diff --git a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/ConstantPattern.java b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/ConstantPattern.java
index 296256e3..d53c9e2c 100644
--- a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/ConstantPattern.java
+++ b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/ConstantPattern.java
@@ -21,7 +21,7 @@ public class ConstantPattern extends VisitorPattern {
 	public Optional<Map<String, Function>> visit(final Variable variable) {
 		if (variable.getType().equals(Variable.V_TYPE.CONSTANT)
 				&& variable.getChar() == symbol) {
-			return Optional.of(new HashMap<>());
+			return Optional.of(Collections.emptyMap());
 		} else {
 			return Optional.empty();
 		}
diff --git a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/EquationsSystemPattern.java b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/EquationsSystemPattern.java
index 9dab3a99..c5ddae4e 100644
--- a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/EquationsSystemPattern.java
+++ b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/EquationsSystemPattern.java
@@ -25,7 +25,7 @@ public class EquationsSystemPattern extends VisitorPattern {
 			return Optional.empty();
 		}
 
-		Optional<Map<String, Function>> subFunctions = Optional.of(new HashMap<>());
+		Optional<Map<String, Function>> subFunctions = Optional.of(Collections.emptyMap());
 		for (int i = 0; i < patterns.length && subFunctions.isPresent(); i++) {
 			final Pattern curPattern = patterns[i];
 			final Function curFunction = equationsSystem.getParameter(i);
diff --git a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/NumberPattern.java b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/NumberPattern.java
index 814c2903..f3212367 100644
--- a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/NumberPattern.java
+++ b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/NumberPattern.java
@@ -21,7 +21,7 @@ public class NumberPattern extends VisitorPattern {
 	@Override
 	public Optional<Map<String, Function>> visit(final Number number) {
 		if (number.getTerm().compareTo(value) == 0) {
-			return Optional.of(new HashMap<>());
+			return Optional.of(Collections.emptyMap());
 		} else {
 			return Optional.empty();
 		}
diff --git a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/SubFunctionPattern.java b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/SubFunctionPattern.java
index 2a7f94b6..a00c7a57 100644
--- a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/SubFunctionPattern.java
+++ b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/SubFunctionPattern.java
@@ -18,9 +18,7 @@ public class SubFunctionPattern implements Pattern {
 
 	@Override
 	public Optional<Map<String, Function>> match(final Function function) {
-		final HashMap<String, Function> subFunctions = new HashMap<>();
-		subFunctions.put(name, function);
-		return Optional.of(subFunctions);
+		return Optional.of(Collections.singletonMap(name, function));
 	}
 
 	@Override
diff --git a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/UndefinedPattern.java b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/UndefinedPattern.java
index 55257d52..148d6478 100644
--- a/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/UndefinedPattern.java
+++ b/core/src/main/java/it/cavallium/warppi/math/rules/dsl/patterns/UndefinedPattern.java
@@ -13,7 +13,7 @@ import java.util.*;
 public class UndefinedPattern extends VisitorPattern {
 	@Override
 	public Optional<Map<String, Function>> visit(Undefined undefined) {
-		return Optional.of(new HashMap<>());
+		return Optional.of(Collections.emptyMap());
 	}
 
 	@Override