}
 	
 	public DataConstraintModel() {
diff --git a/AlgebraicDataflowArchitectureModel/src/parser/Parser.java b/AlgebraicDataflowArchitectureModel/src/parser/Parser.java
index eb41993..d8307eb 100644
--- a/AlgebraicDataflowArchitectureModel/src/parser/Parser.java
+++ b/AlgebraicDataflowArchitectureModel/src/parser/Parser.java
@@ -137,12 +137,27 @@
 		stateTransition.setMessageExpression(((Term) leftTerm).getChild(1));
 		stateTransition.setNextStateExpression(rightTerm);
 		channelMember.setStateTransition(stateTransition);
+		// for type definition
 		if (identifier.getResourceStateType() == null && ((Term) leftTerm).getChild(0) instanceof Variable) {
 			Variable stateVar = (Variable) ((Term) leftTerm).getChild(0);
 			if (stateVar.getType() != null) {
 				identifier.setResourceStateType(stateVar.getType());
 			}
 		}
+		if (((Term) leftTerm).getChild(1) instanceof Term) {
+			Term messageTerm = (Term) ((Term) leftTerm).getChild(1);
+			if (messageTerm.getSymbol().getSignature() == null && messageTerm.getChildren().size() > 0) {
+				Type[] signature = new Type[messageTerm.getChildren().size() + 1];
+				int i = 1;
+				for (Expression e: messageTerm.getChildren()) {
+					if (e instanceof Variable && ((Variable) e).getType() != null) {
+						signature[i] = ((Variable) e).getType();
+					}
+					i++;
+				}
+				messageTerm.getSymbol().setSignature(signature);
+			}
+		}
 		return channelMember;
 	}
 
@@ -168,6 +183,7 @@
 				}
 				Expression exp = null;
 				if (stream.checkNext() != null && stream.checkNext().equals(LEFT_BRACKET)) {
+					// a function symbol
 					Symbol symbol = model.getSymbol(symbolName);
 					if (symbol == null) {
 						symbol = new Symbol(symbolName);
@@ -192,13 +208,15 @@
 						Double d = Double.parseDouble(symbolName);
 						exp = new Constant(symbolName);
 					} catch (NumberFormatException e) {
-						if (symbolName.contains(COLON)) {
-							String variable[] = symbolName.split(COLON);
-							Type type = model.getType(variable[1]);
+						if (stream.checkNext() != null && stream.checkNext().equals(COLON)) {
+							// when a type is specified.
+							stream.next();
+							String typeName = stream.next();
+							Type type = model.getType(typeName);
 							if (type == null) {
-								type = new Type(variable[1], variable[1]);
+								type = new Type(typeName, typeName);
 							}
-							exp = new Variable(variable[0], type);							
+							exp = new Variable(symbolName, type);							
 						} else {
 							exp = new Variable(symbolName);
 						}
@@ -288,17 +306,20 @@
 																			splitBy(
 																					splitBy(
 																							splitBy(
-																									Arrays.asList(line.split("[ \t]")), 
-																									ADD,
-																									ADD_REGX),
-																							MUL,
-																							MUL_REGX),
-																					SUB,
-																					SUB_REGX),
-																			DIV,
-																			DIV_REGX),
-																	COMMA, 
-																	COMMA),
+																									splitBy(
+																											Arrays.asList(line.split("[ \t]")), 
+																											ADD,
+																											ADD_REGX),
+																									MUL,
+																									MUL_REGX),
+																							SUB,
+																							SUB_REGX),
+																					DIV,
+																					DIV_REGX),
+																			COMMA, 
+																			COMMA),
+																	COLON, 
+																	COLON),
 															LEFT_BRACKET, 
 															LEFT_BRACKET_REGX),
 													RIGHT_BRACKET,